Logic, Buddhism, and the Dialetheia


Is it pos­si­ble that some con­tra­dic­tions can be true? If so, how would that af­fect Bayesian Ra­tion­al­ity as well as The­o­ret­i­cal Physics and Quan­tum Com­put­ing? This idea is called “Dialethe­ism”, and it sug­gests that some con­tra­dic­tions (not all con­tra­dic­tions, just para­doxes), are True AND False.

It might sound like a laugh­able claim to even en­ter­tain the idea that some con­tra­dic­tions are op­er­a­tionally “BOTH true and false”, but it could be ex­tremely use­ful for quan­tum me­chan­ics re­search, AI re­search, and ethics (not to men­tion it’s al­most es­sen­tial to un­der­stand­ing east­ern re­li­gions). Let’s go over the his­tor­i­cal con­text to see what this is all about.


INTRO TO WESTERN LOGIC (For those un­fa­mil­iar)


Aris­to­tle was to try and cat­e­go­rize all these op­er­a­tions of the mind and de­rived 3 laws of logic that we can take ab­solutely for granted, laws that self-ev­i­dently ap­ply with­out ques­tion. Aris­to­tle called them “the 3 Laws of Thought”… well… tech­ni­cally he stole them from Plato:

“First, that noth­ing can be­come greater or less, ei­ther in num­ber or mag­ni­tude, while re­main­ing equal to it­self … Se­condly, that with­out ad­di­tion or sub­trac­tion there is no in­crease or diminu­tion of any­thing, but only equal­ity … Thirdly, that what was not be­fore can­not be af­ter­wards, with­out be­com­ing and hav­ing be­come”

1) The law of iden­tity : P=P, also called the law of self-ev­i­dence, the idea that a thing is a thing. For ex­am­ple the sen­tence “the Uni­verse is the Uni­verse” is a self-ev­i­dently valid state­ment.
2) The law of ex­cluded mid­dle : P∨~P=T, the all en­com­pass­ing idea that an op­tion is an op­tion. For ex­am­ple the sen­tence “Either the Uni­verse ex­ists OR the uni­verse doesn’t ex­ist” is a self-ev­i­dent state­ment (show shake­speare’s to be or not to be).
3) The law of non-con­tra­dic­tion : Aris­to­tle made a crit­i­cal de­ci­sion in the his­tory of west­ern civ­i­liza­tion, he de­cided to add a 3rd law, P∧~P=F, the no­tion that we can’t have both a thing and not a thing. It’s the idea that con­tra­dic­tions, not just some, but ALL of them, are out­right false. For ex­am­ple, if you were try­iong to an­swer the ques­tion “why is there some­thing rather than noth­ing?”, then the sen­tence “The uni­verse ex­ists AND the uni­verse doesn’t ex­ist” is a con­tra­dic­tion that should dis­qual­ify your ar­gu­ment right?

Nat­u­rally, you might think there’s noth­ing wrong with call­ing that sen­tence false and that’s what Aris­to­tle thought too. Lit­tle did he know that not all con­tra­dic­tions are the same, be­cause SOME con­tra­dic­tions can ac­tu­ally re­fer to them­selves. Take the state­ment “Ex­is­tence doesn’t ex­ist”, or the state­ment “Non-ex­is­tence ex­ists”. Are those state­ments true or false?

The first to point this out was the philoso­pher Epi­menides, a man from Crete who figured out he could say “all peo­ple from Crete are liars”, cre­at­ing a self-refer­enc­ing con­tra­dic­tion. Th­ese very spe­cial con­tra­dic­tions are what the greeks came to call “Para­doxes”, be­cause not only can they be true or false, they can also be BOTH true and false or NEITHER true or false, what the philoso­pher Pyrrho called “the Te­tralemma”. This is a BIG prob­lem, be­cause the 2nd law, the law of ex­clu­sion says all state­ments must be ei­ther true or false, but we also can’t la­bel para­doxes as solely true or solely false be­cause they are self refer­enc­ing. In or­der to ac­count for para­doxes, we’d first have to rewrite Aris­to­tle’s 2nd law from this P∨~P=T to this P∨~P∨(P∨~P)=T and then rewrite the 3rd law from this P∧~P=F to ei­ther this P∧~P=F∨(T∧F) OR this P∧~P=F∨(~T∧~F).

