# How to Convince Me That 2 + 2 = 3

In “What is Ev­i­dence?” I wrote:1

This is why ra­tio­nal­ists put such a heavy pre­mium on the para­dox­i­cal-seem­ing claim that a be­lief is only re­ally worth­while if you could, in prin­ci­ple, be per­suaded to be­lieve oth­er­wise. If your retina ended up in the same state re­gard­less of what light en­tered it, you would be blind . . . Hence the phrase, “blind faith.” If what you be­lieve doesn’t de­pend on what you see, you’ve been blinded as effec­tively as by pok­ing out your eye­balls.

Cihan Baran replied:2

I can not con­ceive of a situ­a­tion that would make 2 + 2 = 4 false. Per­haps for that rea­son, my be­lief in 2 + 2 = 4 is un­con­di­tional.

I ad­mit, I can­not con­ceive of a “situ­a­tion” that would make 2 + 2 = 4 false. (There are re­defi­ni­tions, but those are not “situ­a­tions,” and then you’re no longer talk­ing about 2, 4, =, or +.) But that doesn’t make my be­lief un­con­di­tional. I find it quite easy to imag­ine a situ­a­tion which would con­vince me that 2 + 2 = 3.

Sup­pose I got up one morn­ing, and took out two earplugs, and set them down next to two other earplugs on my night­table, and no­ticed that there were now three earplugs, with­out any earplugs hav­ing ap­peared or dis­ap­peared—in con­trast to my stored mem­ory that 2 + 2 was sup­posed to equal 4. More­over, when I vi­su­al­ized the pro­cess in my own mind, it seemed that mak­ing xx and xx come out to xxxx re­quired an ex­tra x to ap­pear from nowhere, and was, more­over, in­con­sis­tent with other ar­ith­metic I vi­su­al­ized, since sub­tract­ing xx from xxx left xx, but sub­tract­ing xx from xxxx left xxx. This would con­flict with my stored mem­ory that 3 − 2 = 1, but mem­ory would be ab­surd in the face of phys­i­cal and men­tal con­fir­ma­tion that xxxxx = xx.

I would also check a pocket calcu­la­tor, Google, and per­haps my copy of 1984 where Win­ston writes that “Free­dom is the free­dom to say two plus two equals three.” All of these would nat­u­rally show that the rest of the world agreed with my cur­rent vi­su­al­iza­tion, and dis­agreed with my mem­ory, that 2 + 2 = 3.

How could I pos­si­bly have ever been so de­luded as to be­lieve that 2 + 2 = 4? Two ex­pla­na­tions would come to mind: First, a neu­rolog­i­cal fault (pos­si­bly caused by a sneeze) had made all the ad­di­tive sums in my stored mem­ory go up by one. Se­cond, some­one was mess­ing with me, by hyp­no­sis or by my be­ing a com­puter simu­la­tion. In the sec­ond case, I would think it more likely that they had messed with my ar­ith­metic re­call than that 2 + 2 ac­tu­ally equalled 4. Nei­ther of these plau­si­ble-sound­ing ex­pla­na­tions would pre­vent me from notic­ing that I was very, very, very con­fused.3

What would con­vince me that 2 + 2 = 3, in other words, is ex­actly the same kind of ev­i­dence that cur­rently con­vinces me that 2 + 2 = 4: The ev­i­den­tial cross­fire of phys­i­cal ob­ser­va­tion, men­tal vi­su­al­iza­tion, and so­cial agree­ment.

There was a time when I had no idea that 2 + 2 = 4. I did not ar­rive at this new be­lief by ran­dom pro­cesses—then there would have been no par­tic­u­lar rea­son for my brain to end up stor­ing “2 + 2 = 4” in­stead of “2 + 2 = 7.” The fact that my brain stores an an­swer sur­pris­ingly similar to what hap­pens when I lay down two earplugs alongside two earplugs, calls forth an ex­pla­na­tion of what en­tan­gle­ment pro­duces this strange mir­ror­ing of mind and re­al­ity.

There’s re­ally only two pos­si­bil­ities, for a be­lief of fact—ei­ther the be­lief got there via a mind-re­al­ity en­tan­gling pro­cess, or not. If not, the be­lief can’t be cor­rect ex­cept by co­in­ci­dence. For be­liefs with the slight­est shred of in­ter­nal com­plex­ity (re­quiring a com­puter pro­gram of more than 10 bits to simu­late), the space of pos­si­bil­ities is large enough that co­in­ci­dence van­ishes.4

Un­con­di­tional facts are not the same as un­con­di­tional be­liefs. If en­tan­gled ev­i­dence con­vinces me that a fact is un­con­di­tional, this doesn’t mean I always be­lieved in the fact with­out need of en­tan­gled ev­i­dence.

I be­lieve that 2 + 2 = 4, and I find it quite easy to con­ceive of a situ­a­tion which would con­vince me that 2 + 2 = 3. Namely, the same sort of situ­a­tion that cur­rently con­vinces me that 2 + 2 = 4. Thus I do not fear that I am a vic­tim of blind faith.5

3See “Your Strength as a Ra­tion­al­ist” in Map and Ter­ri­tory.

4For more on be­lief for­ma­tion and be­liefs of fact, see “Feel­ing Ra­tional” and “What Is Ev­i­dence?” in Map and Ter­ri­tory. For more on be­lief com­plex­ity, see “Oc­cam’s Ra­zor” in the same vol­ume.

5If there are any Chris­ti­ans read­ing this who know Bayes’s The­o­rem, might I in­quire of you what situ­a­tion would con­vince you of the truth of Is­lam? Pre­sum­ably it would be the same sort of situ­a­tion causally re­spon­si­ble for pro­duc­ing your cur­rent be­lief in Chris­ti­an­ity: We would push you scream­ing out of the uterus of a Mus­lim woman, and have you raised by Mus­lim par­ents who con­tinu­ally told you that it is good to be­lieve un­con­di­tion­ally in Is­lam.

Or is there more to it than that? If so, what situ­a­tion would con­vince you of Is­lam, or at least, non-Chris­ti­an­ity? And how con­fi­dent are you that the gen­eral kinds of ev­i­dence and rea­son­ing you ap­peal to would have been enough to dis­suade you of your re­li­gion if you had been raised a Mus­lim?

• “To ap­ply the same rea­son­ing the other way, if you aren’t a Chris­tian, what would be a situ­a­tion which would con­vince you of the truth of Chris­ti­an­ity?”

-And Je­sus said unto them, Be­cause of your un­be­lief: for ver­ily I say unto you, If ye have faith as a grain of mus­tard seed, ye shall say unto this moun­tain, Re­move hence to yon­der place; and it shall re­move; and noth­ing shall be im­pos­si­ble unto you. - Matthew 17:20

If moun­tains moved when Chris­ti­ans told them to, ev­ery time, and no one else could effec­tively com­mand moun­tains to move, I think most of us non-be­liev­ers would start go­ing to church.

Alter­na­tively, if the world looked like it was de­signed and reg­u­lated by a lov­ing be­ing, it would help. That might not pro­mote Chris­ti­an­ity speci­fi­cally, but it would be a much bet­ter start than what we ac­tu­ally see.

• At any rate, if the former is true, 2+2=4 is out­side the province of em­piri­cal sci­ence, and ap­ply­ing em­piri­cal rea­son­ing to eval­u­ate its ‘truth’ is wrong.

When I imag­ine putting two ap­ples next to two ap­ples, I can pre­dict what will ac­tu­ally hap­pen when I put two earplugs next to two earplugs, and in­deed, my mind can store the re­sult in a gen­er­al­ized fash­ion which makes pre­dic­tions in many spe­cific in­stances. If you do not call this use­ful ab­stract be­lief “2 + 2 = 4”, I should like to know what you call it. If the be­lief is out­side the province of em­piri­cal sci­ence, I would like to know why it makes such good pre­dic­tions.

To ap­ply the same rea­son­ing the other way, if you aren’t a Chris­tian, what would be a situ­a­tion which would con­vince you of the truth of Chris­ti­an­ity?

You’d have to fix all the prob­lems in be­lief, one by one, by re­vers­ing the ev­i­dence that origi­nally con­vinced me of the be­liefs’ nega­tions. If the Sun stopped in the sky for a day, and then Earth’s ro­ta­tion restarted with­out ap­par­ent dam­age, that would con­vince me there was one heck of a pow­er­ful en­tity in the neigh­bor­hood. It wouldn’t show the en­tity was God, which would be much more com­pli­cated, but it’s an ex­am­ple of how one small piece of my model could be flipped from the nega­tion of Chris­ti­an­ity (in that facet) to the non-nega­tion.

Get­ting all the pieces of the fac­tual model (in­clud­ing the parts I was pre­vi­ously con­vinced were log­i­cally self-con­tra­dic­tory) to al­ign with Chris­ti­an­ity’s fac­tual model, would still leave all the eth­i­cal prob­lems. So the ac­tual end re­sult would be to con­vince me that the uni­verse was in the hands of a mon­strously in­sane and vi­cious God. But then there does not need to be any ob­serv­able situ­a­tion which con­vinces me that it is morally ac­cept­able to mur­der the first-born chil­dren of Egyp­ti­ans—moral­ity does not come from en­vi­ron­men­tal en­tan­gle­ment.

• If you do not call this use­ful ab­stract be­lief “2 + 2 = 4”, I should like to know what you call it.

I call it “2+2=4 is a use­ful model for what hap­pens to the num­ber of earplugs in a place when I put two earplugs beside two other earplugs”. Which is a spe­cial case of the the­ory “ar­ith­metic is a use­ful model for num­bers of earplugs un­der some op­er­a­tions (in­clud­ing but not limited to adding and re­mov­ing)”.

If the be­lief is out­side the province of em­piri­cal sci­ence, I would like to know why it makes such good pre­dic­tions.

The math­e­mat­i­cal claim “2+2=4” makes no pre­dic­tions about the phys­i­cal world. For that you need a phys­i­cal the­ory. 2+2=4 would be true in num­ber the­ory even if your ap­ples or earplugs worked in some com­pletely differ­ent man­ner.

• I hate to break it to you, but if set­ting two things beside two other things didn’t yield four things, then num­ber the­ory would never have con­trived to say so.

Num­bers were in­vented to count things, that is their pur­pose. The first num­bers were sim­ple scratches used as tally marks circa 35,000 BC. The way the counts add up was de­rived from the way phys­i­cal ob­jects add up when grouped to­gether. The only way to change the way num­bers work is to change the way phys­i­cal ob­jects work when grouped to­gether. Phys­i­cal re­al­ity is the ba­sis for num­bers, so to change num­ber the­ory you must first show that it is in­con­sis­tent with re­al­ity.

Thus num­bers have a definite re­la­tion to the phys­i­cal world. Num­ber the­ory grew out of this, and if putting two ob­jects next to two other ob­jects only yielded three ob­jects when num­bers were in­vented over forty thou­sand years ago, then num­ber the­ory must re­flect that fact or it would never have been used. Con­se­quently, sug­gest­ing 2+2=4 would be com­pletely ab­surd, and num­ber the­o­rists would laugh in your face at the sug­ges­tion. There would, in fact, be a log­i­cal proof that 2+2=3 (much like there is a log­i­cal proof that 2+2=4 in num­ber the­ory now).

All of math­e­mat­ics are, in re­al­ity, noth­ing more than ex­tremely ad­vanced count­ing. If it is not re­lated to the phys­i­cal world, then there is no rea­son for it to ex­ist. It fol­lows rules first de­rived from the phys­i­cal world, even if the cur­rent prin­ci­ples of math­e­mat­ics have been ex­trap­o­lated far be­yond the bounds of the strictly phys­i­cal. I think peo­ple lose sight of this far too eas­ily (or worse, never rec­og­nize it in the first place).

Math­e­mat­ics are so firmly grounded in the phys­i­cal re­al­ity that when ob­ser­va­tions don’t line up with what our math tells us, we must change our un­der­stand­ing of re­al­ity, not of math. This is be­cause math is in­ex­tri­ca­bly tied to re­al­ity, not be­cause it is sep­a­rate from it.

• Num­bers were in­vented to count things, that is their pur­pose. The first num­bers were sim­ple scratches used as tally marks circa 35,000 BC.

Ver­bal ex­pres­sions al­most cer­tainly pre­date phys­i­cal no­ta­tions. Un­for­tu­nately the echos don’t last quite that long.

• In your last para­graph you turn ev­ery­thing around and in­ex­pli­ca­bly claim that math is more pri­mary than ob­ser­va­tion of re­al­ity, though you did a good job—and one I agree with—of point­ing out the op­po­site in the pre­vi­ous part of the com­ment.

• When it was no­ticed in the 1800′s that the per­ihe­lion of Mer­cury did not match what New­ton’s in­verse-square law of grav­ity pre­dicted, did we change the way math works? Or did we change our un­der­stand­ing of grav­ity?

Math is the most fun­da­men­tal un­der­stand­ing of re­al­ity that we have. It is the most thor­oughly sup­ported and proven as­pect of sci­ence that I know of. That doesn’t mean that our un­der­stand­ing of math can’t be fun­da­men­tally flawed, but it does mean that math is the last place we ex­pect to find a prob­lem when our ob­ser­va­tions don’t match our ex­pec­ta­tions.

In other words, when as­sign­ing prob­a­bil­ities to whether math is wrong or New­ton’s The­ory of Grav­ity is wrong, the prob­a­bil­ity we as­sign to math it­self be­ing wrong is some­thing like 0.000001% (sorry, I don’t know nearly enough math to make it less than that) and New­ton’s Grav­ity be­ing wrong some­thing like 99.999999%.

See what I’m say­ing?

• Woah, I think that’s a lit­tle over­con­fi­dent...

You’re say­ing that in the mid nine­teenth cen­tury (half a cen­tury be­fore rel­a­tivity), the anoma­lous pre­ces­sion of Mer­cury made it seem 99.999999% likely that New­to­nian me­chan­ics was wrong?

After all, there are other pos­si­bil­ities.

cf. “When it was no­ticed in the 1800′s that the per­ihe­lion of Nep­tune did not match what New­ton’s in­verse-square law of grav­ity pre­dicted, did we change the way math works? Or did we change our un­der­stand­ing of grav­ity?” In this case we ac­tu­ally pos­tu­lated the ex­is­tence of Pluto.

Similar solu­tions were sug­gested for the Mer­cury case, e.g. an ex­tremely dense, small ob­ject or­bit­ing close to Mer­cury.

And that’s leav­ing aside the fact that 99.999999% is an ab­surdly high level of con­fi­dence for pretty much any state­ment at all (see http://​​less­wrong.com/​​lw/​​mo/​​in­finite_cer­tainty/​​ ).

If I were a nine­teenth cen­tury physi­cist faced with the de­vi­a­tions in the per­ihe­lion of Mer­cury, I’d give maybe a 0.1% prob­a­bil­ity to New­ton be­ing in­cor­rect, a 0.001% prob­a­bil­ity to maths be­ing in­cor­rect, and the re­main­ing ~99.9% would be shared be­tween in­cor­rect data /​in­com­plete data/​ other things I haven’t thought of.

How­ever, I agree that we can prob­a­bly be more con­fi­dent of re­sults in maths than re­sults in ex­per­i­men­tal sci­ence. (I was go­ing to dis­t­in­guish be­tween math­e­mat­i­cal/​em­piri­cal re­sults, but given that the OP was to do with the em­piri­cal con­fir­ma­tion of maths, I thought “math­e­mat­i­cal/​ex­per­i­men­tal” would be a safer dis­tinc­tion)

• Yup. I think we agree. My dis­agree­ing post was a mere mi­s­un­der­stand­ing of what you were say­ing.

• After a few re­cent posts of mine it looks like I need to work on my phras­ing in or­der to make my points clear.

No harm no foul.

• For well-es­tab­lished math, sure. We cer­tainly will look for ex­per­i­men­tal mis­takes, un­no­ticed ob­serv­ables (e.g. the hy­poth­e­sized planet Vul­can to ex­plain Mer­cury’s de­vi­a­tion from New­to­nian grav­ity), and bet­ter the­o­ries in about that or­der. How­ever for less well es­tab­lished math­e­mat­ics at the fron­tiers we do con­sider the pos­si­bil­ity that we’ve made a mis­take some­where.

Off the top of my head the biggest ex­am­ple I can think of was von Neu­mann’s proof that hid­den vari­ables were in­con­sis­tent with quan­tum me­chan­ics, which was widely be­lieved and cited at least into the 1980s, de­spite the fact that David Bohm pub­lished a con­sis­tent hid­den vari­ables the­ory of quan­tum me­chan­ics in 1952. I’m cu­ri­ous if any­one can re­call a case in which an ex­per­i­men­tal re­sult led us to re­al­ize that a pre­vi­ously ac­cepted math­e­mat­i­cal “fact” was in­cor­rect.

• I hate to break it to you, but if set­ting two things beside two other things didn’t yield four things, then num­ber the­ory would never have con­trived to say so.

At what point are there two plus two things, and at what point are there four things? Would you not agree that a) the dis­tinc­tion it­self be­tween things hap­pens in the brain and b) the idea of the four things be­ing two sep­a­rate groups with two el­e­ments each is solely in the mind? If not, I’d very much like to see some em­piri­cal ev­i­dence for the ad­di­tion op­er­a­tion be­ing car­ried out.

Math­e­mat­ics are so firmly grounded in the phys­i­cal re­al­ity that when ob­ser­va­tions don’t line up with what our math tells us, we must change our un­der­stand­ing of re­al­ity, not of math.

English is so firmly grounded in the phys­i­cal re­al­ity that when ob­ser­va­tions don’t line up with what our en­glish tells us, we must change our un­der­stand­ing of re­al­ity, not of en­glish.

I hope the ab­sur­dity is ob­vi­ous, and that there are no prob­lems to make mod­els of the world with en­glish alone. So, do you find it more likely that math is con­nected to the world be­cause we link it up ex­plic­itly or be­cause it is an in­trin­sic prop­erty of the world it­self?

• Math­e­mat­ics are so firmly grounded in the phys­i­cal re­al­ity that when ob­ser­va­tions don’t line up with what our math tells us, we must change our un­der­stand­ing of re­al­ity, not of math. This is be­cause math is in­ex­tri­ca­bly tied to re­al­ity, not be­cause it is sep­a­rate from it.

On the other hand...

http://​​en.m.wikipe­dia.org/​​wiki/​​Is_logic_em­piri­cal%3F

• When I imag­ine putting two ap­ples next to two ap­ples, I can pre­dict what will ac­tu­ally hap­pen when I put two earplugs next to two earplugs, and in­deed, my mind can store the re­sult in a gen­er­al­ized fash­ion which makes pre­dic­tions in many spe­cific in­stances. If you do not call this use­ful ab­stract be­lief “2 + 2 = 4”, I should like to know what you call it. If the be­lief is out­side the province of em­piri­cal sci­ence, I would like to know why it makes such good pre­dic­tions.

No, the real world does not work via Peano ar­ith­metic. Your ex­per­i­ments with ap­ples and earplugs are sim­ply ap­pli­ca­tions of con­ser­va­tion of mass and im­mutabil­ity of inan­i­mate ob­jects, and other such prin­ci­ples. Be­fore you learned such things, you were thrilled with the game of peek-a-boo—of how some­one could cease to ex­ist, and then ap­pear out of nowhere.

Con­sider this ex­per­i­ment: Take 2 ap­ples, cut them in half. Take 2 more ap­ples, cut them in half. Put all to­gether. How many ap­ples do you have? The an­swer is not “4 ap­ples”, the an­swer is “8 half-ap­ples”. Fur­ther­more, each in­di­vi­d­ual ap­ple re­mains the same ap­ple as be­fore (minus the effects of time), so that any differ­ences in size, shape, col­ora­tion, bruis­ing, etc would re­main the same. Ap­ples aren’t num­bers, and can’t be sub­sti­tuted for each other.

The world abounds with ex­am­ples where Peano ar­ith­metic does not ap­ply. Con­sider adding two speeds to­gether—they do not add via Peano ar­ith­metic, such that there ex­ists a speed X, such that 2X + 2X = 3X. If we’re us­ing naive mul­ti­pli­ca­tion, that speed is where X=c*sqrt(7/​36). None of this changes my be­liefs about Peano ar­ith­metic—it is nec­es­sar­ily true given its ax­ioms, and its cor­re­spon­dence to the phys­i­cal world is en­tirely co­in­ci­den­tal. Cer­tainly, if Peano ar­ith­metic didn’t cor­re­spond widely to real world prob­lems, I would never have learned about it in high school and it might not even have been in­vented—but it re­mains true all the same.

This all just means that my idea of truth is differ­ent than yours—I think things can be true or false re­gard­less of their pre­dic­tive value. Speci­fi­cally, I value state­ments of the form “If A, then (A worded slightly differ­ently)” and think that al­most all knowl­edge has that form. For ex­am­ple, “If the uni­verse is con­sis­tent and ob­jec­tive, the sci­en­tific method will tend to­ward ac­cu­rately de­scribing the uni­verse”. Once you in­tro­duce in­duc­tive rea­son­ing, even for some­thing as triv­ial as stat­ing “the uni­verse is con­sis­tent and ob­jec­tive”, then you in­tro­duce un­cer­tainty—you switch from bi­nary true/​false to likely/​un­likely and ac­cu­rate/​in­ac­cu­rate and pre­dic­tive/​non-pre­dic­tive.

If you equate “sci­en­tific type truth” with other peo­ple’s “ac­tual truth” you will get into many pointless ar­gu­ments. For ex­am­ple, you seem greatly offended that re­li­gious peo­ple some­times dis­agree with sci­ence. For ex­am­ple, they will point out that sci­ence has always been wrong, and is prob­a­bly still wrong. But they’ll prob­a­bly agree that mod­ern sci­ence more ac­cu­rately and more pre­cisely pre­dicts about our world. In fact, you’ll prob­a­bly get them to agree that sci­ence is per­haps the best method to make ac­cu­rate and pre­cise pre­dic­tions. A state­ment doesn’t need to be true to be use­ful for mak­ing ac­cu­rate pre­dic­tions, for ex­am­ple New­to­nian grav­ity. So why equate “makes ac­cu­rate pre­dic­tions” with “truth”?

• Elez­ier, do you be­lieve that some­day hu­mans could cre­ate an AI and put that AI in a simu­lated en­vi­ro­ment that ac­cu­rately simu­lated all the ob­ser­va­tions hu­man­ity made un­til now?

If you do, what fur­ther ob­ser­va­tions would that AI have to make to ar­rive at the be­lief that they were cre­ated by an in­tel­li­gent en­tity?

• If we as­sume that hu­man­ity has gained ac­cess to effec­tively in­finite com­put­ing power, and has put AIXItl or some­thing similar into a copy of the uni­verse, simu­lated at what­ever level unifies quan­tum me­chan­ics and grav­i­ta­tion into a co­her­ent, leakproof frame­work, AIXItl would have an ex­tremely small be­lief that it was in­side a simu­la­tion. Only if the sim­plest unifi­ca­tion of quan­tum me­chan­ics and grav­ity turns out to be “we’re in a simu­la­tion,” would a hy­per­in­tel­li­gent AI in a perfect simu­la­tion of our uni­verse come to the be­lief that it’s in a simu­la­tion.

So, the epistem­i­cally perfect AI would come to an in­cor­rect de­ci­sion. This does not im­ply a flaw in its method for form­ing be­liefs; it merely im­plies the tau­tol­ogy that there is no way to find out what there is no way to find out.

• In fact I once had this sort of math­e­mat­i­cal ex­pe­rience.

Some­how, while mem­o­riz­ing ta­bles of ar­ith­metic in the first grade, I learned that 11 − 6 = 7. This equa­tion didn’t come up very of­ten in el­e­men­tary school ar­ith­metic, and even more sel­dom in high school alge­bra, and so I sel­dom got any math ques­tions marked wrong. Then one day at uni­ver­sity, I re­ceived back a Math 300 home­work as­sign­ment on which I’d ca­su­ally as­serted that 11 − 6 − 7. My TA had drawn a red cir­cle around the state­ment, punc­tu­at­ing it with three ques­tion marks and the loss of a sin­gle point.

I was con­fused. There was noth­ing wrong with 11 − 6 = 7. Why would my TA have de­ducted a point? Every­one knew that 11 − 6 = 7, be­cause it was just the re­verse of 7 + 6 = wait-a-minute-here.

Pen. Paper. I grabbed eleven coins and care­fully counted six of them away. There were not seven of them left. I started writ­ing down re­mem­bered sub­trac­tion prob­lems. 11 − 4 = 7. 11 − 5 = 6. 11 − 6 = 7. 11 − 7 = 4. One of these sums was clearly not like the oth­ers. I tried ad­di­tion, and found that both 7 + 6 = 13 and 6 + 7 = 13.

The ev­i­dence was over­whelming. I was con­vinced. Con­fused, yes—fas­ci­nated by where my er­ror could have come from, and how I could have held onto it so long—but con­vinced. I set to work mem­o­riz­ing 11 − 6 = 5 in­stead.

It didn’t en­tirely take. Twenty years later, the equa­tion 11 − 6 = 7 still feels so right and fa­mil­iar and un­con­tro­ver­sial that I’ve had to mem­o­rize 11 − 6 = stop. I know the an­swer is prob­a­bly ei­ther 5 or 7, but I work it out man­u­ally ev­ery time.

• I don’t know if the Amer­i­can el­e­men­tary cur­ricu­lum is bet­ter than it was (I hope so) but this mis­take is less likely to hap­pen now. My niece in 2nd grade is learn­ing differ­ent meth­ods of ‘know­ing’ ar­ith­metic. They still mem­o­rize ta­bles, but they also spend a lot of time prac­tic­ing what they call ‘strate­gies for learn­ing the ad­di­tion facts’.

For ex­am­ple..

11-6 = (10-6)+1 = 5 is the com­pen­sa­tion ap­proach.

and 11-6 = 10-5 is the equal ad­di­tions ap­proach.

They also spend a lot of time do­ing men­tal math. I’m im­pressed with how differ­ent things are, and hope that stu­dents are do­ing bet­ter with this more em­piri­cal, con­struc­tivist ap­proach. (My niece is good at math any­way, so I don’t know if she’s get­ting more out of it than av­er­age.)

• I don’t know very much about the Amer­i­can cur­ricu­lum, hav­ing grown up with the Cana­dian one. But I also didn’t pay very much at­ten­tion in math class. I preferred to read the text­book my­self, early in the year, and then play around with as many deriva­tions and the­o­rems as I could figure out, oc­ca­sion­ally pop­ping my head above wa­ter long enough for a test.

I wrote and mem­o­rized my own sub­trac­tion ta­bles, and in­vented a baroque and com­pli­cated sys­tem for writ­ing nega­tive num­bers—for ex­am­ple, 1 − 2 = 9-with-a-cir­cle-around-it, and 5 − 17 = 8-with-two-cir­cles-around-it. Really this is the sort of mis­take which could only have hap­pened to me. :)

I’m glad that they’re teach­ing these sort of strate­gies in US schools. My ex­pe­rience tu­tor­ing el­e­men­tary school math (my son at­tended an al­ter­na­tive school in which par­ents all vol­un­teered their own skills & ex­pe­rience) is that ev­ery kid has a slightly differ­ent con­cep­tion of how num­bers in­ter­act. The most im­por­tant thing I could teach them was that ev­ery con­sis­tent way of ap­proach­ing math is cor­rect; if you don’t un­der­stand the text­book’s pre­scrip­tion for sub­tract­ing, there are dozens of other right ways to think about the prob­lem; it doesn’t mat­ter how you get to the an­swer as long as you fol­low the ax­ioms.

• I never both­ered to mem­o­rize trig equiv­alences. In­stead, I just re­duced sine, co­sine, and tan­gent (and their in­verses) to ra­tios of the sides of a tri­an­gle, and then used the Pythagorean the­o­rem.

• Well, it’s so much eas­ier and more ro­bust that way! In­stead of a long list of con­found­ingly similar equa­tions, you’re left with a sin­gle clear un­der­stand­ing of why tri­gonom­e­try works. After that you can mem­o­rize a few for­mu­las as short­cuts if it helps.

Of course this prin­ci­ple com­pletely breaks down when you start work­ing with a child who’s already con­vinced that they can’t do math—or with a group of 30 kids at once, a third of whose math­e­mat­i­cal in­tu­itions will be far enough from the text­book norm that no one teacher has enough time to guide them through to that first epiphany.

• Your method of sub­trac­tion is similar to be­ing the p-adic num­bers, you might want to look them up!

• it doesn’t mat­ter how you get to the an­swer as long as you fol­low the ax­ioms.

Well, it does also mat­ter in prac­tice that you can com­mu­ni­cate effec­tively (a les­son I had to learn my­self at that age). But learn­ing how to trans­late from an idiosyn­cratic sys­tem into a stan­dard one can be a source of even bet­ter learn­ing, so I agree that kids should not be dis­cour­aged from in­vent­ing non­stan­dard but valid sys­tems.

• I am con­fused by this dis­cus­sion. Are we talk­ing about in­te­gers or things?

An­a­lytic truths may or may not cor­re­spond to our situ­a­tions. When they don’t cor­re­spond, I guess that’s what you all are call­ing “false.” So, if we’re en­g­ineers work­ing on build­ing a GPS sys­tem, I might say to you, “Care­ful now, Eu­clidean ge­om­e­try is false.”

Similarly, quan­tum physi­cists on the job might say, “Watch out now, two and two isn’t nec­es­sar­ily four.”

I’m think­ing of this ex­cel­lent blog post I came across last week:

...Con­sider a bas­ket with 2 ap­ples in it. Now toss in 2 more ap­ples. Ex­am­ine the bas­ket, and you will find (sur­prise!) 4 ap­ples. How­ever, you can­not prove a pri­ori that there will be 4 ap­ples in the bas­ket. It is an em­piri­cal ques­tion, albeit a triv­ial one, whether bas­kets of ap­ples (which are phys­i­cal things) be­have in the same man­ner as the non-nega­tive in­te­gers un­der ad­di­tion (which is an ab­stract log­i­cal con­struct).
This dis­tinc­tion might seem hope­lessly pedan­tic at first, but you can eas­ily go astray by ig­nor­ing it. For ex­am­ple, many peo­ple naively ex­pect pho­tons to be­have in the same man­ner as in­te­gers un­der ad­di­tion, but they don’t. “Num­ber of pho­tons” is not a con­served quan­tity in the way that “num­ber of ap­ples” is; pho­tons can be cre­ated/​de­stroyed, one pho­ton can be split into two, et cetera....
• For a while this con­fused me, be­cause I in­cor­rectly iden­ti­fied what part of Eliezer’s ar­gu­ment I thought was wrong.

Sup­pose I were to make all those ob­ser­va­tions sug­gest­ing that com­bin­ing two ob­jects with two ob­jects pro­duced three ob­jects. I would not con­clude that 2+2=3, rather I would con­clude that ob­jects were not mod­el­led by Peano Arith­metic. (This much has been said by other com­menters). But then I only ‘know’ Peano Arith­metic through the (phys­i­cal) op­er­a­tion of my own brain.

Here’s how to con­vince me that 2+2=3. Sup­pose I look at the proof from (peano ax­ioms) to (2+2=4), and sud­denly no­tice that an in­fer­ence has been made that doesn’t fol­low from the in­fer­ence rules (say, I no­tice that the proof says a + (b⁺) = (a+b)⁺ and I know full well that the cor­rect rule is (a⁺)+(b⁺)=(a+b)⁺). I cor­rect this ‘er­ror’ and fol­low through to the end of the proof, and con­clude the re­sult 2+2=3. What do I do? I con­sider that this ob­ser­va­tion is more likely if 2+2=3 than if 2+2=4, and so I up­date on that. It’s still more likely that 2+2=4, be­cause it’s more likely that I’ve made an er­ror this time than that ev­ery­one who’s analysed that proof be­fore has made an er­ror (or rather, that I have not heard of any­one else spot­ting this er­ror). But clearly there is some­thing to up­date on, so my prior prob­a­bil­ity that 2+2=3 is not zero. How­ever, I also main­tain that if in fact the proof of 2+2=4 is cor­rect, then it re­mains cor­rect whether or not I am con­vinced of it, whether or not I ex­ist, and even whether or not phys­i­cal re­al­ity ex­ists. So it is a pri­ori true, but my knowl­edge of it is not a pri­ori knowl­edge (be­cause the lat­ter does not ex­ist).

I think this is what Eliezer was try­ing to say with “Un­con­di­tional facts are not the same as un­con­di­tional be­liefs.”, but this seems to be glossed over and al­most lost within the con­fu­sion about earplugs. The ar­ti­cle’s failure to dis­t­in­guish be­tween a math­e­mat­i­cal the­ory and a math­e­mat­i­cal model (map and ter­ri­tory, pos­si­bly?) came very close to ob­scur­ing the ac­tual point. This ar­ti­cle does not ex­plain how to con­vince Eliezer that 2+2=3, it ex­plains how to con­vince Eliezer that PA does not model earplugs—and since the lat­ter is not an a pri­ori truth, it is much less in­ter­est­ing that knowl­edge of it is not a pri­ori ei­ther.

• You’re over-think­ing this. Take a look at this real-world ex­am­ple of a “neu­rolog­i­cal fault”:

Now I knew where I was. Soon I would come to in­ter­change 27 with its two ramps, A and B. B led away from my des­ti­na­tion and A di­rectly into it. It had always struck me as strange that one reached 27B be­fore 27A. I re­called draw­ing that on a map to give to some­one who was go­ing to visit me. My breath­ing has re­turned to nor­mal and my panic had dis­ap­peared. I come up to the first sign for the in­ter­change.

“27A”

I could hardly breathe. That was not pos­si­ble. 27A was af­ter 27B. I knew that. I con­sid­ered for a mo­ment the pos­si­bil­ity that on the pre­vi­ous night, shortly af­ter I drove on this very high­way, con­struc­tion work­ers had de­scended en masse on the in­ter­changes and some­how moved them. That seemed far more pos­si­ble than that my clear (and de­tailed) mem­ory could be so wrong. 27A looked ex­actly as I re­mem­bered, ex­cept that now I could see 27B clearly in the dis­tance and in the past I had to turn my head to see it.

I ex­ited on the ramp that I knew wasn’t there twenty-four hours pre­vi­ously to find my­self on a well-re­mem­bered road. And soon I was home.

Now imag­ine that hap­pen­ing on a mas­sive scale. Say that right af­ter read­ing this com­ment you ex­pe­rience ev­i­dence, like that which the OP de­scribes, go­ing against your mem­o­ries of what hap­pens when you put one pair of ob­jects next to an­other pair. (This in­cludes “men­tal con­fir­ma­tion that XXX—XX = XX”, though not a for­mal proof in PA.) Would that make you doubt your mem­o­ries of what PA says? Would you want to check the proof that it says (2+2=4) in case your cur­rent mem­ory is ly­ing about that as well?

• Maybe “earplugs do not model PA,” not the other way around? (Edit: just saw this ex­cel­lent clar­ifi­ca­tion.)

Num­ber-han­dling is an older sci­ence than Peano ar­ith­metic, and es­pe­cially older than model the­ory. The num­bers 2 and 3 would “ex­ist” even if PA were shown to have no mod­els. At least, the no­ta­tion 2 and 3 would still be rele­vant to things that re­ally ex­ist.

It is very eas­ily ver­ified that 2 + 2 does not equal 3, but not effortlessly ver­ified. It takes a pos­i­tive amount of effort to ver­ify it, and there is a pos­i­tive amount risk of hav­ing made a mis­take while do­ing so.

• The ar­ti­cle’s failure to dis­t­in­guish be­tween a math­e­mat­i­cal the­ory and a math­e­mat­i­cal model (map and ter­ri­tory, pos­si­bly?)

Ex­actly. This is one of Eliezer’s few gen­uine philo­soph­i­cal mis­takes, one which, four years later, he’s still mak­ing.

• I know very well the differ­ence be­tween a col­lec­tion of ax­ioms and a col­lec­tion of mod­els of which those ax­ioms are true, thank you.

A lot of peo­ple seem to have trou­ble imag­in­ing what it means to con­sider the hy­poth­e­sis that SS0+SS0 = SSS0 is true in all mod­els of ar­ith­metic, for pur­poses of de­riv­ing pre­dic­tions which dis­t­in­guish it from what we should see given the al­ter­na­tive hy­poth­e­sis that SS0+SS0=SSSS0 is true in all mod­els of ar­ith­metic, thereby al­low­ing in­ter­nal or ex­ter­nal ex­pe­rience to ad­vise you on which of these al­ter­na­tive hy­pothe­ses is true.

• I, at least, was not sug­gest­ing that you don’t know the differ­ence, merely that your ar­ti­cle failed to take ac­count of the differ­ence and was there­fore con­fus­ing and ini­tially un­con­vinc­ing to me be­cause I was tak­ing ac­count of that differ­ence.

How­ever (and it took me too damn long to re­al­ise this; I can’t wait for Logic and Set The­ory this com­ing year), I wasn’t talk­ing about “mod­els” in the sense that peb­bles are a Model of the The­ory PA. I was talk­ing in the sense that PA is a model of the be­havi­our ob­served in peb­bles. If PA fails to model peb­bles, that doesn’t mean PA is wrong, it just means that peb­bles don’t fol­low PA. If a Model of PA ex­ists in which SS0+SS0 = SSS0, then the The­ory PA ma­te­ri­ally can­not prove that SS0+SS0 ≠ SSS0, and if such a proof has been con­structed from the ax­io­mata of the The­ory then ei­ther the proof is in er­ror (ex­ists a step not jus­tified by the in­fer­ence rules), or the com­bi­na­tion of ax­io­mata and in­fer­ence rules con­tains a con­tra­dic­tion (which can be rephrased as “un­der these in­fer­ence rules, the The­ory is not con­sis­tent”), or the claimed Model is not in fact a Model at all (in which case one of the ax­io­mata does not, in fact, ap­ply to it).

I should prob­a­bly write down what I think I know about the epistemic sta­tus of math­e­mat­ics and why I think I know it, be­cause I’m pretty sure I dis­agree quite strongly with you (and my prior prob­a­bil­ity of me be­ing right and you be­ing wrong is rather low).

• Scien­tists and math­e­mat­i­ci­ans use the word “model” in ex­actly op­po­site ways. This is oc­ca­sion­ally con­fus­ing.

• I know very well the differ­ence be­tween a col­lec­tion of ax­ioms and a col­lec­tion of mod­els of which those ax­ioms are true, thank you.

Then why do you per­sist in say­ing things like “I don’t be­lieve in [Ax­iom X]/​[Math­e­mat­i­cal Ob­ject Y]”? If this dis­tinc­tion that you are so aptly able to re­hearse were truly in­te­grated into your un­der­stand­ing, it wouldn’t oc­cur to you to dis­cuss whether you have “seen” a par­tic­u­lar car­di­nal num­ber.

I un­der­stand the point you wanted to make in this post, and it’s a valid one. All the same, it’s ex­tremely easy to slip from em­piri­cism to Pla­ton­ism when dis­cussing math­e­mat­ics, and parts of this post can in­deed be read as be­tray­ing that slip (to which you have ex­plic­itly fallen vic­tim on other oc­ca­sions, the most re­cent be­ing the thread I linked to).

• I don’t think peo­ple re­ally un­der­stood what I was talk­ing about in that thread. I would have to write a se­quence about

• the differ­ence be­tween first-or­der and sec­ond-or­der logic

• why the Lowen­heim-Skolem the­o­rems show that you can talk about in­te­gers or re­als in higher-or­der logic but not first-or­der logic

• why third-or­der logic isn’t qual­i­ta­tively differ­ent from sec­ond-or­der logic in the same way that sec­ond-or­der logic is qual­i­ta­tively above first-or­der logic

• the gen­er­al­iza­tion of Solomonoff in­duc­tion to an­thropic rea­son­ing about agents re­sem­bling your­self who ap­pear em­bed­ded in mod­els of sec­ond-or­der the­o­ries, with more com­pact ax­iom sets be­ing more prob­a­ble a priori

• how that ad­dresses some points Wei Dai has made about hy­per­com­pu­ta­tion not be­ing con­ceiv­able to agents us­ing Solomonoff in­duc­tion on com­putable Carte­sian en­vi­ron­ments, as well as for­mal­iz­ing some of the ques­tions we ar­gue about in an­thropic theory

• why see­ing ap­par­ently in­finite time and ap­par­ently con­tin­u­ous space sug­gests, to an agent us­ing sec­ond-or­der an­thropic in­duc­tion, that we might be liv­ing within a model of ax­ioms that im­ply in­finity and continuity

• why be­liev­ing that things like a first un­countable or­di­nal can con­tain re­al­ity-fluid in the same way as the wave­func­tion, or even be uniquely speci­fied by sec­ond-or­der ax­ioms that pin down a sin­gle model up to iso­mor­phism the way that sec­ond-or­der ax­ioms can pin down in­te­gerness and re­al­ness, is some­thing we have rather less ev­i­dence for, on the sur­face of things, than we have ev­i­dence fa­vor­ing the phys­i­cal ex­ista­bil­ity of mod­els of in­finity and con­ti­nu­ity, or the math­e­mat­i­cal sen­si­bil­ity of talk­ing about the in­te­gers or real num­bers.

• I would like very very much to read that se­quence. Might it be writ­ten at some point?

• Every­thing sounded perfectly good un­til the last bul­let:

why be­liev­ing that things like a first un­countable or­di­nal can con­tain re­al­ity-fluid in the same way as the wavefunction

ERROR: CATEGORY. “Wave­func­tion” is not a math­e­mat­i­cal term, it is a phys­i­cal term. It’s a name you give to a math­e­mat­i­cal ob­ject when it is be­ing used to model the phys­i­cal world in a par­tic­u­lar way, in the spe­cific con­text of that mod­el­ing-task. The ac­tual math­e­mat­i­cal ob­ject be­ing used as the wave­func­tion has a math­e­mat­i­cal ex­is­tence to­tally apart from its phys­i­cal ap­pli­ca­tion, and that math­e­mat­i­cal ex­is­tence is of the ex­act same na­ture as that of the first un­countable or­di­nal; the (math­e­mat­i­cal) wave­func­tion does not gain any “on­tolog­i­cal bonus points” for its role in physics.

or even be uniquely speci­fied by sec­ond-or­der ax­ioms that pin down a sin­gle model up to iso­mor­phism the way that sec­ond-or­der ax­ioms can pin down in­te­gerness and realness

Pin­ning down a sin­gle model up to iso­mor­phism might be a nice prop­erty for a set of ax­ioms to have, but it is not “re­al­ity-con­fer­ring”: there are two groups of or­der 4 up to iso­mor­phism, while there is only one of or­der 3; yet that does not make “group of or­der 3“ a “more real” math­e­mat­i­cal ob­ject than “group of or­der 4”.

• Lowen­heim-Skolem, maybe?

But that does not im­ply that you can’t talk about in­te­gers or re­als in first or­der logic. And in­deed you can talk about in­te­gers and real num­bers us­ing first-or­der logic, peo­ple do so all the time.

• Only in the same sense that you can talk about kit­tens by say­ing “Those furry things!” There’ll always be some am­bi­guity over whether you’re talk­ing about kit­tens or li­ons, even though kit­tens are in fact furry and have all the prop­er­ties that you can de­duce to hold true of furry things.

• Not in the same sense at all. All of the num­bers that you have ever phys­i­cally en­coun­tered were name­able, defin­able, com­putable. More­over they came to you with al­gorithms for ver­ify­ing that one of them was equal to an­other.

• Yes, and that’s OK. I sus­pect you can’t do qual­i­ta­tively bet­ter than that (viz am­bi­ent set-the­o­retic uni­verse for sec­ond-or­der logic), but it’s still pos­si­ble (nec­es­sary?) to work un­der this ap­par­ent lack of ab­solute con­trol over what it is you are deal­ing with. Even though (first or­der) PA doesn’t know what “in­te­gers” are, it’s still true that the state­ments it be­lieves valid are true for “in­te­gers”, it’s use­ful that way (just as AIs or hu­mans are use­ful for mak­ing the world bet­ter). It is a de­vice that per­ceives some of the prop­er­ties of the ob­ject we study, but not all, not enough to re­build it com­pletely. (Other de­vices can form similarly im­perfect pic­tures of the ob­ject of study and its re­la­tion­ship with the de­vice per­ceiv­ing it, or of them­selves per­ceiv­ing this pro­cess, or of the ob­ject of study be­ing af­fected by be­hav­ior of some of these de­vices.)

Like­wise, we may fail to ac­count for all wor­lds that we might be af­fect­ing by our de­ci­sions, but we mostly care about (or maybe rather have non-neg­ligible con­se­quen­tial­ist con­trol over) “real world” (or wor­lds), what­ever this is, and it’s true that our con­clu­sions cap­ture some truth about this “real world”, even if it’s gen­uinely im­pos­si­ble for us to ever know com­pletely what it is. (We of course “know” plenty more than was ever un­der­stood, and it’s a big ques­tion how to com­mu­ni­cate to a FAI what we do know.)

• In other words, a first un­countable or­di­nal may be perfectly good math, but it’s not physics?

