You’re Entitled to Arguments, But Not (That Particular) Proof

Fol­lowup to: Log­i­cal Rudeness

“Modern man is so com­mit­ted to em­piri­cal knowl­edge, that he sets the stan­dard for ev­i­dence higher than ei­ther side in his dis­putes can at­tain, thus suffer­ing his dis­putes to be set­tled by philo­soph­i­cal ar­gu­ments as to which party must be crushed un­der the bur­den of proof.”
-- Alan Crowe

There’s a story—in ac­cor­dance with Poe’s Law, I have no idea whether it’s a joke or it ac­tu­ally hap­pened—about a cre­ation­ist who was try­ing to claim a “gap” in the fos­sil record, two species with­out an in­ter­me­di­ate fos­sil hav­ing been dis­cov­ered. When an in­ter­me­di­ate species was dis­cov­ered, the cre­ation­ist re­sponded, “Aha! Now there are two gaps.”

Since I’m not a pro­fes­sional evolu­tion­ary biol­o­gist, I couldn’t be­gin to rat­tle off all the ways that we know evolu­tion is true; true facts tend to leave traces of them­selves be­hind, and evolu­tion is the hugest fact in all of biol­ogy. My spe­cialty is the cog­ni­tive sci­ences, so I can tell you of my own knowl­edge that the hu­man brain looks just like we’d ex­pect it to look if it had evolved, and not at all like you’d think it would look if it’d been in­tel­li­gently de­signed. And I’m not re­ally go­ing to say much more on that sub­ject. As I once said to some­one who ques­tioned whether hu­mans were re­ally re­lated to apes: “That ques­tion might have made sense when Dar­win first came up with the hy­poth­e­sis, but this is the twenty-first cen­tury. We can read the genes. Hu­man be­ings and chim­panzees have 95% shared ge­netic ma­te­rial. It’s over.

Well, it’s over, un­less you’re crazy like a hu­man (iron­i­cally, more ev­i­dence that the hu­man brain was fash­ioned by a sloppy and alien god). If you’re crazy like a hu­man, you will en­gage in mo­ti­vated cog­ni­tion; and in­stead of fo­cus­ing on the un­think­ably huge heaps of ev­i­dence in fa­vor of evolu­tion, the in­nu­mer­able signs by which the fact of evolu­tion has left its heavy foot­prints on all of re­al­ity, the un­counted ob­ser­va­tions that dis­crim­i­nate be­tween the world we’d ex­pect to see if in­tel­li­gent de­sign ruled and the world we’d ex­pect to see if evolu­tion were true...

...in­stead you search your mind, and you pick out one form of proof that you think evolu­tion­ary biol­o­gists can’t provide; and you de­mand, you in­sist upon that one form of proof; and when it is not pro­vided, you take that as a re­fu­ta­tion.

You say, “Have you ever seen an ape species evolv­ing into a hu­man species?” You in­sist on video­tapes—on that par­tic­u­lar proof.

And that par­tic­u­lar proof is one we couldn’t pos­si­bly be ex­pected to have on hand; it’s a form of ev­i­dence we couldn’t pos­si­bly be ex­pected to be able to provide, even given that evolu­tion is true.

Yet it fol­lows illog­i­cally that if a video tape would provide definite proof, then, like­wise, the ab­sence of a video­tape must con­sti­tute definite dis­proof. Or per­haps just ren­der all other ar­gu­ments void and turn the is­sue into a mere mat­ter of per­sonal opinion, with no one’s opinion be­ing bet­ter than any­one else’s.

So far as I can tell, the po­si­tion of hu­man-caused global warm­ing (an­thro­pogenic global warm­ing aka AGW) has the ball. I get the im­pres­sion there’s a lot of ev­i­dence piled up, a lot of peo­ple try­ing and failing to poke holes, and so I have no rea­son to play con­trar­ian here. It’s now heav­ily poli­ti­cized sci­ence, which means that I take the as­ser­tions with a grain of skep­ti­cism and worry—well, to be hon­est I don’t spend a whole lot of time wor­ry­ing about it, be­cause (a) there are worse global catas­trophic risks and (b) lots of other peo­ple are wor­ry­ing about AGW already, so there are much bet­ter places to in­vest the next marginal minute of worry.