What all this means is that there are now only two ways pos­si­ble ways to an­swer what a para­dox is.

OPTION A: The first way is to deem all con­tra­dic­tions false but a para­dox as BOTH true AND false si­mul­ta­neously, writ­ten like this P∧~P=F∨(T∧F).

OPTION B: The sec­ond way is we in­ter­pret all con­tra­dic­tions as false but a Para­dox as NEITHER true nor false, writ­ten like this P∧~P=F∨(~T∧~F).

By pure cir­cum­stance, the philoso­phers of an­cient Greece de­cided to in­ter­pret para­doxes us­ing method 2, Nei­ther True NOR False, which dis­qual­ifies para­doxes from ever be­ing used in ar­gu­ments again, per­ma­nently ban­ish­ing them from our civ­i­liza­tion, and thus, ban­ish­ing them from your very lan­guage. Most peo­ple in the world grew up in a civ­i­liza­tion grounded in Aris­totelian philos­o­phy, think­ing there’s ab­solutely noth­ing wrong with ig­nor­ing para­doxes, but what if we only think that way due to a life­time of so­cial con­di­tion­ing? If you ask any­one on the street if para­doxes counted as sen­si­ble state­ments they’d prob­a­bly say no, and not sur­pris­ingly, so did Aris­to­tle.


INTRO TO EASTERN LOGIC (Also for those un­fa­mil­iar)


While Aris­to­tle was lay­ing the ground­work for mod­ern lan­guage, sci­ence, and law, there was a philoso­pher on the other side of the world who couldn’t dis­agree more, Sid­dartha Gau­tama, the Bud­dha. If a con­tra­dic­tion is NEITHER True or False, then we can rewrite it as NOT TRUE and NOT FALSE, which we can then rewrite as con­tra­dic­tions are FALSE and TRUE, but that’s ac­tu­ally the same thing as all con­tra­dic­tions are TRUE and FALSE, so could Aris­to­tle have been wrong?

1) The Cha­tuskoti : In the Su­tras, one of the Bud­dha’s stu­dents cu­ri­ous about the af­ter­life asks him:
“Master Go­tama, does mas­ter hold the view that af­ter death, a Tatha­gata ex­ists, where only one thing is true and any­thing else is false?”.
The Bud­dha re­sponds:
“Vac­cha, I do not hold the view that a Tatha­gata ex­ists af­ter death. Nor do I hold the view that a Tatha­gata does ex­ist. I also do not hold the view that a Tatha­gatha nei­ther ex­ists nor does not ex­ist. Nor do I hold the view that a Tatha­gata ex­ists and does not ex­ist”.
In Bud­dhist logic this is called the “Catuṣkoṭi“ or “four cor­ners”, writ­ten like this P∨~P=F∨T∨(T∧F)∨(~T∧~F), which means it’s the para­dox of all para­doxes from which all other para­doxes arise. A su­per­po­si­tion of “Oness” from which we de­rive all other pos­si­ble sys­tems of logic. It holds that the first foun­da­tion of all re­al­ity is a di­v­ine con­tra­dic­tion called “Sun­y­ata” or “empti­ness”, a kind of su­per­po­si­tion-like state that is nei­ther true, nor false, nor true and false, nor nei­ther true OR false.
2) The Law of Con­tra­dic­tion : 600 years later, the philoso­pher Na­gar­juna, founder of Ma­hayana Bud­dhism, worked out that you can di­vide that one di­v­ine su­per­po­si­tion into fur­ther su­per­po­si­tions. Rather than in­ter­pret­ing a Para­dox as nei­ther true or false like Aris­to­tle did P∧~P=F∨(~T∧~F), Na­gar­juna ac­tu­ally choses the first op­tion, to in­ter­pret para­doxes as BOTH true AND false P∧~P=F∨(T∧F), what we call “a Dialetheia”. Be­cause if the ground of re­al­ity is it­self a para­dox as the Bud­dha says, then it should sub­di­vide into fur­ther para­doxes rather than fur­ther nega­tions. Na­jar­juna’s ver­sion of Aris­to­tle’s 3rd law was called the “2 truths doc­trine”, man­dat­ing that all meta­phys­i­cal sys­tems must ac­count for the pos­si­bil­ity of Dialethias, what the Zen Bud­dhists came to call “Koans”.