• I don’t be­lieve it’s good math un­til it be­comes pos­si­ble to talk about the first un­countable or­di­nal, in the way that you can talk about the in­te­gers. Any first-or­der the­ory of the in­te­gers, like first-or­der PA, will have some mod­els con­tain­ing su­per­nat­u­ral num­bers, but there are many differ­ent sorts of mod­els of su­per­nat­u­ral num­bers, you couldn’t talk about the su­per­nat­u­rals the way you can talk about 3 or the nat­u­ral num­bers. My skep­ti­cism about “the first un­countable or­di­nal” is that there would not ex­ist any canon­i­cal­iz­able math­e­mat­i­cal ob­ject—noth­ing you could ever pin down uniquely—that would ever con­tain the first un­countable or­di­nal in­side it, be­cause of the in­definitely ex­ten­si­ble char­ac­ter of well-or­der­ing. This is a sort of skep­ti­cism of Pla­tonic ex­is­tence—when that which you thought you wanted to talk about can never be pinned down even in sec­ond-or­der logic, nor in any other lan­guage which does not per­mit of para­dox.

• You seem to keep for­get­ting that the whole no­tion of “sec­ond-or­der logic” does not make sense with­out some am­bi­ent set the­ory. (Un­less I am greatly mi­s­un­der­stand­ing how sec­ond-or­der logic works?) And if you have that, then you can pin down the nat­u­ral num­bers (and the first un­countable or­di­nal) in first-or­der terms in this larger the­ory.

• Only to the same de­gree that first-or­der logic re­quires an am­bi­ent group of mod­els (not nec­es­sar­ily sets) to make sense. It’s just that the am­bi­ent mod­els in the sec­ond-or­der the­ory in­clude col­lec­tions of pos­si­ble pred­i­cates of any ob­jects that get pred­i­cates at­tached, or if you pre­fer, peo­ple who speak in sec­ond-or­der logic think that it makes as much sense to say “all pos­si­ble col­lec­tions that in­clude some ob­jects and ex­clude oth­ers, but still in­clude and ex­clude only in­di­vi­d­ual ob­jects” as “all ob­jects”.

• Only to the same de­gree that first-or­der logic re­quires an am­bi­ent group of mod­els (not nec­es­sar­ily sets) to make sense.

Well, it makes sense to me with­out any mod­els. I can com­pute, prove the­o­rems, ver­ify proofs of the­o­rems and so on hap­pily with­out ever pro­duc­ing a “model” for the nat­u­ral num­bers in toto, what­ever that could mean.

• Hmmm…

::goes and learns some more math from Wikipe­dia::

Okay… I now know what an or­di­nal num­ber ac­tu­ally is. And I’m try­ing to make more sense out of your com­ment...

or even be uniquely speci­fied by sec­ond-or­der ax­ioms that pin down a sin­gle model up to iso­mor­phism the way that sec­ond-or­der ax­ioms can pin down in­te­gerness and re­al­ness, is some­thing we have rather less ev­i­dence for

So if I un­der­stand you cor­rectly, you don’t trust any­thing that can’t be defined up to iso­mor­phism in sec­ond-or­der logic, and “the set of all countable or­di­nals” is one of those things?

(I never learned sec­ond or­der logic in col­lege...)

• Hmm, funny you should treat “I don’t be­lieve in [Math­e­mat­i­cal Ob­ject Y]” as Pla­ton­ism. I gen­er­ally char­ac­ter­ise my ‘syn­tac­ti­cism’ (wh. I in­tend to ex­plain more fully when I un­der­stand it the hell my­self) as a “Pla­tonic For­mal­ism”; it is promis­cu­ously in­clu­sive of Math­e­mat­i­cal Ob­jects. If you can for­mu­late a set of be­havi­ours (in­fer­ence rules) for it, then it has an ex­ist­ing Form—and that Form is the for­mal­ism (or… syn­tax) that en­cap­su­lates its be­havi­our. So in a sense, un­countable car­di­nals don’t ex­ist—but the the­ory of un­countable car­di­nals does ex­ist; similarly, the the­ory of finite car­di­nals ex­ists but the num­ber ‘2’ doesn’t.

This is of course bass-ack­wards from a map-ter­ri­tory per­spec­tive; I am claiming that the map ex­ists and the ter­ri­tory is just some­thing we naïvely sup­pose ought to ex­ist. After all, a map of non-ex­is­tent ter­ri­tory is ob­ser­va­tion­ally equiv­a­lent to a map of man­i­fest re­al­ity; un­less you can ob­serve the ac­tual ter­ri­tory you can’t dis­t­in­guish the two. Tak­ing as as­sump­tion that the ob­serve() func­tion always re­turns an ob­ject Map, the idea that there is a ter­ri­tory gets Oc­camed out.

There is a good rea­son why I should want to do some­thing so on­tolog­i­cally bizarre: by re­mov­ing refer­ents, and se­man­tics, and man­i­fest re­al­ity; by re­tain­ing only syn­tax, and re­ject­ing the sug­ges­tion that one logic re­ally “mod­els” an­other, we fi­nally solve the prob­lems of Gödel (I’m a math­e­mat­i­cian, not a philoso­pher, so I’m al­lowed to in­voke Gödel with­out los­ing au­to­mat­i­cally) and the in­finite de­scent when we say “first or­der logic is con­sis­tent be­cause sec­ond-or­der logic proves it so, and we can be­lieve sec­ond-or­der logic be­cause third-or­der logic proves it con­sis­tent, and...”. When all you are do­ing is play­ing sym­bol games stripped of any se­man­tics, “P ∧ ¬P” is just a string, and who cares if you can de­rive it from your ax­io­mata? It only stops be­ing a string when you ap­ply your sym­bol games to what you un­know­ingly la­bel as “man­i­fest re­al­ity”, when you (es­sen­tially) claim that sym­bol game A (Peano ar­ith­metic) mod­els sym­bol game B (that part of the Physics game that deals with the ob­jects you’ve iden­ti­fied as peb­bles).

Pla­ton­ism is not a means of ex­clud­ing a math­e­mat­i­cal ob­ject be­cause it’s not one of the Forms; it is a means of al­low­ing any math­e­mat­i­cal ob­ject to have a Form whether you like it or not. I don’t be­lieve in God, but there still ex­ists a Form for a math­e­mat­i­cal ob­ject that looks a lot like “a uni­verse in which God ex­ists”. It’s just that con­ceiv­ing of a pos­si­ble world only makes an ar­row from your world to its, not an ar­row in the re­verse di­rec­tion, hence why “A perfect God would have the qual­ity of ex­is­tence” is such a laugh­able non-starter :) What if some­one broke out of a hy­po­thet­i­cal situ­a­tion in your room right now?

• (I’m a math­e­mat­i­cian, not a philoso­pher, so I’m al­lowed to in­voke Gödel with­out los­ing au­to­mat­i­cally)

As a fel­low math­e­mat­i­cian, I want to point out that it doesn’t mean you win au­to­mat­i­cally, ei­ther. Just look at Vo­evod­sky’s re­cent FOM talk at the IAS.

• Well, of course I don’t win au­to­mat­i­cally. It’s just that there’s a kind of God­win’s Law of philos­o­phy, whereby the first to in­voke Gödel loses by de­fault.

• Read­ing your es­say I won­dered whether it would have been more effec­tive if you had cho­sen big­ger num­bers than 2, 2, and 3. e.g. “How to con­vince me that 67+41 = 112.”

• A lot of peo­ple seem to have trou­ble imag­in­ing what it means to con­sider the hy­poth­e­sis that SS0+SS0 = SSS0 is true in all mod­els of arithmetic

Maybe I’m mis­in­ter­pret­ing you, but could you ex­plain how any non-sym­met­ric equa­tion can pos­si­bly be true in all mod­els of ar­ith­metic?

• Maybe I’m mis­in­ter­pret­ing you, but could you ex­plain how any non-sym­met­ric equa­tion can pos­si­bly be true in all mod­els of ar­ith­metic?

The pur­pose of the ar­ti­cle is only to de­scribe some sub­jec­tive ex­pe­riences that would cause you to con­clude that SS0+SS0 = SSS0 is true in all mod­els of ar­ith­metic. But Eliezer can only de­scribe cer­tain prop­er­ties that those sub­jec­tive ex­pe­riences would have. He can’t make you have the ex­pe­riences them­selves.

So, for ex­am­ple, he could say that one such ex­pe­rience would con­form to the fol­low­ing de­scrip­tion: “You count up all the S’s on one side of the equa­tion, and you count up all the S’s on the other side of the equa­tion, and you find your­self get­ting the same an­swer again and again. You show the equa­tion to other peo­ple, and they get the same an­swer again and again. You build a com­puter from scratch to count the S’s on both sides, and it says that there are the same num­ber again and again.”

Such a de­scrip­tion gives some fea­tures of an ex­pe­rience. The de­scrip­tion pro­vides a test that you could ap­ply to any given ex­pe­rience and an­swer the ques­tion “Does this ex­pe­rience satisfy this de­scrip­tion or not?” But the de­scrip­tion is not like one in a novel, which, ideally, would in­duce you to have the ex­pe­rience, at least in your imag­i­na­tion. That is a sep­a­rate and ad­di­tional task be­yond what this post set out to ac­com­plish.

• Yes, I am aware of that. How­ever, I don’t think two peb­bles on the table plus an­other two peb­bles on the table re­sult­ing in three peb­bles on the table could cause any­one sane to con­clude that SS0 + SS0 = SSS0 is true in all mod­els of ar­ith­metic. In or­der to be con­vinced of that, you would have to as­sign “PA doesn’t ap­ply to peb­bles” a lower prior prob­a­bil­ity than “PA is wrong”.

The state­ment “PA ap­plies to peb­bles” (or any­thing else for that mat­ter) doesn’t fol­low of the peano ax­ioms in any way and is there­fore not part of peano ar­ith­metic. So what if peano ar­ith­metic doesn’t ap­ply to peb­bles, there are other ar­ith­metics that don’t ei­ther, and that doesn’t make them any wrong. You’re us­ing them ev­ery­day in situ­a­tions where they do ap­ply.

A math­e­mat­i­cal the­ory doesn’t con­sist of be­liefs that are based on ev­i­dence; it’s an ax­io­matic sys­tem. There is no way any real-life situ­a­tion could con­vince me that PA is false. Say­ing “SS0 + SS0 = SSS0 is true in all mod­els of ar­ith­metic” sounds like “0 = S0″ or “gar­ble asdf qw­erty sputz” to me. It just doesn’t make any sense.

Math­e­mat­ics has noth­ing to do with ex­pe­rience, only to what ex­tent math­e­mat­ics ap­plies to re­al­ity does.

• Math­e­mat­ics has noth­ing to do with ex­pe­rience.

That you have cer­tain math­e­mat­i­cal be­liefs has a lot to do with the ex­pe­riences that you have had. This ap­plies in par­tic­u­lar to your be­liefs about what the the­o­rems of PA are.

• Sorry, I ed­ited the state­ment in ques­tion right be­fore you posted that be­cause I an­ti­ci­pated a similar re­ac­tion. How­ever, you’re still wrong. It has only to do with my be­liefs to what ex­tent peano ar­ith­metic ap­plies to re­al­ity, which is some­thing com­pletely differ­ent.

Edit: Ok, you’re prob­a­bly not wrong, but it rather seems we are talk­ing about differ­ent things when we say “math­e­mat­i­cal be­liefs”. Whether peano ar­ith­metic ap­plies to re­al­ity is not a math­e­mat­i­cal be­lief for me.

• Con­sider the ex­pe­riences that you have had while read­ing and think­ing about proofs within PA. (The ex­pe­rience of de­vis­ing and con­firm­ing a proof is just a par­tic­u­lar kind of ex­pe­rience, af­ter all.) Are you say­ing that the con­tents of those ex­pe­riences have had noth­ing to do with the be­liefs that you have formed about what the the­o­rems of PA are?

Sup­pose that those ex­pe­riences had been sys­tem­at­i­cally differ­ent in a cer­tain way. Say that you con­sis­tently made a cer­tain kind of mis­take while con­firm­ing PA proofs, so that cer­tain proofs seemed to be valid to you that don’t seem valid to you in re­al­ity. Would you not have ar­rived at differ­ent be­liefs about what the the­o­rems of PA are?

That is the sense in which your be­liefs about what the the­o­rems of PA are de­pend on your ex­pe­riences.

• I’m not sure I 100% un­der­stand what you’re say­ing, but the ques­tion “which be­liefs will I end up with if log­i­cal rea­son­ing it­self is flawed” is of lit­tle in­ter­est to me.

• Is the ques­tion “Which be­liefs will I end up with if my fac­ulty of log­i­cal rea­son­ing is flawed” also of lit­tle in­ter­est to you?

• Yes, be­cause if I as­sume that my fac­ulty of log­i­cal rea­son­ing is flawed, no de­duc­tions of log­i­cal rea­son­ing I do can be con­sid­ered cer­tain, in which case ev­ery­thing falls: Math­e­mat­ics, physics, bayesi­anism, you name it. It is there­fore (haha! but what if my fac­ulty of log­i­cal rea­son­ing is flawed?) very ir­ra­tional to as­sume this.

• But you know that your fac­ulty of log­i­cal rea­son­ing is flawed to some ex­tent. Hu­mans are not perfect lo­gi­ci­ans. We man­age to find use in mak­ing long chains of log­i­cal de­duc­tions even though we know that they con­tain mis­takes with some nonzero prob­a­bil­ity.

• I don’t know that. Can you prove that un­der the as­sump­tion you’re mak­ing?

As I see it, my fac­ulty of log­i­cal rea­son­ing is not flawed in any way. The only thing that’s flawed is my fac­ulty of do­ing log­i­cal rea­son­ing, i.e. I’m not always do­ing log­i­cal rea­son­ing when I should be. But that’s hardly the mat­ter here.

I would be very in­ter­ested in how you can come to any con­clu­sion un­der the as­sump­tion that the log­i­cal rea­son­ing you do to come to that con­clu­sion is flawed. If my fac­ulty of log­i­cal rea­son­ing is flawed, I can only say one thing with cer­tainty, which is that my fac­ulty of log­i­cal rea­son­ing is flawed. Ac­tu­ally, I don’t think I could even say that.

Edit:

We man­age to find use in mak­ing long chains of log­i­cal de­duc­tions even though we know that they con­tain mis­takes with some nonzero prob­a­bil­ity.

I don’t con­sider this to be a prob­lem of ac­tual fac­ulty of log­i­cal rea­son­ing be­cause if some­one finds a log­i­cal mis­take I will agree with them.

• So you don’t con­sider mis­takes in log­i­cal rea­son­ing a prob­lem be­cause some­one might point them out to you? What if it’s an easy mis­take to make, and a lot of other peo­ple make the same mis­take? At this point, it seems like you’re ar­gu­ing about the defi­ni­tion of the words “prob­lem with”, not about states of the world. Can you clar­ify what dis­agree­ment you have about states of the world?

• I think the point is that math­e­mat­i­cal rea­son­ing is in­her­ently self-cor­rect­ing in this sense, and that this cor­rec­tive force is in­ten­tion­is­tic and La­mar­ck­ian—it is be­ing cor­rected to­ward a math­e­mat­i­cal ar­gu­ment which one thinks of as a time­less perfect Form (be­cause come on, are there re­ally any math­e­mat­i­ci­ans who don’t, se­cretly, be­lieve in the Pla­tonic re­al­ism of math­e­mat­ics?), and not just away from an ar­gu­ment that’s flawed.

An in­cor­rect the­ory can ap­pear to be sup­ported by ex­per­i­men­tal re­sults (with prob­a­bil­ity go­ing to 0 as the sam­ple size goes to \in­fty), and if you have the finite set of ex­per­i­men­tal re­sults point­ing to the wrong con­clu­sion, then no amount of mind-in­ter­nal ex­am­i­na­tion of those re­sults can cor­rect the er­ror (if it could, your the­ory would not be pre­dic­tive; con­ser­va­tion of prob­a­bil­ity, you all know that). But mind-in­ter­nal ex­am­i­na­tion of a math­e­mat­i­cal ar­gu­ment, with­out any fur­ther en­tan­gling (so no new in­for­ma­tion, in the Bayesian sense, about the out­side world; only new in­for­ma­tion about the world in­side your head), can dis­cover the er­ror, and once it has done so, it is typ­i­cally a me­chan­i­cal pro­cess to ver­ify that the er­ror is in­deed an er­ror and that the cor­rec­tion has in­deed cor­rected that er­ror.

This re­mains true if the er­ror is an er­ror of omis­sion (We haven’t found the proof that T, so we don’t know that T, but in fact there is a proof of T).

So you’re not get­ting new bits from ob­served re­al­ity, yet you’re mak­ing new dis­cov­er­ies and over­throw­ing past mis­takes. The bits are com­ing from the pro­cess­ing; your ig­no­rance has de­creased by com­pu­ta­tion with­out the ac­qui­si­tion of bits by en­tan­gling with the world. That’s why de­duc­tive knowl­edge is cat­e­gor­i­cally differ­ent, and why er­rors in log­i­cal rea­son­ing are not a prob­lem with the idea of log­i­cal rea­son­ing it­self, nor do they ex­clude a math­e­mat­i­cal state­ment from be­ing un­con­di­tion­ally true. They just ex­clude the pos­si­bil­ity of un­con­di­tional knowl­edge.

Can you con­ceive of a world in which, say, ⋀∅ is false? It’s cer­tainly a lot harder than con­ceiv­ing of a world in which earplugs obey “2+2=3”-ar­ith­metic, but is your be­lief that ⋀∅ un­con­di­tional? What is the ab­solutely most fun­da­men­tally ob­vi­ous tau­tol­ogy you can think of, and is your be­lief in it un­con­di­tional? If not, what kind of ev­i­dence could there be against it? It seems to me that ¬⋀∅ would re­quire “there ex­ists a false propo­si­tion which is an el­e­ment of the empty set”; in or­der to make an er­ror there I’d have to have made an er­ror in look­ing up a defi­ni­tion, in which case I’m not re­ally talk­ing about ⋀∅ when I as­sert its truth; nonethe­less the thing I am talk­ing about is a tau­tolog­i­cal truth and so one still ex­ists (I may have gained or lost a ‘box’, here, in which case things don’t work).

My mind is be­gin­ning to melt and I think I’ve drifted off topic a lit­tle. I should go to bed. (Sorry for ram­bling)

• I guess there are my be­liefs-which-pre­dict-my-ex­pec­ta­tions and my aliefs-which-still-weird-me-out. In the sense of be­liefs which pre­dict my ex­pec­ta­tion, I would say the fol­low­ing about math­e­mat­ics: as far as logic is con­cerned, I have seen (with my eyes, con­nected to neu­rons, and so on) the proof that from P&-P any­thing fol­lows, and since I do want to dis­t­in­guish “truth” from “false­hood”, I view it as (un­less I made a mis­take in the proof of P&-P->Q, which I view as highly un­likely—an easy mil­lion-to-one against) as false. Any­thing which leads me to P&-P, there­fore, I see as false, con­di­tional on the pos­si­bil­ity I made a mis­take in the proof (or not no­ticed a mis­take some­one else made). Since I have a proof from “2+2=3” to “2+2=3 and 2+2!=3″ (which is fairly sim­ple, and I checked mul­ti­ple times) I view 2+2=3 as equally un­likely. That’s surely en­tan­gle­ment with the world—I ma­nipu­lated sym­bols writ­ten by a phys­i­cal pen on a phys­i­cal pa­per, and at each stage, the line fol­low­ing obeyed a re­la­tion­ship with the line be­fore it. My be­lief that “there is some truth”, I guess, can be called un­con­di­tional—noth­ing I see will con­vince me oth­er­wise. But I’m not even cer­tain I can con­ceive of a world with­out truth, while I can con­ceive of a world, sadly, where there are mis­takes in my proofs :)

• You’re miss­ing the es­sen­tial point about de­duc­tives, which is this:

Chang­ing the sub­strate used for the calcu­la­tions does not change the ex­per­i­ment.

With a nor­mal ex­per­i­ment, if you re­peat my ex­per­i­ment it’s pos­si­ble that your ap­para­tus differs from mine in a way which (un­be­knownst to ei­ther of us) is salient and af­fects the out­come.

With math­e­mat­i­cal de­duc­tion, if our re­sults dis­agree, (at least) one of us is sim­ply wrong, it’s not “this da­tum is also valid but it’s data about a differ­ent set of con­di­tions”, it’s “this da­tum con­tains an er­ror in its deriva­tion”. It is the same ex­per­i­ment, and the same com­pu­ta­tion, whether it is car­ried out on my brain, your brain, your brain us­ing pen and pa­per as an ex­ter­nal sin­gle-write store, the­o­rem-prover soft­ware run­ning on a Pen­tium, the same soft­ware run­ning on an Athlon, differ­ent soft­ware in a differ­ent lan­guage run­ning on a Bab­bage An­a­lyt­i­cal Eng­ine… it’s still the same ex­per­i­ment. And a mis­take in your proof re­ally is a mis­take, rather than the laws of math­e­mat­ics hav­ing been mo­men­tar­ily false lead­ing you to a false con­clu­sion. To quote the ar­ti­cle, “Un­con­di­tional facts are not the same as un­con­di­tional be­liefs.” Con­tra­pos­i­tive: con­di­tional be­liefs are not the same as con­di­tional facts.

The only way in which your calcu­la­tion en­tan­gled with the world is in terms of the re­li­a­bil­ity of pen-and-pa­per sin­gle-write stor­age; that re­li­a­bil­ity is not con­tin­gent on what the true laws of math­e­mat­ics are, so the bits that come from that are not bits you can use­fully en­tan­gle with. The bits that you can ob­tain about the true laws of math­e­mat­ics are bits pro­duced by com­pu­ta­tion.

• I don’t con­sider these mis­takes to be no prob­lem at all. What I meant to say is that the ex­is­tence of these noise er­rors doesn’t re­duce the rea­son­abli­ness of me go­ing around and us­ing log­i­cal rea­son­ing to draw de­duc­tions. Which also means that if re­al­ity seems to con­tra­dict my de­duc­tions, then ei­ther there is an er­ror within my de­duc­tions that I can the­o­ret­i­cally find, or there is an er­ror within the line of thought that made me doubt my de­duc­tions, for ex­am­ple eyes be­ing in­ad­e­quate tools for count­ing peb­bles. To put it more gen­er­ally: If I don’t find er­rors within my de­duc­tions, then my per­cep­tion of re­al­ity is not an ap­pro­pri­ate mea­sure for the truth of my de­duc­tions, un­less said de­duc­tions deal in any way with the ap­pli­ca­bil­ity of other de­duc­tions on re­al­ity, or re­al­ity in gen­eral, which math­e­mat­ics does not.

It’s not as if er­rors in per­ceiv­ing re­al­ity weren’t much more nu­mer­ous and harder to de­tect than er­rors in any­one’s fac­ulty of do­ing log­i­cal rea­son­ing.

• It’s not as if er­rors in per­ceiv­ing re­al­ity weren’t much more nu­mer­ous and harder to de­tect than er­rors in any­one’s fac­ulty of do­ing log­i­cal rea­son­ing.

And the prob­a­bil­ity of an er­ror in a given log­i­cal ar­gu­ment gets smaller as the chain of de­duc­tions gets shorter and as the num­ber of ver­ifi­ca­tions of the ar­gu­ment gets larger.

Nonethe­less, the prob­a­bil­ity of er­ror should never reach zero, even if the ar­gu­ment is as short as the proof that SS0 + SS0 = SSSS0 in PA, and even if the proof has been ver­ified by your­self and oth­ers billions of times.

ETA: Where ever I wrote “proof” in this com­ment, I meant “alleged proof”. (Erm … ex­cept for in this ETA.)

• the prob­a­bil­ity of er­ror should never reach zero

The prob­a­bil­ity that there is an er­ror within the line of thought that lets me come to the con­clu­sion that there is an er­ror within any the­o­rem of peano ar­ith­metic is always higher than the prob­a­bil­ity that there ac­tu­ally is an er­ror within any the­o­rem of peano ar­ith­metic, since prob­a­bil­ity the­ory is based on peano ar­ith­metic and if SS0 + SS0 = SSSS0 were wrong, prob­a­bil­ity the­ory would be at least equally wrong.

• the prob­a­bil­ity that there ac­tu­ally is an er­ror within any the­o­rem of peano ar­ith­metic.

(Em­pha­sis added.) Where ever I wrote “proof” in the grand­par­ent com­ment, I should have writ­ten “alleged proof”.

We prob­a­bly agree that the idea of “an er­ror in a the­o­rem of PA” isn’t mean­ingful. But the idea that ev­ery­one was mak­ing a mis­take the whole time that they thought that SS0 + SS0 = SSSS0 was a the­o­rem of PA, while, all along, SS0 + SS0 = SSS0 was a the­o­rem of PA — that idea is mean­ingful. After all, peo­ple are all the time alleg­ing that some state­ment is a the­o­rem of PA when it re­ally isn’t. That is to say, peo­ple make ar­ith­metic mis­takes all the time.

• That is true. How­ever, if your per­cep­tion of re­al­ity leads you to the thought that there might be an er­ror with SS0 + SS0 = SSSS0, and you can’t find that er­ror, then it is ir­ra­tional to as­sume that there ac­tu­ally is an er­ror with SS0 + SS0 = SSSS0 rather than with your per­cep­tion of ra­tio­nal­ity or the con­cept of ap­ply­ing SS0 + SS0 = SSSS0 to re­al­ity.

Can we agree on that?

• Can we agree on that?

I think so, if I un­der­stand you. But I think that you’re refer­ring to a more re­stricted class of “per­cep­tions of re­al­ity” than Eliezer is.

In the kind of sce­nario that Eliezer is talk­ing about, your per­cep­tions of re­al­ity in­clude seem­ing to find an er­ror in the alleged proof that SS0 + SS0 = SSSS0 (and con­firm­ing your per­cep­tion of an er­ror suffi­ciently many times to out­weigh all the times when you thought you’d con­firmed that the alleged proof was valid). If that is the kind of “per­cep­tion of re­al­ity” that we’re talk­ing about, then you should con­clude that there was an er­ror in the alleged proof of SS0 + SS0 = SSSS0.

• That is all good and valid, and of course I don’t be­lieve in any re­sults of de­duc­tions with er­rors in them just based on said de­duc­tions. But that has noth­ing to do with re­al­ity. Two peb­bles plus two peb­bles re­sult­ing in three peb­bles is not what con­vinces me that SS0 + SS0 = SSS0; find­ing the er­ror is, which is noth­ing that is per­ceived (i.e. it is purely ab­stract).

If we’re defin­ing “situ­a­tion” in a way similar to how it’s used in the top-level post (peb­bles and stuff), then there sim­ply can’t ex­ist a situ­a­tion that could con­vince me that SS0 + SS0 = SSSS0 is wrong in peano ar­ith­metic. It might con­vince me to check peano ar­ith­metic, of course, but that’s all.

I try to not ar­gue about defi­ni­tion of words, but it just seems to me that as soon as you define words like “per­cep­tion”, “situ­a­tion”, “be­lieve” etcetera in a way that would re­sult in a situ­a­tion ca­pa­ble of con­vinc­ing me that SS0 + SS0 = SSS0 is true in peano ar­ith­metic, we are not talk­ing about re­al­ity any­more.

• Okay, I just thought of a pos­si­ble situ­a­tion that would in­deed “con­vince” me of 2 + 2 = 3: Dis­able the mod­ule of my brain re­spon­si­ble for log­i­cal rea­son­ing, then show me some stage magic in­volv­ing peb­bles or earplugs, and then my poor ra­tio­nal­iza­tion mod­ule would prob­a­bly end up with some ex­pla­na­tion along the lines of 2 + 2 = 3.

But let’s not go there.

• As I see it, my fac­ulty of log­i­cal rea­son­ing is not flawed in any way. The only thing that’s flawed is my fac­ulty of do­ing log­i­cal rea­son­ing, i.e. I’m not always do­ing log­i­cal rea­son­ing when I should be.

Sorry for not be­ing clear. By “fac­ulty of log­i­cal rea­son­ing”, I mean noth­ing other than “fac­ulty of do­ing log­i­cal rea­son­ing”.

• In that case I have prob­a­bly an­swered your origi­nal ques­tion here.

• And an­other thing: It might be pos­si­ble that if peano ar­ith­metic didn’t ap­ply to re­al­ity I wouldn’t have any be­liefs about peano ar­ith­metic be­cause I might not even think of it. How­ever there is no way I could es­tab­lish the peano ax­ioms and then be­lieve that SS0 + SS0 = SSS0 is true within peano ar­ith­metic. It’s just not pos­si­ble.

• SS0 isn’t a free vari­able like “x”, it is, in any given model of ar­ith­metic, the unique ob­ject re­lated by the suc­ces­sor re­la­tion to the unique ob­ject re­lated by the suc­ces­sor re­la­tion to the unique ob­ject which is not re­lated by the suc­ces­sor re­la­tion to any ob­ject, which is how math­e­mat­i­ci­ans say “Two”.

• Although as a mathmo my­self I should point out that, to save time, we usu­ally pro­nounce it “Two”. :)

• I am quite fa­mil­iar with TNT. How­ever ei­ther you are talk­ing about mod­els of ar­ith­metic based on peano ax­ioms, in which case e.g. SS0 + SS0 = SSS0 sim­ply can­not be true, for it con­tra­dicts these ax­ioms and if both the peano ax­ioms and said equa­tion were true, you wouldn’t have a model of ar­ith­metics; or (what I’m as­sum­ing) you are ac­tu­ally talk­ing about non-peano ar­ith­metics, in which case there is no com­pel­ling rea­son why any equa­tion of this kind should gen­er­ally be true any­way.

On an­other note, it seems that bayesi­anism is heav­ily based on peano ar­ith­metic, so re­fut­ing peano ar­ith­metic by means of bayesi­anism seems like re­fut­ing bayesi­anism rather than re­fut­ing peano ar­ith­metic, at least to me.

• There seem to be far too many peo­ple hung up on the math­e­mat­ics which ig­nores the pur­pose of the post as I un­der­stand it.

The post is not about truth but about con­vic­tion. Eliezer is not say­ing that there could be a sce­nario in which the rules of math­e­mat­ics didn’t work, but that there could be a sce­nario un­der which he was con­vinced of it.

De­con­struct­ing all el­e­ments of neu­rol­ogy, physics and so­cial­ogy that make up the path­way from com­plete ig­no­rance to solid con­vic­tion is not some­thing I could even be­gin to at­tempt—but if one were able to list such steps as a se­ries bul­let points I could con­ceive that the ma­nipu­la­tion of cer­tain steps could lead to a differ­ent out­come, which ap­pears to me to be the ul­ti­mate point of the post (al­though not hugely ground-break­ing, but an in­ter­est­ing thought ex­per­i­ment).

It is not a claim that the strongly held con­vic­tion rep­re­sents fact or that the con­vic­tion would not be shaken by a fu­ture event or pre­sen­ta­tion of ev­i­dence. As a fun­da­men­tal be­liever in sci­en­tific thought and ra­tio­nal­ity there is much that I hold as firm con­vic­tion that I would not hes­i­tate to re-think un­der valid con­tra­dic­tory ev­i­dence.

• I wish I could vote you up so much more! The dis­tinc­tion be­tween a-con­vinc­ing-ar­gu­ment and what-it-would-take-to-con­vince-me is very real and over­looked by al­most ev­ery­one post­ing here.

To take my own ex­pe­rience in be­com­ing con­vinced of athe­ism, I some­times like to think I ac­cept athe­ism for the same rea­son that I ac­cept evolu­tion—be­cause of the ev­i­dence/​lack thereof/​etcetera. But that is sim­ply not the case. I ac­cept athe­ism be­cause of a highly per­sonal his­tory of what it took to get me, per­son­ally, to stop be­liev­ing in Chris­ti­an­ity, and start be­liev­ing in some­thing else that, as much as I would like to pat my ra­tio­nal self on the back, has fairly lit­tle to do with the ar­gu­ments and ev­i­dence I heard on the mat­ter.

When ask­ing some­one why they be­lieve some­thing or are con­vinced of it, “what is the rea­son?” and “what is your rea­son?” are two to­tally differ­ent ques­tions.

• To take my own ex­pe­rience in be­com­ing con­vinced of athe­ism, I some­times like to think I ac­cept athe­ism for the same rea­son that I ac­cept evolu­tion—be­cause of the ev­i­dence/​lack thereof/​etcetera. But that is sim­ply not the case. I ac­cept athe­ism be­cause of a highly per­sonal his­tory of what it took to get me, per­son­ally, to stop be­liev­ing in Chris­ti­an­ity, and start be­liev­ing in some­thing else that, as much as I would like to pat my ra­tio­nal self on the back, has fairly lit­tle to do with the ar­gu­ments and ev­i­dence I heard on the mat­ter.

It’s pos­si­ble that the rea­son you ac­cepted athe­ism is differ­ent to the rea­son you cur­rently ac­cept athe­ism. To make an anal­ogy, I use the QWERTY key­board now be­cause it’s the in­dus­try stan­dard and there­fore the most likely key­board lay­out for me to en­counter on an un­fa­mil­iar ma­chine, re­gard­less of the fact that I learned the QWERTY key­board be­cause that’s what was the set­ting on my com­puter when I started post­ing ob­ses­sively in the Do­minic Dee­gan fo­rums.

• “A pri­ori rea­son­ing” takes place in­side the brain; which is to say, any par­tic­u­lar form of “a pri­ori rea­son­ing” is part of a sim­ple phys­i­cal pro­cess unified with the em­piri­cal ques­tions that we are rea­son­ing about. It is no great sur­prise by se­lect­ing the right form of “a pri­ori rea­son­ing” we can man­age to mir­ror the out­side world. In­side and out­side are part of the same world.

When you think about math­e­mat­ics, your thoughts are not tak­ing place in­side an­other uni­verse, though I can see why peo­ple would feel that way.

• As Within, So Without?

[ducks the rot­ten toma­toes]

• Wikipe­dia on a pri­ori: Re­la­tions of ideas, ac­cord­ing to Hume, are “dis­cov­er­able by the mere op­er­a­tion of thought, with­out de­pen­dence on what is any­where ex­is­tent in the uni­verse”.

This points out clearly the prob­lem that I have with “a pri­ori”. It is a fun­da­men­tally Carte­sian-du­al­ist no­tion. The “mere op­er­a­tion of thought” takes place INSIDE THE UNIVERSE, as op­posed to any­where else.

To ob­serve your own thoughts is a kind of ev­i­dence, if the spik­ings of your neu­rons be en­tan­gled with the ob­ject of your in­quiry (rel­a­tive to your cur­rent state of un­cer­tainty about both). If, for ex­am­ple, I do not know what will hap­pen with two earplugs and two earplugs on the night­stand, I can vi­su­al­ize two ap­ples plus two ap­ples to find out. All of this takes place in the same, unified, phys­i­cal uni­verse, with no on­tolog­i­cal bor­der be­tween the atoms in my skull and the atoms out­side my skull. That’s why the trick works. It would work just as well if I used a pocket calcu­la­tor. Is the out­put of a pocket calcu­la­tor an a pri­ori truth? Why not call the earplugs them­selves a pri­ori truths, then? But if nei­ther of these are a pri­ori, why should I treat the out­puts of my neu­rons as “a pri­ori”? It’s all the same uni­verse.

It ap­pears to me that “a pri­ori” is a se­man­tic stop­sign; its only visi­ble mean­ing is “Don’t ask!”

Vas­sar: It sure seems to me that our evolu­tion and cul­ture con­structed eth­i­cal at­ti­tudes are en­tan­gled with the world.

They’re causal prod­ucts of the world, and yes, if I was ig­no­rant about some evolu­tion-re­lated fac­tual ques­tion, I might be able to use my eth­i­cal at­ti­tudes as ev­i­dence about con­di­tions ob­tain­ing in my an­ces­tral en­vi­ron­ment. That’s not the same as my stat­ing an ex­ter­nal truth-con­di­tion for it be­ing wrong to slaugh­ter the first-born male chil­dren of the sub­jects of an un­elected Pharaoh. It is perfectly ac­cept­able for me to say, “I can think of no en­coun­ter­able situ­a­tion that would trans­form the ter­mi­nal value of this event from nega­tive to pos­i­tive.”

Spear: The test of any re­li­gion is whether cul­tures be­liev­ing it tend to thrive and im­prove the qual­ity of their lives or not.

Ah, yes, the old the­ory that there are rea­sons to be­lieve2 in an as­ser­tion-of-fact be­sides its be­ing true.

Lee: If he pro­claims “two and two makes three,” then he must be talk­ing about some­thing other than the in­te­gers. You can­not be mis­taken about the in­te­gers, you can only mi­s­un­der­stand them.

Just to be clear, when I say “be con­vinced that 2 + 2 = 3”, I mean be­ing con­vinced that the sys­tem of Peano ax­ioms with stan­dard de­duc­tive logic and:

\a.(a + 0 = a) \ab.(a + Sb = S(a + b))

does not have as a theorem

SS0 + SS0 = SSSS0

but does have as a theorem

SS0 + SS0 = SSS0

and is con­sis­tent. Just as I cur­rently be­lieve that PA is con­sis­tent and has a the­o­rem SS0+SS0=SSSS0 but not SS0+SS0=SSS0. So yes, this blog post is about what it would take to con­vince me that 2 + 2 ac­tu­ally equalled 3. I am not sup­posed to be con­vinced of this, if I am sane, and if it is not true. But at the same time, my be­lief in it should not be un­con­di­tional or nonev­i­den­tial, be­cause there are par­tic­u­lar ev­i­dences which con­vinced me that 2 + 2 = 4 in the first place.

I also note that if you do not be­lieve that there is a finite pos­i­tive in­te­ger which en­codes a proof of Godel’s State­ment, then you clearly are not us­ing Peano Arith­metic to define what you mean by the word “in­te­ger”.

• In re­gards to Hume’s in­ter­est­ing con­tri­bu­tions to the ques­tion, I stum­bled across this video a while back which I think will be in­ter­est­ing: http://​​www.youtube.com/​​watch?v=BVZG0G-jnAM (don’t let the ti­tle throw you off; there is con­tent within it).

• What would con­vince me that 2 + 2 = 3, in other words, is ex­actly the same kind of ev­i­dence that cur­rently con­vinces me that 2 + 2 = 4: The ev­i­den­tial cross­fire of phys­i­cal ob­ser­va­tion, men­tal vi­su­al­iza­tion, and so­cial agree­ment.

What has this to do with Peano Arith­metic and a math­e­mat­i­cal proof “PA proofs 2+2=4” which is merely a string of sym­bols? On the other hand, what has PA to do with re­al­ity of earplugs ex­cept the ev­i­dence that PA is a good model for them?

Please ex­plain the mirac­u­lous cor­re­spon­dence to ap­ples and earplugs, then.

There is no mirac­u­lous cor­re­spon­dence, there is in fact a lot of ev­i­dence that FALSIFIES 2 + 2 = 4, like if it is 11 o’clock and 3 hours pass, it is 2 o’clock, and you can pour one glass of wa­ter and one glass of wa­ter into one glass of wa­ter, not to men­tion the already men­tioned pho­tons.

So 2 + 2 = 4 seems acu­tally to be true only when we “know what we are do­ing”, when we are ap­ply­ing it “cor­rectly”. (and I am sure that in the world where 2+2 earplugs lead 3 earplugs, you may still find in­stances where 2+2=4 (like pho­tons or what­ever).) But ap­ply­ing “cor­rectly” bears a lot of in­for­ma­tion about how and where you should be en­tan­gled with re­al­ity in or­der to claim 2+2=4.

That in­for­ma­tion is the differ­ence be­tween pure and ap­plied math­e­mat­ics. Also that is why there are two mean­ings of 2+2=4 which seem to have been mixed up in some of the dis­cus­sion above. And that is what is meant by “2+2=4 is true in (pure) math­e­mat­ics in­de­pen­dently on whether or not it is true in the re­al­ity [when ap­plied]”. Us­ing “a pri­ory” is mis­lead­ing, here I agree.

Of course it is also con­ciev­able that you wake up one morn­ing and PA proofs 1+1=3 BUT 2 ear plugs + 2 ear plugs is still 4 earplugs! Isn’t it?

...now I’m get­ting con­fused… if 2 ear plugs placed next to 2 earplugs lead 3, then how can you re­li­ably write more than 3 syb­mols next to each other to give a proof of any­thing from PA? spooky

• I think you’ve pointed out an is­sue of se­man­tics, not falsified 2 + 2 = 4. If you pour one glass of wa­ter into an­other glass of wa­ter, you have one glass of wa­ter—but ” one glass”, in that case, is qual­i­ta­tive and not quan­ti­ta­tive; it’s not math.

• I am not mak­ing claims about other uni­verses. In par­tic­u­lar I am not as­sert­ing pla­tonic ideal­ism is true. All I am say­ing is “2+2=4” is an a pri­ori claim and you don’t use rules for in­cor­po­rat­ing ev­i­dence for such claims, as you seemed to im­ply in your origi­nal post.

Please ex­plain the mirac­u­lous cor­re­spon­dence to ap­ples and earplugs, then.

I con­fess that I’m also not en­tirely sure what you mean by “a pri­ori” or why you think it re­quires no ev­i­dence to lo­cate an “a pri­ori claim” like “2 + 2 = 4” in the vast space of pos­si­ble a pri­ori claims that in­cludes “2 + 2 = 498034″. I’m sus­pi­cious of claims that sup­pos­edly do not re­quire jus­tifi­ca­tion and yet seem to be uniquely preferred within a rather large space of pos­si­bil­ities. Are you sure “a pri­ori” isn’t just func­tion­ing as a se­man­tic stop­sign?

I’ll ac­cept as di­v­ine any en­tity that can con­sis­tently re­duce the en­tropy of a closed, iso­lated system

This could just be a man­i­fes­ta­tion of an en­tity run­ning our world as a com­puter simu­la­tion. Or even sim­pler, it could be an alien that knows an im­por­tant fact you don’t know about the real laws of physics. Even if the en­tity is run­ning our world as a com­puter simu­la­tion, it could it­self be made of atoms, go to the bath­room, have a boss scream­ing at it, etc.

As Damien Brod­er­ick ob­served: “If you build a snazzy al­ife sim … you’d be a kind of bridg­ing first cause’, and might even have the power to in­ter­vene in their lives—even obliter­ate their en­tire ex­pe­rienced cos­mos—but that wouldn’t make you a god in any in­ter­est­ing sense. Gods are on­tolog­i­cally dis­tinct from crea­tures, or they’re not worth the pa­per they’re writ­ten on.”

• I’m sus­pi­cious of claims that sup­pos­edly do not re­quire justification

Math­e­mat­i­cal claims do re­quire jus­tifi­ca­tion. They even re­quire stronger jus­tifi­ca­tion than em­piri­cal claims: math­e­mat­i­cal proof. As Doug S ex­plained, the proof that 2+2=4 is

2+2 = 2+(1+1) = (2+1)+1 = 3+1 = 4 QED.

(Us­ing the defi­ni­tion of 2, the as­so­ci­a­tivity of +, the defi­ni­tion of 3 and the defi­ni­tion of 4 in that or­der).

Em­piri­cal claims, such as “2+2=4 is re­lated to earplugs or ap­ples” do not re­quire proofs, but they do re­quire ev­i­dence.

• Ac­tu­ally, does the Bible ever say that God is on­tolog­i­cally dis­tinct from crea­tures, in any such way? I’ve read very lit­tle of it my­self, but based on what I’ve heard I would ex­pect that the early Old Tes­ta­ment might not in­clude such dis­tinc­tions (and ba­si­cally por­trays God in a similar man­ner to poly­the­is­tic deities, just with all their power con­cen­trated in one en­tity). Ob­vi­ously there’s plenty of lines about how great God is, but some of that could be seen as mor­al­iz­ing rather than mak­ing fac­tual claims. (al­though I do imag­ine that God hav­ing a boss scream­ing at him prob­a­bly con­tra­dicts a lot of fac­tual state­ments made in some holy books. So sup­pose that God is a con­struct of mun­dane physics in an­other uni­verse, but is ei­ther the only sen­tient en­tity in that uni­verse or the only one with any power in that uni­verse.)

If an en­tity ex­isted which is ca­pa­ble of do­ing ev­ery act un­der­taken by God as de­scribed in any holy book, and which did in fact un­der­take ev­ery ac­tion un­der­taken by God as de­scribed in one spe­cific holy book (like the Bible or the Old Tes­ta­ment), then that holy book could cer­tainly be said to be “true” in some very im­por­tant sense, would it not?

• ...the early Old Tes­ta­ment might not in­clude such dis­tinc­tions (and ba­si­cally por­trays God in a similar man­ner to poly­the­is­tic deities, just with all their power con­cen­trated in one en­tity).

Some schol­ars of re­li­gion have claimed that a straight-for­ward read­ing of the early Old Tes­ta­ment sug­gests it is bet­ter de­scribed as henothe­is­tic than monothe­is­tic.

• “Gods are on­tolog­i­cally dis­tinct from crea­tures, or they’re not worth the pa­per they’re writ­ten on.”

What an in­ter­est­ing ar­gu­ment… but I know of at least one re­li­gion that would tend to dis­agree with this anti-defi­ni­tion of God.