But if I pre­tend for a mo­ment to live in the main­stream men­tal uni­verse in which there is noth­ing scarier to worry about than global warm­ing, and a 6 °C (11 °F) rise in global tem­per­a­tures by 2100 seems like a top is­sue for the care and feed­ing of hu­man­ity’s fu­ture...

Then I must shake a dis­ap­prov­ing finger at any­one who claims the state of ev­i­dence on AGW is in­definite.

Sure, if we waited un­til 2100 to see how much global tem­per­a­tures in­creased and how high the seas rose, we would have definite proof. We would have definite proof in 2100, how­ever, and that sounds just a lit­tle bit way the hell too late. If there are cost-effec­tive things we can do to miti­gate global warm­ing—and by this I don’t mean ethanol-from-corn or cap-and-trade, more along the lines of stan­dard­iz­ing on a liquid fluoride tho­rium re­ac­tor de­sign and build­ing 10,000 of them—if there’s some­thing we can do about AGW, we need to do it now, not in a hun­dred years.

When the hy­poth­e­sis at hand makes time valuable—when the propo­si­tion at hand, con­di­tional on its be­ing true, means there are cer­tain things we should be do­ing NOW—then you’ve got to do your best to figure things out with the ev­i­dence that we have. Sure, if we had an­nual data on global tem­per­a­tures and CO2 go­ing back to 100 mil­lion years ago, we would know more than we do right now. But we don’t have that time-se­ries data—not be­cause global-warm­ing ad­vo­cates de­stroyed it, or be­cause they were ne­glect­ful in gath­er­ing it, but be­cause they couldn’t pos­si­bly be ex­pected to provide it in the first place. And so we’ve got to look among the ob­ser­va­tions we can perform, to find those that dis­crim­i­nate be­tween “the way the world could be ex­pected to look if AGW is true /​ a big prob­lem”, and “the way the world would be ex­pected to look if AGW is false /​ a small prob­lem”. If, for ex­am­ple, we dis­cover large de­posits of frozen methane clathrates that are re­leased with ris­ing tem­per­a­tures, this at least seems like “the sort of ob­ser­va­tion” we might be mak­ing if we live in the sort of world where AGW is a big prob­lem. It’s not a nec­es­sary con­nec­tion, it’s not suffi­cient on its own, it’s some­thing we could po­ten­tially also ob­serve in a world where AGW is not a big prob­lem—but un­like the perfect data we can never ob­tain, it’s some­thing we can ac­tu­ally find out, and in fact have found out.

Yes, we’ve never ac­tu­ally ex­per­i­mented to ob­serve the re­sults over 50 years of ar­tifi­cially adding a large amount of car­bon diox­ide to the at­mo­sphere. But we know from physics that it’s a green­house gas. It’s not a priv­ileged hy­poth­e­sis we’re pul­ling out of nowhere. It’s not like say­ing “You can’t prove there’s no in­visi­ble pink uni­corn in my garage!” AGW is, ce­teris paribus, what we should ex­pect to hap­pen if the other things we be­lieve are true. We don’t have any ex­per­i­men­tal re­sults on what will hap­pen 50 years from now, and so you can’t grant the propo­si­tion the spe­cial, su­per-strong sta­tus of some­thing that has been sci­en­tifi­cally con­firmed by a repli­ca­ble ex­per­i­ment. But as I point out in “Scien­tific Ev­i­dence, Le­gal Ev­i­dence, Ra­tional Ev­i­dence”, if sci­ence couldn’t say any­thing about that which has not already been ob­served, we couldn’t ever make sci­en­tific pre­dic­tions by which the the­o­ries could be con­firmed. Ex­trap­o­lat­ing from the sci­ence we do know, global warm­ing should be oc­cur­ring; you would need spe­cific ex­per­i­men­tal ev­i­dence to con­tra­dict that.