The idea that a thing could both ex­ist AND not ex­ist sounds ab­solutely ab­surd to us to­day, but for the Bud­dhists it was just life as usual. The uni­verse is both some­thing and noth­ing, and for Na­gar­juna, the idea that the uni­verse caused it­self is a perfectly valid state­ment, since he never posited any iron­clad ban on con­tra­dic­tions like Aris­to­tle did. Right now, you might be re­ally tempted to ig­nore the 2 truths doc­trine as mys­ti­cal new age ram­bling, but when it comes to com­put­ers, the laws of physics, and the very lan­guage we speak, the val­idity of self-refer­en­tial para­doxes couldn’t be a more se­ri­ous mat­ter. Un­for­tu­nately, af­ter the Em­pire of the Bud­dhist King Ashoka fell, Bud­dhist libraries, ab­hi­darma schools, and tem­ples in In­dia were burned and monks were slaugh­tered.

Na­gar­juna faded into ob­scu­rity while Aris­to­tle’s 3 laws spread around the world through Euro­pean em­pires, form­ing the next 2000 years of global civ­i­liza­tion. Zen Bud­dhism and Dao­ism were the only ma­jor philoso­phies in hu­man his­tory that ever per­mit­ted con­tra­dic­tions, but it was Aris­to­tle who shap­ing the world’s uni­ver­si­ties, le­gal cus­toms, and so­cial in­sti­tu­tions, all dic­tat­ing what kinds of thoughts our minds can and can’t think.

Even in the west, there were only ever 5 ma­jor west­ern thinkers to base their en­tire philos­o­phy on di­aletheic logic, the con­ti­nen­tal philoso­phers Ge­org Hegel, Friedrich Niet­zsche, Martin Hei­deg­gar, Gilles Deleuze, and the an­cient pre­so­cratic, Her­a­cli­tus. All of them were also largely ig­nored by main­stream sci­ence and main­stream re­li­gion, never never stop­ping to ques­tion whether or not our re­al­ity could se­cretly be a won­drous world of para­con­sis­tent si­mul­tane­ity. A higher plane of con­tem­pla­tion where our ethics, meta­physics, and over­all un­der­stand­ing of re­al­ity could all be differ­ent. As Lud­wig Wittgen­stein once said, “the limits of our lan­guage mean the limits of our world”, and un­for­tu­nately, our logic dic­tates our lan­guage.


DIALETHEISM (The Real Ar­gu­ment Starts Here)


Up un­til the 21st cen­tury, Aris­to­tle’s 3rd law went on ig­nored un­til one man, de­cided to bring the ques­tion of the Para­dox back from the dead. Dr. Gra­ham Priest is a dis­t­in­guished pro­fes­sor of an­a­lytic philos­o­phy at the city uni­ver­sity of New York and he has spent his en­tire ca­reer work­ing on one phrase, a pesky state­ment called “this sen­tence is false”. This is the well known “Liar’s Para­dox”, the state­ment that ev­ery­thing be­ing said is a lie. So if the liar is in­deed ly­ing, then the liar is tel­ling the truth, which means the liar just lied, which means.. they’re tel­ling the.. truth.

The liar’s para­dox used to be noth­ing more than a party trick, un­til the 20th cen­tury, where we needed to take it se­ri­ously for us to ground math­e­mat­ics and con­struct quan­tum com­put­ers and more ad­vanced ma­chine learn­ing sys­tems.


1) THE PROBLEM OF BIVALENCE


The Prin­ci­ple of Bi­valence is the idea that a thing can’t have 2 truth val­ues, but is it le­git?