• It’s of­ten poor form to quote one­self, but since this post (de­servedly) con­tinues to get vis­its, it might be good to bring up the line of thought that con­vinced me that this post made perfect sense:

The space of all pos­si­ble minds in­cludes some (aliens/​men­tal pa­tients/​AIs) which have a no­tion of num­ber and count­ing and an in­tu­itive men­tal ar­ith­metic, but where the last of these is skewed so that 2 and 2 re­ally do seem to make 3 rather than 4. Not just lex­i­cally, but ac­tu­ally; the way that our brains can in­stantly subitize four ob­jects as two dis­tinct groups of two, their minds mis­tak­enly “see” the pat­tern 0 0 0 as com­posed of two dis­tinct 0 0 groups. Although such a mind would be un­likely to arise within nat­u­ral se­lec­tion, there’s noth­ing im­pos­si­ble about en­g­ineer­ing a mind with this er­ror, or rewiring a mind within a simu­la­tion to have this er­ror.

Th­ese minds, of course, would no­tice em­piri­cal con­tra­dic­tions ev­ery­where: they would put two ob­jects to­gether with two more, count them, and then count four in­stead of three, when it’s ob­vi­ous by vi­su­al­iz­ing in their heads that two and two ought to make three in­stead. They would even en­counter proofs that 2 + 2 =4, and be un­able to find an er­ror, al­though it’s patently ab­surd to write SSSS0 = SS0 + SS0. Even­tu­ally, a suffi­ciently re­flec­tive and ra­tio­nal mind of this type might en­ter­tain the pos­si­bil­ity that maybe two and two do ac­tu­ally make four, and that its sys­tem of vi­su­al­iza­tion and men­tal ar­ith­metic are in fact wrong, as ob­vi­ous as they seem from the in­side. We would con­sider such a mind to be more ra­tio­nal than one that de­cided that, no mat­ter what it en­coun­tered, it could never be con­vinced that 2 and 2 made 4 rather than 3.

Now, given all that, why ex­actly should I re­fuse to ever up­date my ar­ith­meti­cal be­liefs if given the sort of ex­pe­riences in Eliezer’s thought ex­per­i­ment? Wouldn’t the hy­poth­e­sis that I am such an agent get a lot of con­fir­ma­tion? (Of course, I very strongly don’t ex­pect to en­counter such ex­pe­riences, be­cause of all the con­tin­u­ing ev­i­dence be­fore me that 2 + 2 = 4; but if I did wake up in that situ­a­tion, I’d have to ac­cept that some part of my mind is prob­a­bly bro­ken, and the part that tells me 2 + 2 = 4 is as likely a can­di­date as any.)

• I had par­allel thoughts at one time, and dis­cov­ered with some effort that I could train my­self to be­lieve that 1+1=3. It took about five min­utes of men­tal prac­tice. What even­tu­ally hap­pened was that ev­ery time I com­bined two ob­jects to­gether men­tally (ab­stractly), I si­mul­ta­neously imag­ined a third which had the bizarre prop­erty that it only ex­isted when the two ob­jects were con­sid­ered si­mul­ta­neously. If I thought of just one ob­ject, the third dis­ap­peared, if I thought of the other ob­ject, it again dis­ap­peared—it only ap­peared as an emer­gent prop­erty of the pair. Thus imag­in­ing 1+1=3 was dis­cov­er­ing the fol­low­ing “op­er­a­tion”:

{E} + {F} = { {E} , {F} , { {E},{F} } }

Look­ing at the car­di­nal­ity of the sets, we have: 1 + 1 = 3

Could such an op­er­a­tion be ‘log­i­cal’ and yield a con­sis­tent num­ber the­ory? (I don’t know. I think it’s a ques­tion in ab­stract alge­bra. (Rings, fields, groups, etc.) Are there any alge­braists here that can com­ment?)

Yet or­thonor­mal is sug­gest­ing the case that 2+2=3 doesn’t re­sult in a log­i­cal, con­sis­tent the­ory—the pos­si­ble minds just be­lieve it due to an in­ter­nal er­ror, and they can use the in­con­sis­tency of their the­ory to de­duce the in­ter­nal er­ror. How­ever, I find it re­ally difficult to think of 2+2=3 hap­pen­ing as a mis­taken Peano ar­ith­metic in­stead of the as­ser­tion of an­other type of ar­ith­metic. The pos­si­ble log­i­cal self-con­sis­tency of this ar­ith­metic fur­ther con­founds: if it’s self-con­sis­tent, they may never de­duce that they got Peano ar­ith­metic wrong. If its not self-con­sis­tent, they can prove all propo­si­tions and how will they know where the er­ror lies? Or even un­der­stand what er­ror means? If there is an er­ror in our rea­son­ing, it can­not be so fun­da­men­tally em­bed­ded in our un­der­stand­ing of logic.

• Nice, but the differ­ence with this “be­lief” is that you’re talk­ing about sen­sory “count­ing” (vi­sual group­ing), and I was talk­ing about the num­bers them­selves, as mod­els for games, other phe­nom­ena, etc., and not just as a “count­ing” tool.

In the 1+1=3 ex­am­ple, to define the car­di­nal­ity, he/​she used the Peano’s ax­ioms, didn’t he/​she?

I don’t see the “vi­sual sen­sory count­ing” as the only use for “2+2=4″, that’s why I don’t think this ex­per­i­ment would re­fute such a pri­ori con­tent.

Another idea: let Ann be a girl with hemis­pa­tial ne­glect in a ex­tinc­tion con­di­tion. Ann has prob­lems de­tect­ing any­thing on the left, and she can pos­si­bly see 2+2=3 as ideal­ized above, due her brain dam­age. Will she think that 2+2=3? I don’t think so...but if she does...will that be a model for all “in­te­ger num­bers” apli­ca­tions? I think in “in­te­ger” as a frame­work for sev­eral phe­nom­ena, other mod­els, other knowl­edge, not only the count­ing one.

For the minds that see 2+2=4 as some­thing patently ab­surd, be­cause 2+2=3 is part of their in­tu­itive ar­ith­metic, these minds prob­a­bly won’t see the 2+2=4 even when brought to a world like ours. After a time in the 2+2=4 world, they prob­a­bly won’t for­get that 2+2=3, un­less the 2+2=3 wasn’t mod­el­ing any­thing else. But the 2+2=3 was mod­el­ing some­thing in their past his­tory, at least the count­ing prin­ci­ple of their world. So they still have the 2+2=3 be­lief in their lives while they re­mem­ber their past. If they for­get their past, the 2+2=3 be­lief might be­came un­use­ful, but that still don’t make the 2+2=3 an ab­surd or re­placed by the 2+2=4: there are 2 num­ber sys­tems here.

For me, 2+2=3 isn’t an ab­surd. That might be seem as a “com­mon sum with a 34 mul­ti­plier” or a “X + Y = X p Y/​X” where “p” is our com­mon sum and ”/​” is our di­vi­sion, etc.. This way, like the 1+1=3 ex­am­ple above, only over­loads the “+” op­er­a­tor. But, again, this “+” isn’t the same from the “2+2=4”

• Upon sud­denly dis­cov­er­ing that the whole world looks differ­ent this morn­ing than it did last night is the ra­tio­nal be­lief “I guess I was de­luded for my whole life up to this point” or “I guess I’m de­luded now”?

Con­sid­er­ing the fact that you’re not wak­ing up in a men­tal in­sti­tu­tion, but the world still seems to con­tain them (and if you get 2 sets of 2 of them, you have 3); the lat­ter is a much more likely situation

• Upon sud­denly dis­cov­er­ing that the whole world looks differ­ent this morn­ing than it did last night is the ra­tio­nal be­lief “I guess I was de­luded for my whole life up to this point” or “I guess I’m de­luded now”?

Why com­pletely leave out the pos­si­bil­ity that you aren’t de­luded at all? Depend­ing on just what kind of ‘differ­ent’ you wake up in that is a dis­tinct pos­si­bil­ity.

I would, by the way, start with a high prior for ‘de­luded now’ which would be al­tered one way or the other by ex­ten­sive re­al­ity test­ing. I ex­pe­rience that in dreams all the time. I know from per­sonal ex­pe­rience it is eas­ier for me to be con­fused about the tran­sient sen­sory ex­pe­rience of the pre­sent than the broad struc­ture of all my mem­o­ries. Re­sults may vary some­what.

• Good point, in the case of wak­ing up in a log­i­cally pos­si­ble world, re­mem­ber­ing a pre­vi­ous log­i­cally pos­si­ble world, there is a non-zero pos­si­bil­ity that you’ve ac­tu­ally gone from one to the other some­how. How low the prob­a­bil­ity is de­pends on the na­ture of the differences

I was too caught up in the case of wak­ing up in a world where the world you re­mem­ber is log­i­cally im­pos­si­ble.

• Good point, in the case of wak­ing up in a log­i­cally pos­si­ble world, re­mem­ber­ing a pre­vi­ous log­i­cally pos­si­ble world, there is a non-zero pos­si­bil­ity that you’ve ac­tu­ally gone from one to the other some­how. How low the prob­a­bil­ity is de­pends on the na­ture of the differences

Ex­actly. And with slightly differ­ent word­ing a world in which it seems like you have changed from one log­i­cal world to an­other is it­self a just a log­i­cally pos­si­ble world.

I was too caught up in the case of wak­ing up in a world where the world you re­mem­ber is log­i­cally im­pos­si­ble.

That would be awk­ward! It would re­quire an awful lot of re­al­ity test­ing on the ques­tion of just how log­i­cally im­pos­si­ble things were. Even af­ter that your con­fi­dence in just about any­thing would be fubared.

• You’re ne­glect­ing the hy­poth­e­sis “my mem­o­ries of the past are be­ing dis­torted to con­vince me that 2 and 2 make 4 in­stead of 3”. Given how eas­ily we dis­tort our mem­o­ries un­der con­di­tions of san­ity, this is as likely as “I’m de­luded now”.

• If you sud­denly gain a set of mem­o­ries in­di­cat­ing that the rap­tor con­spir­acy is tak­ing over the world, you would be con­sid­ered de­luded.

If you sud­denly gain a set of mem­o­ries in­di­cat­ing that 2+2 equals some­thing other than what it DOES in fact equal, you are like­wise de­luded.

So your sug­ges­tion is in fact a sub­set of be­ing de­luded*. At which point you should vol­un­tar­ily seek out psy­cholog­i­cal/​psy­chi­a­tric help.

• (which I as­sign a low prob­a­bil­ity, as I have never heard of such a type of delu­sion ex­ist­ing)

If you be­lieve (as you seem to sug­gest by use of the aac­tive rather than the pas­sive voice) that this delu­sion is be­ing de­liber­ately in­duced, it is im­por­tant to re­mem­ber that any­one with the power to in­duce that delu­sion could also re­duce you to a gib­ber­ing wreck; and hence that go­ing to get help is highly un­likely to be “part of their plan”.

• This is a dis­trac­tion from the ac­tual point; of course if this hap­pened to me, then my first pri­or­ity would be get­ting help (I might be hav­ing a stroke, for in­stance). But once I’m at the hos­pi­tal and they tell me that I’m all right, but some­thing strange hap­pened to my brain so that it falsely re­mem­bers 2 and 2 hav­ing made 4, in­stead of the ob­vi­ously cor­rect 3...

If you don’t agree that some set of cir­cum­stances like this should con­spire to make me ra­tio­nally ac­cept 2+2=3, then if the sce­nario hap­pened to you (with 3 and 4 re­versed), you’re as­sert­ing that you could never ra­tio­nally re­cover from that metal event. Since I’d pre­fer, should I go through a hal­lu­ci­na­tion that 2 and 2 always made 3, to be able to re­cover given enough ev­i­dence, I have to take the “risk” of be­ing con­vinced of some­thing false, in a world where events con­spired against me just so.

• Nice, but the differ­ence with this “be­lief” is that you’re talk­ing about sen­sory “count­ing” (vi­sual group­ing), and I was talk­ing about the num­bers them­selves, as mod­els for games, other phe­nom­ena, etc., and not just as a “count­ing” tool.

In the 1+1=3 ex­am­ple (byrnema an­swer, just be­low), to define the car­di­nal­ity, he/​she used the Peano’s ax­ioms, didn’t he/​she?

I don’t see the “vi­sual sen­sory count­ing” as the only use for “2+2=4″, that’s why I don’t think this ex­per­i­ment would re­fute such a pri­ori con­tent.

Another idea: let Ann be a girl with hemis­pa­tial ne­glect in a ex­tinc­tion con­di­tion. Ann has prob­lems de­tect­ing any­thing on the left, and she can pos­si­bly see 2+2=3 as ideal­ized above, due her brain dam­age. Will she think that 2+2=3? I don’t think so...but if she does...will that be a model for all “in­te­ger num­bers” apli­ca­tions? I think in “in­te­ger” as a frame­work for sev­eral phe­nom­ena, other mod­els, other knowl­edge, not only the count­ing one.

For the minds that see 2+2=4 as some­thing patently ab­surd, be­cause 2+2=3 is part of their in­tu­itive ar­ith­metic, these minds prob­a­bly won’t see the 2+2=4 even when brought to a world like ours. After a time in the 2+2=4 world, they prob­a­bly won’t for­get that 2+2=3, un­less the 2+2=3 wasn’t mod­el­ing any­thing else. But the 2+2=3 was mod­el­ing some­thing in their past his­tory, at least the count­ing prin­ci­ple of their world. So they still have the 2+2=3 be­lief in their lives while they re­mem­ber their past. If they for­get their past, the 2+2=3 be­lief might be­came un­use­ful, but that still don’t make the 2+2=3 an ab­surd or re­placed by the 2+2=4: there are 2 num­ber sys­tems here. The “2” in the “2+2=3“ is differ­ent from the “2” in the “2+2=4”.

For me, 2+2=3 isn’t an ab­surd. That might be seem as a “com­mon sum with a 34 mul­ti­plier” or a “X + Y = X p Y/​X” where “p” is our com­mon sum and ”/​” is our di­vi­sion, etc.. This way, like the 1+1=3 ex­am­ple, only over­loads the “+” op­er­a­tor. But, again, this “+” isn’t the same from the “2+2=4”

• Eliezer: When you are ex­per­i­ment­ing with ap­ples and earplugs you are in­deed do­ing em­piri­cal sci­ence, but the claim you are try­ing to ver­ify isn’t “2+2=4” but “count­ing of phys­i­cal things cor­re­sponds to count­ing with nat­u­ral num­bers.” The lat­ter is, in­deed an em­piri­cal state­ment. The former is a state­ment about num­ber the­ory, the truth of which is ver­ified wrt some model (per Tarski’s defi­ni­tion).

• To ap­ply the same rea­son­ing the other way, if you aren’t a Chris­tian, what would be a situ­a­tion which would con­vince you of the truth of Chris­ti­an­ity?

• The Se­cond Com­ing? An op­por­tu­nity to have a chat with the Lord Him­self? An anal­y­sis of a com­mu­nion wafer re­veal­ing it to, in fact, be liv­ing hu­man flesh? It’s se­ri­ously not that hard to think of these.

• Which is more likely “God ex­ists” or “I just hal­lu­ci­nated that” For the third one, prob­a­bly that He ex­ists, for the sec­ond one, definitely hal­lu­ci­na­tion, for the first, I’m not sure.

• Se­cond one: de­pends. I was kind of as­sum­ing that you have some way of ver­ify­ing it, like you ask Him to cre­ate some­thing and some­one who wasn’t there later de­scribes some of its pre­vi­ously de­ter­mined prop­er­ties ac­cu­rately with­out be­ing clued in. First: you’d need a mas­sive global hal­lu­ci­na­tion, and could use a similar ver­ifi­ca­tion method.

• That seems ac­cu­rate. Re­mem­ber that a sin­gle per­son can hal­lu­ci­nate that some­one else ver­ified some­thing, but this has low prior prob­a­bil­ity.

• I once con­ducted an ex­per­i­ment in which I threw a die 500 times, and then prayed for an hour ev­ery day for a week that that die con­sis­tently land on a four, and then threw the die 500 more times. Cor­re­la­tion was next to zero, so I con­cluded that God does not an­swer prayers about dice from me.

• Haven’t you ever heard the say­ing, “God does not throw dice games”?

• Wasn’t that what Ein­stein said about QM?

• Al­most. Eliezer is mak­ing a bad word­play with what Ein­stein said.

• I wouldn’t ex­pect a de­ity to an­swer that sort of prayer. You’re not be­ing sincere, just try­ing to test them, which many canon­i­cally find an­noy­ing be­cause it shows mis­trust; you don’t need that die to land on a four; it sug­gests you’d use prayer to lowly ends (e.g. “Let me score a touch­down” rather than “Please solve world hunger”); it gives an eas­ily pub­lish­able re­sult, which no de­ity would char­ac­ter­is­ti­cally ac­cept—if they didn’t want to be dis­creet they’d still be do­ing showy mir­a­cles. Stud­ies where you pray to cure can­cer or some­thing are much stronger ev­i­dence.

• You’re not be­ing sincere.

Ac­tu­ally, if you run the test, you are. Given that you’d have changed your mind if it had gone the other way, of course.

• I read about a study like that, in which Chris­ti­ans prayed for peo­ple to re­cover from can­cer. There was barely any differ­ence be­tween the pa­tients that weren’t prayed for, the pa­tients that were prayed for and knee that they were be­ing prayed for, and the pa­tients that didn’t know that they were be­ing prayed for.

• I re­call the same study—and I seem to re­mem­ber that the pa­tients who knew they were be­ing prayed for did a bit worse.

• Do those stud­ies have a placebo group?

• Given my cur­rent men­tal ca­pac­i­ties, I think that any “proof” of God would be more eas­ily at­tributed to hal­lu­ci­na­tion. How­ever, it should still be pos­si­ble for God to prove His ex­is­tence. If He is om­nipo­tent, then he can in­crease my men­tal ca­pac­ity to the ex­tent that I can dis­t­in­guish be­tween di­v­ine in­ter­ven­tion and a hal­lu­ci­na­tion of di­v­ine in­ter­ven­tion.

• But what if you’re hal­lu­ci­nat­ing the in­crease in men­tal ca­pac­ity and re­sult­ing dis­cern­ment?

• It may be the­o­ret­i­cally pos­si­ble to in­crease my men­tal ca­pac­ity in some way such that I can dis­t­in­guish men­tal ca­pac­ity from hal­lu­ci­na­tion. I can­not con­ceive of how that would be done, but it may be pos­si­ble.

P.S. I love when peo­ple re­ply to com­ments that are two and a half years old. It feels like we’re talk­ing to the past.

• There’s no situ­a­tion which would con­vince me that Chris­ti­an­ity had a 100% prob­a­bil­ity of be­ing true, be­cause the idea that the en­tire sce­nario since I first en­coun­tered ev­i­dence of Chris­ti­an­ity be­ing true was a hal­lu­ci­na­tion or that I was a Brain-in-a-Vat could never be dis­proved, but I can eas­ily imag­ine sce­nar­ios that could make me raise my es­ti­mated prob­a­bil­ity of Chris­ti­an­ity much higher, to 50%, 90%, per­haps higher.

If I were tele­ported into an al­ter­nate world where world his­tory and the like seemed more con­sis­tent with Chris­ti­an­ity be­ing true, I could eas­ily en­vi­sion my prob­a­bil­ity rank­ing to as high as my cur­rent one for Athe­ism, to the point that I would act based on the as­sump­tion that it had a 100% prob­a­bil­ity.

• Per­haps ‘a pri­ori’ and ‘a pos­te­ri­ori’ are too loaded with his­toric con­text. Eliezer seems to as­so­ci­ate a pri­ori with du­al­ism, an as­so­ci­a­tion which I don’t think is nec­es­sary. The im­por­tant dis­tinc­tion is the pro­cess by which you ar­rive at claims. Scien­tists use two such pro­cesses: in­duc­tion and de­duc­tion.

De­duc­tion is rea­son­ing from premises us­ing ‘agreed upon’ rules of in­fer­ence such as modus po­nens. We call (con­di­tional) claims which are ar­rived at via de­duc­tion ‘a pri­ori.’

In­duc­tion is up­dat­ing be­liefs from ev­i­dence us­ing rules of prob­a­bil­ity (Bayes the­o­rem, etc). We call (con­di­tional) claims which are ar­rived at via in­duc­tion ‘a pos­te­ri­ori.’

Note: both the rules of in­fer­ence used in de­duc­tion and rules of ev­i­dence ag­gre­ga­tion used in in­duc­tion are agreed upon as an em­piri­cal mat­ter be­cause it has been ob­served that we get use­ful re­sults us­ing these par­tic­u­lar rules and not oth­ers.

Fur­ther­more: both de­duc­tion and in­duc­tion hap­pen only (as far as we know) in the phys­i­cal world.

Fur­ther­more: de­duc­tive claims by them­selves are ‘ster­ile,’ and mak­ing them use­ful im­me­di­ately en­tails coat­ing them with a pos­te­ri­ori claims.

Nev­er­the­less, there is a clear al­gorith­mic dis­tinc­tion be­tween de­duc­tion and in­duc­tion, a dis­tinc­tion which is mir­rored in the claims ob­tained from these two pro­cesses.

• Ha! Creepy. :3

• Eliezer is right; num­bers are first an ab­strac­tion of the world around us. There are a vast num­ber of pos­si­ble ab­strac­tions; the rea­son we have been so very in­ter­ested in num­bers, com­pared to all the other pos­si­ble ab­strac­tions, is that num­bers hap­pen to de­scribe the world around us. It need not have been so.

• What’s an ex­am­ple of an­other pos­si­ble ab­strac­tion?

• Yes it does need be so. Pre­cisely be­cause num­bers are an ab­strac­tion of the world around us, an ab­strac­tion which we as won­der­ful hu­man be­ings have ad­vanced into a more and more so­phis­ti­cated ab­strac­tion for many years, they re­flect (if that is the right word) the world around us.

It is not “the un­prece­dented suc­cess of math,” but of man.

• Lee, the situ­a­tions I talked about for con­vinc­ing me that “2 + 2 = 3” could only ac­tu­ally oc­cur if 2 + 2 ac­tu­ally equalled three within the realm of the in­te­gers. This is right and proper: why should I al­low my­self to be con­vinced by some­thing that would not be valid ev­i­dence?

I do not, there­fore, ever ex­pect my­self to ac­tu­ally en­counter any of these situ­a­tions, be­cause I cur­rently be­lieve that 2 + 2 = 4.

If I ex­pected to en­counter such ev­i­dence in the fu­ture, the ex­pec­ta­tion of my prob­a­ble fu­ture prob­a­bil­ity es­ti­mates must equal my pre­sent prob­a­bil­ity es­ti­mate, so I would have to not re­ally be­lieve that 2 + 2 = 4 in or­der to ex­pect to en­counter ev­i­dence that 2 + 2 = 3.

• Let me take an­other crack at this...

I do not be­lieve any situ­a­tion could ever con­vince Eliezer that 2+2=3.

If he pro­claims “two and two makes three,” then he must be talk­ing about some­thing other than the in­te­gers. You can­not be mis­taken about the in­te­gers, you can only mi­s­un­der­stand them. It’s like say­ing “some women are bach­e­lors.” You are not mis­taken about the world, you’ve merely lost your grasp of the ter­minol­ogy.

• Ooh, ooh! I’ll do you one bet­ter. I’m not just a Chris­tian; I’m a Mor­mon. :P

My good­ness, what would con­vince me of non-Chris­ti­an­ity? The prob­lem here is that Mor­monism has pre­sented me with enough pos­i­tive ev­i­dence that I’m rea­son­ably cer­tain of its ve­rac­ity. So the con­ver­sion pro­cess would be two-tiered: first a strong pos­i­tive ev­i­dence for Is­lam/​Ju­daism/​what­ever, and sec­ond a strong dis­con­fir­ma­tion of Mor­monism, which I would then seek to cor­rob­o­rate by figur­ing out why on earth I re­ceived so many out­landishly un­likely false pos­i­tives.

Both of the tiers may be ex­plained by tel­ling you about the pos­i­tive ev­i­dences I’ve re­ceived for the re­li­gion I cur­rently es­pouse.

Many of you may be aware that Mor­mons (obli­ga­tory se­man­tic note: we are tech­ni­cally called the Church of Je­sus Christ of Lat­ter-Day Saints; the ‘Mor­mon’ ap­pel­la­tion is non-offi­cial and in fact was origi­nally a term of offense, but it sure makes for a good ab­bre­vi­a­tion!) have a bit more scrip­ture than most Chris­tian de­nom­i­na­tions: in ad­di­tion to the Bible (we use the KJV, thanks!) we have the Book of Mor­mon (hence our nick­name) and a few other bits and pieces. But it is the Book of Mor­mon that’s the most well-known book of our scrip­ture, and rightly so: it is of­ten referred to as the “key­stone of our re­li­gion”, in that, were it to be dis­proved, our church would crum­ble like an arch with its key­stone dis­placed.

Those of you who are not fa­mil­iar with the cir­cum­stances of the trans­la­tion of the Book of Mor­mon may seek to en­lighten your­selves; I will pro­ceed from this point un­der the as­sump­tion that you are fa­mil­iar with the ac­tual story, and not with the, erm, South Park drama­ti­za­tion.

(In ad­di­tion, you may wish you ed­u­cate your­selves re­gard­ing the differ­ences be­tween Mor­monism and main­stream Chris­ti­an­ity; they are many. Here is a primer on what we be­lieve.)

Here we have an ex­am­ple of God talk­ing to Joseph Smith, giv­ing him the power to speak in His name, and giv­ing him phys­i­cal ev­i­dence of such: the Book of Mor­mon. There­fore, the ve­rac­ity of the Church of Je­sus Christ of Lat­ter-Day Saints de­pends wholly on the ve­rac­ity of the Book of Mor­mon: if it is false, then Joseph made ev­ery­thing up and the Church is false. If the book is true, then the Church upon which it is founded must also be true.

I will here make an aside to state that yes, I am treat­ing the truth of the Book of Mor­mon as a bi­nary value. There are three pos­si­bil­ities: Either the vi­sion(s) were true, the trans­la­tion was by God, and the Book re­ally is what it claims to be; the vi­sion(s) never hap­pened, the “trans­la­tion” was a lie, and the Book is fic­tion; or the vi­sion(s) were false vi­sions, the trans­la­tion oc­curred by a su­per­nat­u­ral power (Oc­cam sug­gests the same power be­hind the vi­sions), and the Book is still fic­tion (which, be­ing backed by a su­per­nat­u­ral power, may have false ev­i­dence to back it up), and also “God” is a per­verse and con­niv­ing crea­ture act­ing with mo­tives be­yond our ken. Th­ese pos­si­bil­ities will for­ward be referred to, re­spec­tively, as P-True, P-False, and P-Alien.

There­fore we have re­duced the prob­lem of whether this re­li­gion is true to a much sim­pler one: If the Book is true, then ei­ther the Church is true (P-True) or P-Alien. If the Book is false, then the Church is false (P-False).

Now we will dwell for a mo­ment on what it means for the Book of Mor­mon to be true. In this case, we have a very pre­cise work­ing defi­ni­tion: The Book makes sev­eral his­tor­i­cal claims, which would, if true, leave ar­chae­olog­i­cal ev­i­dences. So, if the ar­chae­olog­i­cal ev­i­dences cor­rob­o­rate the Book’s story, then we must con­sider the Book to be “true”, and thereby ac­cept ei­ther P-True or P-Alien. Keep in mind that, in or­der to dis­prove P-False, we must use ar­chae­olog­i­cal ev­i­dence that would not have been available to Joseph Smith; that is, ev­i­dence lack­ing from what we must as­sume would be the knowl­edge available to a 21-year old un­schooled farm­hand in up­state New York in 1827.

So does such ar­chae­olog­i­cal ev­i­dence ex­ist? Why yes, it does.

(com­ment split for length)

• ...what would con­vince me of non-Chris­ti­an­ity? Mor­monism has pre­sented me with enough pos­i­tive ev­i­dence...the con­ver­sion pro­cess would be two-tiered: first a strong pos­i­tive ev­i­dence for Is­lam/​Ju­daism/​what­ever, and sec­ond a strong dis­con­fir­ma­tion of Mormonism

This seems like a sub­tle at­tempt to shift the bur­den of proof.

The prob­a­bil­ity of some­thing be­ing true plus the prob­a­bil­ity of it not be­ing true is one. Other things be­ing true may en­tail the first thing’s not be­ing true. But it’s all re­lated and of the same type, as the prob­a­bil­ity of “not Mor­monism” is ag­gre­gated out of an uni­mag­in­ably large num­ber of pos­si­bil­ities.

To have a similarly peremp­tory (I can’t think of a good word for what I mean, but I hope it’s clear) be­lief sys­tem as Mor­monism, one would only re­quire what would look like the first tier, suffi­cient strong pos­i­tive ev­i­dence for Is­lam/​Ju­daism/​what­ever, and that would it­self dis­con­firm Mor­monism.

To make Mor­monism un­rea­son­able, one would only need what would look like the sec­ond tier, though what would look like the sec­ond tier of ev­i­dence would work too.

When I was very young, I thought that the in­gre­di­ents sec­tion of a food la­bel had to list, as the first in­gre­di­ent, some­thing that com­prised over 50% of the product. If I still be­lieved this, it would be easy to prove to me that a five-bean salad was mostly kid­ney beans. Sim­ply show that none of the other four bean types made up a ma­jor­ity of the salad, and there you’d have it!

Like­wise, re­li­gions ille­gi­t­i­mately try to prove them­selves true or prob­a­ble by show­ing other be­liefs un­likely, but not only doesn’t this suffice to show them prob­a­ble, it isn’t even the case that the most likely thing is nec­es­sar­ily prob­a­ble.

Im­prob­a­ble things can be co­her­ently amalga­mated into sets, so ma­te­ri­al­ist ex­pla­na­tion of con­scious­ness1+ma­te­ri­al­ist ex­pla­na­tion of con­scious­ness2… > du­al­ist ex­pla­na­tion of con­scious­ness1+du­al­ist ex­pla­na­tion of con­scious­ness2.

• It is true that a proof of Is­lam, or one of any other re­li­gion, would nec­es­sar­ily con­sti­tute a dis­proof of Mor­monism. But in or­der for any other the­ory to gain enough cre­dence for me to pay at­ten­tion to it, one would first have to lessen my con­fi­dence in Mor­monism, so that I could, as it were, hear the back­ground noise. The ques­tion was not what would con­vince some­one with­out prior be­lief; the ques­tion was what would con­vince me as a Chris­tian, and in or­der to do that, first you would have to con­vince me to step off my Chris­ti­an­ity tower.

Is this a bias? I don’t be­lieve so. I’ve tried my hard­est to erase my pre­con­ceived no­tions and start from scratch. I’ve tried it three ways. Start­ing with­out priv­ileg­ing any hy­poth­e­sis led to rather a paral­y­sis of thought; I re­al­ized that, with­out any prior hint as to which di­rec­tion I should start search­ing for truth, I could only rely on the ev­i­dence of my senses; hence athe­ism. Start­ing by priv­ileg­ing Mor­monism led to a reaf­fir­ma­tion of the ve­rac­ity of Mor­monism. Start­ing by priv­ileg­ing Catholi­cism, for com­par­i­son, led to Mor­monism.

This is ei­ther a proof of deep-rooted bias in my own mind, or ev­i­dence—that suffices for me, at least—that Mor­monism is the most cor­rect re­li­gion. :3 But of course, this is an ex­per­i­ment I will re­hash over the course of my en­tire life, work­ing ever to perfect my strength as a ra­tio­nal­ist.

When I was very young, I thought that the Nutri­tion In­for­ma­tion per­centages had to to­tal up to 100%. x3 I just thought I’d share that with you.

I like your point that the most likely thing isn’t nec­es­sar­ily prob­a­ble. I apol­o­gize if I’m tak­ing this the wrong way, but that seems to ac­tu­ally be a point in my fa­vor (though not mine speci­fi­cally! Please don’t ac­cuse me of ar­ro­gance!): Just be­cause Mor­monism is im­prob­a­ble doesn’t nec­es­sar­ily mean it’s not the most prob­a­ble thing out there. But time will tell, and in the mean­time, I will at­tempt to keep my mind wide open.

• The ques­tion was not what would con­vince some­one with­out prior be­lief; the ques­tion was what would con­vince me as a Chris­tian,

This could mean at least two things, one right, one wrong. I do not know what you mean.

If I pick up a book, and read page 54, and then 53, and then 55, I will think cer­tain things about the world. If in­stead I had read 53, then 54, then 55, and if do­ing so would have led me to think differ­ent things about the world upon con­clud­ing my read­ing, there is a prob­lem with me as an in­for­ma­tion col­lect­ing and judg­ing agent.

• It means that, hav­ing been born into the covenant, and not hav­ing any of the qualms and con­fu­sion that ap­par­ently are a com­mon re­sult of be­ing born into re­li­gion, I there­fore have a bias, which may or may not be ir­reparable, which, if it is, may or may not be un­for­tu­nate. Eliezer said that notic­ing one’s con­fu­sion was the first step to chang­ing one’s mind. I can boldly state, with­out qualm: I am not con­fused. Every­thing I have learned about Mor­monism is in­ter­nally con­sis­tent, and con­sis­tent with my own ideas on moral­ity. There is a God, and He is my Father, who loves each of us as a child. Joseph Smith was a true prophet, or­dained of said God to re­store His church in these, the lat­ter days of the world.

• Every­thing I have learned about Mor­monism is in­ter­nally con­sis­tent, and con­sis­tent with my own ideas on moral­ity.

This sounds very con­ve­nient for you. Do you con­sider the church’s con­sis­tency with your moral­ity to be ev­i­dence that your moral­ity is cor­rect, or that the church is? Espe­cially if the lat­ter, what ev­i­den­tial sta­tus do you con­sider peo­ple whose moral­ity dis­agrees at least partly with the church to have?

• Oh, yes, it’s very con­ve­nient. :P Well, not always. A good ex­am­ple is the re­cent fight over Prop 8, wherein the Church’s moral­ity came into sharp con­trast with the moral­ity of many out­side it. (I will not say “most”, be­cause it was in fact the vote of Cal­ifor­nia cit­i­zens which de­cided the mat­ter, and not the Church.) To show­case the in­con­ve­nience with­out re­veal­ing over­much about my per­sonal life, I will sim­ply state that I have many per­sonal friends who were out­raged at my de­ci­sion to stand with my Church on the mat­ter.

The church’s con­sis­tency with my own moral­ity is, I think, ev­i­dence that the Church is cor­rect. Without the church, my moral­ity would still ex­ist. As far as oth­ers’ con­flict­ing moral­ities...

.....

That’s an in­ter­est­ing ques­tion, ac­tu­ally. What ev­i­den­tial sta­tus does my con­flict­ing moral­ity have on yours?

• I saw this on the side while read­ing an un­re­lated post...

The church’s con­sis­tency with my own moral­ity is, I think, ev­i­dence that the Church is cor­rect. Without the church, my moral­ity would still ex­ist.

I’m much more in­clined to think it’s ev­i­dence that you were raised in the church, or in a cul­ture in­fluenced by the church, etc...

If I rephrase what you said, it’s “Party X’s agree­ment with me on sub­ject Y is ev­i­dence that Party X can think well and is prob­a­bly right about other things, too.” Please tell me you meant some­thing else...

PS: You seem ca­pa­ble of up­dat­ing, judg­ing from a few of the com­ments in this thread, and you seem to care about the truth. The next step is to stop hold­ing your own be­liefs to a differ­ent stan­dard of ev­i­dence than you do other be­liefs. I hope you find your time in the soon-to-be-formerly-the­is­tic camp more fun than I did.

• Your point is only ap­pli­ca­ble inas­much as you took my quote out of con­text. I was asked to choose one of two op­tions; I chose the one that seemed most right to me. I could be wrong, but your point doesn’t an­swer to the origi­nal ques­tion.

• The church’s con­sis­tency with my own moral­ity is, I think, ev­i­dence that the Church is cor­rect. Without the church, my moral­ity would still ex­ist.

Without your moral­ity, the church would still ex­ist, too, wouldn’t it?

What ev­i­den­tial sta­tus does my con­flict­ing moral­ity have on yours?

Some, but not more than the av­er­age dis­sen­ter—less than a typ­i­cal clever con­se­quen­tial­ist found around these parts, and not even as much as the ide­olog­i­cally similar votes of Mor­mons I’m friends with and have had a chance to ques­tion in more de­tail. But that’s not quite the same ques­tion, be­cause I de­vel­oped the frame­work of my own moral­ity in­de­pen­dently, and am not backed by a large in­sti­tu­tion. What I want to know is more along the lines of: why is your moral­ity agree­ing with the LDS church ev­i­dence for the LDS church, which is not over­whelmed by the ma­jor­ity of hu­man be­ings whose moral­ities dis­agree with yours/​the church’s, or over­bal­anced by the hu­mans whose moral­ities agree with those of other re­li­gions?

(If you were us­ing “ev­i­dence” in a suffi­ciently tech­ni­cal sense that this over­whelming­ness/​over­bal­anced­ness was in fact noted and sim­ply left un­men­tioned as strictly ir­rele­vant to what I origi­nally asked, I re­tract the ques­tion, but I sus­pect oth­er­wise.)

• I was in fact us­ing ev­i­dence in that tech­ni­cal a sense, but I’ll an­swer your ques­tion any­way.

...why is your moral­ity agree­ing with the LDS church… not over­whelmed by the ma­jor­ity of hu­man be­ings whose moral­ities dis­agree with yours/​the church’s, or over­bal­anced by the hu­mans whose moral­ities agree with those of other re­li­gions?

Be­cause moral­ity is not a bi­nary at­tribute. You can’t go out on the street and ask them, “Do you agree with the Mor­mons, yes or no?” Well, you could, but then if they an­swered no, you’d have to ask them how many peo­ple they kil­led to­day. It’s ex­actly that fal­lacy that leads fun­da­men­tal­ist Chris­ti­ans /​shud­der/​ to claim that athe­ists love to rape and mur­der and… I dunno, en­gage in bes­tial­ity or some­thing.

So no, other peo­ples’ moral­ities don’t sway me par­tic­u­larly much, be­cause a) they don’t mat­ter as much to me as my own moral­ity—as I think you’d agree with, say­ing “not more than the av­er­age dis­sen­ter”; and b) be­cause the con­so­nance be­tween my moral­ity and Mor­monism isn’t that much of an ev­i­dence in its fa­vor. I was us­ing it mainly as a con­trast be­tween my­self and all the peo­ple who have posted say­ing that Chris­ti­an­ity made them feel “wrong”.

• may or may not be unfortunate

Let pos­si­ble states of the world be rep­re­sented by A, B, C, etc. Let’s say A is true.

An agent that de­cides to be­lieve that the world is rep­re­sented by the the­ory that comes ear­liest alpha­bet­i­cally will be for­tu­nate as it will be­lieve true things, but it isn’t dis­cern­ing at all.

An agent that be­lieves the con­tents of books when it reads the book’s chap­ters in se­quen­tial or­der and dis­be­lieves the con­tents of books when it chooses to read the chap­ters in re­verse or­der is not an agent de­signed to dis­cern truth, how­ever lucky it gets de­cid­ing how to read each book it reads.

I’m just try­ing to ask to what ex­tent you don’t re­sem­ble an op­ti­mal thinker in this par­tic­u­lar way no hu­man to­tally suc­ceeds at, one pos­si­bil­ity would be for you to deny that this hu­man ten­dency is a flaw. Some peo­ple may dis­pro­por­tionately be in­fluenced by the last book they read, oth­ers by the first, oth­ers by the one’s with nice cov­ers, etc.. All I’m try­ing to get at is to see if you agree it’s bad to be a de­cider that is in­fluenced by the or­der it gets in­for­ma­tion in (ex­cept for to the ex­tent the or­der con­sti­tutes in­for­ma­tion, but this isn’t re­ally an ex­cep­tion).

Some­one could claim that truth of a propo­si­tion is com­men­su­rate with the age of the old­est book con­tain­ing it, and such a per­son would not mean what any­one else means by “truth”, and would be wrong to the ex­tent they are try­ing to com­mu­ni­cate.

Like­wise truth isn’t usu­ally bound to the or­der of ev­i­dence. If I read a pam­phlet ad­vo­cat­ing Is­lam, and then one ad­vo­cat­ing Mor­monism, I ought to reach the same ex­act con­clu­sions as if I had read them in the other or­der. If I don’t, I may hap­pen to come to be­lieve the cor­rect thing, but this is true of any de­ci­sion pro­cess, even the alpha­bet­i­cal one.

The ques­tion was not what would con­vince some­one with­out prior be­lief; the ques­tion was what would con­vince me as a Chris­tian, and in or­der to do that, first you would have to con­vince me to step off my Chris­ti­an­ity tower.

the con­ver­sion pro­cess would be two-tiered: first a strong pos­i­tive ev­i­dence for Is­lam/​Ju­daism/​what­ever, and sec­ond a strong dis­con­fir­ma­tion of Mormonism

I’ve tried my hard­est to erase my pre­con­ceived no­tions and start from scratch.

hav­ing been born into the covenant, and not hav­ing any of the qualms and con­fu­sion that ap­par­ently are a com­mon re­sult of be­ing born into re­li­gion, I there­fore have a bias, which may or may not be irreparable

In the first two quotes above, you seem to dis­agree with what I say, in the lat­ter two, you seem to agree.

• The con­fu­sion, I reckon, comes from my in­abil­ity to step out­side my­self. I am not a perfect ra­tio­nal­ist; I am trapped to an ex­tent by the con­cepts taught to me since birth, just as I find my­self un­com­fortable with my gen­der iden­tity due to grow­ing up in an abu­sive house­hold. It is difficult to step out­side one’s own bi­ases. So yes, my bias may be ir­reparable. As for “un­for­tu­nate”, the odds of it be­ing an un­for­tu­nate bias are ex­actly the odds of Mor­monism be­ing true. If I be­lieve the truth, then I am for­tu­nate. It is the chance that my bias is un­for­tu­nate that drives me ever to re­fine my un­der­stand­ing, and never stop ques­tion­ing my premises.

I’m just try­ing to ask to what ex­tent you don’t re­sem­ble an op­ti­mal thinker in this par­tic­u­lar way no hu­man to­tally suc­ceeds at, one pos­si­bil­ity would be for you to deny that this hu­man ten­dency is a flaw.

It’s not not a flaw. I’m just strug­gling to de­ter­mine to what ex­tent my be­lief in my re­li­gion is due to prior bias, and to what ex­tent it’s due to ra­tio­nal thought.

• waits for wedrifid

• waits for wedrifid

I hadn’t ac­tu­ally read the grand­par­ent be­yond skim­ming and cat­e­go­rized it as an en­tirely non-trol­lish ex­pres­sion of per­sonal be­lief. Given the prompt in the post it was ap­pro­pri­ate to the con­text and as ra­tio­nal as can be ex­pected given that the guys’ be­liefs are ut­ter non­sense.

Hav­ing read through the first com­ment (be­fore the “to be con­tinued”) the fol­low­ing part jumped out at me as the pri­mary non se­quitur.

So, if the ar­chae­olog­i­cal ev­i­dences cor­rob­o­rate the Book’s story, then we must con­sider the Book to be “true”, and thereby ac­cept ei­ther P-True or P-Alien.

That just isn’t case. Ar­chae­olog­i­cal cor­rob­o­ra­tion pro­vides ev­i­dence for the Book’s story. That is, part of the story is val­i­dated which elimi­nates a whole lot of the bits that could be wrong and we can as­sume a cor­re­lated truthi­ness with the re­main­der of the story. We up­date p(Book’s Story) up­ward, but not to one. Some­thing along the lines of:

p(Arch | BS) = x
p(Arch | !BS) = y

p(BS | Arch) = p(Arch | BS) * p(BS) /​ p(Arch)

We do not have the log­i­cal de­duc­tion “IF Arch THEN BS” but rather a likely­hood ra­tio such that BS is more likely the less likely it is for the ar­chael­og­i­cal ev­i­dence is to ex­ist given that the BS is false. Be­cause p(Arch | BS) > p(Arch | !BS), Arch does some­thing to over­come the in­cred­ibly low prior prob­a­bil­ity p(BS).

To put it an­other way there is a crit­i­cal ob­ser­va­tion that de­duc­tively “(Book’s Story) = (Arche­olog­i­cally ver­ifi­able parts) && (parts that are not arche­olog­i­cally ver­ifi­able)”. This is be­fore we go ahead and calcu­late p(Mor­monism | BS) vs p(Alien | BS).

Another in­ter­est­ing prob­a­bil­ity calcu­la­tion to con­sider is how likely it is that wedrifid will write out a bunch of prob­a­bil­ity calcu­la­tions given the clearly false ‘truth’ propo­si­tion is the acronym of “Book’s Story” vs wedrifid writ­ing out a bunch of calcu­la­tions about bul­lshit given the acronym is not BS. From this we can go ahead and chain our in­fer­ences to calcu­late p(wedrifid is peurile | wedrifid writes out the calcu­la­tions). For what it is worth I think you should find that the likely­hood ra­tio is small even if your pos­te­rior is enor­mous.

• I take offense to any im­pli­ca­tions about my pos­te­rior.