We are, I think, deal­ing with that old prob­lem of mo­ti­vated cog­ni­tion. As Gilovich says: “Con­clu­sions a per­son does not want to be­lieve are held to a higher stan­dard than con­clu­sions a per­son wants to be­lieve. In the former case, the per­son asks if the ev­i­dence com­pels one to ac­cept the con­clu­sion, whereas in the lat­ter case, the per­son asks in­stead if the ev­i­dence al­lows one to ac­cept the con­clu­sion.” Peo­ple map the do­main of be­lief onto the so­cial do­main of au­thor­ity, with a qual­i­ta­tive differ­ence be­tween ab­solute and non­ab­solute de­mands: If a teacher tells you cer­tain things, and you have to be­lieve them, and you have to re­cite them back on the test. But when a stu­dent makes a sug­ges­tion in class, you don’t have to go along with it—you’re free to agree or dis­agree (it seems) and no one will pun­ish you.

And so the im­plicit emo­tional the­ory is that if some­thing is not proven—bet­ter yet, proven us­ing a par­tic­u­lar piece of ev­i­dence that isn’t available and that you’re pretty sure is never go­ing to be­come available—then you are al­lowed to dis­be­lieve; it’s like some­thing a stu­dent says, not like some­thing a teacher says.

You de­mand par­tic­u­lar proof P; and if proof P is not available, then you’re al­lowed to dis­be­lieve.

And this is flatly wrong as prob­a­bil­ity the­ory.

If the hy­poth­e­sis at hand is H, and we have ac­cess to pieces of ev­i­dence E1, E2, and E3, but we do not have ac­cess to proof X one way or the other, then the ra­tio­nal prob­a­bil­ity es­ti­mate is the re­sult of the Bayesian up­date P(H|E1,E2,E3). You do not get to say, “Well, we don’t know whether X or ~X, so I’m go­ing to throw E1, E2, and E3 out the win­dow un­til you tell me about X.” I can­not be­gin to de­scribe how much that is not the way the laws of prob­a­bil­ity the­ory work. You do not get to screen off E1, E2, and E3 based on your ig­no­rance of X!

Nor do you get to ig­nore the ar­gu­ments that in­fluence the prior prob­a­bil­ity of H—the stan­dard sci­ence by which, ce­teris paribus and with­out any­thing un­known at work, car­bon diox­ide is a green­house gas and ought to make the Earth hot­ter.

Nor can you hold up the nonob­ser­va­tion of your par­tic­u­lar proof X as a triumphant re­fu­ta­tion. If we had time cam­eras and could look into the past, then in­deed, the fact that no one had ever “seen with their own eyes” pri­mates evolv­ing into hu­mans would re­fute the hy­poth­e­sis. But, given that time cam­eras don’t ex­ist, then as­sum­ing evolu­tion to be true we don’t ex­pect any­one to have wit­nessed hu­mans evolv­ing from apes with our own eyes, for the laws of nat­u­ral se­lec­tion re­quire that this have hap­pened far in the dis­tant past. And so, once you have up­dated on the fact that time cam­eras don’t ex­ist—com­puted P(Evolu­tion|~Cam­era) - and the fact that time cam­eras don’t ex­ist hardly seems to re­fute the the­ory of evolu­tion—then you ob­tain no fur­ther ev­i­dence by ob­serv­ing ~Video, i.e., P(Evolu­tion|~Video,~Cam­era) = P(Evolu­tion|~Cam­era). In slo­gan-form, “The ab­sence of un­ob­tain­able proof is not even weak ev­i­dence of ab­sence.” See ap­pendix for de­tails.

(And while we’re on the sub­ject, yes, the laws of prob­a­bil­ity the­ory are laws, rather than sug­ges­tions. It is like some­thing the teacher tells you, okay? If you’re go­ing to ig­nore the Bayesian up­date you log­i­cally have to perform when you see a new piece of ev­i­dence, you might as well ig­nore out­right math­e­mat­i­cal proofs. I see no rea­son why it’s any less epistem­i­cally sin­ful to ig­nore prob­a­bil­ities than to ig­nore cer­tain­ties.)

Throw­ing E1, E2 and E3 out the win­dow, and ig­nor­ing the prior prob­a­bil­ity of H, be­cause you haven’t seen un­ob­tain­able proof x; or hold­ing up the nonob­ser­va­tion of X as a triumphant re­fu­ta­tion, when you couldn’t rea­son­ably ex­pect to see X even given that the un­der­ly­ing the­ory is true; all this is more than just a for­mal prob­a­bil­ity-the­o­retic mis­take. It is log­i­cally rude.