a) The Para­dox: We can write out the para­dox as a syl­l­o­gism. “This sen­tence is false is true”, “This sen­tence is false is false”, “there­fore this sen­tence is false is BOTH True and False” (rather than NEITHER true or false), thereby vi­o­lat­ing aris­to­tle’s 3rd law:
1) P∧~P→T
2) P∧~P→F
C: P∧~P→T∧F.
b) The Re­but­tal: In­ter­est­ingly enough, the Liar’s para­dox sup­ports Na­ga­juna’s in­ter­pre­ta­tion, mean­ing Aris­to­tle’s law of con­tra­dic­tion could be changed. How­ever, this usu­ally hand waved away with com­mon re­but­tal to the Liar’s para­dox. If the liar’s para­dox is both true and false then it’s not true. If the liar’s para­dox is both true and false then it is not false, there­fore there­fore the liar’s para­dox is ac­tu­ally NEITHER true nor false like Aris­to­tle said:
1. (P∧~P=T)→~F.
2. (P∧~P=F)→~T.
C: ∴(P∧~P=F)→~F∧~T.
c) The Re­but­tal to the Re­but­tal: At first glance, the re­but­tal seems to have de­bunked the Liar’s para­dox, but if we write out the logic we will see that all this re­but­tal did was try to dis­tract us from the ac­tual prob­lem. If we as­sume the con­clu­sion of that re­but­tal, where the liar’s para­dox is nei­ther not true or not false, then as the sec­ond premise we can point out that the phrase “Not true AND Not false” is just the same thing as “False AND True”, mean­ing we have proven that Aris­to­tle was wrong and there’s no such thing as a state­ment that’s nei­ther true nor false, leav­ing the only re­main­ing in­ter­pre­ta­tion of the Liar’s Para­dox as true AND false:
1. (P∧~P=F)→~F∧~T,
2. ~F∧~T→T∧F ,
C: ∴(P∧~P=F)→T∧F.

2) THE PROBLEM OF TRUTH VALUE GAPS

We could always just clas­sify the liar’s para­dox as a so-called “truth value gap”, mean­ing not only is it nei­ther true or false, para­doxes aren’t even de­serv­ing of a truth value.

Let’s give an ex­am­ple of a sen­tance with­out a truth value. “What’s your fa­vorite color?” That’s a ques­tion, so it’s an ex­am­ple of a TVG (truth value gap). But what about a sen­tence like “Ex­is­tence doesn’t ex­ist”?

a) the para­dox : One might say a para­dox like that has zero truth value be­cause we don’t re­spond to it with “that’s true” or “that’s false”. But let’s try a spe­cial state­ment, “the pre­sent king of france is bald”.
b) the re­but­tal : It makes an as­sump­tion that there is a pre­sent king of france, so it’s nei­ther true nor false, but it MUST have a truth value be­cause it is cer­tainly in the cat­e­gory of “state­ment”. I sup­pose we can in­fer that a Dialetheia works only in-so-far as it’s talk­ing about things that ac­tu­ally ex­ist (there is no such thing as a “king of france” to­day).
c) the re­but­tal to the re­but­tal : The state­ment “uni­corns are white and not white” is not a Dialethia, it’s quite fairly a TVG. But for some­thing “pre­sent” that IS le­gi­t­i­mately be­ing talked about, a para­dox is not a TVG, it’s perfectly gram­mat­i­cal, doesn’t com­mit cat­e­gory mis­takes, and it doesn’t suffer from failure of refer­ence. Mean­ing things pre­sent at hand (like prob­lems of quan­tum me­chan­ics) do de­mand a truth value.

3) THE PROBLEM OF EXPLOSION

The is­sue of bi­valence is solved, but if so, would a Dialethia mean that all of re­al­ity is sub­jec­tive and a mat­ter of opinion?

Well, no, it’s just say­ing SOME parts of ob­jec­tive re­al­ity are struc­tured through para­doxes.

This kind of at­tack on Dialethe­ism is called “The Prin­ci­ple of In­fer­ence”, but Lo­gi­ci­ans just call it “Ex­plo­sion”, be­cause what it sug­gests is that if we break the law of con­tra­dic­tion then peo­ple can just make any ar­gu­ment they want.

The prin­ci­ple of ex­plo­sion has been around since the mid­dle ages and it’s the very rea­son that Aris­to­tle’s law of con­tra­dic­tion never gets ques­tioned (be­cause if we vi­o­late the law of con­tra­dic­tion, then peo­ple can pretty much say any­thing what­ever, thereby mak­ing all of logic pointless). This is why it’s strongly recom­mended that we must ABSOLUTELY NEVER break Aris­to­tle’s law.