Heck, even I up­voted this. Your point is well made, and well taken; even if ar­chae­olog­i­cal ev­i­dence cor­rob­o­rates parts of the Book of Mor­mon, that does not up­date its prob­a­bil­ity to 1. I should have been more clear… no, rather, I should have thought of it that ra­tio­nally, but I was blinded by my own cer­tainty. I apol­o­gize; thank you for show­ing me my er­ror.

Were I to rewrite the above, it would take the form of some­thing like this:

The Book con­sists of two pieces of in­for­ma­tion: data that are ar­chae­olog­i­cally ver­ifi­able, and data that are not ar­chae­olog­i­cally ver­ifi­able. If ar­chae­olog­i­cal ev­i­dences cor­rob­o­rate the Book’s story, then there are two pos­si­bil­ities: ei­ther the non-ar­chae­olog­i­cally-ver­ifi­able bits are also true, or they are not. If the former is the case, then Joseph Smith’s story is cor­rect, the Church is true, etc. etc. If the non-ar­chae­olog­i­cally-ver­ifi­able bits are not true, given that the a.v. bits are, then we must con­clude one of two things: ei­ther a co­in­ci­dence (which prob­a­bil­ity be­comes smaller with each ad­di­tional cor­rob­o­rat­ing ev­i­dence), or some­thing Stranger, e.g. alien teenagers. I am in­clined, given the cur­rent state of the ev­i­dence, to be­lieve the above sce­nar­ios in the fol­low­ing or­der, in de­scend­ing or­der of prob­a­bil­ity: a) The Book Is True, b) Aliens Are Trol­ling Us, c) Mag­nifi­cent Coin­ci­dence. I also think that these three pos­si­bil­ities, and their sub­groups, com­prise the en­tirety of the prob­a­bil­ity space, but please cor­rect me if there’s a pos­si­bil­ity I have over­looked.

Oh, as an aside: The propo­si­tion that “The main­stream LDS church is not true, but the truth is had by one of the hand­ful of splin­ter groups that split off from the LDS church and still be­lieve in the Book of Mor­mon” does in fact fall un­der pos­si­bil­ity a, though con­sid­er­ing the le­gal trou­bles sur­round­ing some of these groups, this seems rather un­likely to me. After all, Joseph Smith pub­lished this as one of our thir­teen Ar­ti­cles of Faith: “We be­lieve in be­ing sub­ject to kings, pres­i­dents, rulers, and mag­is­trates; in obey­ing, hon­or­ing, and sus­tain­ing the law.”

• Oh, as an aside: The propo­si­tion that “The main­stream LDS church is not true, but the truth is had by one of the hand­ful of splin­ter groups that split off from the LDS church and still be­lieve in the Book of Mor­mon” does in fact fall un­der pos­si­bil­ity a, though con­sid­er­ing the le­gal trou­bles sur­round­ing some of these groups, this seems rather un­likely to me. After all, Joseph Smith pub­lished this as one of our thir­teen Ar­ti­cles of Faith: “We be­lieve in be­ing sub­ject to kings, pres­i­dents, rulers, and mag­is­trates; in obey­ing, hon­or­ing, and sus­tain­ing the law.”

I don’t un­der­stand this—why would le­gal trou­bles make their be­liefs any more or less likely to be true? Seems like an en­tirely ir­rele­vant is­sue.

• I think the point is that not get­ting into le­gal trou­ble is an im­por­tant tenet of Mor­monism (since obey­ing the law was one of those 13 “Ar­ti­cles of Faith”), so that a group that’s got into a lot of le­gal trou­ble is un­likely to be The One True LDS Church.

• Cheers. I un­der­stand what he means now, but it still seems like a par­tic­u­larly pe­cu­liar be­lief.

• While I do not ac­cept cer­tain of your premises (sur­pris­ing­ness of cor­rob­o­rated ev­i­dence) your rea­son­ing from there is co­gent and the up­date wor­thy of re­spect!

• Oh! Well, thank you! I will at­tempt to be co­gent the first time in the fu­ture. :3

• Again in 2008 that same team of ge­netic sci­en­tists re­pub­lished es­sen­tially the same ar­ti­cle un­der the same ti­tle, mak­ing a similar point: “Here we show, by us­ing 86 com­plete mi­to­chon­drial genomes, that all Na­tive Amer­i­can hap­logroups, in­clud­ing hap­logroup X, were part of a sin­gle found­ing pop­u­la­tion, thereby re­fut­ing mul­ti­ple-mi­gra­tion mod­els.” (http://​​www.ncbi.nlm.nih.gov/​​pmc/​​ar­ti­cles/​​PMC2427228/​​?tool=pm­cen­trez)

Only solid piece of ev­i­dence i found on the DNA route, most of the rest seems to be ar­gu­ing that there re­mains a minis­cule chance de­spite the cur­rent con­sen­sus on DNA data.

• I’m not sure why you chose to post this as a re­sponse to my rewrite, but that doesn’t de­tract form the val­idity of the post.

I’m well ac­quainted with the fal­lacy you linked to; that’s ac­tu­ally been one of my fa­vorite of Eliezer’s ar­ti­cles. It is un­for­tu­nate that this and other fal­la­cies abound in real-world ar­gu­ments… how­ever, I trust you un­der­stand that the ex­is­tence of fal­la­cies does not equate to a false con­clu­sion. If I base my con­clu­sion X on ar­gu­ments A, B, C and D, and D is fal­la­cious, X may still hap­pily rest on A, B and C.

In par­tic­u­lar, there’s a differ­ence be­tween the hope­less grasp­ing-at-straws of the “there’s a chance it’s a co­in­ci­dence!” ar­gu­ment and the “This does not nec­es­sar­ily con­tra­dict what we’re say­ing” ar­gu­ment. In the lat­ter, there are also pos­i­tive ev­i­dences to bolster the con­clu­sion; it is true then that nega­tive ev­i­dences (by that I mean, ev­i­dences which show no sup­port for the con­clu­sion, but do not dis­prove it) nudge the prob­a­bil­ity does, but not as much as the pos­i­tive ev­i­dences nudge it up. In the former, all there is is wish­ful think­ing.

• I trust you un­der­stand that the ex­is­tence of fal­la­cies does not equate to a false con­clu­sion. If I base my con­clu­sion X on ar­gu­ments A, B, C and D, and D is fal­la­cious, X may still hap­pily rest on A, B and C.

I just think that if the DNA ev­i­dence isn’t there then how can i con­sider the pos­si­bil­ity of the book of Mor­mon hav­ing any truth to it. It feels a lot like con­sid­er­ing the pos­si­bil­ity of In­tel­li­gent De­sign as the ori­gin of hu­man­ity. If A, B, and C pre­clude the ex­is­tence of D then X is weak­ened more by the dis­proof of D then if it is a stan­dalone piece of ev­i­dence.

• But the DNA ev­i­dence is there. You pointed to a piece of it, and then said “but the rest is mostly bull”. But that doesn’t mean that the ev­i­dence you found ceases to be valid.

• Upvoted for amuse­ment value.

• I gather the dis­cus­sion of the whole thread rests on this un­ex­pected premise:

we can as­sume a cor­re­lated truthi­ness with the re­main­der of the story

Sto­ries always have a blend of fact and fic­tion. Ac­counts of trav­els, cul­ture and civ­i­liza­tions may have some seeds of truth, but other parts about God’s in­ten­tions and an­gels needn’t be true.

My sense is that you are col­lec­tively un­der­es­ti­mat­ing how un­pre­dictably in­for­ma­tion can pass down fam­ily lines and through trav­el­ing story-tel­lers, schol­ars and his­to­ri­ans.

we must use ar­chae­olog­i­cal ev­i­dence that would not have been available to Joseph Smith; that is, ev­i­dence lack­ing from what we must as­sume would be the knowl­edge available to a 21-year old un­schooled farm­hand in up­state New York in 1827

There’s a lot packed into this. To give an anal­ogy for a non-the­is­tic ex­am­ple, if some de­tails prove cor­rect about the col­lec­tive com­mu­nity’s aware­ness of the lost lo­ca­tion of At­lantis, Hans Chris­tian An­der­son shouldn’t get credit for ‘know­ing’ these de­tails when he in­cluded them in The Lit­tle Mer­maid.

• The en­tirety of Lehi’s jour­ney from Jerusalem to the sea has been found to match up with ac­tual ge­o­graph­i­cal and cul­tural sites in the Ara­bian Pen­in­sula. Lehi’s jour­ney fol­lows what we now know to be an­cient trad­ing routes. Lehi’s fam­ily buried Ish­mael at a place which Nephi called Na­hom, which has been found by name, ex­actly where it should be. More or less di­rectly east of that site, on the coast of Oman, have been found two can­di­date sites for Boun­tiful, Wadi Sayq and Salalah, right where they ought to be, with ev­ery fea­ture de­scribed in the book in­clud­ing: rea­son­able ac­cess from Na­hom (i.e. no moun­tains in the way!), an in­let for launch­ing a ship, fer­tile ground with “much fruit and… honey”, tim­ber to build a durable ship, year-round ac­cess to fresh wa­ter, a nearby moun­tain upon which Nephi could offer his prayer, available ore and flint, and wind and ocean cur­rents fa­vor­able for launch­ing a ship out to sea. Can­di­date sites for the Valley of Le­muel and the River of La­man have been found, right where they ought to be.

• The prac­tice of writ­ing on metal plates, laugh­able in 1830, has now been well es­tab­lished as a le­gi­t­i­mate an­cient prac­tice; one that Joseph Smith could never have known. He was mocked for his claim of re­ceiv­ing a “book writ­ten on gold plates” more than any other he made… even to this day! The prac­tice of bury­ing said records in stone boxes in the earth has been similarly cred­ited.

• The prac­tice of writ­ing in what Mor­mon called “re­formed Egyp­tian” (Mor­mon 9:32-34) has re­cently been shown to be rather more ac­cu­rate than might be ex­pected, as demon­strated by Daniel C. Peter­son in Re­view of Books on the Book of Mor­mon, Vol. 5, 1993:

The state­ment “When mod­ern Jews copy their scrip­ture, they use He­brew. They do not use Egyp­tian or Ara­bic, the lan­guage of their his­toric en­e­mies” is quite an as­ton­ish­ing dis­play of ig­no­rance. Since the Egyp­tian lan­guage has been dead for cen­turies, it is hardly re­mark­able that mod­ern Jews do not read the Bible in Egyp­tian. On the other hand, “the first and most im­por­tant ren­der­ing [of the Old Tes­ta­ment] from He­brew [into Ara­bic] was made by Sa’adya the Ga’on, a learned Jew who was head of the rab­binic school at Sura in Baby­lon (died 942)” (Ge­orge A. But­trick, ed., The In­ter­preter’s Dic­tionary of the Bible [here­after IDB], 4 vols. and sup­ple­ment [Nashville: Abing­don, 1962-1976], 4:758b). Thus, Jews have in­deed trans­lated the Bible into “Ara­bic, the lan­guage of their his­toric en­e­mies.” They also have trans­lated it into the lan­guage of their “his­toric en­e­mies” the Greeks (IDB 4:750b on the Sep­tu­ag­int) and Ara­maeans (IDB 1:185-93; 4:749-50, on the Ara­maic Tar­gums).

• Many tourists to Mex­ico will be well fa­mil­iar with the use of ce­ment in an­cient Amer­ica, for ex­am­ple in Teotihua­can; this in­for­ma­tion is had in the Book of Mor­mon, but was un­known in Joseph Smith’s time.

• Ja­cob chap­ter 5 offers many, many de­tails re­gard­ing olive cul­ti­va­tion which match pre­cisely with what is now known about an­cient prac­tices in Is­rael.

• Many seem­ingly non-He­braic per­sonal names in the Book of Mor­mon (Alma, Sariah, Lehi, Mosiah, Aha) have been in­de­pen­dently at­tested. Th­ese names are not just “He­brew-ish”, mind. They have been shown to be ac­tual at­tested He­brew names.

There are more ev­i­dences, but these are the strongest, in my opinion.

Now, are there nega­tive ar­chae­olog­i­cal ev­i­dences for the Book of Mor­mon? Un­for­tu­nately, there is rarely such a thing as a “nega­tive ar­chae­olog­i­cal ev­i­dence”; there are cer­tainly none that dis­prove any­thing the Book of Mor­mon says. All that can be said is that the Book of Mor­mon makes claims that do not match up with our cur­rent ar­chae­olog­i­cal knowl­edge… but the same was said, at var­i­ous points in the past, for all the above claims. It is true that the state­ment “lack of ev­i­dence is not ev­i­dence of lack” is blatantly false… but “lack of ev­i­dence” cer­tainly has a lot less weight than the pos­i­tive ev­i­dence above.

Eliezer, you said that it is more ra­tio­nal to be­lieve that Oc­cam’s Ra­zor will always yield use­ful re­sults than to be­lieve that, al­though it has yielded use­ful re­sults up to the pre­sent, it will cease to at some fu­ture date. For­give me if I make an er­ror here, but by ap­pli­ca­tion of the same ar­gu­ment, I should think that it is more likely that the Book of Mor­mon will cor­rob­o­rate with all fu­ture ar­chae­olog­i­cal ev­i­dence than that the Book of Mor­mon will fail to match up, hav­ing so far met all of the above and more.

It is true that I do not have a 100% cer­tainty that the Book of Mor­mon is true. But hav­ing seen all the ev­i­dence for its ve­rac­ity, I am con­vinced enough of it to base my life and wor­ld­view on the re­li­gion pred­i­cated upon it.

So in or­der to con­vert me to Is­lam? First, you’d have to con­vince me that the Book of Mor­mon is not true, in or­der to get me back to a baseline. Then you’d have to con­vince me that Is­lam is true… and you’ve seen above the weight of ev­i­dence that will con­vince me.

DISCLAIMER: The above is not an at­tempt to con­vert any­one. It is an hon­est re­sponse to the ques­tion (challenge?) that Eliezer posed. I do not be­lieve that any­one can or ought to be con­verted to a re­li­gion solely based upon log­i­cal ev­i­dence… though log­i­cal ev­i­dence can cer­tainly be a gate­way drug! :3 If you’re in­trigued, I would urge you to read the Book of Mor­mon for your­self. If you have ques­tions, I urge you to com­ment, or email me at vl (pe­riod) aran­dur (at) gmail (dot) com.

• The en­tirety of Lehi’s jour­ney...

The places ex­ist, but is there ev­i­dence of the ac­tual jour­ney? If I adopt this the­ory of ev­i­dence, I ac­cept Amer­i­can Gods as non-fic­tion, be­cause most of the places in that book ex­ist.

The prac­tice of writ­ing on metal plates, laugh­able in 1830, has now been well es­tab­lished as a le­gi­t­i­mate an­cient prac­tice; one that Joseph Smith could never have known.

What ev­i­dence is there that Smith knew noth­ing of the prac­tice of writ­ing on metal plates? Who says it was laugh­able in 1830?

Many tourists to Mex­ico will be well fa­mil­iar with the use of ce­ment in an­cient Amer­ica, for ex­am­ple in Teotihua­can; this in­for­ma­tion is had in the Book of Mor­mon, but was un­known in Joseph Smith’s time.

It was known in Europe—used al­most ev­ery­where in Rome. Are there spe­cific ar­chi­tec­tural de­tails that were un­prece­dented?

Ja­cob chap­ter 5 offers many, many de­tails re­gard­ing olive cul­ti­va­tion which match pre­cisely with what is now known about an­cient prac­tices in Is­rael.

Ja­cob 5 agrees with what, as Dar­win would say, “ev­ery an­i­mal hus­ban­der knows.” What ex­actly are the de­tails that match? Are they un­ex­pected?

Many seem­ingly non-He­braic per­sonal names...

What pro­por­tion of ran­dom 3-char­ac­ter He­brew strings do not cor­re­spond to per­sonal names?

I have read the Book of Mor­mon in the past, but I hereby pre­com­mit to read­ing it again and “search­ing in my heart” (I have a copy on my book­shelf) if you can demon­strate that my skep­ti­cism re­gard­ing your ev­i­dence is un­war­ranted.

• I will an­swer your points in the or­der re­ceived.

First: your anal­ogy is flawed, and, I’m sorry to say, rather ob­vi­ously so. Neil Gaiman knew of the places where he set the events of Amer­i­can Gods, hav­ing ei­ther trav­eled there him­self or else at least seen them on a map. (I can’t name any speci­fi­cally, never hav­ing read the book, but I can sur­mise as much from the con­text of your ob­jec­tion, I should think! x3) Smith, on the other hand, could not have cred­ibly known any­thing about the lo­ca­tion or name of an an­cient burial site in the Ara­bian Pen­in­sula, or of the lo­ca­tion of such a place as “Boun­tiful” in the same part of the world… par­tic­u­larly since “com­mon knowl­edge” of the Ara­bian Pen­in­sula makes the no­tion of find­ing any­thing that could be de­scribed as “boun­tiful” there sub­ject to skep­ti­cism.

Se­cond: Here are var­i­ous sources de­rid­ing Joseph’s claim of metal plates. John Hyde, Jr., Mor­monism: Its Lead­ers and De­signs (New York: Fetridge, 1857), 217-18; M.T. Lamb, The Golden Bible (New York: Ward and Drum­mond, 1887), 11; Stu­art Martin, The Mys­tery of Mor­monism (Lon­don: Od­hams Press, 1920), 27. A quote by Hugh Nibley in 1957 seems amus­ingly pre­scient: “it will not be long be­fore men for­get that in Joseph Smith’s day the prophet was mocked and de­rided for his de­scrip­tion of the plates more than any­thing else.” (Hugh Nibley, Lehi in the Desert, CWHN 5:107). A quote I have on hand: “No such records were ever en­graved upon golden plates, or any other plates, in the early ages” /​[M.T. Lamb, The Golden Bible, or, the Book of Mor­mon: Is It from God? (New York: Ward & Drum­mond, 1887), p. 11/​]. More in­for­ma­tion can be had here, thanks to Jeff Lind­say, who is my pri­mary (though not my sole!) source for Book of Mor­mon ev­i­dences. He has done a won­der­ful job com­piling them.

I must, for the sake of com­plete­ness, humbly ad­mit fault: To say that the prac­tice was one “that Joseph Smith could never have known” is in fact false; it is within the realm of pos­si­bil­ity that Joseph might have heard of such a thing. In my opinion, the like­li­hood that he could have known any­thing about the prac­tice is so small as makes no odds, but I must con­cede that the prob­a­bil­ity is not 0. But the ridicule that he re­ceived for his claim is well-doc­u­mented.

Third: I did not mean to im­ply that the use of ce­ment to make dwellings was un­heard of. How­ever, the use of ce­ment by pre-Columbian Amer­i­cans was un­known to the hoi pol­loi in Palmyra, late 1820′s. Even as late as 1929, ridicule abounded for the sake of this idea:

In 1929, He­ber J. Grant (former Pres­i­dent of the Church) told the story of a man with a doc­torate who had ridiculed him for be­liev­ing in the Book of Mor­mon. That learned man cited the men­tion of ce­ment work as an ob­vi­ous lie “be­cause the peo­ple in that early age knew noth­ing about ce­ment.” Pres­i­dent Grant, who was a young man at the time of that con­ver­sa­tion, said:

“That does not af­fect my faith one par­ti­cle. I read the Book of Mor­mon prayer­fully and sup­pli­cated God for a tes­ti­mony in my heart and soul of the di­v­inity of it, and I have ac­cepted it and be­lieve it with all my heart.” I also said to him, “If my chil­dren do not find ce­ment houses, I ex­pect that my grand­chil­dren will.” He said, “Well, what is the good of talk­ing with a fool like that?” (April 1929 Con­fer­ence Re­port, p. 128 ff.)

For more on this, please see Matthew G. Wells and John W. Welch, “Con­crete Ev­i­dence for the Book of Mor­mon,” In­sights (May 1991): 2.

• First: Very well, the anal­ogy was flawed. I’m un­clear as to what the name “Boun­tiful” is sup­posed to re­fer to. Do ei­ther of the places men­tioned as can­di­dates trans­late to “Boun­tiful”? Fur­ther, I want to point out that “Crit­ics doubt the link be­tween Na­hom and NHM, as well as hav­ing other crit­i­cisms.” This will dove­tail with our forth­com­ing con­ver­sa­tion on He­brew/​English transliter­a­tion.

Se­cond: While such things were un­known ar­chae­olog­i­cally, the prac­tic­ing of in­scrip­tion on gold is refer­enced in the Bible; some googling un­cov­ers Ex 39:30; see also the refer­ences here. Who­ever the au­thor of the BoM was, they were very well versed in the Bible.

Third: The quote demon­strates that the ac­tual ex­is­tence of pre-Columbian Amer­i­can ce­ment houses is ir­relel­vant. If they had not been found in our time, surely you also would main­tain that they would be found… even­tu­ally. As you do el­se­where.

• First: The name “Boun­tiful” has no sig­nifi­cance other than in­di­cat­ing a place of bounty. The can­di­date sites are those which match the de­scrip­tion I noted above:

...rea­son­able ac­cess from Na­hom (i.e. no moun­tains in the way!), an in­let for launch­ing a ship, fer­tile ground with “much fruit and… honey”, tim­ber to build a durable ship, year-round ac­cess to fresh wa­ter, a nearby moun­tain upon which Nephi could offer his prayer, available ore and flint, and wind and ocean cur­rents fa­vor­able for launch­ing a ship out to sea.

The only rea­son I am able to use the Na­hom—NHM the­ory as ev­i­dence is be­cause the lan­guage Nephi uses in­di­cates that the name of the place was given by some­one prior to Lehi’s travel. Speak­ing of which, yes, Crit­ics do doubt the link, but if you read on, those crit­i­cisms are some­what less than mov­ing...

• The fact that the Book of Mor­mon does not ex­plic­itly men­tion con­tact with out­siders dur­ing Lehi’s jour­ney.

• It is sug­gested that there is no ev­i­dence dat­ing NHM be­fore A.D. 600.

• It is sug­gested that the pro­nun­ci­a­tion of NHM is un­known and may not re­late to Na­hom at all.

• It has been sug­gested that Joseph Smith sim­ply cre­ated the name Na­hom as a var­i­ant of the Bibli­cal names Na­ham (1 Chron. 4:19), Ne­hum (Ne. 7:7) and Nahum (Na. 1:1).

The first is not re­ally com­pre­hen­si­ble as a counter-ar­gu­ment; con­tact with out­siders is not req­ui­site for Lehi to know the name. The sec­ond is a mere lack of ev­i­dence. The third is merely a com­plaint of am­bi­guity in­her­ent in He­brew, and is an­swered el­se­where in the ar­ti­cle. The fourth is sim­ply an al­ter­nate the­ory, and a right flimsy one at that, if it’s meant to ex­plain away the con­so­nance be­tween Joseph’s “guess” and the ac­tual place.

Se­cond: I’ll just note that the prac­tice of en­grav­ing on metal jew­elry and plaques is some­thing much differ­ent than the prac­tice of writ­ing sa­cred records on books of pre­cious metal.

Third: The story of Ein­stein’s Ar­ro­gance is rele­vant. :3 But at this point, I have enough pos­i­tive ev­i­dence be­hind the Book of Mor­mon to start tak­ing some of its as-of-yet un­ver­ified claims on faith.

And what about you? What of the ev­i­dences that do stand? What is the chance that these could have come about by pure luck? Cer­tainly we’ve ac­quired enough bits of ev­i­dence to raise the Book of Mor­mon to the level where it mer­its our at­ten­tion, at least.

• What is the chance that these could have come about by pure luck?

Rea­son­ably high. We have many ex­am­ples of charis­matic peo­ple con­struct­ing ob­vi­ously fic­tive re­li­gions whose fol­low­ers then retroac­tively find ev­i­dence, ex­ploit­ing hind­sight/​con­fir­ma­tion bias. Scien­tol­ogy, Baha’i, Theos­o­phy, and the var­i­ous ti­be­tan tulkus are ex­am­ples.

• In each of these cases, the amount of retroac­tive ev­i­dence is far out­weighed by the num­ber of ev­i­dences against the re­li­gion’s teach­ings. The op­po­site is true of Mor­monism. None of its claims are dis­proven; we are only lack­ing ev­i­dence to sup­port them. And the num­ber of claims un­sub­stan­ti­ated by phys­i­cal ev­i­dence is shrink­ing. Every time a dis­cov­ery has been made that re­lates to the Book of Mor­mon, it sup­ports the text.

I will ad­mit that there have been dis­cov­er­ies that have challenged pop­u­lar un­der­stand­ings of the Book of Mor­mon. Once upon a time, it was in vogue to sup­pose that the nar­ra­tive spanned the en­tire Amer­i­can con­ti­nent (that is, both of them). This has been shown to be prob­a­bly false, and in fact the text of the Book of Mor­mon it­self seems to con­tra­dict that no­tion. How­ever, the differ­ence be­tween, say, Scien­tol­ogy and the Book of Mor­mon is that we have in the lat­ter a doc­u­ment that is not chang­ing, but is still match­ing up to the ev­i­dence thrown at it. This doc­u­ment has been around for some 200 years in its pre­sent form, and the only al­ter­a­tions that have been made to it have been to re­pair gram­mat­i­cal er­rors—er­rors that, in fact, speak more strongly for the Book of Mor­mon than against it, since the first print­ing had “er­rors” that, while atro­cious English, ac­tu­ally made very good He­brew. I will sup­ply you with refer­ences to this claim if you wish, but I thought it be­hooved me to stick to phys­i­cal ev­i­dence first, as those are, in my opinion, the strongest claims.

But you say “rea­son­ably high”. I’m afraid I’ll have to hand you the bur­den of proof. With this counter, you chose to com­ment on an af­terthought of a ques­tion and dis­miss it out of hand, in­stead of talk­ing about my ar­gu­ments. We started this con­ver­sa­tion—at least I did—un­der the premise that the phys­i­cal ev­i­dences I sup­plied were worth dis­cussing. I thought that you were un­der the same premise, but now with this post you at­tempt to dis­miss any phys­i­cal ev­i­dences as “hind­sight/​con­fir­ma­tion bias”. I call foul.

• None of its claims are dis­proven; we are only lack­ing ev­i­dence to sup­port them. And the num­ber of claims un­sub­stan­ti­ated by phys­i­cal ev­i­dence is shrink­ing. Every time a dis­cov­ery has been made that re­lates to the Book of Mor­mon, it sup­ports the text.

Ab­sence of ev­i­dence is ev­i­dence of ab­sence. The book of Mor­mon makes many claims for which, if they were true, we would ex­pect to find ev­i­dence, but we do not. If you only look at the writ­ings of Mor­mon apol­o­gists, you’re go­ing to get an ex­tremely slanted pic­ture of how well the Book of Mor­mon agrees with ex­ist­ing ar­chae­olog­i­cal ev­i­dence, but if you look el­se­where, it’s not hard to find strong ev­i­dence against it. The fact that the Book of Mor­mon refer­ences as be­ing pre­sent an­i­mals that did not ex­ist in Me­soamer­ica, or any­where in the New World at the time, while not men­tion­ing any of nu­mer­ous com­mon an­i­mals that were, is, as I see it, a knock­down ar­gu­ment all by it­self. If these an­i­mals ex­isted at that time and place, we have an ex­tremely strong ex­pec­ta­tion of ev­i­dence for it given the ar­chae­olog­i­cal and pa­le­on­tolog­i­cal re­search we’ve done, but in­stead there is none. And the chance that le­gi­t­i­mate writ­ings from that time and place would refer­ence as pre­sent an­i­mals which were not ap­prox­i­mates to zero. This is ex­tremely strong ev­i­dence against the Book of Mor­mon be­ing true, and it’s only one among its ev­i­den­tial failings.

• I am well ac­quainted with the no­tion of ab­sence of ev­i­dence, thank you; I touched on this point above, stat­ing that, al­though ab­sence of ev­i­dence does count as points against the case I make, pos­i­tive ev­i­dence makes stronger points. Were this not the case, then physi­cists wouldn’t be search­ing for the Higgs Bo­son; they’d be re­stricted to the­o­ries which are read­ily ex­plained by only the par­ti­cles we have ev­i­dence of.

A dis­proof of the Book of Mor­mon, then, must rest upon just that: dis­proof. With that in mind, let us ex­am­ine fur­ther those points raised in the link you pro­vided.

Ar­chae­olog­i­cal Fal­la­cies
First, four tech­nolo­gies are men­tioned which were “un­known to Me­soamer­ica”: char­i­ots, steel swords, bel­lows, and silk.

An ex­pla­na­tion of the word ‘char­iot’ can be found here.

Many ex­pla­na­tions have been made re: steel swords; the refer­ence made in this case comes from the book of Ether, speak­ing of the Jared­ites. I offer the be­low quote as a counter:

In light of con­tem­po­rary con­di­tions in Me­soamer­ica, one can un­der­stand this pas­sage a num­ber of ways. Although the blades of most macuahuitls in Me­soamer­ica were made from ob­sidian, the Aztecs are known to have had war clubs stud­ded with iron in­stead of the usual ob­sidian. There are even ex­am­ples in Me­soamer­ica of cer­e­mo­nial macuahuitls with feathers re­plac­ing the ob­sidian blades.

Var­i­ous types of ma­te­rial, in­clud­ing iron, re­placed the usual ob­sidian of the macuahuitl, and such a weapon could thus be de­scribed as a sword with a metal “blade.” Another pos­si­bil­ity is to equate this Jared­ite steel with the “steel” of the King James trans­la­tion of the Old Tes­ta­ment, which ac­tu­ally refers to the He­brew word for “bronze.”

Fi­nally, we need to un­der­stand that Mosiah trans­lated Ether’s plates into so­cial and lin­guis­tic con­cepts with which he was fa­mil­iar. Mosiah, as king, pos­sessed La­ban’s sword, a steel weapon that was passed down as one of the in­signia of roy­alty. In trans­lat­ing Ether’s record, Mosiah might thus have given the Jared­ite kings steel swords, like the one he him­self pos­sessed, be­cause in Mosiah’s so­ciety a king was ex­pected to have a steel sword as his royal weapon.

Bel­lows are only men­tioned in the lo­cale of the old world, not in Amer­ica, mak­ing this a non-point.

Re­gard­ing silk: An LDS pub­li­ca­tion, and a non-LDS pub­li­ca­tion, “Silk­worm of the Aztecs” by Richard S. Pei­gler, Ph.D., Cu­ra­tor of En­to­mol­ogy, in Mu­seum Quar­terly, Vol. 2, No. 1 (Spring, 1993): pp. 10-11 (pub­lished by the Den­ver Mu­seum of Nat­u­ral His­tory, both show ev­i­dence of silk in the Amer­i­cas.

A note on cities in Amer­ica comes again from Jeff Lind­say:

As for the ac­count deal­ing with peo­ples in the New World, Book of Mor­mon ge­og­ra­phy best fits the Isth­mus of Te­huan­te­pec (south­ern Mex­ico, Gu­atemala), where a num­ber of sites, cities, etc., have been ten­ta­tively cor­re­lated with Book of Mor­mon lo­ca­tions. The best treat­ment of this is in John Soren­son’s An An­cient Amer­i­can Set­ting for the Book of Mor­mon. He offers fas­ci­nat­ing cor­re­la­tions, very strong (in my opinion), though only a small frac­tion of the ar­chae­olog­i­cal work has been done that is needed to con­firm most of the spe­cific pro­pos­als. The La­man­ites in the Book of Mor­mon may cor­re­late well with a part of the early Mayan civ­i­liza­tion or one of the other cul­tural groups in an­cient Me­soamer­ica. The peo­ples de­scribed in the Book of Ether could very well be part of the Olmec peo­ples from the same area. A num­ber of Mayan leg­ends and the few sur­viv­ing writ­ings provide in­ter­est­ing par­allels with Book of Mor­mon con­cepts. Could write much more on this if you’re in­ter­ested. Bot­tom line: yes, there are real places and there were real peo­ple de­scribed in what is truly an au­then­tic an­cient record. But we are in our in­fancy when it comes to un­der­stand­ing Me­soamer­ica. Un­til schol­ars are able to do more work there, the ar­gu­ment from silence should be ap­plied with cau­tion.

Fur­ther, as noted above, the de­tails of Lehi’s jour­ney through the Ara­bian pen­in­sula have been well cor­re­lated with ac­tual places, some with names match­ing those found in ar­chae­olog­i­cal stud­ies.

An­thro­polog­i­cal fal­la­cies

Most stun­ning of all, the BoM never once in­di­cates that the Amer­i­can con­ti­nent was any­thing but un­in­hab­ited when the re­fugees from Jerusalem ar­rived.

I’m sorry, but this is plainly wrong. We have known for quite some time that the Nephites were not the only in­hab­itants of an­cient Amer­ica; the Jared­ites are an ex­am­ple at­tested in the Book of Mor­mon.

Biolog­i­cal fal­la­cies
My good­ness, what an in­trigu­ing ques­tion this is. I’ll defer to Jeff Lind­say, who has done much work on this sub­ject, and who has cited many good pri­mary sources, lest there be a com­plaint against my us­ing his work too many times.

Lin­guis­tic fal­la­cies
I once again defer to Jeff Lind­say:

One of the most in­ter­est­ing ev­i­dences of transoceanic con­tact be­tween the Old and New Wor­lds is the Bat Creek He­brew in­scrip­tion found by a Smith­so­nian ex­pe­di­tion in Ten­nessee in 1889. (The Bat Creek Stone and other in­ter­est­ing odd­i­ties of ar­chae­ol­ogy, in­clud­ing pre-Columbian maize in In­dia, can be seen at the Ar­chae­olog­i­cal Out­liers site.) Anti-Mor­mon writ­ers such as the Tan­ners have spent much effort try­ing to ar­gue that the writ­ing on the Bat Creek Stone is not He­brew. How­ever, non-LDS scholar J. Hus­ton McCul­loch has now shown that the Bat Creek in­scrip­tion, once thought to be Chero­kee, “fits sig­nifi­cantly bet­ter as Pa­leo-He­brew” (J. Hus­ton McCul­loch, “The Bat Creek In­scrip­tion: Chero­kee or He­brew?” Ten­nessee An­thro­pol­o­gist, Vol. 13, Fall 1988, p. 116, as cited by Matthew Roper, Re­view of Books on the Book of Mor­mon, Vol. 4, 1992, p. 212). McCul­loch’s re­cent work con­firms Cyrus Gor­don’s origi­nal hy­poth­e­sis about the in­scrip­tion, namely, that it was from be­tween 70 A.D. and 135 A.D. and rep­re­sented Old World writ­ing (Science Vol. 2, May 1971, pp. 14-16, as cited by Paul R. Cheesman, BYU Stud­ies, Vol. 13, No. 1, p. 85). Car­bon-14 dated wood and brass bracelets as­so­ci­ated with the in­scrip­tion date to be­tween A.D. 32 and A.D. 769 (Ibid., pp.107-12, 116) - definitely be­fore Colum­bus. Cyrus Gor­don, a re­spected non-LDS scholar, wrote:

The Bat Creek In­scrip­tion is im­por­tant be­cause it is the first sci­en­tifi­cally au­then­ti­cated pre-Columbian text in an Old World script or lan­guage found in Amer­ica; and, at that, in a flawless ar­chae­olog­i­cal con­text. It proves that some Old World peo­ple not only could, but ac­tu­ally did, cross the At­lantic to Amer­ica be­fore the Vik­ings and Colum­bus....The dis­cred­ited pre-Columbian in­scrip­tions in Old World scripts or lan­guages will have to be re­ex­am­ined and reeval­u­ated, each on the mer­its of the ev­i­dence, case by case. (Cyrus Gor­don, “A He­brew In­scrip­tion Authen­ti­cated,” in Lundquist and Ricks, eds., By Study and Also by Faith, 1:71,80, as cited by Roper, op. cit.; for more on this con­tro­ver­sial is­sue, see also J. Hus­ton McCul­loch, “The Bat Creek In­scrip­tion: Did Judean Re­fugees Es­cape to Ten­nessee?” Bibli­cal Ar­chae­ol­ogy Re­view, July/​Au­gust 1993, pp. 46-53, 82, and the differ­ing view of P. Kyle McCarter, Jr., “Let’s Be Se­ri­ous about the Bat Creek Stone,” Bibli­cal Ar­chae­ol­ogy Re­view, July/​Au­gust 1993, pp. 54-55, 83.)

While crit­ics will re­peat old ar­gu­ments that the Bat Creek Stone is a forgery, it is im­por­tant to rec­og­nize that “there is ab­solutely no in­di­ca­tion that the in­scrip­tion is a forgery, in the first place, other than the cir­cu­lar, and there­fore un­scien­tific, ar­gu­ment that be­ing He­brew, it must surely be a fake” (J. Hus­ton McCul­loch, “The Bat Creek Stone: A Re­ply to Main­fort and Kwas,” Ten­nessee An­thro­pol­o­gist, Vol. 18, No. 1, Spring 1993, p. 16, em­pha­sis added, as cited by Matthew Roper, FARMS Re­view of Books, Vol. 9, No. 1, 1997, p. 142). David H. Kelly has also found se­ri­ous ev­i­dence of sev­eral pre-Columbian in­scrip­tions of Euro­pean ori­gin: “We need to ask . . . where we have gone wrong as ar­chae­ol­o­gists in not rec­og­niz­ing such an ex­ten­sive Euro­pean pres­ence in the New World” (David H. Kelly, “Proto-Tif­nagh and Proto-Ogham in the Amer­i­cas,” Re­view of Ar­chae­ol­ogy, Vol. 2, Spring 1990, p. 10, as cited by Roper, op. cit.). More ev­i­dence for schol­arly ac­cep­tance of Old World scripts in the an­cient Amer­i­cas can be found in W.R. McGlone et al., An­cient Amer­i­can In­scrip­tions: Plow Marks or His­tory? (Long Hill, Mass.: Early Sites Re­search So­ciety, 1993, as cited by Soren­son, 1993, p. 21) and Jac­ques de Mahieu, “Cor­pus des in­scrip­tions ru­iniques d’Amerique du Sud,” Ka­dath 68, Brus­sels, 1988, pp. 11-42 (cited by Soren­son, 1993, p. 21). More rele­vant re­search has ten­ta­tively iden­ti­fied hun­dreds of pos­si­ble links be­tween Uto-Aztecan lan­guages (in Book of Mor­mon ter­ri­tory) with the an­cient He­brew lan­guage (work by Brian D. Stubbs, in­clud­ing “A Cu­ri­ous Ele­ment in Uto-Aztecan,” The Epi­graphic So­ciety Oc­ca­sional Papers, Vol. 23, 1998 [ac­cord­ing to sec­ond-hand sources—I have not yet read this ar­ti­cle]; “Ele­ments of He­brew in Uto-Aztecan: A Sum­mary of the Data,” F.A.R.M.S. pa­per, 1988; “Look­ing Over vs. Over­look­ing Na­tive Amer­i­can Lan­guages: Let’s Void the Void,” Jour­nal of Book of Mor­mon Stud­ies, Vol. 5, No. 1, Spring 1996, pp. 1-49).

It Takes a Thief...
I will not deign to jus­tify this. Any ex­am­i­na­tion of the story, from ei­ther side, will show that this is nei­ther a rigor­ous dis­proof or in fact un­rea­son­able.

Lost in Trans­la­tion
B. F. Sperry writes a re­sponse here to the ques­tion of Har­ris vs. An­thon. As for the Book of Abra­ham, I would be re­miss not to re­fer you to Jeff Lind­say’s ex­cel­lent three-part piece.

• Edit: I meant to cover this point first, but I left it out be­fore.

I am well ac­quainted with the no­tion of ab­sence of ev­i­dence, thank you; I touched on this point above, stat­ing that, al­though ab­sence of ev­i­dence does count as points against the case I make, pos­i­tive ev­i­dence makes stronger points. Were this not the case, then physi­cists wouldn’t be search­ing for the Higgs Bo­son; they’d be re­stricted to the­o­ries which are read­ily ex­plained by only the par­ti­cles we have ev­i­dence of.

This re­ally isn’t how it works. Ab­sence of ev­i­dence is ev­i­dence of strength pro­por­tional to the ex­pec­ta­tion of ev­i­dence if a given propo­si­tion is true. So if, for ex­am­ple, you pro­pose that there is an elephant in a room, and then you in­ves­ti­gate the room and see no sign of an elephant, then that is very strong ev­i­dence that there is no elephant in the room. But if you pro­pose that there is a mouse in a room, and you in­ves­ti­gate and see no sign of the mouse, then that is only weak ev­i­dence that there is no mouse. You will have to up­date your con­fi­dence that there is a mouse in the room down­wards, but much, much less than you had to up­date in the case of the elephant.

In both the case of the elephant and the mouse, ac­tu­ally ob­serv­ing the elephant or mouse would be ex­tremely strong ev­i­dence; you could still be wrong if you were hal­lu­ci­nat­ing or some­one had con­trived an ex­tremely clever way of cre­at­ing an illu­sion of ei­ther, but it would still force you to greatly strengthen your prob­a­bil­ity es­ti­mate for an elephant or mouse be­ing in the room. It’s psy­cholog­i­cally com­pel­ling to try to gen­er­al­ize this into an broad prin­ci­ple, that pos­i­tive ev­i­dence is always stronger, but in fact as with the case of the elephant, nega­tive ev­i­dence can reach ar­bi­trar­ily high strengths de­pend­ing on how strong the ex­pec­ta­tion of ev­i­dence is. Like­wise, pos­i­tive ev­i­dence can reach ar­bi­trar­ily low strengths de­pend­ing on how likely it is that the ob­ser­va­tion would be forth­com­ing with­out the propo­si­tion be­ing true. For in­stance, if an alleged psy­chic de­scribes a crime scene, and the po­lice con­firm that the de­scrip­tion is ac­cu­rate, this is not strong ev­i­dence that the psy­chic had any sort of vi­sion of the scene if their de­scrip­tion is statis­ti­cally likely to ap­ply to any crime scene of that type.

The defenses you’ve linked are ex­tremely weak. Apol­o­gists of any re­li­gion can ra­tio­nal­ize this de­gree of agree­ment with ev­i­dence, but the fact re­mains that given what we know about Me­soamer­i­can civ­i­liza­tion, the Book of Mor­mon does not re­motely re­sem­ble what we would ex­pect a le­gi­t­i­mate text from that time and place to be like, the most we can say is that it is not strictly im­pos­si­ble for it to be so.

If you’re already strongly in­vested in a re­li­gious nar­ra­tive be­ing true, then some­thing like

After read­ing about the dis­cov­ery of fos­silized bi­son along with the mam­moths re­cently found in Mex­ico (As­so­ci­ated Press, Oct. 30, 1996), per­haps one could spec­u­late that bi­son were treated and named as cat­tle. If buf­falo or bi­son had been in Joseph Smith’s vo­cab­u­lary in 1829, per­haps a more spe­cific term might have been used in the trans­la­tion, but “cat­tle” (per­haps as a generic term) may have been the most ac­cu­rate trans­la­tion for what­ever word was used in the Nephite lan­guage.

may seem like an ad­e­quate defense, but a per­son who is merely im­par­tial to the re­li­gion will sim­ply ask “How likely is that?” Well, given that when an­i­mals are raised do­mes­ti­cally for food like cat­tle, ar­chae­ol­o­gists can con­sis­tently find con­cen­tra­tions of their re­mains in hu­man set­tle­ments along with food re­fuse, and there is no ev­i­dence what­so­ever of bi­son be­ing do­mes­ti­cated in Me­soamer­ica, or any­where in pre­mod­ern Amer­ica at all, and be­sides which this was over twenty years af­ter the Lewis and Clark ex­pe­di­tion and Joseph Smith should have been quite aware of the ex­is­tence of buf­falo, the an­swer seems to be “very un­likely”. Other defenses given on that page are similarly un­com­pel­ling.

I recom­mend check­ing out this ar­ti­cle. It’s about mar­tial arts, but it gen­er­al­izes ex­tremely well. Once you be­come per­son­ally in­vested in a set of be­liefs, your de­mands for ar­gu­ments in its defense will be much weaker than a per­son with­out the same in­vest­ment. Works of apolo­get­ics such as the ones you’ve linked may satisfy a be­liever to keep their pack­age of be­liefs, but this is very differ­ent from singling them out to an im­par­tial in­di­vi­d­ual to adopt them.

Hav­ing read a con­sid­er­able num­ber of works of apolo­get­ics for var­i­ous re­li­gions, I can­not say that Mor­monism stands out for hav­ing an atyp­i­cal de­gree of sup­port. It is at best typ­i­cal, and the ev­i­den­tial stan­dards among re­li­gions are already ex­tremely low.

• Your point is well taken, and I will med­i­tate upon it. Thank you.

• Re “Silk­worms of the Aztecs”, have you read it? Be­cause these peo­ple say that the ev­i­dence for it ex­ist­ing is weak. I don’t have ac­cess to JSTOR and I don’t have Aaron Swartz’s hard drive, so I can’t look it up my­self.

• Well, that’s dis­con­cert­ing. Sounds like ev­ery­one’s copy­ing off ev­ery­one else. ;3 Prob­lems in academia, in­deed. The fi­nal post on that thread does seem to in­di­cate that the ar­ti­cle does ex­ist; would you like me to at­tempt to gain a pho­to­copy, so I can ver­ify your sus­pi­cions?