After all—in the ab­sence of your un­ob­tain­able par­tic­u­lar proof, there may be plenty of other ar­gu­ments by which you can hope to figure out whether you live in a world where the hy­poth­e­sis of in­ter­est is true, or al­ter­na­tively false. It takes work to provide you with those ar­gu­ments. It takes work to provide you with ex­trap­o­la­tions of ex­ist­ing knowl­edge to prior prob­a­bil­ities, and items of ev­i­dence with which to up­date those prior prob­a­bil­ities, to form a pre­dic­tion about the un­seen. Some­one who does the work to provide those ar­gu­ments is do­ing the best they can by you; throw­ing the ar­gu­ments out the win­dow is not just ir­ra­tional, but log­i­cally rude.

And I em­pha­size this, be­cause it seems to me that the un­der­ly­ing metaphor of de­mand­ing par­tic­u­lar proof is to say as if, “You are sup­posed to provide me with a video of apes evolv­ing into hu­mans, I am en­ti­tled to see it with my own eyes, and it is your re­spon­si­bil­ity to make that hap­pen; and if you do not provide me with that par­tic­u­lar proof, you are defi­cient in your du­ties of ar­gu­ment, and I have no obli­ga­tion to be­lieve you.” And this is, in the first place, bad math as prob­a­bil­ity the­ory. And it is, in the sec­ond place, an at­ti­tude of try­ing to be defen­si­ble rather than ac­cu­rate, the at­ti­tude of some­one who wants to be al­lowed to re­tain the be­liefs they have, and not the at­ti­tude of some­one who is hon­estly cu­ri­ous and try­ing to figure out which pos­si­ble world they live in, by what­ever signs are available. But if these con­sid­er­a­tions do not move you, then even in terms of the origi­nal and flawed metaphor, you are in the wrong: you are en­ti­tled to ar­gu­ments, but not that par­tic­u­lar proof.

Ig­nor­ing some­one’s hard work to provide you with the ar­gu­ments you need—the ex­trap­o­la­tions from ex­ist­ing knowl­edge to make pre­dic­tions about events not yet ob­served, the items of ev­i­dence that are sug­ges­tive even if not definite and that fit some pos­si­ble wor­lds bet­ter than oth­ers—and in­stead de­mand­ing proof they can’t pos­si­bly give you, proof they couldn’t be ex­pected to provide even if they were rightthat is log­i­cally rude. It is in­valid as prob­a­bil­ity the­ory, fool­ish on the face of it, and log­i­cally rude.

And of course if you go so far as to act smug about the ab­sence of an un­ob­tain­able proof, or chide the other for their cre­dulity, then you have crossed the line into out­right or­di­nary rude­ness as well.

It is like­wise a mad­ness of de­ci­sion the­ory to hold off pend­ing pos­i­tive proof un­til it’s too late to do any­thing; the whole point of de­ci­sion the­ory is to choose un­der con­di­tions of un­cer­tainty, and that is not how the ex­pected value of in­for­ma­tion is likely to work out. Or in terms of plain com­mon sense: There are signs and por­tents, smoke alarms and hot door­knobs, by which you can hope to de­ter­mine whether your house is on fire be­fore your face melts off your skull; and to de­lay leav­ing the house un­til af­ter your face melts off, be­cause only this is the pos­i­tive and par­tic­u­lar proof that you de­mand, is de­ci­sion-the­o­ret­i­cal in­san­ity. It doesn’t mat­ter if you cloak your de­mand for that un­ob­tain­able proof un­der the head­ing of sci­en­tific pro­ce­dure, say­ing, “Th­ese are the proofs you could not ob­tain even if you were right, which I know you will not be able to ob­tain un­til the time for ac­tion has long passed, which surely any sci­en­tist would de­mand be­fore con­firm­ing your propo­si­tion as a sci­en­tific truth.” It’s still nuts.


Since this post has already got­ten long, I’ve moved some de­tails of prob­a­bil­ity the­ory, the sub­text on cry­on­ics, the sub-sub­text on molec­u­lar nan­otech­nol­ogy, and the sub-sub-sub­text on Ar­tifi­cial In­tel­li­gence, into:

De­mands for Par­tic­u­lar Proof: Ap­pen­dices.