The prin­ci­ple of ex­plo­sion can be writ­ten as p and not p im­ply q ( ~P∧P→Q ) where p and not p is any given con­tra­dic­tion and q is what­ever con­clu­sion you feel like prov­ing.

a) The Para­dox : For ex­am­ple, take this ridicu­lous ar­gu­ment where we treat a con­tra­dic­tion as true: as­sume a con­tra­dic­tion like the uni­verse does ex­ist and doesn’t ex­ist, an idea some east­ern philoso­phers ac­tu­ally ac­cept, premise two, ei­ther the uni­verse doesn’t ex­ist or uni­corns ex­ist, seems fair so far. But then we see the con­clu­sion, if the uni­verse does ex­ists, which it does, then uni­corns ex­ist too.
1) ~P∧P=T
2) ~P∨Q=T
C) ∴P→Q=T
b) The Re­but­tal : In fact, not just uni­corns, re­place Q with what­ever you want and it will be true. Con­sid­er­ing con­tra­dic­tions true is a night­mare be­cause you make liter­ally any ar­gu­ment and have it be valid. The prin­ci­ple of ex­plo­sion con­cludes that only way to avoid ridicu­lous ar­gu­ments like that is to de­clare the first premise of the ar­gu­ment, the con­tra­dic­tion, as false, thus mak­ing uni­corns and all other fan­tasies an un­sound ar­gu­ment:
1) ~P∧P=F.
2) ~P∨Q=T
C) ∴P→Q=F.
c) The Re­but­tal to the Re­but­tal : It seems like a rock solid re­but­tal, how­ever ex­plo­sion misses one key de­tail, Dialethe­ism never made the as­sump­tion that EVERY con­tra­dic­tion is nec­es­sar­ily true. Con­sid­er­ing a con­tra­dic­tion to be BOTH true and false is not the same thing as con­sid­er­ing it true. Dialethe­ism says that if we re­ject most con­tra­dic­tions BUT ac­cept the ex­is­tence of self-refer­enc­ing con­tra­dic­tions, AKA para­doxes, then we can vi­o­late Aris­to­tle’s 3rd law with­out per­mit­ting ridicu­lous ar­gu­ments that can claim what­ever they want. Let’s look at that uni­corn ar­gu­ment again, but in­stead of just hav­ing true and false, this time let’s al­low 3 pos­si­ble truth val­ues, True, False, or Dialethia:
Premise one, “the uni­verse does ex­ist and doesn’t ex­ist”, in­stead of mak­ing this true or false we’ll make it a di­alethia, as some east­ern thinkers have posited. Premise two, “ei­ther the uni­verse doesn’t ex­ist or uni­corns ex­ist”, the same premise as last time. Sur­pris­ingly, we see that us­ing the Dialetheia still makes the uni­corn ar­gu­ment false. Con­clu­sion, if the uni­verse ex­ists then we still can’t in­fer that uni­corns ex­ist since that con­clu­sion no longer fol­lows from premise 2:
1) ~P∧P=T∧F.
2) ~P∨Q=T,
C) ∴P→Q=F.

Over­all, we’ve shown that you can still break the law of con­tra­dic­tion with­out be­ing be­ing al­lowed to say just any­thing, thereby de­con­struct­ing the prin­ci­ple of Ex­plo­sion and challeng­ing Aris­to­tle’s 3rd law. In the 21st cen­tury, any sys­tem of logic that re­jects ex­plo­sion and con­sid­ers para­doxes valid is what we call a “Para­con­sis­tent logic”, while any logic that keeps the prin­ci­ple is called a “Clas­si­cal Logic”.

Now note one key de­tail, I’m not say­ing Clas­si­cal Log­ics should be done away with. Over 99% of sci­en­tists still use clas­si­cal logic, and you know what, that’s perfectly okay, be­cause they never have to deal with para­doxes. How­ever, that last 1% of of sci­en­tists, like quan­tum physi­cists, have to deal with para­doxes all the time, so we can’t just force them to use clas­si­cal logic too, they need a more ac­cu­rate set of ax­ioms. To­day, there’s a des­per­ate need to cre­ate com­put­ers, per­haps quan­tum com­put­ers, that can vi­o­late the law of non-con­tra­dic­tion so physi­cists can fi­nally solve their prob­lems. If we put Para­con­sis­tent log­ics into com­put­ers it means they’re go­ing to start col­lect­ing a lot more in­for­ma­tion and draw­ing a lot more con­clu­sions, since there’s now more than two pos­si­ble truth val­ues: “true”, “false”.. and “di­aletheia”.