• Well, I have to ad­mit that I’m cu­ri­ous, but re­ally only mildly. I mostly gave up trol­ling Mor­mon mis­sion­ar­ies af­ter high school. I just thought it might be an in­ter­est­ing ar­ti­cle, which is why, while skim­ming this thread, it is one of the two things I googled—the other be­ing the Bat Creek stone.

• :3 I am glad to hear you gave up on trol­ling the mis­sion­ar­ies. I re­al­ize that they can be an­noy­ing… and some of them may de­serve a bit of trol­ling, from the sto­ries I’ve heard… but most of them are hard-work­ing young men who re­ally do be­lieve in what they’re say­ing.

• In each of these cases, the amount of retroac­tive ev­i­dence is far out­weighed by the num­ber of ev­i­dences against the re­li­gion’s teach­ings.

Really? I can’t think of any ev­i­dence con­tra­dict­ing the be­lief that His Holi­ness the Dalai Lama is the rein­car­na­tion of the pre­vi­ous Dalai Lama. Yet the ev­i­dence in fa­vor is much of the same kind of ev­i­dence pre­sented here, namely, “How could the young Dalai Lama have known which of many ob­jects were the per­sonal pos­ses­sions of the pre­vi­ous Dalai Lama, were he not the rein­car­na­tion thereof?” In the same vein, “How could Joseph Smith have known X?”, asked rhetor­i­cally, doesn’t provide ev­i­dence in it­self.

In any case, this was never meant to be an ar­gu­ment about me con­vert­ing to Mor­monism. I wanted to know why you thought a non-Mor­mon shouldn’t be skep­ti­cal of these ev­i­dences. I’ll leave oth­ers to judge whether or not you’ve satis­fied the con­di­tion of the pre­com­mit­ment in a par­allel dis­cus­sion thread.

• If you look at the votes for our posts, I think you’ll find that they’ve already been judg­ing. :3 Yes, I’m sorry if you felt I was jump­ing onto the “Hey, I’ve con­vinced you, now you should con­vert!” band­wagon; that was far from my in­tent. But I have offered my ar­gu­ments about why a non-Mor­mon shouldn’t be skep­ti­cal—rather, ought to be skep­ti­cal, but should be swayed any­way by the weight of ev­i­dence—but if it is not enough to con­vince you, then so be it. It is said that two Bayesi­ans, work­ing from the same set of pri­ors, can­not agree to dis­agree… but I think we have differ­ent pri­ors, which dis­turbs me to an ex­tent. I will go med­i­tate on this; I hope you will, too.

EDIT: As to the Dalai Lama ex­am­ple, whose word do we have that these ob­jects did in fact be­long to the pre­vi­ous Dalai Lama? If the hon­esty of the cer­e­mony is well-doc­u­mented, then I would be in­ter­ested to learn more.

• Beh, half of LW down­votes ev­ery­thing re­motely the­ist on sight. It wasn’t a judg­ment of the ev­i­dence.

I do worry that I have been in­suffi­ciently dili­gent in eval­u­at­ing the many re­li­gions. Hope­fully any ex­tant gods will turn out to be un­der­stand­ing.

• ″ Ra­tion­al­ity can’t be used to ar­gue for a fixed side, its only pos­si­ble use is de­cid­ing which side to ar­gue.” Peo­ple ar­gu­ing for their own re­li­gion au­to­mat­i­cally fail this rather ba­sic premise of ra­tio­nal­ity, so what’s the point get­ting into a dis­cus­sion with them on finer points of re­li­gious doc­trine, given that they have no clue about ra­tio­nal­ity to be­gin with, re­gard­less of what they say?

My ques­tion would in­stead be “Is it im­por­tant to you for your re­li­gion to be right? If so, how does this mesh with ra­tio­nal­ity, if not, what are the odds that all the available ev­i­dence you eval­u­ated pointed you in this con­ve­nient di­rec­tion with­out any bias in­volved?”.

• If a re­li­gion were cor­rect, what would you ex­pect de­bates with fol­low­ers of that re­li­gion to look like?

• Depends on what you mean by “cor­rect”.

For ex­am­ple, if $re­li­gion’s teach­ings cor­rectly con­strain ex­pec­ta­tions in ver­ifi­able ways, I ex­pect such de­bates to look some­thing like this: Skep­tic: “Why do you fol­low the teach­ings of$re­li­gion?” Believer: “Be­cause its teach­ings cor­rectly con­strain ex­pec­ta­tions. Here, I’ll show you: here’s a real-world situ­a­tion. What do you ex­pect to hap­pen next?” Skep­tic: “I ex­pect $A.” Believer: “Well, ap­ply­ing$re­li­gion’s teach­ings I con­clude that $B is more likely.” Skep­tic: “Ex­cel­lent! Let’s see what hap­pens.” (lather, rinse, re­peat) Even­tu­ally one of them says to the other: “Huh. Yeah, it seems you were right!” • “$re­li­gion’s teach­ings cor­rectly con­strain ex­pec­ta­tions in ver­ifi­able ways”—that’s where it fails ev­ery time. That the uni­verse was cre­ated 6000 years ago “should not be taken liter­ally” now, though it was back when it was not testable. There is some nice stuff about it in HPMoR, Ch 22, Belief in Belief. There is no ra­tio­nal ar­gu­ment you can make that would change some­one’s be­lief if they are de­ter­mined to keep it. Our Mor­mon friend here is a typ­i­cal ex­am­ple. An hon­estly re­li­gious per­son would say that “this is what I choose to be­lieve, leave logic out of it.”

• I’m not sure if you think I dis­agree with you, or if you’re just echo­ing me for em­pha­sis.

Just to be clear, I was an­swer­ing JGWeiss­man’s ques­tion: if a re­li­gion were cor­rect, for at least that un­der­stand­ing of “cor­rect” (which I en­dorse), that’s what I would ex­pect de­bates with its fol­low­ers to look like.

I’ve never en­coun­tered a re­li­gious tra­di­tion for which de­bates with its fol­low­ers ac­tu­ally looked like that, which I take as ev­i­dence that no re­li­gious tra­di­tion I’m fa­mil­iar with cor­rectly con­strains ex­pec­ta­tions in ver­ifi­able ways.

• My point was that the rea­son you never en­coun­tered it is be­cause it would im­ply ra­tio­nal­ity, which is in­com­pat­i­ble with faith. Not to say that a re­li­gious per­son can­not be ra­tio­nal about other things, just not about their own be­liefs. Thus “if a re­li­gion were cor­rect” is not a mean­ingful state­ment.

• Ah. Thanks for clar­ify­ing.

I think your pro­posed ex­pla­na­tion for the ob­served event is un­der­de­ter­mined by the ev­i­dence we’re dis­cussing, but it could cer­tainly be true.

Nev­er­the­less, I’m still in­clined to at­tend more to how well a prac­tice is ob­served to con­strain an­ti­ci­pated ex­pe­rience than to how ra­tio­nal its prac­ti­tion­ers can be in­ferred to be on gen­eral prin­ci­ples… though I’ll grant you that in­ferrable level of ra­tio­nal­ity cor­re­lates pretty well to how much en­ergy I’ll de­vote to mak­ing the ob­ser­va­tions in the first place.

• First, it would be in­ter­est­ing to know how one can con­vince a neu­tral and mildly ra­tio­nal ob­server what it means for a given re­li­gion to be cor­rect and ex­plain how this cor­rect­ness can be tested ex­per­i­men­tally. I don’t have Yud­kowsky’s imag­i­na­tion, so it’s not some­thing I can eas­ily con­ceive.

• If I in­ter­pret JGW’s com­ment cor­rectly, the rhetor­i­cal ques­tion wouldn’t suffer much were it phrased “If X were true, what would you ex­pect de­bates with peo­ple who be­lieved X was true to look like?”

The an­swer is that as hu­mans speak­ing col­lo­quially, they would first say “X is true” and then rat­tle off rea­sons, in the same for­mat apol­o­gists use. This pat­tern of speak­ing does not strongly im­ply that the pat­tern of speak­ing was the pat­tern of think­ing, it’s just how peo­ple speak.

Some peo­ple do think in this pat­tern, in­clud­ing many the­ists, so one can lose sight of the fact that the mode of speak­ing and mode of think­ing are not perfectly cor­re­lated.

ex­plain how this cor­rect­ness can be tested experimentally

As hard as they try, I don’t think re­li­gions can avoid mak­ing testable claims. The untestable claim X is im­plic­itly paired with the testable claim that one should be­lieve X.

Even prob­a­bil­is­tic be­liefs are held be­cause be­lief sys­tems lead peo­ple to ex­pect things. when con­fronted with in­puts.

If a Uni­tar­ian Univer­sal­ist says “(One ought to be­lieve that) there is a 99.9% chance Je­sus ex­isted,” and the sci­en­tific con­sen­sus is “(One ought to be­lieve that) there is a 99.5% chance Je­sus ex­isted,” and we fire up the ol’ AIXI and it out­puts the lat­ter, the UU is wrong even if Je­sus ex­isted as one his­tor­i­cal char­ac­ter.

The UU might as well claim that the Noah’s ark tale liter­ally hap­pened, if he isn’t his be­lief sys­tem is in one way worse than the fun­da­men­tal­ist’s, as his con­tains the propo­si­tion “To hell with re­al­ity when it con­tra­dicts my re­li­gion, if I can defy it with­out do­ing so in a fla­grant enough way that peo­ple no­tice, in­clud­ing my­self”, whereas the lat­ter’s con­tains the propo­si­tion “To hell with re­al­ity when it con­tra­dicts my re­li­gion.” Much sim­pler.

• I reck­oned that was the case, but I wanted to ver­ify my un­ease. :3

And don’t worry! If we Mor­mons turn out to be right, then the sal­va­tion/​damna­tion schema isn’t bi­nary. ^_~ We be­lieve that if you’re a good per­son who didn’t com­plete all the mys­ti­cal rit­u­als you need in or­der to be “saved”, then you’ll go to the next-lower de­gree of heaven, which is still a fair sight bet­ter than this place.

Also that you’ll prob­a­bly get am­ple ev­i­dence to pe­ruse dur­ing the mil­len­nium, so you’ll be able to make an in­formed de­ci­sion. (My own un­der­stand­ing; may be dis­proven upon fur­ther pe­rusal of Church doc­trine, but I think I’ve got it pretty right.)

• Fourth: In this case, I defer en­tirely to the ex­perts.

Below is an ex­cerpt from John Gee and Daniel C. Peter­son, “Graft and Cor­rup­tion: On Olives and Olive Cul­ture in the Pre-Modern Med­iter­ranean,” in The Alle­gory of the Olive Tree, pp. 186-247, taken from pages 223-224:

And here is an ex­cerpt from “Botan­i­cal Aspects of Olive Cul­ture Rele­vant to The Alle­gory of the Olive Tree” by Wilford M. Hess, Daniel J. Fair­banks, John W. Welch, and Jonathan K. Driggs in The Alle­gory of the Oliver Tree (pp. 552-554):

Based on the botan­i­cal and hor­ti­cul­tural in­for­ma­tion pre­sent in the ar­chae­olog­i­cal and his­tor­i­cal record, and re­flected in Ja­cob 5, we can con­clude that the an­cients were su­perb hor­ti­cul­tur­ists and had a profound un­der­stand­ing of vi­tal biolog­i­cal and plant cul­tural prin­ci­ples. Most of the botan­i­cal and hor­ti­cul­tural prin­ci­ples in Ja­cob 5 are sound and are very im­por­tant for olive cul­ture. In ad­di­tion, the one or two points, ac­cord­ing to our in­ter­pre­ta­tion, that rep­re­sent un­usual or anoma­lous cir­cum­stances are nec­es­sary en­hance­ments to the mes­sage of the alle­gory. In this sin­gle chap­ter of the Book of Mor­mon there are many de­tailed hor­ti­cul­tural prac­tices and pro­ce­dures that were not likely known by an un­trained per­son, and may not have been fully ap­pre­ci­ated by pro­fes­sional botanists or hor­ti­cul­tural­ists at the time the Book of Mor­mon was trans­lated. Even to­day, out­side of olive-grow­ing ar­eas, pro­fes­sional hor­ti­cul­tural­ists may not fully ap­pre­ci­ate some of the unique as­pects of olive cul­ture. Given the ex­ten­sive de­tail about olive cul­ture pre­sent in Ja­cob 5, we must give Zenos much credit for a high de­gree of hor­ti­cul­tural knowl­edge, which many take for granted. Ex­am­ples of what the an­cients and Zenos ev­i­dently knew were how to prune, dig about, dung, and nour­ish; how to graft tame to wild and wild to tame, and how to graft tame back into tame; how to bal­ance tops and roots by prun­ing, and the rea­sons for do­ing this; how to save the roots of trees whose branches had de­cayed, and how to trans­plant branches to pre­serve the de­sired traits of good plants; how to pre­serve and store fruit and how to dis­t­in­guish be­tween good and bad fruit; how well plants grow on good and bad soil; how to care for trees to cause young and ten­der branches to shoot forth; that they could graft wild to tame to re­ju­ve­nate tame; that spe­cific cul­ti­vars pro­duced well in cer­tain ar­eas; . . . that they could burn an or­chard to reestab­lish a new one; that plants grown from seeds would not have de­sir­able char­ac­ter­is­tics; the im­por­tance of elimi­na­tion of old wood and de­bris by burn­ing, and how to deal with pests and pathogens; how to pre­vent heavy bear­ing one year and no bear­ing the next by proper prun­ing; the ne­ces­sity to plant more than one cul­ti­var for pol­li­na­tion; and how to prop­a­gate scions with the de­sir­able ge­netic ma­te­rial. In­ter­est­ingly, much of this so­phis­ti­cated tech­nol­ogy was prob­a­bly lost in the Nephite civ­i­liza­tion, for the olive is not men­tioned again in the Book of Mor­mon af­ter Ja­cob 5, an in­di­ca­tion that the lands of the Book of Mor­mon may not have been suit­able for grow­ing olives … The only re­gions on the Amer­i­can con­ti­nents with Med­iter­ranean cli­mates where olive cul­ture is eco­nom­i­cally fea­si­ble are the re­gions of Cal­ifor­nia, Chile, and Ar­gentina. Joseph Smith prob­a­bly knew how to prune, dig about, dung, and nour­ish lo­cal fruit trees; he prob­a­bly knew a lit­tle about graft­ing, and he may have been fa­mil­iar with some other hor­ti­cul­tural prin­ci­ples, but not likely those pe­cu­liarly re­lated to olive cul­ture.

Fifth: That is en­tirely the wrong ques­tion to ask; so wrong that I won­der if you un­der­stood my point. Your ques­tion should have been, “What pro­por­tion of ran­dom 3-6 English char­ac­ter strings cor­re­spond both to pro­nounce­able words and as-of-that-time undis­cov­ered He­braic names”. Or per­haps you are act­ing un­der the as­sump­tion that these names are at­tested only by con­so­nant matches? That’s not quite true. For ex­am­ple, the name “Alma” is not sim­ply writ­ten as “lm” in he­brew, but is writ­ten with four char­ac­ters, es­sen­tially com­ing out to ‘lm’. For schol­ars of He­brew, there is good ev­i­dence that the name should be “Alma,” which is ex­actly how the non-LDS scholar, Yi­gael Yadin, transliter­ated it. As far as the ac­tual pro­por­tion, I have no idea, but one must as­sume that there are more dis­al­lowed com­bi­na­tions than al­lowed ones, or else the lan­guage would be­come in­com­pre­hen­si­ble. :P

• Fourth: I’m not an ex­pert, so I too defer.

EDIT: Wait, these aren’t ran­dom ex­perts. They’re all Mor­mon apol­o­gists, with ob­vi­ous in­cen­tive to defend their faith. Where are the un­af­fili­ated ar­chae­ol­o­gists on this?

Fifth: I am ad­mit­tedly an am­a­teur at bibli­cal He­brew, so I sup­pose I should have asked for 3-4 char­ac­ter strings. If I were an evil Joseph Smith, I would con­struct such plau­si­ble-sound­ing He­brew strings, and then transliter­ate them into English. Un­der this pro­ce­dure, whether I gen­er­ate aleph-lamed-mem-aleph, aleph-lamed-mem, ayin-lamed-mem, and etc, I still plau­si­bly gen­er­ate “Alma”. After some fa­mil­iar­ity with He­brew, it does not be­come overly difficult to guess at vow­els; hence the leg­i­bil­ity of un­pointed text.

• Fourth: No, of course not. If you were a non-LDS scholar, would you come out and say, “Oh, by the way, ac­cord­ing to this ev­i­dence we found, the Book of Mor­mon might well be true af­ter all.” First off, it would be ca­reer suicide, and sec­ond, if you found sci­en­tific ev­i­dence sup­port­ing the Book of Mor­mon, I imag­ine you’d be in­trigued, start seek­ing for more in­for­ma­tion, and even­tu­ally be­come LDS. :P But very well; I can offer what non-LDS schol­ars have said about olive cul­ture, and you can com­pare to Ja­cob 5 and draw your own con­clu­sions. The fol­low­ing quote cour­tesy of Jeff Lind­say.

For on­line ver­ifi­ca­tion of olive cul­ture prin­ci­ples from non-LDS re­sources, con­sider “The Se­crets of Olive Trees” from BienManger.com (also LeGourmetMar­ket.com), from which the fol­low­ing ex­cerpts are taken. That page ver­ifies sev­eral con­cepts in Ja­cob 5, such as the abil­ity of olive trees to grow in rich and poor soils, the im­por­tance of graft­ing, the abil­ity to re­gen­er­ate or re­ju­ve­nate a de­cay­ing olive tree, and the prac­tice of ap­ply­ing dung:

SOILS The olive tree of­ten grows on poor and dry soils, but gives re­mark­able re­sults on rich soils (Cal­ifor­nia) or by ir­ri­ga­tion (Spain and Oranie). . . . GRAFTING : the prop­a­ga­tion of a given va­ri­ety of table olives is done by graft­ing, ex­cept in spe­cial cases (cut­tings, stump chips of the same va­ri­ety). Depend­ing on what has to be grafted, the fol­low­ing tech­niques are be­ing used : For the seedlings and the sprouts com­ing from stocks of a differ­ent va­ri­ety, you can use cleft graft­ing or bud­ding. In the case of older trees, be it the graft­ing of wild olive trees or of olive groves whose pro­duc­tion is to be mod­ified, it is ad­vised to use inarch­ing or bark graft­ing. . . . REGENERATION : It may be nec­es­sary to re­ju­ve­nate an olive grove if it has not been main­tained for a long pe­riod or if it has suffered ac­ci­dents, thus be­com­ing un­able to pro­duce a nor­mal crop. It is suffi­cient to cut away all branches, ex­cept the largest ones and then graft the re­main­ing stumps. The grove should then bear a unique va­ri­ety of table olives and be able of bear­ing fruit in ex­cel­lent con­di­tions. A trunk in very bad shape should be cut at the base in or­der to start with three re­plac­ing shoots. . . . MANURE : Although ma­nur­ing largely pays off, olive trees are still too rarely ma­nured. Ma­nure should be or­ganic, on a ba­sis of dung or cat­tle cake. When pos­si­ble, a cul­ture of green fer­til­iz­ers (vetch, lupin, etc.), mowed at ma­tu­rity and ploughed in, will com­plete the dress­ing of or­ganic mat­ter. . . . Here is some in­for­ma­tion from a mod­ern olive-tree cul­ti­va­tor, as viewed April 27, 2008: Some an­cient olive trees in Jerusalem at the Mount of Olives date back 2000 years. When old large limbs are pruned on large aged olive trees, new branches grow and a new olive crop grows. . . . The leaves of olive trees are gray-green and are re­placed at 2-3 year in­ter­vals dur­ing the spring af­ter new growth ap­pears. Prun­ing yearly and severely is very im­por­tant to in­sure con­tinued pro­duc­tion. The trees have the un­pro­duc­tive limbs re­moved, “so that it will be more fruit­ful” John 15:2. An olive tree can grow to 50 feet with a limb spread of 30 feet, but most grow­ers will keep the tree pruned to 20 feet to as­sure max­i­mum pro­duc­tion. >>New sprouts and trees will emerge from the olive tree stump roots, even if the trees are cut down. Some olive trees are be­lieved to be over a thou­sand years old, and most will live to the ripe old age of 500 years. Olives gen­er­ally are beaten off trees with poles, har­vested me­chan­i­cally or by shak­ing the fruit from the trees onto can­vas. Most ripen­ing olives are re­moved from the trees af­ter the ma­jor­ity of the fruit be­gins to change in color. It is im­por­tant to squeeze out the olive oil within a day af­ter har­vest­ing or else fer­men­ta­tion or de­cline in fla­vor and qual­ity will oc­cur. The olive oil can be con­sumed or used in cook­ing im­me­di­ately af­ter its col­lec­tion from the press. Olive oils are unique and dis­tinct, each brand of olive oil hav­ing its own char­ac­ter, as de­ter­mined by many fac­tors, like those unique fla­vor differ­ences found in fine wines. Pre­pared com­mer­cial olive oils can vary greatly in aroma, fruit fla­vor; whether the taste is, flow­ery, nutty, del­i­cate, or mild, and the col­or­ing of olive oil is quite vari­able. . . . Olive trees can sur­vive droughts and strong winds, and they grow well on well drained soils up to a pH of 8.5 and the trees can tol­er­ate salt wa­ter con­di­tions. In Europe, olive trees are nor­mally fer­til­ized ev­ery other year with an or­ganic fer­til­izer. Alter­nate bear­ing can be avoided by heavy prun­ing and gen­er­ally the trees re­spond to this very quickly and fa­vor­ably. Olive trees should be pur­chased that have been veg­e­ta­tively prop­a­gated or grafted, be­cause the seed grown trees will re­vert to a wild type that yields small olives with an in­sipid taste. Olive trees are more re­sis­tant to dis­eases and in­sects than any other fruit tree and, there­fore, are sprayed less than any other crop. Other olive-re­lated re­sources are pro­vided by the Univer­sity of Ge­or­gia (note the dis­cus­sion of soils, in­di­cat­ing that olive trees can grow on soil too poor for or­di­nary cul­ti­va­tion, con­sis­tent with Ja­cob 5) and the Cal­ifor­nia Rare Fruit Grow­ers.

Fifth: Yes, of course you’re cor­rect about the leg­i­bil­ity of un­pointed text, but again, this does not mean that a ma­jor­ity of vi­able con­so­nant strings are el­i­gible names. We can roughly do the same thing in English, ndrst­ndng t wtht hvng vwls, but this wouldn’t work if all of the prior con­so­nant strings were vi­able names. There must be rather large gaps in mor­pheme-space for any lan­guage to be in­tel­ligible, oth­er­wise any er­rors in pro­nun­ci­a­tion or data lost in trans­fer would ren­der the com­mu­ni­ca­tion un­in­tel­ligible, or worse, change its mean­ing en­tirely. I’ll claim a minor po­si­tion of au­thor­ity on this point; I’m in col­lege, work­ing on a ma­jor in Lin­guis­tics.

• If 2+2 equals 3, I de­sire to be­lieve that 2+2 equals 3. I want my con­clu­sion to be con­trol­led by the ab­stract fact I seek to dis­cern.

• I can imag­ine a world in which the math­e­mat­ics we have de­vel­oped is not use­ful, or in which com­monly as­sumed ax­ioms are false in that world. How­ever, “The Pythagorean The­o­rem is a the­o­rem of Eu­clidean ge­om­e­try” is still true even if you’re liv­ing on a sphere. If I say “I can­not be con­vinced that 2 + 2 = 4″, I mean some­thing like “I can­not be con­vinced that S(S(0)) + S(S(0))) = S(S(S(S(0)))) is not a the­o­rem of Peano ar­ith­metic.”

On the re­li­gion is­sue: I’ll ac­cept as di­v­ine any en­tity that can con­sis­tently re­duce the en­tropy of a closed, iso­lated sys­tem, and will demon­strate this abil­ity on de­mand. ;)

• If the en­tity is ma­nipu­lat­ing the sys­tem, then it’s not closed or iso­lated any­more, is it? The sys­tem of en­tity+sys­tem could be iso­lated, but to know if the en­tropy of that was re­duced you’d need to know the in­ter­nal en­tropy of God. But if he can pro­duce in­finite neg-en­tropy, then his in­ter­nal en­tropy is a mean­ingless con­cept.

• Eliezer: “Gray Area, if num­ber the­ory isn’t in the phys­i­cal uni­verse, how does my phys­i­cal brain be­come en­tan­gled with it?”

I am not mak­ing claims about other uni­verses. In par­tic­u­lar I am not as­sert­ing pla­tonic ideal­ism is true. All I am say­ing is “2+2=4” is an a pri­ori claim and you don’t use rules for in­cor­po­rat­ing ev­i­dence for such claims, as you seemed to im­ply in your origi­nal post.

A pri­ori rea­son­ing does take place in­side the brain, and neu­ro­scien­tists do use a pos­te­ri­ori rea­son­ing to as­so­ci­ate phys­i­cal events in the brain with a pri­ori rea­son­ing. De­spite this, a pri­ori claims ex­ist and have their own rules for es­tab­lish­ing truth.

• Gray Area, if num­ber the­ory isn’t in the phys­i­cal uni­verse, how does my phys­i­cal brain be­come en­tan­gled with it?

Rozen­daal, sounds like you bought into one of re­li­gion’s Big Lies.

• You seem to be us­ing the word ‘re­li­gion’ when you are more speci­fi­cally talk­ing about Pla­ton­ism, right?

• The core is­sue is whether state­ments in num­ber the­ory, and more gen­er­ally, math­e­mat­i­cal state­ments are in­de­pen­dent of phys­i­cal re­al­ity or en­tailed by our phys­i­cal laws. (This ques­tion isn’t as ob­vi­ous as it might seem, I re­mem­ber read­ing a pa­per claiming to con­struct a con­sis­tent set of phys­i­cal laws where 2 + 2 has no definite an­swer). At any rate, if the former is true, 2+2=4 is out­side the province of em­piri­cal sci­ence, and ap­ply­ing em­piri­cal rea­son­ing to eval­u­ate its ‘truth’ is wrong.

• I don’t think this is at all the core is­sue.

Eliezer’s origi­nal post stated that be­liefs need to come from mind-re­al­ity en­tan­gling pro­cesses.

If math is a part of “re­al­ity”, then Eliezer’s point stands and em­piri­cal rea­son­ing makes perfect sense.

If math is not a part of “re­al­ity”, then we would ex­pect it to in­fluence noth­ing at all, in­clud­ing our be­liefs. Or even sup­pose that knowl­edge came from some­where and could in­fluence be­lief but still did not oth­er­wise cor­re­late with re­al­ity: Then it would be ir­rele­vant. This, of course, is not the case—as any­one who’s ever used any mass-man­u­fac­tured de­vice as well as bridges and roads, should re­al­ize. Math DOES have util­ity in real life. And I dare­say that if it sud­denly stopped helping us re­li­ably pre­dict the load-bear­ing limit of bridges, we’d treat is as sus­pect and false.

The ACTUAL core is­sue re­mains that a be­lief that can­not be re­versed is use­less.

• There are some points of view that some­times do re­quire math­e­mat­i­cal state­ments to be de­pen­dent on re­al­ity (i.e. con­struc­tivism, ac­tual ver­sus po­ten­tial in­finity de­bate, etc).

Some­times it is in­tu­itive to re­quire math­e­mat­ics to be­have this way, i.e. ‘nat­u­ral’ num­bers are called that for a rea­son, and they bet­ter be­have like the ap­ples or I’m pos­tu­lat­ing a change in nomen­cla­ture.

P.S. Ii seems to me the OP’s word­ing wasn’t pre­cise enough. I can very well imag­ine a situ­a­tion in which some ba­sic ad­di­tion would yield non ob­vi­ous re­sults (like ad­di­tion in­side mod­ulo N num­ber space).

• When I rea­son in­side a fully ax­io­m­a­tized for­mal sys­tem, the ax­ioms don’t de­pend on re­al­ity, but the rules for ma­nipu­lat­ing sym­bols de­pend on … some­thing. You could define it as “if I perform these ma­nipu­la­tions in re­al­ity, I will get this re­sult” but what if perform­ing the ma­nipu­la­tions in differ­ent places gets differ­ent re­sults?

What if, when you ap­plied the rule “(x+Sy) ⇒ S(x+y)” twice and the rule “(x+0)=>x” once, to “(SS0+SS0)”, you got “SSS0″ in­stead of “SSSS0”?

• I guess when one rea­sons in­side a fully ax­io­m­a­tized for­mal sys­tem, this some­thing the rules for sym­bol ma­nipu­la­tion de­pend on is the set of ax­ioms.

Now I’m putting on my un­e­d­u­cated hat, so ex­cuse me if this is heresy: Start­ing with the ax­ioms you ap­ply logic to for­mu­late more spe­cific rules (in this case the ab­stract is em­piri­cally falsifi­able, since we’re work­ing on nat­u­ral num­bers).

So, to ar­rive at SS0+SS0=SSS0, you’d have to ven­ture out­side the realm of rea­son I’m afraid.Tthat would maybe man­i­fest it­self as magic—get­ting 4 ap­ples on the table dur­ing night, but 3 dur­ing day when you put 2 and 2 ap­ples side by side. And could mean abil­ity to pro­duce some­thing from noth­ing by clever ar­range­ment of ap­ples. and waste dis­posal would be­come easy :)

In other words my opinion is it’s not pos­si­ble even as thought ex­per­i­ment un­less you in­tro­duce some ran­dom fac­tor from be­yond the scope of ax­ioms.

• well there’s the spe­cial other thing, the rea­son you can’t ex­plain Peano Arith­metic to a rock, which is that ax­ioms are static se­quences of sig­nals, but in ad­di­tion you have these dy­nam­ics.

Best source on this is Lewis Car­roll http://​​www.di­text.com/​​car­roll/​​tor­toise.html

Th­ese dy­nam­ics are con­tained within the struc­ture of our thoughts, which is why they’re pre­served in a thought ex­per­i­ment. But we still have to ac­tu­ally check our thoughts, which are part of re­al­ity.

Sorry if this wasn’t very co­her­ent.

• P.S. Ii seems to me the OP’s word­ing wasn’t pre­cise enough. I can very well imag­ine a situ­a­tion in which some ba­sic ad­di­tion would yield non ob­vi­ous re­sults (like ad­di­tion in­side mod­ulo N num­ber space).

Hm… not pre­cise enough for what? I think we all know what was meant… un­less Eliezer did a ninja edit af­ter you posted ;) this seems to cover it:

There are re­defi­ni­tions, but those are not “situ­a­tions”, and then you’re no longer talk­ing about 2, 4, =, or +.

What you sug­gested, that’s not a “ba­sic ad­di­tion” any more, is it?

• Hi, I am a math­e­mat­i­cian and I guess most math­e­mat­i­ci­ans would not agree with this. I am quite new here and I am look­ing for­ward to re­ac­tions of ra­tio­nal­ists :-)

I, per­son­ally, dis­t­in­guish “real world” and “math­e­mat­i­cal world”. In real world, I could be per­suaded that 2+2=3 by ex­pe­rience. There is no way to per­suade me that 2+2=3 in math­e­mat­i­cal world un­less some­body shows me a proof of it. But I already have a proof of 2+2=4, so it would lead into great re­form of math­e­mat­ics, similar to the re­form af­ter Rus­sel para­dox. Just em­piri­cal ex­pe­rience would definitely not suffice. The ex­am­ple of 2+2=4 looks weird be­cause the state­ment holds in both “wor­lds” but there are other para­doxes which demon­strate the differ­ence bet­ter.

For ex­am­ple, there is so called Banach-Tarski para­dox, (see Wikipe­dia). It is proven (by set the­ory) that a solid ball can be di­vided into finitely many parts and then two an­other balls of the same size as the origi­nal one can be com­posed from the pieces. It is a phys­i­cal non­sense, mass is not pre­served. Yet, there is a proof… What can we do with that? Do we say that physics is right and math­e­mat­ics is wrong?

Rea­son­able ex­pla­na­tion: The phys­i­cal in­ter­pre­ta­tion of the math­e­mat­i­cal the­o­rem is just over­sim­plified. This part of math­e­mat­ics does not fit to this part of physics. The false state­ment about physics is just differ­ent from the true math­e­mat­i­cal state­ment.

But the Banach-Tarski para­dox has no phys­i­cal equiv­a­lent. We can not test it em­piri­cally, we can just be­lieve the proof. This is prob­a­bly what I would think if my ex­pe­riences showed me that 2+2=3. It would ap­pear that in our real mys­te­ri­ous world just 2+2=3 but in math­e­mat­i­cal world, which was de­signed to be sim­ple and rea­son­able, still 2+2=4.

Similarly, we can guess whether and how the phys­i­cal uni­verse is curved, yet the Eu­clidean space will be straight and in­finite by defi­ni­tion, no mat­ter what we will ex­pe­rience.

Sure, it can be ar­gued that if math­e­mat­ics does not re­flect the real world then it is use­less. Well, set the­ory is a base for al­most all math fields. Even though the par­tic­u­lar re­sult called Banach-Tarski para­dox have no prac­ti­cal use, more com­pli­cated ob­jects in the math­e­mat­i­cal uni­verse are used in physics well. Restric­tion to just “em­piri­cally testable” ob­jects in math­e­mat­ics is a counter-in­tu­itive use­less ob­sta­cle. In such view, there is no sixth Ack­er­mann num­ber or the twin prime con­jec­ture has no mean­ing. I can barely imag­ine such math­e­mat­ics.

I un­der­stand that you may want a sim­ple way to han­dle the­ists but aban­don­ing ab­stract math­e­mat­ics (or call­ing it “false”) is definitely not a wise one.

• The point was less about the phys­i­cal world ap­pli­ca­tions of 2+2=4, and more about the fact that any be­lief you have is ul­ti­mately based on the ev­i­dence you’ve en­coun­tered. In the case of purely the­o­ret­i­cal proofs, it’s still based on your sub­jec­tive ex­pe­rience of hav­ing read and un­der­stood the proofs.

Hu­mans are some­times liter­ally in­sane (for ex­am­ple, not be­ing able to tell that they’re miss­ing an arm). Also, even the best of us some­times mi­s­un­der­stand or mis­re­mem­ber things. So you need to leave prob­a­bil­ity mass for hav­ing mi­s­un­der­stood the proof in the first place.

(The fol­lowup to this post is this one: http://​​less­wrong.com/​​lw/​​mo/​​in­finite_cer­tainty/​​ which ad­dresses this in some more de­tail)

• I see. It seemed to me that it was about the ex­per­i­men­tal method which did not fit to a math­e­mat­i­cal state­ment. I un­der­stand the pos­si­bil­ity of be­ing mis­taken. I was mis­taken many times, I am not sure with some proofs and I know some per­sua­sive fake proofs… De­spite this, I am not very con­vinced that I should do such things with my prob­a­bil­ity es­ti­mates. After all, it is just an es­ti­mate. More­over it is a bit self-refer­enc­ing when the es­ti­mate uses a more com­pli­cated for­mula then the state­ment it­self. If I say that I am 1-sure, that 1 is not 12, it is safe, isn’t it? :-D Well, it does not mat­ter :-) I think that I got the point, “I know that I know noth­ing” is a well known quote.

• Ahem. I can think of many ways that some broadly defined “ex­per­i­men­tal method” could come into play there.

• (I think this may have came across a bit more con­fronta­tional than was op­ti­mal)

((Also, on that note, mirefek, if I came across as more con­fronta­tional than seemed ap­pro­pri­ate, apolo­gies.))

• Please, be more spe­cific. I am not sure ex­actly what are you re­spond­ing to. Do you mean that a math proof (or knowl­edge of it) can be con­sid­ered as ex­per­i­men­tal method in some sense?

• I don’t think you’ve re­sponded to my linked com­ment. But OK, look­ing up a re­sult in a math book could count as an ex­per­i­ment, as could any method by which you might learn about dyslexia or what­ever you sus­pect might be con­fus­ing you. If you don’t be­lieve any­thing like that could hap­pen to you, ei­ther you made that judge­ment based on ex­pe­rience and sci­ence or you are very badly mis­guided.

• To be hon­est, your com­ments con­fuse me. I knew about the link but I didn’t see a con­nec­tion be­tween the link and ex­per­i­men­tal method and where the cita­tions in the link came from. I am not sure what you mean by “any­thing like that” in your last com­ment and I am not very in­ter­ested in it.

But I pre­fer to keep the origi­nal prob­lem: If look­ing up a re­sult in a math book could count as an ex­per­i­ment what is the (broader) defi­ni­tion of an ex­per­i­ment, then?

• I think that I got the point, “I know that I know noth­ing” is a well known quote.

It’s ac­tu­ally a some­what differ­ent point he’s try­ing to make (it’s spaced out over sev­eral blog­posts) - the idea is not to say “all knowl­edge is fal­lible.” You should be very con­fi­dent in math proofs that have been well vet­ted. It’s use­ful to have a sense of how cer­tain your knowl­edge is. (like, could you make 100 similar state­ments with­out be­ing wrong once? 1,000? 10,000?)

(i.e. “the sun will rise to­mor­row” is a prob­a­bil­ity, not a cer­tainty, and “Ghosts could be real” is a prob­a­bil­ity, not a cer­tainty, but they are very differ­ent prob­a­bil­ities.)

If you’re in­ter­ested, I do recom­mend the se­quences in more de­tail—a lot of their points build on each other. (For ex­am­ple, there are mul­ti­ple other posts that ar­gue about what it’s use­ful to think in prob­a­bil­ities, and how to ap­ply that to other things).

• Hello, I’m a Chris­tian. And, yes, I’m also a ra­tio­nal­ist gasp!. I was born and raised a Chris­tian, and I hon­estly am not sure if I would be­lieve, say, Bud­hism if I was raised that way- My gut an­swer is ‘No’, but I can­not re­ally be sure, as I would be a com­pletely differ­ent per­son. There’s no way no one can truth­fuly say yes or no for sure to that ques­tion.

Right, any­ways, I do have rea­sons I would stop be­liev­ing… There are a cou­ple very spe­cific situ­a­tions that pop to mind in which I would be con­vinced that my whole life has been a lie:

1. The apoc­a­lypse hap­pens in a fash­ion other than is pre­dicted in Reve­la­tions (In parts of it that seem strictly fac­tual, not sym­bolic)- Such as a Zom­bie Apoca­lypse with no Se­cond Com­ing from the clouds.

2. Hu­mans elimi­nat­ing death- In Reve­la­tions, peo­ple die, so if that stopped be­ing an op­tion, well...

3. Time travel (Yes, re­ally- it’s only a lit­tle less plau­si­ble than your rea­sons, no offense).

• Edit: Also, wel­come to Less Wrong. Sorry, po­lite­ness should have come first.

Really...that’s all you mean when you say I’m a Chris­tian? Do you just mean “The book of Reve­la­tion is true, we’ll never com­pletely defeat death, and time travel is im­pos­si­ble?” In that case, prob­a­bly even a lot of peo­ple here agree with 23 of that.

I as­sume the an­swer to the first ques­tion is “no”. In that case, please ex­plain more of what you mean by call­ing your­self a Chris­tian. That will open up more ground for a se­ri­ous dis­cus­sion, if you ac­tu­ally do want to change your mind if it is the case that Chris­ti­an­ity is false.

• Well, I should have speci­fied- those are the first ex­am­ples that jumped to mind. I mean a whole lot more by say­ing that I am a Chris­tian, I sup­pose I would define it as I be­lieve that all the Bible says is true- that God cre­ated the uni­verse, Je­sus is our Savi­our, and we ex­ist to glo­rify God (I know, cached thought, but that one I have thought about.).

I re­ally do mean that I do not want to be­lieve in any­thing that is wrong, but I have yet to see any­thing that is defini­tive ev­i­dence that my be­liefs are in­cor­rect. (And I also ad­mit that I do not want to give up my cur­rent be­liefs, and I’m go­ing to be heav­ily bi­ased against any in­for­ma­tion shown me, but I will try.)

• My first ques­tion would be, why do you be­lieve in Chris­ti­an­ity, speci­fi­cally, in­stead of Hin­duism, Is­lam, or some­thing else (like that there are 4 gods, and they cre­ated the Earth with 4 sea­sons)? Why would you say that the Chris­tian God cre­ated the uni­verse, rather than say­ing that you just don’t know?

• First, from a sci­en­tific stand­point, there’s a good bit of ev­i­dence for cre­ation as is told in the Bible- a flood and all.

And it re­ally isn’t any­thing I can con­vince you of from there on- rea­sons such as that it makes sense that we can­not make our­selves good enough, the Bible makes far more sense than the Quaran (which I have read a good bit of), ex­pe­riences, so on, so forth. And just pure faith, which of course makes no sense to a good athe­ist like you. (No offense. No offense.)

• First, from a sci­en­tific stand­point, there’s a good bit of ev­i­dence for cre­ation as is told in the Bible—a flood and all.

I have never heard of such ev­i­dence. Could you di­rect me to where to find it? I think the ev­i­dence points in the op­po­site di­rec­tion. See the Wikipe­dia ar­ti­cle on flood ge­ol­ogy, to be­gin with. If you be­lieve the Earth is un­der 10000 years old, then you should also read this ar­ti­cle, “Is There Really Scien­tific Ev­i­dence for a Young Earth?”. It was writ­ten by a Chris­tian, and I’d like to point out the fol­low­ing quote from the in­tro­duc­tion:

It is not the pur­pose of this pa­per to dis­cuss the­ol­ogy, but this au­thor firmly be­lieves that a literal in­ter­pre­ta­tion of Ge­n­e­sis al­lows for an Old-Earth view that is con­sis­tent with main­stream sci­ence. I say this only to em­pha­size that this pa­per is not in­tended to op­pose any Chris­tian be­liefs, or to tear down any­one’s faith. Rather, the pur­pose of this pa­per is to en­sure that our Faith is based firmly on Truth, and not merely wish­ful think­ing.

Ex­plain what you mean when you use the phrase, “pure faith”.

• I sup­pose I would define it as I be­lieve that all the Bible says is true

Liter­ally, to the last dec­i­mal point, or do you make some al­lowances for figu­ra­tive lan­guage, im­pre­cise mea­sure­ment and/​or un­marked parables?

• The prob­lem with go­ing there is that it’s easy to go to far, to a point where the Bible isn’t true any­more and it’s just your in­ter­pre­ta­tion of bits and pieces of the Bible. Any­ways, I don’t re­ally think of figu­ra­tive lan­guage as some­thing you need to make al­lowances for, it just is how it was writ­ten- and most of the time is fairly ob­vi­ous too. I’ve never seen one in­stance of im­pre­cise mea­sure­ment, but if you know of one, fire away, and un­marked parables are also fairly easy to spot.

• The prob­lem with go­ing there is that it’s easy to go to far, to a point where the Bible isn’t true any­more and it’s just your in­ter­pre­ta­tion of bits and pieces of the Bible.

Yes, true. But it’s pos­si­ble to go too far the other way, too, which causes a lot of prob­lems (see: the cre­ation­ist move­ment in Amer­ica).

I’ve never seen one in­stance of im­pre­cise mea­sure­ment, but if you know of one, fire away

2 Cor­in­thi­ans 4:2:

He also made a round tank of bronze, 7½ feet deep, 15 feet in di­ame­ter, and 45 feet in cir­cum­fer­ence.

I con­sider it more prob­a­ble that the mea­sure­ment is im­pre­cise than that pi is three for that tank.

I mean, it’s a minor de­tail, but it’s there.

un­marked parables are also fairly easy to spot.

That’s what I thought, too, but ap­par­ently some peo­ple take the Gar­den of Eden liter­ally.

• And he made a molten sea, ten cu­bits from the one rim to the other it was round all about, and...a line of thirty cu­bits did com­pass it round about...

1 Kings 7:23

• If there are any Chris­ti­ans in the au­di­ence who know Bayes’s The­o­rem (no nu­mero­phobes, please) might I in­quire of you what situ­a­tion would con­vince you of the truth of Is­lam?

Why does this need to go out to Chris­ti­ans? I sus­pect that most, if not all, peo­ple read­ing this are non-Mus­lims who know Bayes’s The­o­rem. What would con­vince you of the truth of Is­lam?

• What would con­vince you of the truth of Is­lam?

If some fun­da­men­tal con­stant, or the ra­tio be­tween two fun­da­men­tal con­stants, en­coded in its bi­nary digits the Qu’ran, that would cause me to be­lieve with greater than 50% cer­tainty in the truth of Is­lam.

• It’s be­lieved by some (but not proven) that you can find any se­quence of digits you’d like in Pi.

And even though ev­ery­body knows that 2Pi is the much more sen­si­ble con­stant, that trans­for­ma­tion helpfully changes the se­quence of bi­nary digits not at all.

• It’s be­lieved by some (but not proven) that you can find any se­quence of digits you’d like in Pi.

But you gen­er­ally need a num­ber that has about as many bits as the se­quence it­self just to pin­point which digit to start read­ing from.