In CLASSICAL LOGICS we only have “1” and “0″



In PARACONSISTENT LOGICS we now have “1” and “0″ and “#”. I imag­ine this is some­thing that could come in handy for quan­tum com­put­ers.


Im­por­tant Note: I’m not say­ing Aris­to­tle was stupid for in­vent­ing the Law of Non-Con­tra­dic­tion, I’m just point­ing out that para­doxes are ex­cep­tions to the rule. It’s the same prin­ci­ple be­hind New­ton’s clas­si­cal dy­nam­ics be­ing not en­tirely ac­cu­rate and get­ting re­placed with Ein­stein’s Gen­eral Rel­a­tivity, it de­pends on what you’re us­ing it for. 99% of sci­en­tists would get by just fine us­ing New­ton’s laws of me­chan­ics, but physi­cists do­ing Black Hole re­search would need to use Gen­eral Rel­a­tivity to get a more ac­cu­rate an­swer. This is the same rea­son­ing for why we should ex­pand Aris­to­tle’s clas­si­cal law of con­tra­dic­tion P∧~P=F into the para­con­sis­tent law of con­tra­dic­tion P∧~P=F∨(T∧F), al­low­ing us to dis­cover the deeper philo­soph­i­cal truths of the uni­verse.


4) THE PROBLEM OF GROUNDEDNESS


Now al­low me to stop at­tack­ing Pseudo-straw­men and get to the REAL re­but­tals posed by ac­tual philoso­phers. The ul­ti­mate at­tack on the Liar’s Para­dox comes from the lo­gi­cian Saul Kripke.

a) The Para­dox : Kripke says the Liar’s Para­dox isn’t grounded and is just a vis­cious cy­cle of adding fake truth-pred­i­cates, thus mak­ing it a val­ue­less state­ment.
b) The Re­but­tal : Kripke’s clar­ifi­ca­tion of the para­dox is called “ground­ed­ness”, where we re­move all “falsity pred­i­cates” from the state­ment, we’re left with the root of the state­ment “this sen­tence”. In other words, if we use the sym­bol P to rep­re­sent “this sen­tence” and the words “is false” rep­re­sented as the falsity pred­i­cate on P (~), then we’ll see that just as “ques­tions” lack truth value, the state­ment “this sen­tence” ALSO has no truth value.
c) The Re­but­tal to the Re­but­tal : This brings us to the “Proof of Re­venge”, which Dr. Priest evokes as a re­but­tal to Kripke us­ing what’s called “the Strength­ened Liar’s Para­dox”, where we change the syn­tax of “this sen­tence is false” into “this sen­tence is not true” or even bet­ter yet “this sen­tence is ei­ther not true or val­ue­less”.

Now when you try Kripke’s re­but­tal it no longer works. If Kripke, like be­fore, points out that the state­ment is val­ue­less, then it’s not true, and if we ad­mit it’s not true then the state­ment “this sen­tence is ei­ther not true or val­ue­less” is true, again giv­ing us a Dialethia where both true­ness and false­ness are si­mul­ta­neously valid.

Kripke’s method only works on phrases like “this sen­tence is true” be­cause it has a re­dun­dancy of it’s own truth value. How­ever, Kripke’s ground­ed­ness DOES NOT work on “this sen­tence is false” which refers to the ex­is­tence of it­self then over­turns it’s own truth value.

“This sen­tence is true” un­de­ter­mines it’s own truth value while “this sen­tence is false” overde­ter­mines it, which is to say it cre­ates a truth value within a truth value.


5) THE PROBLEM OF REDUNDANCY


Philoso­pher Arthur Prior had his own re­sponse to Para­doxes, which was es­sen­tially, “so what?”. SO WHAT if the phrase “this sen­tence” refers to it’s own ex­is­tence? If that’s the case, then don’t ALL sen­tences re­fer to their own ex­is­tence? If all sen­tences im­plic­itly re­fer to their own truth, then “the proof of Re­venge” is re­dun­dant.