If that num­ber is rep­re­sented by some other con­stant, that counts.
If we just have to figure it out our­selves, in the same way that we’d be able to figure out which digit to start if we wanted to find “The Hob­bit” en­coded in the digits of pi, it doesn’t count.

• Are you con­strain­ing the en­cod­ing scheme at all?

• In just com­mon­sense ways, e.g. it must not be en­coded in a way so ar­bi­trary that you would be able to de­rive any other similar-length piece of liter­a­ture by similar method­olo­gies.

• Why? It would cer­tainly be an as­tound­ing thing (sub­ject to the ob­vi­ous caveats about the com­plex­ity of the en­cod­ing scheme), but why would it im­ply that the en­coded ma­te­rial was true?

• If I find the text of Moby Dick suit­ably en­coded (what­ever that means) into the foun­da­tion of a build­ing, and I don’t find other texts en­coded into that build­ing, it seems rea­son­able to take se­ri­ously the the­ory that there ex­ists some pro­cess or en­tity which has a spe­cial re­la­tion­ship both with that build­ing, and with the text of Moby Dick, differ­ent from the re­la­tion­ship it has with any other text.

If I find the text of the Ko­ran suit­ably en­coded into the fun­da­men­tal con­stants of the uni­verse, it seems equally rea­son­able to take se­ri­ously the the­ory that there ex­ists some pro­cess or en­tity which has a spe­cial re­la­tion­ship both with that uni­verse, and with the text of the Ko­ran, differ­ent from the re­la­tion­ship it has with any other text.

You’re right, of course, that it doesn’t fol­low from that that ei­ther the Ko­ran or Moby Dick is true. Nei­ther does it fol­low from the truth of the Ko­ran (what­ever that means) that Is­lam is true (what­ever that means).

OTOH, con­vert­ing to a be­lief in Is­lam on the ba­sis of that ev­i­dence seems more jus­tified than re­main­ing in­differ­ent to Is­lam in the face of that ev­i­dence.

Of course, those aren’t the only op­tions.

Granted, it’s not re­ally clear to me what is a rea­son­able re­sponse to that ev­i­dence. “In­ves­ti­gate the Ko­ran,” of course, but I have no sense of what such an in­ves­ti­ga­tion might even look like.

• I don’t think it’s a ques­tion that de­serves an an­swer, if you’re truly ask­ing whether find­ing the Qu’ran em­bed­ded into the phys­i­cal/​math­e­mat­i­cal struc­ture of the uni­verse should be con­sid­ered ev­i­dence sup­port­ing the truth of Is­lam.

It would quite ob­vi­ously not be ev­i­dence AGAINST Is­lam, nor would it be ev­i­dence UNCORRELATED to the re­al­ity of Is­lam. As such it can only be ev­i­dence in sup­port of Is­lam.

If you’re just ar­gu­ing that it shouldn’t make me raise my con­fi­dence level to over 50%, to what per­centage do you think one should raise it to, given such a find­ing?

• It would quite ob­vi­ously not be ev­i­dence AGAINST Is­lam, nor would it be ev­i­dence UNCORRELATED to the re­al­ity of Is­lam.

Where did you pull that out of? I mean, we’re talk­ing blue ten­ta­cle sce­nar­ios here.

• A blue ten­ta­cle sce­nario, how­ever un­likely, is not ev­i­dence against the hy­poth­e­sis that I am a changeling from the oc­to­pus peo­ple.

• Hehe, it shouldn’t be long un­til some­one de­mands rule 34 of this.

• Down­voted for lack of clar­ity. What ex­actly are you say­ing here? Are you truly say­ing that if the Qu’ran is firmly em­bed­ded in the physics of the world, that’s un­cor­re­lated to Is­lam hav­ing val­idity? Stop be­ing coy with your re­sponses please, then per­haps I”ll also be able to an­swer what­ever-your-ACTUAL-ques­tion-is bet­ter.

• Are you truly say­ing that if the Qu’ran is firmly em­bed­ded in the physics of the world, that’s un­cor­re­lated to Is­lam hav­ing val­idity?

I see no rea­son to pre­sume any­thing about this cor­re­la­tion. P(the Qu’ran is em­bed­ded in pi or similar) is so low as to ren­der the prob­a­bil­ity of any­thing con­di­tional on the hy­poth­e­sis in­calcu­la­ble. That is what I mean by the refer­ence to blue ten­ta­cle sce­nar­ios.

I re­peat, why would dis­cov­er­ing a large and com­plex yet parochial as­ser­tion, such as the Qu’ran, em­bed­ded eter­nally in the world with­out hu­man agency, lead you to be­lieve it? You have done no more than as­sert this as “ob­vi­ous”.

• Okay, sim­ple logic here: There’s a num­ber of given pos­si­bil­ities.
A) The Qu’ran is a com­pletely hu­man con­struc­tion, much like any other work of liter­a­ture.
B) The Qu’ran is a false mes­sage by some non-hu­man (but still lo­cated within our uni­verse) en­tity to hu­man­ity (e.g. teenage alien pranksters, fairies, Satan, what­ever)
C) The Qu’ran is a false mes­sage by some en­tity/​en­tities that con­structed (or helped con­struct) the uni­verse (e.g. ly­ing “simu­la­tors”)
D) The Qu’ran is a true mes­sage by God to hu­man­i­ty
E) …other pos­si­bil­ities I may be ne­glect­ing.

Th­ese op­tions must sum up to 100%.

(A) is what I (and pretty much all other athe­ists) cur­rently be­lieve.
(B) is be­lieved by e.g. those Chris­ti­ans who think that Qu’ran is the work of the devil.
(D) is what Mus­lims be­lieve.

If we have enough data to ex­clude pos­si­bil­ities (A) and (B), don’t you see that this must in­crease the prob­a­bil­ity of both (C) and (D)? That now the pos­si­bil­ities (C) and (D) must sum up to al­most 100%, much like prob­a­bil­ities (A), (B), (C) and (D) pre­vi­ously did?

This is ob­vi­ous to me.

• That now the pos­si­bil­ities (C) and (D) must sum up to al­most 100%, much like prob­a­bil­ities (A), (B), (C) and (D) pre­vi­ously did?

I don’t think this is ob­vi­ous. Since (E) is nonzero and un­speci­fied, it might be sig­nifi­cant once (A) and (B) are ex­cluded. Prob­a­bly af­ter ex­clud­ing (A) and (B), it would be worth spend­ing some time flesh­ing out (E) a bit bet­ter.

In my case, the pri­ors on (C) and (D) are so low I’d just as well in­clude them in (E) from the out­set.

• I can’t see why (B) got ex­cluded, but more sig­nifi­cantly, what hap­pened to (E)? In blue ten­ta­cle sce­nar­ios, that’s the most im­por­tant one, the un­known un­knowns. You list it ex­plic­itly, then com­pletely ig­nore it.

Un­known un­knowns are im­por­tant long be­fore the outer wilds of twenty sigma. It’s those that kill you when you thought you had all bases cov­ered. And out in the weird realms where parochial mes­sages can be hid­den in eter­nal math­e­mat­ics or cos­molog­i­cal en­g­ineer­ing, it is im­pos­si­ble to con­ceive what else may be lurk­ing there.

• I can’t see why (B) got ex­cluded, but more sig­nifi­cantly, what hap­pened to (E)?

You’re miss­ing the point. Keep in­clud­ing (B) as a pos­si­bil­ity if you like (I could de­bate with you on the prob­a­bil­ity of aliens so pow­er­ful that they can al­ter the fun­da­men­tal con­stants of the uni­verse they in­habit and be will­ing to do so just to prank hu­man­ity with a re­li­gion—but it’s not worth the trou­ble). Also add as many (E)s, (F)s, (G)s you like. Add a hun­dred differ­ent pos­si­bil­ities if you want.

Either way, if (A) gets sig­nifi­cantly re­duced as a prob­a­bil­ity, and we have no rea­son to si­mul­ta­neously re­duce the prob­a­bil­ity of (D) (or ad­just the rel­a­tive like­li­hood of the re­main­ing prob­a­bil­ities in a man­ner that dis­ad­van­tages (D)), then (D)’s es­ti­mated prob­a­bil­ity must in­crease by a fac­tor analo­gous to the weight that (A) pre­vi­ously held.

If I cur­rently be­lieve (A) to be 99.99% per­cent likely, then its ex­clu­sion au­to­mat­i­cally in­creases the prob­a­bil­ity of (D) by a fac­tor of 10,000 -- no mat­ter how many al­ter­nate pos­si­bil­ities Es, Fs, Gs you also provide.

At this point I think you’re just be­ing aller­gic at the idea of any­thing even hy­po­thet­i­cally in­creas­ing the prob­a­bil­ity of Is­lam be­ing true. What hy­po­thet­i­cal amount of ev­i­dence would cause you to be­lieve in Is­lam, if the sce­nario I pro­vided isn’t suffi­cient?

• Either way, if (A) gets sig­nifi­cantly re­duced as a prob­a­bil­ity, and we have no rea­son to si­mul­ta­neously re­duce the prob­a­bil­ity of (D) (or ad­just the rel­a­tive like­li­hood of the re­main­ing prob­a­bil­ities in a man­ner that dis­ad­van­tages (D)), then (D)’s es­ti­mated prob­a­bil­ity must in­crease by a fac­tor analo­gous to the weight that (A) pre­vi­ously held.

Why D in par­tic­u­lar? Why not E?

At this point I think you’re

End of con­ver­sa­tion.

• Why D in par­tic­u­lar? Why not E?

E too, ob­vi­ously, like­wise with C. But the ques­tion that be­gan this thread was about (D), not about (C) or any Es. So that’s what I’m talk­ing about.

End of con­ver­sa­tion.

Se­ri­ously? You got offended af­ter I pa­tiently spend long para­graphs ex­plain­ing ba­sic prob­a­bil­ity to you? And you don’t even bother an­swer­ing my ques­tion, af­ter I an­swer all of yours?

I’ll keep this in mind next time I am tempted to re­spond to you.

• B got ex­cluded be­cause in-uni­verse agents don’t write the uni­verse’s laws.

• P(the Qu’ran is em­bed­ded in pi or similar) is so low

If pi is a nor­mal num­ber, which it likely is, then the Qu’ran is em­bed­ded in it, and so is any other text.

• Yeah. As some­one said here, even true “mir­a­cles” aren’t proof of a the­is­tic God (much less a par­tic­u­lar ver­sion of one) - it might be e.g. some alien teenagers pul­ling a prank.

• “even”? The ev­i­dence I men­tioned would be much more im­pres­sive than a mere mir­a­cle. And the Qu’ran is quite clearly in­dica­tive of the Is­lamic ver­sion of God.

And you may also be an alien teenager pul­ling a prank, but I’m nonethe­less con­vinced you’re hu­man.

De­mand­ing an in­finite amount of proof be­fore you’re con­vinced of any­thing isn’t ac­tu­ally ra­tio­nal­ity. No­body’s talk­ing about 100% cer­tainty here.

• And you may also be an alien teenager pul­ling a prank, but I’m nonethe­less con­vinced you’re hu­man.

That’s be­cause I’m in­ter­act­ing with you in an en­tirely or­di­nary hu­man way and not dis­play­ing any “mir­a­cles” or such.

• I think we must be hav­ing differ­ent dis­cus­sions, be­cause I don’t un­der­stand what your point is, and you don’t seem to un­der­stand my point ei­ther.

• Your point is that you’re for­get­ting about pri­ors. This should also be Mul­ti­headed’s point, how­ever poorly ex­pressed.

Our prior for “alien pranksters” is not high—the ques­tion is just how low it is com­pared to al­ter­nate ex­pla­na­tions. Any rea­son­able pri­ors as­sign vastly more prob­a­bil­ity that Mul­ti­headed is hu­man than… well, any­thing else, but even if we re­jected that it would take a while be­fore we got to aliens. The ques­tion of whether aliens or the su­per­nat­u­ral is to be as­signed higher prob­a­bil­ity when faced with some­thing as strik­ing as ap­par­ent ma­nipu­la­tion of the phys­i­cal con­stants un­der­ly­ing this uni­verse is a much harder ques­tion.

• Eliezer: I am us­ing the stan­dard defi­ni­tion of ‘a pri­ori’ due to Kant. Given your re­sponses, I con­clude that ei­ther you don’t be­lieve a pri­ori claims ex­ist (in other words you don’t be­lieve de­duc­tion is a valid form of rea­son­ing), or you mean by ar­ith­metic state­ments “2+2=4” some­thing other than what most math­e­mat­i­ci­ans mean by them.

• 2+2=4 is a truth about math­e­mat­ics. It is not a truth about the world.

Truths in the world have no bear­ing on math­e­mat­i­cal truths. While we learn math­e­mat­ics from ob­ser­va­tions about the world, it is not from ob­ser­va­tion that math­e­mat­ics de­rive truth. Math­e­mat­i­ci­ans do not test the­o­ries em­piri­cally; such the­o­ries would be­come the do­main of physics or biol­ogy or the like. Thus, the only ev­i­dence one could in­fer 2+2=3 from would be mis­lead­ing math­e­mat­i­cal ev­i­dence.

Since 2+2=4 is so sim­ple, there are not too many peo­ple who could be effec­tively mis­lead in this way, and Eliezer is most likely not one of them. One could prob­a­bly con­vince some­one to be­lieve a false math­e­mat­i­cal for­mula if it were suffi­ciently com­pli­cated for the in­di­vi­d­ual to have trou­ble un­der­stand­ing it, and it had a suffi­ciently crafty ex­pla­na­tion.

Ba­si­cally, be­liev­ing 2+2=3 to be true would re­quire the ev­i­dence nec­es­sary to be­lieve in mar­ried bach­e­lors: ev­i­dence that con­fuses the hell out of you effec­tively.

Some peo­ple are ar­gu­ing that math­e­mat­ics is not a pri­ori. If so, then the situ­a­tion with putting two pairs of ap­ples to­gether and get­ting 3 ap­ples would be the ap­pro­pri­ate type of ev­i­dence. If math­e­mat­ics is a pos­te­ri­ori, the an­swer is thus quite sim­ple.

Sorry if this is overly re­dun­dant with pre­vi­ous posts.

• There is an ex­am­ple that of­ten floats around, where it is ‘proven’ math­e­mat­i­cally that 1=2 (or some other such equal­ity, by the prin­ci­ple of ex­plo­sion it doesn’t re­ally mat­ter). The trick is that at some step in the proof, a non ob­vi­ous di­vi­sion by zero oc­curred.

• I imag­ine it’s the same proof that makes 2+2=5. There is a point in the proof where the cor­rect re­sult is ob­vi­ously 0=0 (though never ex­plic­itly writ­ten), yet it con­tinues as though it didn’t hap­pen.

It’s an ex­am­ple of mak­ing the prob­lems so com­plex that you make a mis­take, it’s not a valid proof.

The proof for 2+2=4, in­ci­den­tally, is al­most 400 pages long. The sim­plis­tic ver­sions most use take for granted many things for granted (like + and = and 2) that the ac­tual proof does not.

• Eliezer: “Gray Area, if num­ber the­ory isn’t in the phys­i­cal uni­verse, how does my phys­i­cal brain be­come en­tan­gled with it?”

I am not mak­ing claims about other uni­verses. In par­tic­u­lar I am not as­sert­ing pla­tonic ideal­ism is true. All I am say­ing is “2+2=4” is an a pri­ori claim and you don’t use rules for in­cor­po­rat­ing ev­i­dence for such claims, as you seemed to im­ply in your origi­nal post.

A pri­ori rea­son­ing does take place in­side the brain, and neu­ro­scien­tists do use a pos­te­ri­ori rea­son­ing to as­so­ci­ate phys­i­cal events in the brain with a pri­ori rea­son­ing. De­spite this, a pri­ori claims ex­ist and have their own rules for es­tab­lish­ing truth.

• In­te­gers are slip­pery in a way that ap­ples and poo­dles are not. If you say some­thing un­con­ven­tional about in­te­gers, you cease to talk about them. --- Does any­one dis­agree with that?

(1) Peter de Blanc asks what hap­pens when I can­not fol­low a proof prop­erly. I count that as a failure of ra­tio­nal­ity rather than an in­stance of be­ing mis­lead by ev­i­dence. That is not, I think, what Eliezer in­tends when he says “con­vinced.”

(2) If I ob­serve some trick and say, “wow, two and two makes three,” then I am drop­ping the in­te­ger sys­tem and adopt­ing some other. My “wow” is the same one that we all said when we learned that Eu­clidean ge­om­e­try doesn’t hold in our uni­verse.

• The truth of an ar­ith­matic equa­tion and the truth of the con­tent of a re­li­gion like Is­lam or Chris­ti­an­ity are re­ally not com­pa­rables at all. Within the do­main of math­e­mat­ics, “two plus two” is one defi­ni­tion of “four”. Con­versely, “four” is one defi­ni­tion of “two.” (In a sense these truths are tau­ta­log­i­cal.)

The Greeks no­ticed that math­e­mat­ics is a field of knowl­edge that can be de­vel­oped en­tirely in the mind. The ma­nipu­la­tive ob­jects that we use to teach chil­dren ba­sic ar­ith­metic op­er­a­tions are not ac­tu­ally the sub­jects of ar­ith­metic, but crude illus­tra­tions of ideas (ideals) that are uni­ver­sal in the most ab­solute sense of the word—they are part of the uni­verse.

Reli­gions seek knowl­edge by en­tirely differ­ent meth­ods, meth­ods that are not sub­ject to any kind of proofs ore ver­ifi­ca­tions. (I think it weird that re­li­gious peo­ple con­sider it a virtue to cling to ideas for which no data of any kind can be sum­moned for sup­port.)

• I’m an evan­gel­i­cal protes­tant and I’d like to give my an­swer to the ‘what would it take to con­vince me to be­come a Mus­lim’ ques­tion. This is go­ing to be a nar­ra­tive ex­am­ple and thus show only one of many pos­si­ble routes. I’ve cho­sen a rout that does not de­pend on pri­vate knowl­edge, fresh mir­a­cle in the pre­sent day, or even or even changed facts in things it would be in­con­ceiv­able for me to be wrong about, be­cause I see this rout as the hard­est and there­fore most re­veal­ing.

Mus­lim schol­ars pro­pose a com­peti­tor to the Doc­u­men­tary Hy­poth­e­sis (JEPD) for the Pen­ta­teuch and/​or Two-source Hy­poth­e­sis a.k.a. Four-Source The­ory for the syn­op­tic gospels that showed in­stead how these Bible books de­vel­oped as cor­rup­tions of a proto-Ko­ran. This shouldn’t be too hard as the ex­ist­ing pop­u­lar the­o­ries are mostly nar­ra­tive fal­lacy + an af­fec­tive death spiral. It would at­tract enough at­ten­tion as poli­ti­cally fash­ion­able that I would hear about it and look it up on bibli­cal Stud­ies blogs. If it ac­tu­ally had plau­si­bil­ity that would in­crease my ex­pec­ta­tion that an in­ves­ti­ga­tion of the Ko­ran would be fruit­ful and I would start check­ing into it more. One of the things I would be look­ing for is out­side ev­i­dence such as signs of the su­per­nat­u­ral in its ori­gin, speci­fi­cally mir­a­cles done by Mo­hamed. Not the in­fancy gospel of Thomas type mir­a­cles where it seems likely these are leg­endary ac­cre­tions af­ter the fact, but more like what we see in the canon­i­cal gospels and epis­tles where we seem to have a record of con­tem­po­rary eye­wit­nesses think­ing they saw the laws of na­ture re­peat­edly vi­o­lated. I would also be look­ing for more in­ter­nal con­fir­ma­tions like was a con­sis­tent but nu­anced pic­ture of hu­man na­ture and how God in­tends to deal with it pre­sented. Or how is theod­icy re­garded? As I was eval­u­at­ing ques­tions like this I would be look­ing at: One, was the world view pre­sented con­sis­tent with the world as it ac­tu­ally is? Two, does the world view pre­sented provide a foun­da­tion you can build an ap­proach to life on? To help me eval­u­ate all this I would be look­ing into both Cris­tian and Mus­lim apol­o­gist’s an­swers to these ques­tions. To be con­vinced to the Mus­lim po­si­tion I’d need to run into Mus­lim apol­o­gists who are con­sid­er­ably more ra­tio­nally co­her­ent than any I have so far heard of. But given what mushy headed non­sense third par­ties some­times re­port as “Chris­tian teach­ing” there is a se­lec­tion bias in fa­vor of mushy head­ed­ness in what is promi­nently available to the pub­lic. (It’s in­ter­est­ing read­ing Less Wrong to see that many of the ar­gu­ments against Chris­ti­an­ity are ex­actly the same ar­gu­ments that con­ser­va­tive Chris­ti­ans use against Liberal Chris­ti­ans.) Over­all I would need to be con­vinced that Is­lam was both in­ter­nally and ex­ter­nally con­sis­tent and that in ar­eas where it con­flicts with Chris­ti­an­ity, Chris­ti­an­ity is con­sid­er­ably less cred­ible than I cur­rently find it. This would prob­a­bly mean find­ing a large num­bers of spe­cific in­con­sis­ten­cies that I have found only a cou­ple of in the past. But the fact that I have found a few means it is con­ceiv­able I could find more in the fu­ture.

One last ob­jec­tion I need to ad­dress is “If the one ad­mits ev­i­dence for Is­lam might be out there, why hasn’t the one check it out yet?” Well it would take months and mouths of work and there are so many other things it might also be prof­itable to in­ves­ti­gate. (Like LessWrong where not only do I get to in­ves­ti­gate an al­ter­na­tive world view, that in­ves­ti­ga­tion is just a bonus to get­ting all these neat ra­tio­nal think­ing tools that will be of on­go­ing use to me.) More­over a nega­tive re­sult would not re­ally be defini­tive; there would always be the pos­si­bil­ity that I had just not found the right Moslem apol­o­gists or was not dig­ging into the right ver­sion of Is­lamic the­ol­ogy. So there is no rea­son I would pick Is­lam as the thing to in­vest my time in­ves­ti­gat­ing with­out an ad­di­tional rea­son. But if, for ex­am­ple, there was an Is­lamic the­olo­gian who offered to de­bate the is­sues with me then I would be in­clined to do it and fol­low where the be­lief up­dates lead.

• “if, for ex­am­ple, there was an Is­lamic the­olo­gian who offered to de­bate the is­sues with me then I would be in­clined to do it and fol­low where the be­lief up­dates lead.”

Is that an open offer to the­olo­gians of all stripes?

• Yes, the­olo­gians of all strips, and philoso­phers and lo­gi­ci­ans of all per­spec­tives. As long a they are will­ing to re­spond to my ques­tions as well as hav­ing me re­spond to their’s. (Though if some­one is rude, en­gages in rhetor­i­cal hy­per­bola, etc. I re­serve the right to do those things back to them.)

I’ll try to check back here to see if any­one wants to do that or e-mail me at alia1dx@gmail.com and I’ll give you my pri­vate e-mail to carry on a di­a­log.

• Email sent about a week ago. Did it get spam-filtered?

• For a 5-year-old, say­ing “You’re not not not not fat” is just an­other way of say­ing “You’re fat.”

For an adult, say­ing “(the sum of) 2 + 2” is just an­other way of say­ing “4.”

For an en­tity far more in­tel­li­gent than hu­mans, stat­ing the ap­pro­pri­ate set of ax­ioms is just an­other way of stat­ing Euler’s iden­tity, Cauchy’s in­te­gral the­o­rem, and all sorts of other things.

• For the state­ment 2+2=4 to be true there are some as­sump­tions that needs to be. That is 2+2=4 is true within a sys­tem, math­e­mat­ics, but this sys­tem is in fact a con­struc­tion!

The ba­sic as­sump­tion here is that we can define and iden­tify ‘one’ thing—say a ball, a man or any other “item”—for this to be true you would fur­ther need to have ‘iden­ti­cal’ items… that is items that have very similar at­tributes.

As you can see this leads to a in­finite regress, where one as­sump­tion leads to oth­ers, and in fact we don’t have such sys­tems in re­al­ity, that is such sys­tems are only ‘real’ in our minds.

Thus we can con­struct sys­tem where one ob­ject can be ex­changed 1:1 di­rectly, say money in a com­puter sys­tem,, but there are few if any such sys­tems in the real world. In our con­struc­tions we can agree that one ant is equal to an other, but in the real world they may be very differ­ent.

So the idea of the piles of sand are very much to the point. There is never such a thing as one man or one cow—and 2 + 2 cows is 4 cows only if we agree to what one cow can be.

Re­gards Per

• Cloud, you might want to read Steven Pinker’s “The Blank Slate”.

• There are re­ally two ques­tions in there:

• Whether the Peano ar­ith­metic ax­ioms cor­rectly de­scribe the phys­i­cal world.

• Whether, given those ax­ioms and ap­pro­pri­ate defi­ni­tions of 2 and 4 (per­haps as Church nu­mer­als), 2 + 2 = 4.

One is a ques­tion about the world, the other about a nec­ces­sary truth.

The first is about what as­pect of the world we are look­ing at, un­der what defi­ni­tions. 2 rab­bits plus 2 rab­bits may not re­sult in 4 rab­bits. So I have to as­sume Eliezer refers to the sec­ond ques­tion.

Can we even mean­ingfully ask the sec­ond ques­tion? Kind of. As David Deutsch warns, we shouldn’t mis­take the study of ab­solute truths for the pos­ses­sion of ab­solute truths. We can ask our­selves how we com­puted whether 2+2=4, con­scious that our means of com­put­ing it may be flawed. We could in prin­ci­ple try many means of com­put­ing whether 2+2=4 that seem to obey the Peano ax­ioms: fingers, aba­cus, other phys­i­cal coun­ters, etc. Then we could call into ques­tion our means of ag­gre­gat­ing the com­pu­ta­tions into a sin­gle very con­fi­dent an­swer and then our means of re­tain­ing the an­swer in mem­ory.

Seems a pointless ex­er­cise to me, though. Evolu­tion ei­ther has en­dowed us with men­tal tools that cor­re­spond to some ba­sic nec­ces­sary truths or it hasn’t. If it hadn’t, we would have no good means of ex­plor­ing the ques­tion.

• (some ar­gu­ments)
Don’t care. If you can re­verse en­tropy, you might as well be a god. If some alien gives me tech­nol­ogy to re­verse en­tropy, then A God Am I.

• Lee B, Gray Area: what if you had a proof that 2 + 2 = 3, and, al­though you seem to re­call hav­ing once seen a proof that 2 + 2 = 4, you can’t re­mem­ber ex­actly how it went?

• I am a jew (born and raised). I can eas­ily imag­ine that if I were raised in the mus­lim world to a mus­lim fam­ily that I would be a mus­lim to­day. How­ever, were I born to a chris­tian fam­ily (and per­haps this is sim­ply my in­ner bi­ases talk­ing) I sus­pect that I would have been at­tracted to var­i­ous as­pect of the Jewish re­li­gion which are not pre­sent (or not nearly as strong) in chris­ti­an­ity, like the idea of a “con­tract with God”.

In full dis­clo­sure, I do not con­tinue to call my­self a Jew be­cause I be­lieve the To­rah to be more likely than any other main­stream re­li­gious text, but be­cause I find the eth­i­cal frame­work to be su­pe­rior.

• Chris­ti­ans sub­sti­tute the heavy yoke of the law for a lighter bur­den (faith and hope) in Christ. So yes, you can ap­pre­ci­ate a more rigor­ous eth­i­cal code, but Chris­ti­ans wish not to live un­der the law. You can call it weak­ness but I think it is hu­mil­ity grounded in the re­al­iza­tion that we all know the good we ought to do but fail in do­ing, and the bad we hate we find our­selves do­ing.

If a su­pe­rior eth­i­cal frame­work makes it easy to do that good and shun that evil, we’re back to keep­ing con­tracts with God and herein lies the real challenge—con­tracts are hard to keep and easy to break. What you have is a stu­dent with a text­book who has to get a perfect score on a test. I’d pre­fer a test where I don’t need a perfect score to pass, and even bet­ter if the pro­fes­sor (Je­sus) takes it for me. This my con­cept of Chris­ti­an­ity and I hope other Chris­ti­ans will agree.

• This prob­a­bly isn’t the web­site for you.

• Are you sure Ali­corn? As a former chris­tian now athe­ist thanks to LW(es­pe­cially EY’s writ­ings) I’ve learned a lot here.

• I wouldn’t turn away ar­bi­trary Chris­ti­ans, but this one in par­tic­u­lar at least needs to lurk more and would prob­a­bly be bet­ter served by a differ­ent web­site with more ba­sic ma­te­rial and a differ­ent mix in the au­di­ence.

• Well, he just wrote one com­ment so I’m won­der­ing how you ar­rived at that con­clu­sion. Wouldn’t it be bet­ter to give some pos­i­tive re­in­force­ment to new­com­ers?

• Yaro’s com­ment is en­tirely about the­ol­ogy. It’s ac­tu­ally an on-topic re­sponse to its im­me­di­ate par­ent, but it ap­pears com­pletely iso­lated from any other con­text or rele­vance. It makes as­ser­tions and states opinions with­out demon­strat­ing the un­der­ly­ing com­pre­hen­sion of pro­duc­tive ar­gu­ment that is nec­es­sary for a the­ist, or any­one, to make worth­while com­ments (at least within a topic which is this kind of sub­stan­tive mat­ter of fact.)

Pos­i­tive re­in­force­ment is to re­ward be­hav­iors that I would like to see con­tinue. I think the gap be­tween yaro’s level and the level I want to see on this site is big enough that it is not worth a re­in­force­ment pro­ject.

• Ali­corn,

Good effort, you are al­most there, if you used the ex­pla­na­tion you gave above to Yaro he prob­a­bly would be more en­light­ened than by “this is not the right web­site for you.”

Quot­ing from The Power of Re­in­force­ment:

The rea­son you should ig­nore poor perfor­mance if you say “No, you’re do­ing it wrong!” you are in­ad­ver­tently pun­ish­ing the effort. A bet­ter re­sponse to a mis­take would be to re­in­force the effort: “Good effort! You’re al­most there! Try once more.”

In spite of his com­ment be­ing not in line, why not praise the effort, es­pe­cially con­sid­er­ing that this was his first com­ment on LW. I’m as­sum­ing he did an hon­est effort to pre­sent his point of view, why not praise that and point out the way this site works?

• I do not wish to re­ward yaro’s effort, and thereby get more of it. I be­lieve that more of yaro’s effort here would re­sult in more com­ments that are of com­pa­rable qual­ity and top­i­cal­ity at least for a pro­longed learn­ing curve, and do not be­lieve that the pro­ject of nudg­ing them to­wards im­prove­ment is worth com­mu­nity time.

Please don’t use an ar­ti­cle about the use of re­ward to en­courage good be­hav­ior as a way to say that all be­hav­ior is worth re­ward­ing.

Good effort, you are al­most there

...

Dude. Subtlety?

• I do not wish to re­ward yaro’s effort, and thereby get more of it. I be­lieve that more of yaro’s effort here would re­sult in more com­ments that are o

Straw man, I’m not talk­ing about re­ward­ing his com­ment, but his par­ti­ci­pa­tion. Isn’t one of the goals of LW to raise the san­ity wa­ter­line?

do not be­lieve that the pro­ject of nudg­ing them to­wards im­prove­ment is worth com­mu­nity time.

I agree here but I see you are wast­ing pre­cious com­mu­nity time(ac­tu­ally it’s your time) by en­gag­ing in a dis­cus­sion with me. You would have wasted less of our time if you were to give a more con­struc­tive re­ply in the first place.

Please don’t use an ar­ti­cle about the use of re­ward to en­courage good be­hav­ior as a way to say that all be­hav­ior is worth re­ward­ing.

Another straw man, I didn’t say that.

Please don’t use straw men when ar­gu­ing with me.

I won’t waste any more time with this, so I’ll leave you the last an­swer.

• You quoted this:

A bet­ter re­sponse to a mis­take would be to re­in­force the effort: “Good effort! You’re al­most there! Try once more.”

and pre­vi­ously said of the larger pas­sage:

Now that we all know this, shouldn’t we abol­ish down­votes?

But when you tried it out:

Ali­corn,

Good effort, you are al­most there

this was her re­sponse:

Good effort, you are al­most there

...

Dude. Subtlety?

Didn’t work. Shall I praise your effort and urge you to do bet­ter next time? Would that work for you any bet­ter than it did for Ali­corn?

• We hardly have enough ev­i­dence af­ter just one at­tempt. Ad­di­tion­ally, sub­tlety is a form of de­ceit, and not gen­er­ally en­couraged in ra­tio­nal dis­cus­sion.

Any­way, my com­plaint would have to be to­ward the out-of-hand dis­mis­sal of yaro’s post, rather than offer­ing a sub­stan­tive dis­agree­ment or at least a link re­gard­ing the per­ceived flaws in yaro’s ar­gu­ment. That’s proper ra­tio­nal­ist en­courage­ment. No sub­tlety re­quired.

• Re­in­force­ment is for things one wants more off. I can’t say I want more posts with­out know­ing some­thing about the con­tent. In this case, I think Ali­corn is right that this poster is not ready to con­tribute things this com­mu­nity would find valuable.

• Doesn’t LW want more par­ti­ci­pa­tion?

I agree that the com­ment is not in line with the think­ing of LW, but why not point it out to the com­menter in a po­lite man­ner if you want to say any­thing at all?

• Doesn’t LW want more par­ti­ci­pa­tion?

Not es­pe­cially. I want bet­ter par­ti­ci­pa­tion. Not ab­solutely ridicu­lous re­li­gious tripe. The per­son Yaro is wel­come to stay, so long as he leaves his bul­lshit at the door. Mak­ing that kind of com­ment will, and should, prompt a nega­tive re­sponse.

• I would dis­agree with you com­pletely on this. You are out­right dis­miss­ing a point of view with no sup­port­ing ev­i­dence other than a vague, in­sult­ing com­ment. It ap­pears you haven’t ac­tu­ally learned what this site is pro­mot­ing. It’s one thing to dis­agree with Yaro here, it’s an­other to out­right in­sult his be­liefs and sim­ply raise his bar­ri­ers in agree­ing with any­thing you be­lieve.

I’ve seen similar in­stances oc­cur enough times to know (within a rea­son­able mar­gin of doubt) that if you want to ac­tu­ally make a per­son agree with you, you start by mak­ing your­self agree­able.

• Do we con­sider it to be ev­i­dence in Chris­ti­an­ity’s fa­vor that more peo­ple be­lieve in it than Is­lam? Does the av­er­age IQ of ad­her­ents of a re­li­gious be­lief cause it to be­come more plau­si­ble to us?

In the in­ter­ests of dis­clo­sure, I am an ag­nothe­ist who was bap­tized Catholic and raised main­line Protes­tant, so we’re still wait­ing for Eliezer’s re­quested com­ment.

• Cer­tainly. The prob­a­bil­ity of Chris­ti­an­ity hav­ing more fol­low­ers than Is­lam is greater if Je­sus rose from the dead and less if he did not.

It’s not nec­es­sar­ily strong ev­i­dence of course. Disavow­ing Is­lam has enor­mous so­cial con­se­quences, so I would ex­pect there to be a large num­ber of Mus­lims in both the world where Muham­mad re­ceived the Qu­ran from Gabriel and the world where Muham­mad hal­lu­ci­nated. But I still ex­pect there to be more Chris­ti­ans if Je­sus rose from the dead than if he did not.

IQ is only weakly cor­re­lated to ra­tio­nal­ity. A much bet­ter thing to do is to ask Chris­ti­ans why they be­lieve. If you know the rea­sons a Chris­tian be­lieves, then the ev­i­den­tial weight of their rea­son­ing will re­place the ev­i­den­tial weight that comes from the fact that they be­lieve.

The causal flow looks like this:

Real­ity --> Rea­son to be­lieve → Per­son believes

By d-sep­a­ra­tion, once you know a per­son’s rea­sons for be­liev­ing, the fact that they be­lieve is no longer use­ful in­for­ma­tion to you.

In the in­ter­ests of dis­clo­sure, I am an ex-Chris­tian who spent a year learn­ing Ara­bic be­cause I be­lieved that God was call­ing me to be a mis­sion­ary to Mus­lims. When I learned Bayes the­o­rem, I at­tempted to use it to con­struct an ar­gu­ment that Je­sus be­ing di­v­ine was more prob­a­ble than him be­ing or­di­nary. Need­less to say, I didn’t get very far be­fore I re­al­ized I was fal­ling into the base rate fal­lacy, and this is what ul­ti­mately led to my de-con­ver­sion.

Some sim­ple Fermi es­ti­mates:

The United States with it’s cur­rent pop­u­la­tion of 300 mil­lion has around 5,000 cults. The en­tire world had a pop­u­la­tion around 300 mil­lion dur­ing Je­sus’s time, so we can guess that they also had about 5,000 re­li­gions. Only ten of them be­came ma­jor world re­li­gions (let’s say). So the prob­a­bil­ity of a false re­li­gion be­com­ing a ma­jor world re­li­gion is about 1 in 500. The prob­a­bil­ity of a true re­li­gion be­com­ing a ma­jor world re­li­gion is near 100%. So the ev­i­den­tial weight of Chris­ti­an­ity’s large fol­low­ing is about 499 to 1.

If the prob­a­bil­ity of a ran­domly se­lected hu­man ris­ing from the dead is less than 1 out of 500 (and I had to ad­mit that it was sub­stan­tially less, even when I was a be­liever), then these two con­sid­er­a­tions sug­gest it more likely that Je­sus did not rise from the dead.

There’s lots of other ev­i­dence that could be taken into ac­count. But as a non-be­liever I don’t hes­i­tate to ad­mit that Chris­ti­an­ity’s pop­u­lar­ity counts as pos­i­tive ev­i­dence; I just think the nega­tive ev­i­dence adds up to more than the pos­i­tive ev­i­dence.

• Peo­ple can be­lieve wrong things by the mil­lions (Yay! the Earth is flat), that does not make it right. Stupid peo­ple can be­lieve cor­rect things and in­tel­li­gent peo­ple can be­lieve in­cor­rect things. And if you were bas­ing the be­lief sys­tem you be­lieve in on av­er­age IQ, you’d go with athe­ism any­way.

But none of these things are ev­i­dence. Some­thing would be ev­i­dence even if ev­ery­body in the world dis­agreed. Rel­a­tivity was true even when ev­ery sin­gle physi­cist (a group of rather ed­u­cated peo­ple) just knew that New­to­nian physic was truth.

• Peo­ple’s be­lief in some­thing is ev­i­dence for that thing in the sense that in gen­eral it’s more likely for peo­ple to be­lieve in a thing if it’s true. Less Wrongers some­times use the phrase “Bayesian ev­i­dence” when they want to ex­plic­itly in­clude this type of ev­i­dence that is ex­cluded by other stan­dards of ev­i­dence.

One way to think about this: Imag­ine that there are a bunch of par­allel uni­verses, some of which have a flat Earth and some of which have a spher­i­cal Earth, and you don’t know which type of uni­verse you’re in. If you look around and see that a bunch of peo­ple be­lieve the Earth is flat, you should judge it as more likely you’re in a flat-Earth uni­verse than if you looked around and saw few or no flat-Earthers.

How­ever, peo­ple’s be­liefs are of­ten weak ev­i­dence that can be out­weighed by other ev­i­dence. The fact that many peo­ple be­lieve in a god is ev­i­dence that there is a god, but (I think) it’s out­weighed by other ev­i­dence that there is not a god.

• ‘Peo­ple’s be­lief in some­thing is ev­i­dence for that thing in the sense that in gen­eral it’s more likely for peo­ple to be­lieve in a thing if it’s true’. What’s the ev­i­dence for this state­ment?

• The over­whelming ma­jor­ity of all hu­man be­liefs are (triv­ially) true. Things like “If I drop a rock, it will fall down”, “If I touch hot fire it will hurt”, etc. and “I am sit­ting down”, “I am typ­ing on a key­board”, etc.

The hu­man brain has evolved to de­ter­mine truths about the world around it, es­pe­cially in cases where the knowl­edge di­rectly af­fects sur­vival chances (“Tiger is dan­ger­ous”), but also for cases where the knowl­edge could help in­di­rectly (ba­si­cally all hu­man progress in­clud­ing first tool us­age—achieved es­pe­cially through cu­ri­os­ity and strive to find truth). It fails catas­troph­i­cally in some cases, but most of the time it does an ex­cel­lent job.

• Some­thing to con­sider is that if you al­low your be­liefs to be in­fluenced by the be­liefs of oth­ers you are in dan­ger of cre­at­ing a feed back loop. When de­cid­ing what to be­lieve based on what oth­ers be­lieve you must rule out those who are sim­ply fol­low­ing oth­ers as well

• In dis­cussing New­comb’s prob­lem, Eliezer at one point stated, “Be care­ful of this sort of ar­gu­ment, any time you find your­self defin­ing the “win­ner” as some­one other than the agent who is cur­rently smil­ing from on top of a gi­ant heap of util­ity.”

This al­igns well with a New Tes­ta­ment state­ment from Je­sus, “Ye shall know them by their fruits...ev­ery good tree bringeth forth good fruit, but a cor­rupt tree bringeth forth evil fruit.”

So, I’m only a novice of the Bayesian Con­spir­acy, but I can calcu­late the breast can­cer per­centages and the red vs blue pearl prob­a­bil­ities. To an­swer Eliezer’s ques­tion, to con­vince me of the truth of Is­lam, it would have to show me bet­ter out­comes, bet­ter fruit, than Chris­ti­an­ity, across the board. In many cases its prin­ci­ples don’t con­flict with Chris­ti­an­ity; but where they do, I would have to es­tab­lish that re­solv­ing the con­flict in fa­vor of Is­lam will lead to bet­ter out­comes.

Con­sider, as just one ex­am­ple, the fruits iden­ti­fied by LW’s own Swim­mer963, at http://​​less­wrong.com/​​lw/​​4pg/​​pos­i­tive_think­ing/​​ Would fol­low­ing Is­lam give me a bet­ter foun­da­tion than that for pos­i­tive think­ing, re­silience, mo­ti­va­tion for mu­tual help? Then I would be in­ter­ested. Not con­vinced by that alone, but in­ter­ested.

If Is­lam con­sis­tently offered a more co­her­ent wor­ld­view that more effec­tively helped me to be­come a bet­ter per­son and achieve my goals, then I would have cause to con­sider that it might have more truth than what I be­lieve now. As far as I have yet de­ter­mined, it doesn’t; its teach­ings seem to be more limited, less use­ful, than what I already have.

• So to be con­verted to a re­li­gion (Is­lam only be­ing an ex­am­ple here) it would have to provide a bet­ter moral and pos­i­tive emo­tional frame­work than Chris­ti­an­ity?

Side-note: This is sep­a­rate to the ques­tion above, but on the topic of the post you pro­vided on pos­i­tive think­ing, I think it may have some­thing to do with re­li­gion be­ing less com­mon in a trend among those who are both wealthy and in a higher qual­ity of ed­u­ca­tion (i.e. ter­tiary ed­u­ca­tion has a lower in­stance of re­li­gion than sec­ondary, pub­lic has a lower in­stance of re­li­gion than pri­vate, CEOs are less re­li­gious than white col­lar work­ers, etc) along with a num­ber of other fac­tors that I can’t re­call, and that these fac­tors do in­crease ten­dency to­wards nega­tive think­ing. There is a truth in the stated Chris­tian doc­trine (as is shared in Bud­dhism, Tao­ism, Hin­duism and oth­ers) that ma­te­rial goods do not bring hap­piness or ‘sal­va­tion’. I per­son­ally do not be­lieve, how­ever, that this makes those who are athe­ists less valid in their be­liefs (I would hope so, be­ing an athe­ist my­self).

• I see a lot of peo­ple ar­gu­ing that “2”, “3″, “+”, and “=” are defined in terms of the Peano ax­ioms, and as such, aren’t ac­tu­ally rele­vant to the be­hav­ior of phys­i­cal ob­jects. They say that the ax­ioms pin down the num­bers, re­gard­less of how phys­i­cal ob­jects be­have or start be­hav­ing.

But the Peano ax­ioms use some­thing called a “suc­ces­sor” to gen­er­ate the nat­u­ral num­bers. And how do we figure out what the suc­ces­sors are? Well, one no­ta­tion is to ap­pend an “S” to the pre­vi­ous num­ber to in­di­cate that num­ber’s suc­ces­sor, such that the suc­ces­sor of “SS0” is “SSS0″. Then “+” would mean “re­peat­edly ap­ply the suc­ces­sor op­er­a­tion to the num­ber to the right of this op­er­a­tor for how­ever many times in­di­cated by the num­ber to the left of this op­er­a­tor”, and “=” would in­di­cate “these two num­bers, when writ­ten out us­ing suc­ces­sor-no­ta­tion, have the char­ac­ter ‘S’ oc­cur the same num­ber of times”.

So how do we calcu­late “2 + 2”? Well, we take the num­ber of oc­cur­rences of the char­ac­ter “S”, count them up, then put the to­tal num­ber of oc­cur­rences in front of a sin­gle “0”: “SSSS0“, which we in­ter­pret as “4”. “2 + 2 = 4”.

But now let’s imag­ine your brain’s vi­sual cor­tex (or what­ever it uses to vi­su­al­ize things) be­ing messed up some­how. Ac­tu­ally, let’s go fur­ther than that, and sup­pose ev­ery­one’s vi­sual cor­texes got messed up in the same way, so that now, when we vi­su­al­ize two ob­jects and two more ob­jects, and put them to­gether, we see, not four ob­jects, but three. So if you were to try and vi­su­al­ize a group of two dots com­ing to­gether with an­other group of two dots, you would end up see­ing, in your mind’s eye, a fi­nal group of three dots.

Now imag­ine count­ing the num­ber of times “S” oc­curs in “SS0″, then putting two of those groups of “S” char­ac­ters to­gether. How many “S” char­ac­ter are in the fi­nal group? Vi­su­al­ize it, now...

Why, three. Of course there’s three. If you take “SS” and put it with “SS”, of course you get “SSS”. What’s that? You say you’re get­ting “SSSS”? Where are you get­ting that ex­tra “S” from? What? No—can’t you see it? It’s ob­vi­ously three—how can you put those two groups to­gether and get four?

So, “SS0 + SS0 = SSS0”.

My point is this: you can’t just point to the Peano ax­ioms and say, “Ha! Your hy­po­thet­i­cal situ­a­tion in­volv­ing the be­hav­ior of mere phys­i­cal ob­jects is mean­ingless be­fore the might of my ab­solute math­e­mat­i­cal as­sump­tions!” Re­mem­ber, when you try to perform “logic” on those ax­ioms, you’re still us­ing your brain to do it. And how­ever ivory-tower un­touch­able you imag­ine your ax­ioms to be, your brain is a real, phys­i­cal ob­ject perform­ing real phys­i­cal com­pu­ta­tions. If we lived in a slightly differ­ent uni­verse, your brain would take one look at “SS0” and “SS0“, vi­su­ally add to­gether the num­ber of “S” char­ac­ters, and see “SSS0”. Any­one who saw “SSSS0” would be seen as crazy, or brain-dam­aged, or some­thing.

Physics trumps math and logic.

• They say that the ax­ioms pin down the num­bers, re­gard­less of how phys­i­cal ob­jects be­have or start be­hav­ing.

Not sure who “they” are. May I sug­gest read­ing up on model the­ory? Maybe En­der­ton’s “math­e­mat­i­cal logic” (?).

It’s im­por­tant to think sep­a­rately about the “model” (the thing we are study­ing), the “lan­guage” (where we make state­ments about the model), and the “the­ory” (a set of state­ments in a lan­guage). The same the­ory in a par­tic­u­lar lan­guage may and in fact gen­er­ally does ap­ply to mul­ti­ple dis­tinct mod­els. The same model (ob­ject) may be de­scribed by the­o­ries in differ­ent lan­guages of differ­ent strengths.

So in one sense Peano ax­ioms “pin down” the nat­u­ral num­bers, but in an­other sense they don’t be­cause we can in­vent crazy ob­jects that con­tain a lot more than just the nat­u­ral num­bers to which Peano ax­ioms also ap­ply (this is the con­tent of the Lowen­heim-Skolem the­o­rem).

http://​​en.wikipe­dia.org/​​wiki/​​L%C3%B6wen­heim%E2%80%93Skolem_theorem

We can use a more pow­er­ful lan­guage than first or­der logic to de­scribe the nat­u­ral num­bers, and that would rule out some of the crazy mod­els. That will cap­ture more prop­er­ties of the nat­u­ral num­ber line, but not ev­ery­thing.

Physi­cists play a similar game to lo­gi­ci­ans, ex­cept per­haps a bit less for­mally. But their mod­els (in the sense of ‘ob­ject of study’) “bite back.”

It’s con­fus­ing that to a model the­o­rist “the model” refers to the ter­ri­tory, while to a statis­ti­cian “the model” refers to the map.

• Not sure who “they” are.

My bad; I wasn’t clear. “They” refers, not to any per­son or group of peo­ple in academia, but some of the com­menters on this LW post. As an ex­am­ple: this com­ment.

• Um, but the (+) op­er­a­tor in peano ar­ith­metic is ac­tu­ally defined in terms of Sx + y = x + Sy. It would be some­what cir­cu­lar to “sug­gest count­ing the S’s up” in a method of defin­ing num­bers, af­ter all. So the way you calcu­late 2 + 2 is more like

SS0 + SS0

(thing on the left starts with an S)

S(S0) + SS0

(move the S to the right)

S0 + SSS0

(thing on the left starts with an S)

S(0) + SSS0

(move the S to the right)

0 + SSSS0

(elimi­nate “0 + ” with ax­iom)

SSSS0

I imag­ine you’d need a rather more de­vi­ous brain mod­ifi­ca­tion to pre­vent one from car­ry­ing out these steps cor­rectly, in such a way that the re­sult is SSS0.

• I imag­ine you’d need a rather more de­vi­ous brain mod­ifi­ca­tion to pre­vent one from car­ry­ing out these steps cor­rectly, in such a way that the re­sult is SSS0.

All right. Let me take a stab at it.

S(0) + SSS0

(move the S to the right)

Okay. Fol­low­ing you so far...

0 + SSSS0

Eh? Where’d you get the ex­tra “S” from?

(This hack would have the un­for­tu­nate side effect of mak­ing ev­ery ad­di­tion with at least one term less than or equal to 3 and a re­sult greater than 3 come out to 1 less than it’s sup­posed to, how­ever. If you wanted to only make 2 + 2 = 3, and pre­serve all other ad­di­tions as-is, I can’t think of any brain hack that could do that. That’s not to say no such hack is pos­si­ble; I’m sure one is, but I just can’t think of one.)

• This hack would have the un­for­tu­nate side effect of mak­ing ev­ery ad­di­tion with at least one term less than or equal to 3 and a re­sult greater than 3 come out to 1 less than it’s sup­posed to, how­ever.

I think it would even re­sult in any ad­di­tion with a term ≤ 3 and re­sult > 3 come out to ex­actly 3, un­less you have some sort of rule for S + SSS0 some­times be­com­ing SSSS0 in­stead of SSS0.

Note also that an en­ter­pris­ing soul can line up the two steps:

S0  +  SSS0
⁠ 0  +  SSS0


And no­tice that they are con­fused, be­cause the SSS0′s are iden­ti­cal, even though they shouldn’t be, be­cause Sx + y = x + Sy was the rule ap­plied and Sy ≠ y.

A brain hack that made all of this work is surely pos­si­ble, of course, but it seems like it would have to be a bit more sys­tem­atic.

• A brain hack that made all of this work is surely pos­si­ble, of course, but it seems like it would have to be a bit more sys­tem­atic.

That seems fair. Would you agree that my origi­nal point (that your grasp of logic stems from a phys­i­cal brain and can be mud­dled) stands, though?

• Wouldn’t such an oc­cur­rence in­volve an over­haul of the world on part of some Force/​En­tity? And why would you, and only you, be able to note that some­thing changed, i.e. that you be­lieved 2+2=4 and now you no longer don’t? Much more im­por­tantly, since you use it as an ex­am­ple, Win­ston would not bother to write about 2+2=3, he would prob­a­bly ac­tu­ally write about 2+2=4, or even 5, thus shak­ing your world even fur­ther...

• I un­der­stand the point Eliezer’s try­ing to make here. How­ever, you (who­ever’s read­ing this) could not con­vince me that ss0 + ss0 =sss0 in Peano ar­ith­metic (I define the sce­nario in which my mind is di­rectly ma­nipu­lated so that I hap­pen to be­lieve this not to con­sti­tute “con­vinc­ing me”). Here’s why I be­lieve this po­si­tion to be ra­tio­nal:

A)In or­der for me to make this ar­gu­ment, I have to pre­sume com­mu­ni­ca­tion of it. It’s not that I be­lieve the prob­a­bil­ity of that com­mu­ni­ca­tion to be 1. Cer­tainly many peo­ple might read this com­ment and not know Peano ar­ith­metic, mi­s­un­der­stand my lan­guage, not finish read­ing, etc. etc. etc. and the prob­a­bil­ity of this is non­triv­ial. How­ever, ar­gu­ments are di­rected at the pos­si­ble wor­lds in which they are un­der­stood.

B)Com­mu­ni­ca­tion of “ss0 + ss0 =” as a state­ment of Peano ar­ith­metic already fully con­strains the an­swer to be “ssss0“ sim­ply by virtue of what these sym­bols mean. That is to say, that hav­ing un­der­stood these sym­bols and Peano ar­ith­metic, no fur­ther ex­pe­rience is nec­es­sary to know that “sss0” is wrong. Men­tal flaws at any point in this pro­cess or un­der­stand­ing are pos­si­ble, but they ex­ist only within pos­si­ble wor­lds in which com­mu­ni­ca­tion of these ideas does not ac­tu­ally oc­cur be­cause to think that “ss0 + ss0 = sss0” is to mi­s­un­der­stand Peano ar­ith­metic, and un­der­stand­ing Peano ar­ith­metic is a pre­req­ui­site for un­der­stand­ing a claim about it.

Therefore

C)There is no pos­si­ble world within which I can be con­vinced of the prop­erly com­mu­ni­cated con­cept “ss0 + ss0 = sss0”. Of course, this doesn’t mean there’s no pos­si­ble world in which I can be con­vinced that I am ex­pe­rienc­ing a neu­rolog­i­cal fault or be­ing ma­nipu­lated, or that there are no pos­si­ble wor­lds in which I hap­pen to wrongly be­lieve that ss0 + ss0 = sss0. It’s just that some­one ex­pe­rienc­ing a neu­rolog­i­cal fault or be­ing ma­nipu­lated is not the same thing as some­one be­ing con­vinced.

A similar ar­gu­ment holds for the im­pos­si­bil­ity of me con­vinc­ing my­self that ss0 + ss0 = sss0. I un­der­stand ss0 + ss0 = ssss0 in Peano ar­ith­metic well enough that I can re­view in a very short pe­riod of time why it must be so. Thus you would liter­ally have to make me for­get that I know this in or­der to have me be­lieve oth­er­wise, which hardly counts as “con­vinc­ing.” This does not mean that I am pre­sum­ing men­tal er­rors or Dark Lords of the Ma­trix to be im­pos­si­ble. For clar­ifi­ca­tion, here’s what a run­through of me ex­pe­rienc­ing what Eliezer pro­poses would look like:

I get up one morn­ing, take out two earplugs, and set them down next to two other earplugs on my night­table, and no­ticed that there were now three earplugs, with­out any earplugs hav­ing ap­peared or dis­ap­peared—in con­trast to my stored mem­ory that 2 + 2 was sup­posed to equal 4.

Be­cause that stored mem­ory en­tails an un­der­stand­ing of why, I run through those rea­sons. If they’re in­com­plete this con­sti­tutes me “for­get­ting that I know this.” (It does not mean that I don’t know this now. Right now I do.) There­fore I don’t have a “stored mem­ory that 2 + 2 was sup­posed to equal 4.” I have an in­com­plete stored mem­ory which tries to say some­thing about 2, +, =, and 4 (if my per­son­al­ity were in­tact I would prob­a­bly try and re-de­rive the miss­ing parts of it, af­ter call­ing 911). Either way I iden­tify a cog­ni­tive fault. In real life wak­ing up to this my most likely sus­pect would be that my ex­pe­rience of one earplug dis­ap­pear­ing was deleted be­fore I pro­cessed it, but there are lots of other pos­si­bil­ities as well. If I re­peated the ex­per­i­ment mul­ti­ple times I would con­sider ei­ther a sys­tem­atic fault or “be­ing messed with” at a fun­da­men­tal level.

When I vi­su­al­ize the pro­cess in my own mind, it seems that mak­ing XX and XX come out to XXXX re­quires an ex­tra X to ap­pear from nowhere

Still pre­sum­ing an in­tact line of rea­son­ing say­ing why this must not be so, I would again iden­tify a cog­ni­tive fault, and a pretty cool one at that. Some­thing this in­tri­cate might well leave me sus­pect­ing Dark Lords of the Ma­trix as a non­triv­ial pos­si­bil­ity, pro­vided all other cog­ni­tive func­tions seemed fully in­tact. Still wouldn’t be as likely as a weird brain fault, though. I would definitely have fun in­ves­ti­gat­ing this.

I check a pocket calcu­la­tor, Google, and my copy of 1984 where Win­ston writes that “Free­dom is the free­dom to say two plus two equals three.”

Dark Lords of the Ma­trix bump higher, but Psy­chosis has definitely leapt into the front of the pack.

I could keep go­ing, of course. Th­ese last few pre­sume I can still rea­son out some­thing like Peano ar­ith­metic. If I can’t in­ci­den­tally, then of course they look differ­ent but I still don’t think it would be ac­cu­rate to de­scribe any pos­si­ble out­come as “me be­ing con­vinced that 2 + 2 = 3.” If you run all the way down the list un­til you liter­ally delete all things that I know and all ways I might ob­tain them, I would de­scribe that as a pos­si­ble uni­verse in which “me” has been deleted. The strict lower bound on where I can still stum­ble across my cog­ni­tive fault and/​or ma­nipu­la­tion is when my rea­son­ing abil­ity is no longer Tur­ing com­plete. This es­sen­tially re­quires the elimi­na­tion of all com­plex thought, though of course mak­ing it merely un­likely for me to stum­ble upon the fault is much eas­ier—just delete ev­ery­thing I know about for­mal math­e­mat­ics, for ex­am­ple.

tl;dr

I agree with most of what Eliezer is say­ing, but wouldn’t say that I could be con­vinced 2 + 2 = 3. Does this make my be­lief un­con­di­tional? Depen­dant on me un­der­stand­ing what 2 + 2 = 3 means, maybe it does. Maybe an un­der­stand­ing of 2, +, =, 3, and 4 ne­ces­si­tates 2 + 2 = 4 for a ra­tio­nal mind, and any de­vi­a­tion from this, even in in­ter­nal men­tal pro­cesses, would be iden­ti­fi­able as a fault. After all, you can run a soft­ware pro­gram to de­tect flaws in some com­puter pro­ces­sors.

• Ex­trap­o­lat­ing from Eliez­ers line of rea­son­ing you would prob­a­bly find that al­though you re­mem­ber ss0 + ss0 = ssss0, if you try to de­rive ss0 + ss0 from the peano ax­ioms, you also dis­cover it ends up as sss0, and start­ing with ss0 + ss0 = ssss0 quickly leads you to a con­tra­dic­tion.

• OK, I’m a Chris­tian. Bit of his­tory: -raised chris­tian -As a teen be­came ag­nos­tic/​deist, athe­ist at 17 -Con­verted to Chris­ti­an­ity at 18

Based on ra­tio­nal think­ing I drift to­wards deism/​ag­nos­ti­cism. I’m skep­ti­cal of microbes-to-man evolu­tion and abio­ge­n­e­sis. But if abio­ge­n­e­sis could be demon­strated, or if evolu­tion­ary pro­cesses could be demon­strated to be ca­pa­ble of pro­duc­ing the kind of com­plex­ity we see in biol­ogy (e.g. evolu­tion­ary al­gorithms run on su­per­com­puter clusters pro­duc­ing real AI) then I’d prob­a­bly drift to­wards athe­ism.

Any­way, at 18 I be­came a Chris­tian be­cause of di­rect rev­e­la­tion by God him­self, and I was not high.

A similar or bet­ter rev­e­la­tion could con­vince me of a differ­ent re­li­gion, though Is­lam would re­quire a much big­ger rev­e­la­tion. (Ex­traor­di­nary claims re­quire ex­traor­di­nary ev­i­dence, and I con­sider the claim that Is­lam is true much less likely than the claim that Ju­daism, Chris­ti­an­ity or Bud­dhism is true, which in turn I con­sider less likely than the claim that Deism is true.)

Edit: Thanks all for the lovely dis­cus­sion, I think I’ve pre­sented my the­ory of Life, the Uni­verse and Every­thing in enough de­tail to get a fair un­der­stand­ing of it.

I hope you like the data point and a lotta luck syn­the­siz­ing your own the­ory of L,U and E.

• Hello! As you’re no doubt aware, the gen­eral tenor of Less Wrong tends to­ward non-be­lief in re­li­gion. How­ever, in con­trast to many re­li­gious be­liev­ers, you have ex­pressed a will­ing­ness to al­ter your views in the face of ev­i­dence. Watch out! Even your ten­ta­tive sug­ges­tion that you might “drift to­wards athe­ism” might cause you to be re­garded as a heretic or at least un­trust­wor­thy in some churches. But if you’re will­ing to com­mit your­self to pur­su­ing the truth where­so­ever it may lead, then con­grat­u­la­tions!

As has been men­tioned already in this thread, Ju­daism and Chris­ti­an­ity his­tor­i­cally do not claim to be non-dis­prov­able. Eli­jah bet his God against Baal and (in the Bibli­cal nar­ra­tive) won. Do you think this ex­per­i­ment can be repli­cated? Alter­na­tively, is there some­thing equiv­a­lent to a “similar or bet­ter rev­e­la­tion” that could con­vince you that no or­ga­nized re­li­gion is cor­rect at all?

• My par­ents don’t con­sider me a real Chris­tian, some­how I cope. ;-)

Not only do I be­lieve the Eli­jah ex­per­i­ment can be repli­cated, I be­lieve it is be­ing repli­cated to­day along with many other mir­a­cles. Just hid­den for most peo­ple, be­cause in Chris­ti­an­ity, God re­veals the truth to those who he chooses (poor/​hum­ble/​righ­teous peo­ple) and keeps other peo­ple (rich/​wicked/​pride­ful) blind. So God might raise some­one from the dead but in a way that could not be pub­li­cly ver­ified, lest the rich proud peo­ple who think they’re so smart find out the truth.

I fail to see how a su­per­nat­u­ral rev­e­la­tion could prove no (or­ga­nized) re­li­gion is cor­rect, short of God say­ing “no re­li­gion is cor­rect”, which would then cause me to cre­ate my own or­ga­nized re­li­gion...

But Chris­ti­an­ity could surely be dis­proved in many differ­ent ways. For one, aliens or real sen­tient AI would dis­prove Chris­ti­an­ity AFA I’m con­cerned. I’m not yet 30, so maybe I’ll dis­cover it in my life­time.

If Chris­ti­an­ity were dis­proved, that would leave Bud­dhism and Deism as the only vi­able re­li­gions left IMH(cur­rent)O. And Deism is only nec­es­sary in so far as I find the ev­i­dence for abio­ge­n­e­sis and hu­mans-cre­ated-by-evolu­tion lack­ing.

So ex­cept mir­a­cles and cre­ation, I could be an athe­ist.

• Just hid­den for most peo­ple, be­cause in Chris­ti­an­ity, God re­veals the truth to those who he chooses (poor/​hum­ble/​righ­teous peo­ple) and keeps other peo­ple (rich/​wicked/​pride­ful) blind. So God might raise some­one from the dead but in a way that could not be pub­li­cly ver­ified, lest the rich proud peo­ple who think they’re so smart find out the truth.

You can see how non-Chris­ti­ans might find that to be a sus­pi­ciously con­ve­nient ex­cuse, right?

• So be­cause it makes sense it’s sus­pi­ciously con­ve­nient?

Ob­vi­ously if there was a God (e.g. the Chris­tian one) and he wanted the whole world to be nom­i­nal Chris­ti­ans he would do an­other Eli­jah like demon­stra­tion of his power, recorded on cam­era.

This is ob­vi­ously not the case. So ei­ther the Chris­tian god does not ex­ist (sus­pi­ciously con­ve­nient for the non-Chris­tian?) or he does not ac­tu­ally want all those non-Chris­ti­ans to self-iden­tify as Chris­ti­ans (sus­pi­ciously con­ve­nient for the Chris­tian god?)

• So be­cause it makes sense it’s sus­pi­ciously con­ve­nient?

It’s sus­pi­ciously con­ve­nient be­cause your claim im­plies that that ev­i­dence of Chris­ti­an­ity’s truth is only available to peo­ple who already be­lieve in it (or who are already much closer to be­liev­ing it than their epistemic state ac­tu­ally war­rants).

• Ob­vi­ously, if the ev­i­dence of Chris­ti­an­ity’s truth was available to all then all would be Chris­ti­ans. As­sum­ing the Chris­tian god does not want all to be Chris­ti­ans the ev­i­dence should not be available to all.

Any­way, when I re­ceived my ex­pe­rience I cer­tainly did not want to be­lieve in it. And even now many years later, I would pre­fer to aban­don Chris­ti­an­ity and its moral­ity but find my­self un­able be­cause of my ex­pe­riences.

I also know of a few other sto­ries similar to mine, enough to con­vince my­self I’m not delu­sional.

• As some peo­ple have pointed out, it’s not a bi­nary choice be­tween you be­ing crazy or delu­sional, and Chris­ti­an­ity be­ing right. Hu­man brains com­plete pat­terns, in pre­dictable ways. I don’t know what your ex­pe­rience was (since you’re keep­ing that pri­vate) but there are prob­a­bly mul­ti­ple pos­si­ble wor­lds that are con­sis­tent with your ex­pe­rience: not just “Xaway is nuts” or “Je­sus is the Sav­ior.” Think about what might have ac­tu­ally hap­pened and what it might ac­tu­ally mean, and re­sist pat­tern-match­ing for a while.

Just a word of info on this site: this is not a place where peo­ple gen­er­ally de­bate re­li­gion. You sound like you have your doubts; I recom­mend you read the best athe­ist ar­gu­ments (Ber­trand Rus­sell comes to mind), and read about the his­tory of the Bible and early Church from a sec­u­lar aca­demic writer. Let it mar­i­nate for a while. Read widely and see what hap­pens to your views. Some­times de­bat­ing on the in­ter­net isn’t the best way to learn; it crys­tal­lizes what­ever ideas you started off with and makes it hard to change your mind.

If you would “pre­fer to aban­don Chris­ti­an­ity” but your ex­pe­riences won’t let you, you should re­ally take some time to think about whether your ex­pe­riences have re­li­gious im­pli­ca­tions. There are nat­u­ral­is­tic ex­pla­na­tions for re­li­gious vi­sions, and no, they don’t all mean you’re crazy. (Check out Oliver Sacks on Hilde­gard of Bin­gen, and Robert Sapolsky on St. Paul.)

• There are nat­u­ral­is­tic ex­pla­na­tions for re­li­gious vi­sions, and no, they don’t all mean you’re crazy. (Check out Oliver Sacks on Hilde­gard of Bin­gen, and Robert Sapolsky on St. Paul.)

I’d also recom­mend Why God Won’t Go Away: Brain Science and the Biol­ogy of Belief by Gene D’Aquili and Vince Rauss.

• I also know of a few other sto­ries similar to mine, enough to con­vince my­self I’m not delu­sional.

I as­sume you mean sto­ries of re­li­gious ex­pe­riences similar to your own. This should not be ev­i­dence that you are not delu­sional, since many peo­ple through­out his­tory have claimed to have had such ex­pe­riences, with refer­ence to differ­ent, mu­tu­ally ex­clu­sive re­li­gions. On av­er­age, there­fore, most (if not all) peo­ple hav­ing such ex­pe­riences must have been delu­sional. You should have a prob­a­bil­ity that you are mis­taken at least as high as this pro­por­tion.

• Minor quib­ble, but “delu­sional” would seem overly in­flam­ma­tory as it im­plies the delu­sion­al­ity is a per­sis­tent prop­erty of Xaway’s per­son, rather than the one-off oc­cur­rence it more likely was.

• and keeps other peo­ple (rich/​wicked/​pride­ful) blind

Now I’m won­der­ing which of those cat­e­gories I fit in to. They all sound a tad ap­peal­ing. :)

• If you are fa­mil­iar with Chris­ti­an­ity, all hu­mans fall into the wicked and pride­ful cat­e­gories.

The fact that you are on the in­ter­net sug­gests you ad­di­tion­ally fall into the rich one too.

Now whether God sovereignly chooses his peo­ple (calv­inism), or hu­mans can also choose e.g. by hum­bling them­selves (ar­i­anism) is an open ques­tion.

Edit to add: Just be­cause God hasn’t re­vealed the truth to some­one to­day, doesn’t mean he won’t do it to­mor­row or even (though this is heresy) af­ter death.

So I cer­tainly don’t con­sider all non-Chris­ti­ans to be hope­less, af­ter all I was a non-Chris­tian too, once. And I also don’t con­sider all who call them­selves Chrs­tian to be cho­sen.

• If you are fa­mil­iar with Chris­ti­an­ity,

I was sincere Chris­tian right up un­til I re­al­ised the re­li­gion could be bet­ter ex­plained by tribal sig­nal­ling than magic.

all hu­mans fall into the wicked and pride­ful cat­e­gories.

You just finished say­ing:

God re­veals the truth to those who he chooses (poor/​hum­ble/​righ­teous peo­ple) and keeps other peo­ple (rich/​wicked/​pride­ful) blind.

• A ba­sic doc­trine of Chris­ti­an­ity is that poor, hum­ble and righ­teous peo­ple are wicked and pride­ful too.

Only Je­sus is perfect.

Some strains be­lieve God choses for rea­sons we can’t grasp and then those peo­ple be­come more hum­ble and less pride­ful, etc.

Others be­lieve that if you do your best to be hum­ble and righ­teous even­tu­ally God will re­veal him­self (though no guaran­tee that it will hap­pen be­fore your last minute on earth).

I don’t know which of the two it is, or per­haps it is some­thing else en­tirely.

• There were some things I thought of say­ing, but I think I’ll hold my tongue for now. In short, I think your as­ser­tions have some log­i­cal er­rors. This is not a put-down or a per­sonal com­ment—I’m cer­tainly no more than an as­piring ra­tio­nal­ist, at best, my­self. I hope you stick around this fo­rum. In the spirit of Tarski I would ask you to join me in say­ing:

If Chris­ti­an­ity is true I de­sire to be­lieve that Chris­ti­an­ity is true. If Chris­ti­an­ity is not true, I de­sire to be­lieve that Chris­ti­an­ity is not true.

I would say this, and do!

• Chris­ti­an­ity isn’t true.

• You’re just mad they re­fused to can­on­ize Sa­muel B. Fay.

• If you spot a log­i­cal er­ror, bring it on.

Ob­vi­ously I don’t want to be­lieve un­true things.

But if there is two things I am sure about, it’s (1) that hu­mans are not ra­tio­nal, es­pe­cially not me and (2) there are things that are true which can not be proven to be true (the real world analogue to Godels the­o­rems).

I fre­quent this site, but I gen­er­ally do not par­ti­ci­pate in in­ter­net dis­cus­sions. I only reg­istered this ac­count and gave my two cents be­cause Eliezer asked for a Chris­tian who speaks Bayes to chime in.

I’m afraid that once I log off, I will prob­a­bly for­get the pass­word to this ac­count.

• Again, I hope you stick around. No need to burn your­self out as the lone voice of Chris­ti­an­ity—pac­ing your­self is fine.

Also, this truly is a ra­tio­nal­ist site. If you can pre­sent well-thought out ar­gu­ments, peo­ple here will listen to you. If you can make a ra­tio­nal ar­gu­ment demon­strat­ing the truth of Chris­ti­an­ity, then (ac­cord­ing to some de­nom­i­na­tions) you could save some souls. (I un­der­stand the Calv­inists would not nec­es­sar­ily agree.) But ac­cord­ing to some tra­di­tions, good works (not just fide sola) have merit, and evan­ge­liz­ing is one of the great­est of all good works. Is it not?

My ul­te­rior mo­tive in mak­ing that ar­gu­ment is that I also think this fo­rum could benefit from the per­spec­tive of a Chris­tian who speaks Bayes.

• Also, this truly is a ra­tio­nal­ist site. If you can pre­sent well-thought out ar­gu­ments, peo­ple here will listen to you.

That is not ‘truly ra­tio­nal­ist’. Well thought out ar­gu­ments for a pre­s­e­lected bot­tom line are bul­lshit.

• Also, this truly is a ra­tio­nal­ist site. If you can pre­sent well-thought out ar­gu­ments, peo­ple here will listen to you. If you can make a ra­tio­nal ar­gu­ment demon­strat­ing the truth of Christianity

The truth sta­tus of Chris­ti­an­ity is some­thing that Less Wrong should be able to con­sider a set­tled ques­tion. We can de­bate about things like the Si­mu­la­tion Ar­gu­ment, etc. and other re­duc­tion­ist non-su­per­nat­u­ral­ist claims that look sorta like deism if you squint, but Je­ho­vah did not cre­ate the uni­verse, and Je­sus is not Lord, and I don’t think there’s any point in hu­mour­ing some­one who dis­agrees, or en­courag­ing them to come up with smarter-sound­ing ra­tio­nal­iza­tions. Let’s not push Less Wrong in the di­rec­tion of be­com­ing the sort of place where these old de­bates are re­hashed; there are more in­ter­est­ing things to think and talk about. Although it seems that Xaway in par­tic­u­lar may not have come here with the in­ten­tion of ac­tu­ally con­vinc­ing any­one to be­lieve in Chris­ti­an­ity, I would pro­pose in the gen­eral case that any­one who does want to should be referred to some place like /​r/​athe­ism in­stead.

• Well, I cer­tainly don’t think Je­ho­vah cre­ated the uni­verse. On the other hand, this thread is de­voted to the con­sid­er­a­tion of the propo­si­tion that 2 + 2 = 3 -- ar­guably a set­tled ques­tion—with the un­der­stand­ing that “a be­lief is only re­ally worth­while if you could, in prin­ci­ple, be per­suaded to be­lieve oth­er­wise.” I don’t know if Xaway is go­ing to be par­ti­ci­pat­ing any more (hi, Xaway, if you’re read­ing this!), but I was hop­ing that this might be a good ex­er­cise in prac­tic­ing ra­tio­nal dis­cus­sion. In part, I thought we could win him over to the dark side (jok­ing about it be­ing the dark side.)

• I also think this fo­rum could benefit from the per­spec­tive of a Chris­tian who speaks Bayes.

I think I’d rather have a bet­ter cal­ibrated Fre­quen­tist.

• I’d rather have a rock. Or a Chris­tian who doesn’t speak Bayes. At least that im­plies less dou­ble­think.

• Chris­ti­an­ity here is ac­tu­ally a memetic haz­ard. It’s a set of be­liefs that has so many things wrong with it all of us feel com­pel­led to ad­dress all of the bad think­ing and wrong ev­i­dence all at once. It im­me­di­ately draws ev­ery­one away from what­ever pro­duc­tive com­ments they were mak­ing and into an at­tempt to de­con­vert the in­ter­locu­tor. The in­ter­locu­tor then re­sponds to these at­tempts with more non­sense in differ­ent places which draws still more peo­ple in to the bat­tle. Bet­ter to just keep the Hy­dra’s out than try and chop off all those heads.

No one here is ac­tu­ally at risk but we don’t get any­thing to jus­tify the strain on the im­mune sys­tem.

• I can think of some coun­terex­am­ples. We “got” SarahC, for in­stance (ac­cord­ing to her own words), and that was an unadulter­ated boon.

Also, the claims of re­li­gion are varied enough that they provide a range of top­ics, many triv­ial but some in­ter­est­ing. E.g., if we were in a sim and some­body changed it from out­side in vi­o­la­tion of the sim’s in­ter­nal phys­i­cal law, that would con­sti­tute a “mir­a­cle” at this level of re­al­ity. How would we rec­og­nize such an event from in­side?

• A lot of Sarah’s com­ments were made this sum­mer when I wasn’t around, so I may have missed some­thing but I quick glance con­firms that she is not a be­liev­ing Chris­tian. She cer­tainly hasn’t ar­gued for the truth Chris­ti­an­ity, which is re­ally my con­cern.

Also, the claims of re­li­gion are varied enough that they provide a range of top­ics,

Which we can dis­cuss suc­cess­fully with­out real Chris­ti­ans.

• Sorry, I was un­clear in speak­ing. I meant she ac­knowl­edged LW’s in­fluence in her de­con­ver­sion, and is no longer re­li­gious. I think she started out Jewish ac­tu­ally. I can’t seem to find the rele­vant com­ment/​post.

• I was never Chris­tian, I was raised Jewish, and now I don’t be­lieve in God. And, yes, LessWrong con­tributed. (I think, IIRC, we also have a mem­ber who was raised Mus­lim and re­cently be­came an athe­ist since he found LW.)

I don’t think you can ran­domly de­con­vert some­one who isn’t already seek­ing a change. Like most ma­jor changes in be­lief or lifestyle, de­con­ver­sion has to be self-mo­ti­vated. But if a Chris­tian (or other re­li­gious per­son) is hang­ing around LW and not trol­ling, then he’s prob­a­bly look­ing for some al­ter­na­tives, and there’s no harm point­ing him in that di­rec­tion.

• I was never Chris­tian, I was raised Jewish, and now I don’t be­lieve in God. And, yes, LessWrong con­tributed. (I think, IIRC, we also have a mem­ber who was raised Mus­lim and re­cently be­came an athe­ist since he found LW.)

My rea­son to ab­jure God was mainly due to eth­i­cal rea­sons. I didn’t want to fol­low some­thing any­more that had de­liber­ately de­signed such an hel­l­hole of a uni­verse. Later I be­came an athe­ist mainly for notic­ing that noth­ing nat­u­ral re­ally ap­peared to be in­tel­li­gently de­signed. Just look at the moon, the shape of the con­ti­nents etc., or that we live on the sur­face of a sphere rather than in­side a Dyson sphere. The next big step came via sci­ence fic­tion, when I no­ticed how easy it would have been to de­sign a uni­verse where noth­ing could suffer hor­ribly. What Less Wrong added on top of all else I learnt is that Oc­cam’s ra­zor has been for­mal­ized. I didn’t know about that be­fore LW.

I just don’t see that any­one would need Less Wrong to stop be­liv­ing into one of the Abra­hamic re­li­gions. It should be ob­vi­ous to any­one who isn’t morally bankrupt or a psy­chopath that God is not your friend, rather it is your worst en­emy. If that doesn’t con­vince you, why not just read the Bible:

Who­ever is cap­tured will be thrust through; all who are caught will fall by the sword. Their in­fants will be dashed to pieces be­fore their eyes; their houses will be looted and their wives vi­o­lated. See, I will stir up against them the Medes, who do not care for silver and have no delight in gold. Their bows will strike down the young men; they will have no mercy on in­fants, nor will they look with com­pas­sion on chil­dren. (Isa­iah 13:15-18)

• I just don’t see that any­one would need Less Wrong to stop be­liv­ing into one of the Abra­hamic re­li­gions. It should be ob­vi­ous to any­one who isn’t morally bankrupt or a psy­chopath that God is not your friend, rather it is your worst en­emy.

And yet sim­ple ob­ser­va­tion con­firms that it is not ob­vi­ous to many peo­ple who are clearly not so­ciopaths or more morally bankrupt than usual. It’s com­pletely or­di­nary for peo­ple to ra­tio­nal­ize away in­con­sis­ten­cies or flaws in their be­liefs with as lit­tle re­vi­sion as pos­si­ble. Mak­ing large al­ter­a­tions to ac­count for large er­rors is a rare and difficult to learn skill.

• Yes, ob­vi­ously, as I am used to from my par­ents. Sadly none of them would read LW or not ra­tio­nal­ize away what is be­ing said here like so much else. I be­lieve that those who ab­jured re­li­gion be­cause of read­ing some­thing like LW are rather an ex­cep­tion. I was re­ally ad­dress­ing re­li­gious peo­ple, with what I call my shock and awe ap­proach to crack their stronghold of sub­jec­tive moral su­pe­ri­or­ity. To para­phrase what I said, you are dumb, ig­no­rant and morally ab­hor­rent if you do not ab­jure your God. Yep, that might not work, but it does re­flect my weari­ness. So never mind my lit­tle tirade, I lost my sense of lo­ca­tion aware­ness for a mo­ment there ;-)

• I was aware of the moral as­pects; but I was con­fused by the no­tion that I seemed to dis­agree with God and I thought this was my fault. I had a prob­lem with the story of Pin­chas, but I thought that was me just be­ing “soft” or “sec­u­larized” and I was re­ally un­sure whether to trust my own sense of moral­ity. (One thing we should all un­der­stand here is that “con­science” is very far from in­fal­lible.)

What changed my mind is a sense that my brain is all I’ve got. I may be wrong about many things, but I’m not go­ing to be­come less wrong by throw­ing out the ma­jor­ity of what I know in fa­vor of one an­cient and rather bloody book; if “con­science” isn’t trust­wor­thy, it’s still prob­a­bly more trust­wor­thy than sim­ple con­formism.

• I seemed to dis­agree with God and I thought this was my fault. I had a prob­lem with the story of Pin­chas, but I thought that was me just be­ing “soft” or “sec­u­larized” and I was re­ally un­sure whether to trust my own sense of moral­ity.

If you re­place God with Yud­kowsky, story of Pin­chas with AI go­ing FOOM and soft, re­spec­tively sec­u­larized, with ir­ra­tional and sense of moral­ity with ed­u­ca­tion (or worse, in­tel­li­gence), then you got how I feel about an­other topic.

What changed my mind is a sense that my brain is all I’ve got. I may be wrong about many things, but I’m not go­ing to be­come less wrong by throw­ing out the ma­jor­ity of what I know in fa­vor of one an­cient and rather bloody book; if “con­science” isn’t trust­wor­thy, it’s still prob­a­bly more trust­wor­thy than sim­ple con­formism.

I’ve always felt that con­science was just a mat­ter of taste. So it was never re­ally a ques­tion about how trust­wor­thy my moral judge­ment is but that I care about it. I ab­jured God when I still be­lieved that it ex­ists. Only later I be­came an athe­ist. I sup­pose that is the differ­ence be­tween you and me here. You wanted to do the right thing (in an ob­jec­tive sense) and for me the right thing has always been that what I want.

• Although I ap­pre­ci­ate some of the ar­ti­cles on this site, I don’t think I’ll par­ti­ci­pate much in the dis­cus­sion.

Although I speak Bayes and know more logic than a hu­man should know, I do not con­sider my­self a ra­tio­nal­ist, be­cause I doubt my own ra­tio­nal­ity. It wouldn’t make sense for an in­her­ently ir­ra­tional per­son to spend his time try­ing to talk ra­tio­nally when he could be danc­ing or pro­gram­ming.

Also, I firmly be­lieve that Chris­ti­an­ity can not be proven by ar­gu­ment, only by ev­i­dence (mir­a­cles). And only God him­self, not the Chris­tian, can provide the ev­i­dence, which he does on his own terms.

• I do not con­sider my­self a ra­tio­nal­ist, be­cause I doubt my own ra­tio­nal­ity.

This site isn’t called Always Right, you know.

• (2) there are things that are true which can not be proven to be true (the real world analogue to Godels the­o­rems).

Ar­guably this is the case for ev­ery­thing (un­til we solve the prob­lem of in­duc­tion). In the mean­time, I don’t know of any­thing you can’t as­sign a prob­a­bil­ity to or col­lect ev­i­dence about.

As for whether this is an analogue to Godel’s the­o­rem (or, in times gone by, Rus­sel’s para­dox­i­cal cat­a­logues—or in times yet to come, the halt­ing prob­lem) - no. Math­e­mat­i­cal sys­tems are use­ful ways to carve re­al­ity at its joints. So are cat­e­gories, and so is com­pu­ta­tion. They can’t an­swer ques­tions about them­selves. But re­al­ity quite clearly can an­swer ques­tions about it­self.

• there are things that are true which can not be proven to be true (the real world analogue to Godels the­o­rems).

Ar­guably this is the case for ev­ery­thing (un­til we solve the prob­lem of in­duc­tion). In the mean­time, I don’t know of any­thing you can’t as­sign a prob­a­bil­ity to or col­lect ev­i­dence about.

How about the ques­tion of whether there is any­thing you can’t as­sign a prob­a­bil­ity to or col­lect ev­i­dence about?

• You can as­sign a prob­a­bil­ity to that. I hadn’t con­sid­ered the ques­tion strongly enough to have a math­e­mat­i­cal num­ber for you, but I would es­ti­mate there is a 10% chance that there are things which I can­not as­sign a prob­a­bil­ity to or col­lect ev­i­dence about. (Note that I as­sign a much lower prob­a­bil­ity to the claim “you can’t as­sign a prob­a­bil­ity to or col­lect ev­i­dence about x”; em­piri­cally those state­ments have been made prob­a­bly mil­lions of times in his­tory and as far as I know not a sin­gle one has been cor­rect)

That said, “I don’t know of any­thing you can’t as­sign a prob­a­bil­ity to or col­lect ev­i­dence about” is true with a prob­a­bil­ity of 1 − 4x10^-8 (the chance I am hal­lu­ci­nat­ing, or made a gross er­ror given that I dou­ble-checked).

• If you spot a log­i­cal er­ror, bring it on.

Did. Didn’t work. Wrote you off. :)

• I’m afraid that once I log off, I will prob­a­bly for­get the pass­word to this ac­count.

Per­haps you could go to ‘Prefer­ences’ on the right and change your pass­word to some­thing eas­ier to re­mem­ber.

Any­way, at 18 I be­came a Chris­tian be­cause of di­rect rev­e­la­tion by God him­self, and I was not high.

Re­gard­ing your rev­e­la­tion and di­rect ex­pe­rience with God, I am very cu­ri­ous as to whether the rev­e­la­tion speci­fied in any way which re­li­gion God would pre­fer you to par­ti­ci­pate in. (You wrote above that you think the Judeo-Chris­tian re­li­gions seem more likely, only, so this leads me to be­lieve the rev­e­la­tion wasn’t that spe­cific.)

(Echo­ing Costanza’s ques­tions) How much er­ror do you al­low for know­ing about God, but fol­low­ing the wrong re­li­gion? Even if Chris­ti­an­ity seems most likely to you, what prob­a­bil­ity do you as­sign to any cur­rent or­ga­nized re­li­gion be­ing cor­rect? I sup­pose the rea­son why I’m ask­ing is that some­thing like Chris­ti­an­ity seems un­nec­es­sar­ily spe­cific if you are po­ten­tially deist or athe­ist. Prob­a­bil­is­ti­cally, God could ex­ist in a lot of differ­ent ways, and provide true rev­e­la­tions, long be­fore all the spe­cific things are true about Chris­ti­an­ity.

• Many other peo­ple have such ex­pe­riences, high or no. Some Hindu, some Mus­lim, some Pa­gan, some even athe­ists. To be blunt, do you doubt their sincer­ity, or their san­ity? Why are you epistem­i­cally priv­ileged?

• To the ex­tent that their ex­pe­riences do not con­tra­dict mine, I see no rea­son to doubt. There is noth­ing in Chris­ti­an­ity that pre­vents non-Chris­ti­ans from hav­ing re­li­gious ex­pe­riences.

But when the ex­pe­riences of oth­ers do con­tra­dict mine, such as the rev­e­la­tions Joseph Smith or Mo­hammed re­ceived, I have to doubt their sincer­ity or their san­ity (I don’t know which) for the same rea­son you doubt mine: Be­cause I can’t see in their mind and I wasn’t in their body when it hap­pened. And if I have to choose be­tween my own ex­pe­riences and an­other per­sons ex­pe­riences, I choose my own.

But I should men­tion that of all the peo­ple I trust and who have told me their re­li­gious ex­pe­riences (mostly hindu fam­ily mem­bers) to date none of them has proven a challenge to my Chris­ti­an­ity.

I have to doubt their sincer­ity or their san­ity (I don’t know which) for the same rea­son you doubt mine: Be­cause I can’t see in their mind and I wasn’t in their body when it hap­pened. And if I have to choose be­tween my own ex­pe­riences and an­other per­sons ex­pe­riences, I choose my own.

It is im­por­tant to un­der­stand that if no re­li­gious ex­pe­riences were mu­tu­ally ex­clu­sive with Chris­ti­an­ity (no­body ever saw Ganesh or Mo­hammed), then they would count a lot more strongly as ev­i­dence for Chris­ti­an­ity. But many are mu­tu­ally ex­clu­sive, and doubt­ing the sincer­ity of ev­ery Sufi mys­tic who saw God is a move that re­quires strong ev­i­dence.

As to an­other per­son’s ex­pe­riences vs your own: I sym­pa­thize, I re­ally do. But you need to have some epistemic hu­mil­ity here, and re­al­ize that “you” are en­coded in about half a kilo of mushy grey stuff that is of­ten very un­trust­wor­thy. I for one do not doubt your sincer­ity (or the Sufis’) but I do doubt that you cor­rectly in­ter­preted your ex­pe­rience.

• And if I have to choose be­tween my own ex­pe­riences and an­other per­sons ex­pe­riences, I choose my own.

Luck­ily, we need not be limited to those hy­pothe­ses. Nei­ther you nor many of the oth­ers with similar ex­pe­riences need be ly­ing or in­sane. And the ex­is­tence of an om­nipo­tent, om­ni­scient and omni-benefi­cent de­ity need not en­ter into it ei­ther. You just have to have brains.

Wel­come, by the way.

• I’ve con­sid­ered those kind of ex­pla­na­tions, but the na­ture of the par­tic­u­lar ex­pe­riences which caused me to con­vert does not lend it­self to that kind of ex­pla­na­tion.

My policy is to never dis­cuss the de­tails with some­one I do not per­son­ally know and trust, but I will say this much: the ev­i­dence was ex­ter­nal and ob­served and con­firmed by trusted oth­ers.