a) The para­dox : If I had a sen­tence that sim­ply con­tained the word “False”, then should we say the very ex­is­tence of the word false is ALSO a para­dox? Ob­vi­ously not, bea­cause the sen­tences “the sky is blue” and “it’s true that the sky is blue” are ac­tu­ally the ex­act same sen­tence in terms of their truth value.
b) The re­but­tal : In the same sense, the state­ments “this sen­tence is false” and “it’s true that this sen­tences false” are ALSO the same sen­tence, so the liars para­dox is trick­ing us into see­ing a pred­i­cate that isn’t re­ally there.
c) The Re­but­tal to the Re­but­tal : But there’s one in­ter­st­ing thing about Prior’s re­but­tal. Yes the state­ment “this sen­tence is false” can trans­late to “it’s true that this sen­tence is false”, how­ever us­ing Dr. Prior’s ex­act same logic, THAT sen­tence it­self is also iden­ti­cal to the sen­tence “it’s true this sen­tence is true and this sen­tence is false”, which is, you guessed it, a Dialetheia.

How­ever, Prior took this into ac­count and pointed out one more in­ter­est­ing thing, we would be us­ing a Dialethia to prove the ex­is­tence of a Dialetheia, which in it’s own met­al­in­guis­tic way, is a cir­cu­lar ar­gu­ment. We haven’t de­rived a di­alethia from the ar­gu­ment, we’ve just as­serted it, which makes it a con­tra­dic­tion.

Un­for­tu­nately for him, Prior is also us­ing a cir­cu­lar ar­gu­ment, us­ing the law of con­tra­dic­tion to prove that the law of con­tra­dic­tion is true. At first it ap­pears we have a clash be­tween 2 cir­cu­lar ar­gu­ments with both sides beg­ging the ques­tion, but there is a way out, Oc­cam’s ra­zor. What’s in­ter­est­ing is that we make fewer as­sump­tions about logic to get Dialetheia than we do to get Dr.Prior’s an­swer with re­gard to what we call “Contin­gent Facts”.

Dr.Prior’s ar­gu­ment uses the con­text of a sen­tence to make his ar­gu­ment, re­quiring him to mul­ti­ply be­yond ne­ces­sity. Mean­while Dialetheia is self-ev­i­dently de­rived from the sen­tence it­self and needs no com­par­i­son with other sen­tences in or­der to make its point. Lastly, Dialetheia is ac­tu­ally NOT a cir­cu­lar ar­gu­ment be­cause it only makes 2 as­sump­tions, the law of iden­tity and the law of ex­clu­sion, while Prior has made 3 as­sump­tions, the pre­vi­ous 2 plus the law of con­tra­dic­tion.


6) THE PROBLEM OF LANGUAGE


Math­e­mat­i­cian and Philoso­pher Alfred Tarski launched one fi­nal at­tack on the liar’s para­dox, claiming that it’s just a prob­lem of lan­guage. It’s a similar re­sponse to what we’d get from the Post­mod­ernists, be­cause per­haps this whole idea of the Liar’s Para­dox isn’t a self-ecv­i­dent truth and it might just be men­tal mas­ter­ba­tion for one sim­ple rea­son. If we can find a lan­guage where the para­dox doesn’t ex­ist, then Dialethe­ism is not self-ev­i­dent, it’s just a so­cial con­struct. To do this Tarski draws a dis­tinc­tion be­tween quote “se­man­ti­cally closed lan­guages” like en­glish verses what are called “se­man­ti­cally open lan­guages”. While ev­ery hu­man lan­guage on earth is a se­man­ti­cally closed lan­guage where you can use the lan­guage to talk about the lan­guage, the liar’s para­dox CAN’T be ex­pressed in a se­man­ti­cally closed lan­guages. A se­man­ti­cally closed lan­guage has 2 el­e­ments, one, that can re­fer to it’s own ex­pres­sions and two, that it con­tains the pred­i­cates true or false for se­man­tic clo­sure.