In fact if you are fa­mil­iar with Zero Knowl­edge Proofs (I’m a crypto geek) the ev­i­dence was a type of ZKP that al­lows me to know with cer­tainty (to the ex­tent that I can trust my own ra­tio­nal­ity and senses) with­out en­abling me to du­pli­cate the proof.

• Any­way, at 18 I be­came a Chris­tian be­cause of di­rect rev­e­la­tion by God him­self, and I was not high.

What was that like? In par­tic­u­lar, how could you tell that it was re­ally a rev­e­la­tion and not any kind of tem­po­rary brain malfunc­tion?

• I’m skep­ti­cal of microbes-to-man evolu­tion and abio­ge­n­e­sis. But if abio­ge­n­e­sis could be demon­strated, or if evolu­tion­ary pro­cesses could be demon­strated to be ca­pa­ble of pro­duc­ing the kind of com­plex­ity we see in biol­ogy (e.g. evolu­tion­ary al­gorithms run on su­per­com­puter clusters pro­duc­ing real AI) then I’d prob­a­bly drift to­wards athe­ism.

A God is a very com­plex en­tity. Posit­ing one does not, there­fore, help to ex­plain biolog­i­cal com­plex­ity (un­less you have an ex­pla­na­tion for God). Even though we don’t know how abio­ge­n­e­sis hap­pened it is still or­ders of mag­ni­tude more likely than God ex­ist­ing given the rel­a­tive com­plex­ities in­volved. That Chris­ti­an­ity is true is also or­ders of mag­ni­tude more un­likely than you and your com­pan­ions hal­lu­ci­nat­ing your di­rect rev­e­la­tion—the former be­ing an ex­traor­di­nar­ily com­plex hy­poth­e­sis and hal­lu­ci­na­tions and gen­eral ir­ra­tional­ity be­ing quite com­mon.

• Well that is just your bi­ases...

Be­cause a God is su­per­nat­u­ral any prob­a­bil­ity as­signed to it ex­ist­ing is as ar­bi­trary as any other.

Ob­vi­ously, if the P=1/​3^^^^^3 then it would be ab­surd to see bio­ge­n­e­sis or biolog­i­cal com­plex­ity as ev­i­dence for God. But if the P =0.01 then I, for one, see it as very strong ev­i­dence.

I see no rea­son to pre­fer the­ism vs. athe­ism and I con­sider an ex­traor­di­nar­ily low P to be bi­ased to­wards athe­ism, but if that rocks your boat, have fun.

That I am ir­ri­a­tional and delu­sional is highly prob­a­ble, in fact I am sure of it. But I have no choice but to trust my own faulty brain.

I would cer­tainly not con­sider you ra­tio­nal if you were to con­vert to Chris­ti­an­ity solely based on read­ing my story on the in­ter­netz.

• This is re­ally wrong, ob­vi­ously, but my hopes that the in­fer­en­tial dis­tance was man­age­able have been dashed. You might start here. I’m done though.

• I tend to think that a phys­i­cal sys­tem of num­ber­ing and an en­tirely non­phys­i­cal sys­tem of be­lief as ap­ples and or­anges- en­tirely in­com­pa­rable. Speci­fi­cally, adding or sub­tract­ing earplugs is an en­tan­gle­ment of re­al­ity and be­lief whereas choos­ing eg. chris­ti­an­ity or is­lam is sim­ply some­thing of be­lief- yes, that spiritual be­lief is af­fected by your re­al­ity (en­vi­ron­men­tal fac­tors like school­ing, par­ents and lo­ca­tion, ob­vi­ously) but in the end, it is still a be­lief- for ex­am­ple, if a per­son never heard of Je­sus or Muham­mad but nonethe­less be­lieved in a higher power or si­mil­iar dis­po­si­tion, does this make them mus­lim, chris­tian, nei­ther or both? Fur­ther­more, if some­body re­ally wants to be­lieve that sound trav­els in space, then their be­lief may well pre­vail de­spite all ev­i­dence against it as the per­son cre­ates ‘ex­cep­tions’ to their be­liefs that they be­lieve do not dis­prove their the­ory. Hope this made sense...

• One might in­deed “be­lieve” all that. But a be­lief has no use if it isn’t true.

• Ap­ples and or­anges have more ways they are al­ike than not al­ike.

I always have to bring this up when some­one makes the “ap­ples to or­anges” state­ment. It’s only true so long as you are pur­pose­fully ig­nor­ing all the ways they are al­ike.

In other words, it is just as valid to com­pare ap­ples to or­anges as it is to com­pare fuji ap­ples to granny smith ap­ples.

That’s just me be­ing pedan­tic, but it re­ally seems to ap­ply in this par­tic­u­lar case.

• Ap­ples and or­anges are al­ike in more ways than they are not al­ike.

I always have to bring this up when some­one makes the “you can’t com­pare ap­ples to or­anges” state­ment. In fact, it is quite rea­son­able to com­pare ap­ples to or­anges. It’s also rea­son­able to com­pare ap­ples to eigh­teen-wheel­ers. It’s only un­rea­son­able when you are ex­plic­itly ig­nor­ing all the ways they are al­ike. Even then, it isn’t par­tic­u­larly un­rea­son­able to com­pare two things that are com­pletely dis­similar.

I’m be­ing a lit­tle pedan­tic, but it re­ally seems to ap­ply in this par­tic­u­lar case.

• What I gain from this ar­ti­cle is more or less an ex­am­ple of so­ciety’s in­fluence on how you un­der­stand things. For ex­am­ple, for most peo­ple 2+2=4. If the count­ing sys­tem and math op­er­a­tions was com­pletely differ­ent, 2+2 could equal any­thing, un­less one was fa­mil­iar with the high-con­text cul­ture us­ing such a sys­tem. Another ex­am­ple would be the pro­jec­tion of an idea with words. One may say ex­press their emo­tion as the word “happy”. Another may say “joy”. Another “eu­pho­ria”. Un­know­ingly, all three have the same ex­act emo­tion, only their words have their differ­ent con­no­ta­tions. Supris­ingly enough, I seem to have con­fused my­self. Does any­one want to try to dis­cern what I’ve said?

• This time I dis­agree with Eliezer...this ex­per­i­ment won’t con­vince me that 2+2=3...wouldn’t even con­vince me that phys­i­cal maxim “ev­ery­thing goes some­where” is wrong...I would find where the phones are (even if they sub­li­mated). That still don’t make that an “imutable be­lief”.

There’s noth­ing wrong in switch­ing lex­i­cally 3 and 4 ( S(2) = 4; S(4) = 3; S(3) = 5 )...sounds un­use­ful, and don’t at­tack Peano’s ax­ioms. That would make me be­lieve in 2+2=3.

To stop be­liev­ing in the in­te­ger num­bers, it’s needed to prove an in­con­sis­tency in Peano’s ax­ioms (even if their rep­re­sen­ta­tion is phys­i­cal, in­side the brain), and this ex­per­i­ment doesn’t prove that.

If the 2+2=3 gets usual in ev­ery em­piri­cal test I do, as sug­gested in this ar­ti­cle (no mat­ter how ab­surd it can seem to be), I wouldn’t stop be­liev­ing in the in­te­ger num­bers: I would have a NEW num­ber sys­tem (ax­ioms/​defi­ni­tions) with this char­ac­ter­is­tic (2+2=3). That’s a new model, and what was em­piri­cally falsified be­fore, was the link be­tween the old model and the phys­i­cal re­al­ity I could note, but not the old model it­self.

I’ve got cu­ri­ous about para­con­sis­tent log­ics in this case...

• Thanks for an ex­cel­lent post. I think you have summed up the dis­tinc­tion be­tween be­liefs aris­ing out of blind faith and those that are ob­ser­va­tion based.

• In re­sponse to g (a while back, con­cern­ing en­tropy): If physi­cists dis­cov­ered such a tech­nique, om­ni­science of a sort(by ar­bi­trar­ily al­ter­ing and mea­sur­ing the amount of in­for­ma­tion in a given re­gion) would be pos­si­ble, as would a form of om­nipo­tence (we could ar­range any con­ciev­able con­figu­ra­tion of par­ti­cles via Maxwell’s de­mon). Hook­ing it up to a com­puter with some knowl­edge base of usu­ally-ac­cepted morals to this quan­tum en­tropy-de­creas­ing con­struct, we would have om­nibenev­olence, also—hence, such a be­ing would, in­deed, be (an ap­prox­i­mate) God by most stan­dards. Ex­cept for hav­ing cre­ated the uni­verse (could it pos­si­bly be used with some as-yet-un­known the­ory of quan­tum grav­ity to cre­ate some mul­ti­verses, or a loope in space-time back to the Big Bang?), such a be­ing is about as close to a God as is log­i­cally pos­si­ble.

• “Cloud, you might want to read Steven Pinker’s ‘The Blank Slate’.”

Per­haps the term “blank slate” car­ries too much bag­gage. I only mean it with re­spect to the a pri­ori/​pos­te­ri­ori or ra­tio­nal­ism/​em­piri­cism. Dis­claimer: my eclec­tic sur­vey of much of Western thought has blurred the lines defin­ing these terms. So take from this what you will, but I can’t guaran­tee my­self be­ing clear.

• I re­call my mu­sic teacher once put a quote on the board which I shall now ad­just to the prob­lem: Take 2 piles of sand and 2 more piles of sand and add them to­gether. What do you get? 1 or more piles of sand.

Not di­rectly ap­pli­ca­ble to the gen­eral un­der­stand­ing of in­te­gers, but amus­ing to me. You could also do similar quib­bles with mu­si­cal tones or beats.

Then again it could all be rub­bish...for I don’t think I could ar­gue any of the points ar­gued so far, though I do find my at­tempt at un­der­stand­ing it en­joy­able if not com­plete.

• Yet if you counted the grains of sand, you would have as much sand as is con­tained in four piles of sand − 2+2=4.

This is the same as say­ing when I add 2+2 and get 4, I start with two num­bers and only get one num­ber. It’s true, but you’ve fooled your­self into be­liev­ing this is some profound math­e­mat­i­cal truth (and in a sense it is, but not the way you origi­nally thought), when in fact it was so ob­vi­ous to any­body who wasn’t try­ing to fool them­selves that it did not need point­ing out.

This is also the same as start­ing with two groups of two ap­ples, adding them to­gether, and get­ting one group of four ap­ples. I’m not dis­ap­pointed by this re­sult. In fact, the very rea­son I have four ap­ples is be­cause I have merged two groups of two ap­ples into a sin­gle group. The re­sult of this merger is four ap­ples.

• Yet if you counted the grains of sand, you would have as much sand as is con­tained in four piles of sand − 2+2=4.

Could you please define a “pile”? :3

• I’ve not read all of the com­ments, but those that I’ve read from you, Eliezer, in com­bi­na­tion with the origi­nal blog post, con­firm that we are in agree­ment. Re: Locke, I be­lieve we are blank slates when born. There is no such thing as a pri­ori (how do I ital­i­cize?). All think­ing, even log­i­cal and math­e­mat­i­cal rea­son­ing, is done a pos­te­ri­ori. Of what I’ve read, you’ve put it brilli­antly.

• It is pos­si­ble in to­day’s won­der­ful world of com­put­ers to have 2 + 2 = 3, and be both cor­rect and un­der­stand­able.

For In­stance:

We have two in­te­ger vari­ables x and y. Our equa­tion is x + x and the out­come is placed in y (ie. x + x = y) We will view the value of y.

We take the value 1.7 and in­put it into x. Since x is an in­te­ger it will (in most cases) be rounded to 2. There­fore x = 2.

It is pos­si­ble, how­ever, for y to re­ceive the value of 1.7 + 1.7 which, in to­day’s ac­cepted math, equals 3.4.

Plac­ing 3.4 in an in­te­ger vari­able will set y to 3.

There­fore, you have 2 + 2 = 3.

BTW, this is why do­ing float­ing point math with in­te­ger vari­ables on com­put­ers is a very bad idea......

• So the ac­tual end re­sult would be to con­vince me that the uni­verse was in the hands of a mon­strously in­sane and vi­cious God. As I noted here, that is ac­tu­ally pretty much what I be­lieved in the last days of my Chris­ti­an­ity. My per­spec­tive on ethics made it more plau­si­ble to me than I sus­pect it would be to most peo­ple.

The whole point of Chris­ti­an­ity (as I grew up with it) is that by man­i­fest­ing Him­self on earth God re­al­ized that the whole smit­ing peo­ple thing was passe. I always thought the God of the New Tes­ta­ment was just that of the Old with bet­ter mar­ket­ing, though of course I found the lat­ter more in­ter­est­ing.

Eliezer, the things you are say­ing here about math are just the type of things I was at­tempt­ing to here, but you’re much bet­ter at it.

• I draw the line at P AND ~P, though: just un­think­able.

I’ve heard re­li­gious peo­ple pro­fess be­liefs of this na­ture. I don’t think they ac­tu­ally be­lieve it, but I don’t think it’s pure be­lief-in-be­lief ei­ther; I see it as an at­tempt to ex­plain a deeply un­usual sub­jec­tive ex­pe­rience in poorly suited lan­guage. (Which is not to say I think any state­ments like that are meta­phys­i­cally true or any­thing.)

I do think there’s some­thing to “a pri­ori” be­sides a mere se­man­tic stop­sign, though. I could model phys­i­cally pos­si­ble wor­lds with differ­ent con­tents, or log­i­cally pos­si­ble wor­lds with differ­ent physics, but I can’t imag­ine how I could model (as op­posed to loosely imag­ine) a uni­verse where 2+2=3. Eliezer, would you hold that such a world is ac­tu­ally con­structable and mod­e­lable in ad­di­tion to imag­in­able? Do you think “nec­es­sary” and “con­tin­gent” or “log­i­cally pos­si­ble”/​”im­pos­si­ble” are se­man­tic stop­signs too?

• “It ap­pears to me that “a pri­ori” is a se­man­tic stop­sign; its only visi­ble mean­ing is “Don’t ask!”″

No, a pri­ori rea­son­ing is what math­e­mat­i­ci­ans do for a liv­ing. De­spite op­er­at­ing en­tirely by means of se­man­tic stop­signs, math­e­mat­ics seems nev­er­the­less to en­joy rude health.

• I con­cede (a lit­tle)!

In a pre­vi­ous Over­com­ing Bias post we learned that peo­ple some­times be­lieve the con­junc­tion of events R and Q is more prob­a­ble than event Q alone. Thus peo­ple can be­lieve sim­ple and strictly illog­i­cal things, and so I shouldn’t throw around the word “un­think­able.”

If I stretch my imag­i­na­tion, I can just maybe imag­ine this sort of log­i­cal blun­der with small in­te­gers.

I draw the line at P AND ~P, though: just un­think­able.

• This sen­tence of Eliezer’s is where the ac­tion is:

I’m sus­pi­cious of claims that sup­pos­edly do not re­quire jus­tifi­ca­tion and yet seem to be uniquely preferred within a rather large space of pos­si­bil­ities.

“There are no mar­ried bach­e­lors” gets us to nod our heads be­cause we uniquely pre­fer English syn­tax and se­man­tics. We pick it out of the rather large space of pos­si­ble lan­guages be­cause it’s what ev­ery­one else is do­ing.

If Eliezer went around earnestly say­ing, “there are some mar­ried bach­e­lors,” I would guess he had en­tan­gled him­self with an en­vi­ron­ment where peo­ple go around say­ing such things, with a differ­ent pos­si­ble lan­guage.

Eliezer in­sists that he could be en­tan­gled with ev­i­dence such that he be­lieves “there are some mar­ried bach­e­lors” is true in English as we know it. I don’t think he could; that propo­si­tion is un­think­able in good English.

• It is perfectly ac­cept­able for me to say, “I can think of no en­coun­ter­able situ­a­tion that would trans­form the ter­mi­nal value of this event from nega­tive to pos­i­tive.”

Now, don’t make me bring up a trolly prob­lem. :-)

• Math­e­mat­ics is about log­i­cal pat­terns. A world in which you can be mis­taken about such fun­da­men­tals as the value of 2 + 2 is not a world where you can put any trust in your log­i­cal de­duc­tions. As such, if you ever do no­tice such a slip, I sug­gest that the cause is likely to be some­thing deeply wrong with you, your­self, and not that you are liv­ing in a com­puter simu­la­tion.

The test of any re­li­gion is whether cul­tures be­liev­ing it tend to thrive and im­prove the qual­ity of their lives or not. The whole point of the word of God is that fol­low­ing it gives your life “eu­daimo­nia”, as Aris­to­tle put it. The Com­mu­nist re­li­gion, for ex­am­ple, failed mis­er­ably, and the cur­rent sec­u­lar liberal re­li­gion seems to be failing at the “thrive” part. Western fla­vors of the Chris­tian re­li­gion seem to have done pretty well over the last mil­len­nium or so, so the move away from it over the last cen­tury seems strange. Is­lam is good at thriv­ing, but seems poor at im­prov­ing qual­ity of life.

In­ci­den­tally, the most fun­da­men­tal test of Chris­ti­an­ity is meant to be be­lief in the Nicene creed, which is per­haps the best test of whether you be­lieve if “Chris­ti­an­ity is true” or not.

• “The test of any re­li­gion is whether cul­tures be­liev­ing it tend to thrive and im­prove the qual­ity of their lives or not.”

Um, I’m pretty sure the test of a re­li­gion is whether or not the model of re­al­ity pro­posed by that re­li­gion cor­re­sponds with ac­tual re­al­ity or not (sorry I’m not sure how to phrase this in terms of a “test”, with­out as­sum­ing the val­idity of sen­sory in­put). This is par­tic­u­larly no­tice­able in the case of re­li­gions which claim af­ter­lives, where any im­pact of earthly ac­tions on our af­ter­life ut­terly out­weigh any im­pact that a re­li­gion has on earthly con­di­tions. The very idea of de­bat­ing whether a re­li­gion im­proves our qual­ity of life on earth only makes sense from an Athe­ist or Ag­nos­tic view­point, con­sid­er­ing whether that re­li­gion can be used as a prac­ti­cal tool re­gard­less of it’s truth.

• I’m nei­ther Eliezer nor (so far as you know) an AGI, but I think (1) I couldn’t be con­vinced by ev­i­dence that be­liefs should not re­spond to ev­i­dence but (2) I could be led by ev­i­dence to aban­don my be­lief that they should. (Prob­a­bly along with most of my other be­liefs.) What it would take for that would be a sys­tem­atic failure of be­liefs ar­rived at by as­sess­ing ev­i­dence to match any bet­ter with fu­ture ev­i­dence than be­liefs ar­rived at in other ways. I think that would ba­si­cally re­quire that fu­ture ev­i­dence to be ran­dom; in fact that’s roughly what “ran­dom” means. I’m not sure that I can ac­tu­ally imag­ine a world like that, though.

I think Doug should amend his crite­rion to say ”… with no sign of any in­crease in en­tropy el­se­where”. But it seems to me that a be­ing with no power other than (say) be­ing able to in­duce mod­estly sized tem­per­a­ture gra­di­ents would not thereby qual­ify to be called a god. (If physi­cists an­nounce to­mor­row that the sec­ond law of ther­mo­dy­nam­ics can be cheated by some cun­ning tech­nique with the word “quan­tum” in it, are we sud­denly all gods?) And if the power is suffi­ciently limited (it takes time, and only op­er­ates on a small re­gion of space, and the tem­per­a­ture gra­di­ent in­duced is very small) then it doesn’t even qual­ify as god-like power in my book. But I ex­pect Doug wasn’t be­ing perfectly se­ri­ous.

What do you mean by “doesn’t pre­sent any se­ri­ous prob­lems”? That you have no trou­ble think­ing of ev­i­dence that would suffice to con­vince you of those things? (If so, I agree.) (It’s not fair to blame Ben for pick­ing “Chris­ti­an­ity is true” in­stead of some­thing more spe­cific; he was just copy­ing Eliezer.)

• “I’m not sure that I can ac­tu­ally imag­ine a world like that, though.”

A com­puter simu­la­tion with in­finite pro­cess­ing power that runs a per­son from an ini­tial state (the stan­dard one is solely based on their ge­net­ics, but for your ex­per­i­ment we could use a brain down­load of a given hu­man from part­way through their life) through all pos­si­ble se­quences of sen­sory in­puts.

• Eliezer: It sure seems to me that our evolu­tion and cul­ture con­structed eth­i­cal at­ti­tudes are en­tan­gled with the world. By the way, I don’t think that we agree at all about what “I find it quite easy to imag­ine” means, but of course, some words, like “I”, are tricky. It might be more in­ter­est­ing to ask “what data could I give a soundly de­signed AGI that would con­vince it that 2+2=3?” For you and for sound AGI de­signs, I’d like to know what situ­a­tion would be con­vinc­ing re­gard­ing the propo­si­tion “be­liefs should not re­spond to ev­i­dence or to rea­son­ing”.

Doug: we can all re­duce en­tropy in phys­i­cal sys­tems. This does, how­ever, re­quire that we act upon those sys­tems, but the god you are dis­cussing would also be act­ing upon the sys­tems where it re­versed en­tropy, right?

Ben: I’m pretty sure that “Chris­ti­an­ity is true” is not a hy­poth­e­sis. Believ­ing some­thing more spe­cific, like Je­sus was born to a Vir­gin and re­turned 3 days af­ter be­ing buried doesn’t pre­sent any se­ri­ous prob­lems.

• I just op­er­ate un­der the as­sump­tion that I will never ac­tu­ally en­counter a situ­a­tion where 2+2 does not equal 4, and there­fore do not spend time wor­ry­ing about such a hy­po­thet­i­cal situ­a­tion. This as­sump­tion has never failed me be­fore.

• I don’t quite get what hap­pens. Does imag­in­ing two and two to­gether give same men­tal image as imag­in­ing two and one to­gether? Does putting two and two earplugs to­gether give same re­sult as putting two and one earplug to­gether? If it does, then I take 4 earplugs, put two and one to­gether and put other into my ear, then two and one are same as two and two to­gether, so I should be able to sep­a­rate it into two and two, and and then I have two earplugs on my hands, two in a box, and one in my ear. I do it the sec­ond time and I can’t hear any­thing, but I have all the earplugs I had in the box. This would be some very cool magic.

If it does not, I don’t get what ac­tu­ally changed. I would sus­pect le­sion in lex­i­cal re­gion of the brain that makes me con­fused and makes me mi­s­un­der­stand the world from then on, in­ter­pret­ing 4 as 3 ev­ery time, but not when fetch­ing from mem­ory. Alter­na­tively, a failure dur­ing fetch­ing from mem­ory is pos­si­ble. That is plau­si­ble, and might even have hap­pened to some­one. The prob­a­bil­ity that i did screw up in the past would have gone up maybe from 0.001 to 0.01 (num­ber just to illus­trate) but wouldn’t go any higher. The prob­a­bil­ities for fancy al­ter­na­tive world stuff would go from maybe 1E-9 to 1E-8 , edit: scratch that, con­spir­a­cies and gods mess­ing with simu­la­tor i won’t con­sider due to it’s lack of pre­dic­tive value and hence zero ex­pected util­ity from con­sid­er­ing it.

edit: to clar­ify. 2+2=3 is an ill defined state­ment that means noth­ing to me un­til it is speci­fied what ex­actly 2, 3, +, = mean, in such a way that I can at least eval­u­ate truth of 2+2 = 2+1 and a cou­ple other state­ments (such as sep­a­rat­ing 3 into 2 and 2). I could just as well re­ply to you in Chi­nese (and if re­ply is not very long and you have no ac­cess to the suffi­cient body of Chi­nese texts, it will be en­tirely im­pos­si­ble for you to un­der­stand it)

•        A mid­dle aged woman is charged with the task of count­ing ob­jects(or­anges, ap­ples, earplugs) in­di­vi­d­u­ally and in pairs as they roll onto a con­veyer belt she no­tices that they come in or­der of ( OOO,A A, E) and has performed this job for sev­eral years. The woman de­vises a for­mula for count­ing these ob­jects she places a [ 1 in column 3 ] for a set of or­anges that pass by, then a [ 1 in column 2 ] for the pair of ap­ples that pass by, she then places a [ 1 in column 1 ] for the earplug. So by look­ing at her count of the line (OOO,AA,E,OOO,AA,E) or  2+2+2=6 pairs and by sub­sti­tut­ing the for­mula 3(O)+2(A)+E=to­tal ob­jects or 2+2+2=12. One morn­ing the woman looked down at her night table and saw two ap­ples an ear plug then two more ap­ples then an­other earplug lay­ing on the floor is it pos­si­ble that her mind de­ducted 2+2=3?

We learn by ex­pe­rience and shaped by the ge­net­ics passed on to us by our par­ents. We start out as a blank page ex­cept for the most pri­mal urges. We are then feed sights, sounds, tastes, touches and then brain washed into a so­ciety of hyp­ocrites and string pul­lers push­ing us always to­wards medi­ocrity. I be-leave one could be born to Is­lam or any other re­li­gion  and later dis­cover they no longer be­lieve. Man is driven in­stinc­tively by com­fort, if some­thing is painful, un­com­fortable, mi­s­un­der­stood, cheer­ful or calming we al­ign these feel­ings with ac­tions. For ex­am­ple a child born to Is­lam may find the teach­ings com­fort­ing and pro­claim Ala the di­v­ine cre­ator. On the other hand the child may wit­ness hard­ship and loss and re­al­ize through pain and sor­row that the only one listen­ing is him­self and de­nounce Ala, he then will try to find peace through com­fort.
`
• I can­not con­ceive of a pos­si­ble world where “mak­ing XX and XX come out to XXXX re­quired an ex­tra X to ap­pear from nowhere, and was, more­over, in­con­sis­tent with other ar­ith­metic I vi­su­al­ized, since sub­tract­ing XX from XXX left XX, but sub­tract­ing XX from XXXX left XXX.” Un­less, in that pos­si­ble world I did not know how to rea­son. If 2 + 2 re­ally was 3, what would 1 + 2 be? Not 4, since then 2+2 = 2+1 and since sub­trac­tion is defined as the in­verse of ad­di­tion (if its not, its not sub­trac­tion) we would have 0 = 1. Not 3, since in the world you’re imag­in­ing 3 – 2 = 2 so than if 2+1 = 3 we can sub­sti­tute it for 3 (be­cause it ‘is the very same thing as 3’) and get 2+1-2=2 and since ad­di­tion is com­mu­ta­tive (its just putting 2 things to­gether and I can’t con­ceive of the or­der mat­ter­ing) we would again have 1 = 0. Now, you can write a post about an imag­i­nary world where ad­di­tion is not com­mu­ta­tive or where things have differ­ent prop­er­ties than them­selves (so I can’t sub­sti­tute 2+1 for 3) or where the set of in­te­gers is not closed un­der ad­di­tion but they wouldn’t be con­ceiv­able. Yes I can con­ceive of putting 2 ear plugs next to 2 ear plugs and be­ing left with 3 but even if that hap­pened I would still be­lieve that 2+2 = 4

• This time I dis­agree with Eliezer...this ex­per­i­ment won’t con­vince me that 2+2=3...wouldn’t even con­vince me that phys­i­cal maxim “ev­ery­thing goes some­where” is wrong...I would find where the earplugs are (even if they sub­li­mated). That still don’t make that an “imutable be­lief”.

There’s noth­ing wrong in switch­ing lex­i­cally 3 and 4 ( S(2) = 4; S(4) = 3; S(3) = 5 )...sounds un­use­ful, and don’t at­tack Peano’s ax­ioms. That would make me be­lieve in 2+2=3.

To stop be­liev­ing in the in­te­ger num­bers, it’s needed to prove an in­con­sis­tency in Peano’s ax­ioms (even if their rep­re­sen­ta­tion is phys­i­cal, in­side the brain), and this ex­per­i­ment doesn’t prove that.

If the 2+2=3 gets usual in ev­ery em­piri­cal test I do, as sug­gested in this ar­ti­cle (no mat­ter how ab­surd it can seem to be), I wouldn’t stop be­liev­ing in the in­te­ger num­bers: I would have a NEW num­ber sys­tem (ax­ioms/​defi­ni­tions) with this char­ac­ter­is­tic (2+2=3). That’s a new model, and what was em­piri­cally falsified be­fore, was the link be­tween the old model and the phys­i­cal re­al­ity I could no­tice, but not the old model it­self.

I’ve got cu­ri­ous about para­con­sis­tent log­ics in this case...

• I think the key is to look at re­li­gion in eco­nomic terms. Ra­tional be­ings will max­i­mize util­ity. To a sci­en­tist, it may seem ir­ra­tional not to ques­tion ev­ery as­pect about life and our ex­is­tence. To a re­li­gious per­son, eter­nal ques­tion­ing may seem like a waste of time. What is the differ­ence to me, from a purely self­ish point of view, whether or not God cre­ated ev­ery­thing and sent down a son/​prophet/​what have you? I can ac­cept it as truth with no harm to my­self, leav­ing my time free to pur­sue more pro­duc­tive ac­tivity—so why shouldn’t I?

There are many peo­ple who con­vert from one re­li­gion to an­other, thus pro­vid­ing demon­stra­ble ev­i­dence that the be­liefs can be swayed given an ap­pro­pri­ate change in util­ity func­tion. Per­haps it for mar­riage or other so­cial in­ter­ac­tions, per­haps be­cause a differ­ent set of be­liefs car­ries more res­o­nance eth­i­cally or log­i­cally.

As to the “mon­strously in­sane and vi­cious God” you as­so­ci­ate with Chris­ti­an­ity, you (along with a good many Chris­ti­ans) are con­fus­ing Him with the Ju­daic God of the Old Tes­ta­ment. The whole point of Chris­ti­an­ity (as I grew up with it) is that by man­i­fest­ing Him­self on earth God re­al­ized that the whole smit­ing peo­ple thing was passe.

• I’m go­ing to go ahead and offer a differ­ing opinion re­gard­ing Chris­ti­an­ity. o_o; First of all, much of the “God is vile and in­sane” protest can be miti­gated by re­mem­ber­ing that, if the Chris­tian God ex­ists, then this life is a tiny piece of our en­tire ex­is­tence, and that death is far from the worst pos­si­ble out­come. If you try to jus­tify the Chris­tian God’s ethics based on con­clu­sions you’ve reached by dis­be­liev­ing in Him, your premises are con­tra­dic­tory.

And sec­ond, God has in­di­cated many times that He does not change. (Yes, a few of those were not from God di­rectly, but it doesn’t mat­ter). So I don’t know why a brief stint on Earth would change His mind, par­tic­u­larly about moral­ity, since He’s sup­posed to be in­finitely just...

I just… no, I re­ally am cu­ri­ous now. This doc­trine seems to be all sorts of self-con­tra­dic­tory. In which church did you grow up?

• I’m go­ing to go ahead and offer a differ­ing opinion re­gard­ing Chris­ti­an­ity. o_o; First of all, much of the “God is vile and in­sane” protest can be miti­gated by re­mem­ber­ing that, if the Chris­tian God ex­ists, then this life is a tiny piece of our en­tire ex­is­tence, and that death is far from the worst pos­si­ble out­come. If you try to jus­tify the Chris­tian God’s ethics based on con­clu­sions you’ve reached by dis­be­liev­ing in Him, your premises are con­tra­dic­tory.

If you try to jus­tify the Chris­tian God’s ethics based on the bible’s own as­ser­tions of his jus­tice and in­fal­li­bil­ity, your ar­gu­ment is cir­cu­lar. Con­clu­sions based on be­lief or dis­be­lief in God are ir­rele­vant to judg­ing his moral­ity ac­cord­ing to the por­trait painted in holy texts, we already have our own moral toolkit to work with.

I don’t see how it re­motely miti­gates any charges of vile­ness or in­san­ity to posit that God hands out re­wards of eter­nal bliss or pun­ish­ments of eter­nal suffer­ing for be­liefs and/​or ac­tions with­out mak­ing his ex­pec­ta­tions clear. That’s neg­li­gence be­yond the scale of crim­i­nal­ity. No mat­ter how sure you are that you un­der­stand what God wants, if he had ac­tu­ally made his mes­sage clear and well ev­i­denced, your be­liefs would not be a minor­ity wor­ld­wide. Any in­tel­li­gent and com­pe­tent hu­man who wanted to get a co­her­ent mes­sage across could do bet­ter. Hell, schol­ars have bet­ter agree­ment on what Niet­zsche meant, and he was be­ing de­liber­ately ob­scure.

• Con­clu­sions based on be­lief or dis­be­lief in God are ir­rele­vant to judg­ing his moral­ity ac­cord­ing to the por­trait painted in holy texts

As moral­ity is en­tan­gled with re­al­ity, (in­cor­rect) con­clu­sions about any­thing are po­ten­tially rele­vant to judg­ing moral­ity.

I don’t see how it re­motely miti­gates any charges of vile­ness or insanity

I won­der how read­ily be­liev­ers would, in a sort of plea bar­gain, ac­cept and em­brace the charge of in­san­ity, with all its con­no­ta­tions, if it were thought the ob­vi­ously at­trac­tive horn of the dilemma, with no other al­ter­na­tives.

I’m imag­in­ing what re­li­gious in­sti­tu­tions and liter­a­ture would look like if, say, one out of ev­ery ten ad­jec­tives refer­ring to a de­ity in hymns, psalms, etc. were re­placed with “in­sane” or one of its syn­onyms.

• snerk I’m sad to say that the an­swer is “rather read­ily, for some”. I’ve got­ten into heated de­bates—heated be­cause they ended with me throw­ing my hands up in the air, ap­palled at the will­ing ig­no­rance of my op­po­nent—about whether God fol­lows the same ba­sic rules of logic that we do. It’s as­ton­ish­ing. I’m sure if you were to start a Protes­tant move­ment say­ing that “God is in­sane, but we fol­low Him any­way”, you’d get fol­low­ers by the truck­load.

By Oc­cam’s ra­zor, we must con­clude that the ba­sic ten­ants of logic we have in this life will not cease to be true in the next. Then again, Oc­cam’s ra­zor de­pends on Oc­cam’s ra­zor for its ve­rac­ity… :3 If you wanna talk about cir­cu­lar ar­gu­ments.

And I agree with your state­ment re: in­cor­rect con­clu­sions; thank you.

EDIT: Man, this 10-minute lag is kil­ling me. O_o;

• Just out of cu­ri­os­ity, if you for some rea­son val­ued above all else, faith (of the sort where the more ev­i­dence the less faith), how would you go about max­i­miz­ing it? If you made the faith too uni­ver­sal, that it­self might be ev­i­dence of its truth (and thereby re­duce the value of the faith). Can you prove that there is an ab­solute moral­ity, such that valu­ing faith above ra­tio­nal­ity is nec­es­sar­ily im­moral (as op­posed to re­ally in­con­ve­nient, or seems im­moral to most peo­ple)?

PS: Many Chris­ti­ans get an­noyed if you sug­gest that you can just be­lieve in Je­sus af­ter you die, like peo­ple who lived be­fore Je­sus. They’ll get even more an­noyed if you ask them where in the Bible it says oth­er­wise.

• if you for some rea­son val­ued above all else, faith (of the sort where the more ev­i­dence the less faith), how would you go about max­i­miz­ing it?

To op­ti­mize that kind of faith, just put ev­ery per­son in a sep­a­rate uni­verse tai­lored to con­tain max­i­mally weak ev­i­dence for a propo­si­tion P, then make them in­sane (e.g., with tor­ture, brain­wash­ing, or in­nate cog­ni­tive bi­ases) un­til they delu­sively be­lieve in P de­spite the lack of ev­i­dence. Since each per­son gets their own pocket uni­verse, they needn’t be ex­posed to any other per­son ca­pa­ble of com­mu­ni­cat­ing to them sup­port­ing ev­i­dence for P.

Can you prove that there is an ab­solute moral­ity, such that valu­ing faith above ra­tio­nal­ity is nec­es­sar­ily immoral

Define “ab­solute moral­ity” and “prove”. If noth­ing can even be ev­i­denced about moral­ity, then I can safely ig­nore the ques­tion and just ask about what ac­tu­ally benefits peo­ple. Believ­ing true things gen­er­ally helps peo­ple have hap­pier, more peace­ful lives filled with more love and beauty; is the lu­natic in the asy­lum a paradigm of hu­man flour­ish­ing?

If you think that’s not uni­ver­sally the case, then OK. But you must think so be­cause you have ac­tual ev­i­dence for the value of faith. If I have no ev­i­dence that Zeus is Lord but think that’s OK be­cause faith is a virtue, I still need to provide some ev­i­dence that faith in the propo­si­tion ‘Zeus is Lord’ is a virtue. If I ap­peal to faith in faith, as op­posed to just faith in Zeus, then I’ve made the con­tent of faith ar­bi­trary, which means that any re­li­gious claim can be jus­tified, not just my own re­li­gious claim.

• To op­ti­mize that kind of faith, just put ev­ery per­son in a sep­a­rate uni­verse tai­lored to con­tain max­i­mally weak ev­i­dence for a propo­si­tion P, then make them in­sane (e.g., with tor­ture, brain­wash­ing, or in­nate cog­ni­tive bi­ases) un­til they delu­sively be­lieve in P de­spite the lack of ev­i­dence. Since each per­son gets their own pocket uni­verse, they needn’t be ex­posed to any other per­son ca­pa­ble of com­mu­ni­cat­ing to them sup­port­ing ev­i­dence for P.

In other words, lit­tle to no prac­ti­cal differ­ence from what we live in. There’s wide­spread be­lief in God (very weak ev­i­dence but ex­cel­lent priv­ileg­ing of the hy­poth­e­sis), the threat of fu­ture tor­ture (and cur­rent so­cial pres­sures), in­doc­tri­na­tion from an early age, and we cer­tainly have plenty of cog­ni­tive bi­ases (many of which are geared to prefer­ring things with pos­i­tive con­se­quences). The main differ­ence with your sce­nario is the in­ter­ac­tion with other peo­ple—but it can be ar­gued that other peo­ple are very poor ev­i­dence for the ex­is­tence of God, com­pared to eg pro­vid­ing a non-the­is­tic ex­pla­na­tion to where you came from.

I’m point­ing out that P(the world we live in | a God that val­ues faith) is very high, and es­sen­tially in­dis­t­in­guish­able from P(the world we live in | there is no God). This is no co­in­ci­dence, as oth­er­wise peo­ple who be­lieved in a God that val­ues faith would be con­stantly sur­prised by the world we live in. Note that if some­one who be­lieves in a God that val­ues faith, claims to have found strong ob­jec­tive ev­i­dence for the ex­is­tence of their God, they’re co­in­ci­den­tally also claiming to have found strong ev­i­dence that said god doesn’t value faith (ie, ev­i­dence for some other god).

(I’m not try­ing to mi­suse the rep­re­sen­ta­tive­ness heuris­tic, just point­ing out that if our world wasn’t rep­re­sen­ta­tive of some pop­u­lar god, be­lief in that god would die out, like with Zeus.)

Define “ab­solute moral­ity” and “prove”. If noth­ing can even be ev­i­denced about moral­ity, then I can safely ig­nore the ques­tion and just ask about what ac­tu­ally benefits peo­ple.

If noth­ing can be ev­i­denced about moral­ity, than what you just did is called “beg­ging the ques­tion”.

I wrote my above post be­cause I was in­trigued by Des­r­topa’s claim that it would be im­moral and/​or in­sane for God to hand out epic pun­ish­ments and re­wards based on [the per­son’s un­ev­i­denced faith] with­out mak­ing it clear to ev­ery­one that He wanted [un­ev­i­denced faith].

• In other words, lit­tle to no prac­ti­cal differ­ence from what we live in.

.. No. If our uni­verse were op­ti­mized for max­i­mal faith in Chris­ti­an­ity, there would be no Chris­ti­ans other than you, much more con­clu­sive em­piri­cal ev­i­dence (e.g., im­pos­si­ble-to-fake video footage) show­ing that Je­sus did not rise from the dead, etc., and your brain would just come pre-wired to be­lieve in Je­sus with equal and max­i­mal con­fi­dence no mat­ter what ev­i­dence you en­coun­tered. Ba­si­cally your brain would just be a cir­cuit that chants ‘JESUS IS LORD’, as­so­ci­ated with a strong con­vic­tion-feel­ing, and seeks out and ab­sorbs as much Chris­ti­an­ity-re­fut­ing ev­i­dence as pos­si­ble, with­out hav­ing any mechanism for mod­ify­ing the ‘JESUS IS LORD’ con­vic­tion pump in your brain.

If built-in be­liefs aren’t al­lowed, then the sec­ond best step would be to liter­ally tor­ture you—like, you’ve never lived a day of your life with­out un­der­go­ing some­thing roughly as un­pleas­ant as scaphism—un­til you’re driven liter­ally in­sane and can do noth­ing but grind your teeth and gib­ber end­lessly about Je­sus be­ing lord. That’s much, much closer to what a uni­verse op­ti­mized for faith (and faith alone) would look like. We aren’t liter­ally in such a uni­verse; any com­par­i­son of your own day-to-day ex­is­tence to ac­tual tor­ture must sug­gest ei­ther a loose grasp on the English lan­guage, or a fun­da­men­tal mi­s­un­der­stand­ing of just what real tor­ture is like.

Cer­tainly vague, hand-wavey threats are not op­ti­miz­ing for un­jus­tified-be­lief. Threats can’t drive most peo­ple past the brink of mad­ness, ar­guably can’t in­spire be­lief at all. Try wav­ing a gun around and threat­en­ing to kill some­one, or kill eir fam­ily, if ey doesn’t spon­ta­neously be­lieve that the Moon is made of green cheese. The per­son might claim to be­lieve the Moon is made of green cheese, but they wouldn’t ac­tu­ally be­lieve.

oth­er­wise peo­ple who be­lieved in a God that val­ues faith would be con­stantly sur­prised by the world we live in

That’s not how hu­man be­lief works. Hu­mans do not au­to­mat­i­cally no­tice their con­fu­sion in all in­stances, nor do they au­to­mat­i­cally form in­ter­nally con­sis­tent be­lief struc­tures with­out putting any work into it. ‘Per­son X be­lieves strongly in Y’ does not in gen­eral sug­gest ‘the ev­i­dence available to per­son X is over­whelm­ingly pre­dicted by the truth of Y’.

Note that if some­one who be­lieves in a God that val­ues faith, claims to have found strong ob­jec­tive ev­i­dence for the ex­is­tence of their God, they’re co­in­ci­den­tally also claiming to have found strong ev­i­dence that said god doesn’t value faith

Doesn’t this ap­ply to you? You just claimed to have strong ev­i­dence that your God’s ex­is­tence pre­dicts the em­piri­cal world ap­prox­i­mately as well as your God’s nonex­is­tence does. But a God who ac­tu­ally val­ued faith would make sure that his hy­poth­e­sis seemed to do a worse job of pre­dict­ing the world, so that more faith was re­quired to ac­cept him. Every time you re­fute one of my ar­gu­ments, your faith weak­ens.

Doesn’t this strike you as a slightly odd ob­ses­sion for a cre­ator-of-ev­ery­thing? Self-de­cep­tion and bad ar­gu­ments, as ends in them­selves? It at least strikes me as odd.

• Doesn’t this ap­ply to you? You just claimed to have strong ev­i­dence that your God’s ex­is­tence pre­dicts the em­piri­cal world ap­prox­i­mately as well as your God’s nonex­is­tence does.

Yes, but I didn’t claim it as ev­i­dence of any­thing other than that such be­lief isn’t par­tic­u­larly mal­adap­tive (con­se­quence­less be­liefs won’t in­terfere with your pre­dic­tive power). If it helps you un­der­stand my point, P(the world we live in | in­visi­ble uni­corns in a far away galaxy fart rain­bows) is also very high, which is not at all an ar­gu­ment in fa­vor of in­visi­ble uni­corns (only that there’s no ev­i­dence against uni­corns nor will be­liev­ing in uni­corns there­fore re­sult in poor pre­dic­tions).

To the ex­tent that be­lief in a God that val­ues faith is con­se­quence­less, it can’t be mal­adap­tive. To the ex­tent that such be­lief has con­se­quences, it will make pre­dic­tions about the real world. Mak­ing pre­dic­tions about the real world means they can test the be­lief, which re­gard­less of the re­sult will be sus­pect (one way, it is ev­i­dence against their be­lief in God, the other way ev­i­dence against their be­lief that God val­ues faith).

My point is that most Chris­ti­ans don’t think through the con­se­quences of claiming that some­thing is ev­i­dence for God. Why have faith if they’re ar­gu­ing that their be­lief is a sci­en­tifi­cally ver­ifi­able one—in such a case, faith would be more likely to mis­lead them than sci­ence.

Long story short, if you find your­self ar­gu­ing with a Chris­tian about whether some­thing is or isn’t ev­i­dence for God, you could have cut the whole thing short by ask­ing them “Will your sug­ges­tion let me test for the ex­is­tence of God?” Not only is there only one rea­son­able way they can an­swer, there’s speci­fi­cally a com­mand against test­ing God.

• One should be care­ful with con­text here...

I’m en­tirely jus­tified in claiming that 2 + 2 = 1, or 2 + 2 = 0 in some situ­a­tions, and such a claim is quite math­e­mat­i­cally sound.