How­ever, Tarski says we can cre­ate syn­thetic ma­chine lan­guages where self-refer­en­tial sen­tences are blocked or ar­tifi­cial lan­guages that don’t use true or false as pred­i­cates. Th­ese are called “Se­man­ti­cally Open lan­guages”, and they tend to be use­less to hu­mans but nev­er­the­less ARE pos­si­ble. We can cre­ate what’s called “an ob­ject lan­guage” that is struc­ture such that it can’t pos­si­bly talk about it­self in terms of trut­hood or falsity. Without a lan­guage that can talk about it­self, the liars para­dox is just a so­cial con­struct, a prob­lem of hu­man lan­guage and has no ba­sis in logic. In fact, Tarski has even sug­gested get­ting rid of all hu­man lan­guages and cre­at­ing a new ar­tifi­cial se­man­ti­cally-open lan­guage that all hu­mans on earth could speak and this lan­guage would not have the same prob­lems of con­fu­sion we do. In fact, we’d be able to do philos­o­phy and sci­ence with­out mis­in­ter­pret­ing each other or be able to pur­posely mis­lead each other. A lan­guage where it’s im­pos­si­ble to lie. But Tarski’s Solu­tion has one small prob­lem.

While we can build a Se­man­ti­cally open lan­guage that can’t talk about it­self, it’s not pos­si­ble to con­struct one that can’t talk about lan­guage in gen­eral. For ex­am­ple, what’s to stop it from evolv­ing a way to talk about other lan­guages? Lin­guis­tic philoso­phers call the idea of a lan­guage that can talk about other lan­guages “a Me­ta­lan­guage” while the lan­guage be­ing talked ABOUT is called “An Ob­ject Lan­guage”. The prob­lem here is that there’s noth­ing stop­ping an ob­ject lan­guage from mak­ing pred­i­cate state­ments about the met­a­lan­guage, for ex­am­ple “this state­ment’s met­a­lan­guage is false”.

Essen­tially, Tarski can’t give us a bul­let­proof way to keep Dialei­the­ism out of our dis­course and has failed to ban­ish it to the realm of lin­guis­tic con­structs.

No mat­ter what we do, the dreaded liars para­dox will keep re­turn­ing to logic no mat­ter what we do.

So clearly there’s only one thing left to do, in­stead of des­per­ately try­ing to ig­nore the ex­is­tence of Dialetheia, why don’t we just em­brace them?

Why don’t we find a way our lan­guages, math­e­mat­ics, and laws of physics can work WITH IT rather than Against it?


CONCLUSION (What does Bud­dhist Dialethe­ism mean for philos­o­phy?)

If we can ac­cept Na­gar­juna’s no­tion that “SOME con­tra­dic­tions are true” then this changes ev­ery­thing… meta­physics, epistemics, ethics, poli­tics, and Bayesian ra­tio­nal­ity. If so, we might have to rewrite some in­grained so­cial, eco­nomic, and sci­en­tific laws to ad­just for di­aletheia, but I’ll leave that to the prag­ma­tists (I just want to get Dialethe­ist the­ory cor­rect).

This also has se­ri­ous im­pli­ca­tions for what ar­tifi­cial in­tel­li­gence re­ally is. Is ma­chine ra­tio­nal­ity only sub­or­di­nate to hu­man ra­tio­nal­ity be­cause the hu­man brain can op­er­ate on para­con­sis­tent log­ics (Roger Pen­rose’s “Quan­tum Co­her­ence The­ory”) while ma­chine brains can’t, then I be­lieve we might have a way to make ma­chines think more like hu­mans. Per­haps Bud­dhist log­ics could be the key to mak­ing a more “friendly” AI (if it’s able to learn our val­ues, which them­selves con­tain many di­aletheia, we could re­duce ex­is­ten­tial risk).

It of­ten makes me think of my fa­vorite video game “Por­tal 2”, and how in the end of the game, the rogue ar­chailect GLADOS, is fi­nally defeated by a di­aletheia (we ask her to para­con­sis­tently calcu­late “this sen­tence is false” and she self-de­structs). Per­haps if GLaDOS ran on a para­con­sis­tent logic she might not have been so hor­rible in the first place and may have un­der­stood the more nu­anced as­pects of re­al­ity (but that’s just spec­u­la­tion on my part).

So if our AI-god were to have a re­li­gion at all, I’d pre­fer it be Bud­dhism, so it might-then be able to work out how hu­mans un­der­stand suffer­ing and com­pas­sion.


Please tear this post to shreds, I want to make sure I didn’t for­get to ad­dress any ar­gu­ments against the di­aletheia. I’m also cu­ri­ous about your thought son whether Bud­dhist Log­ics are worth pur­su­ing. Every small cri­tique helps, thanks again LW.



PS: Shame­less Plug for my Tran­shu­man­ist Youtube Chan­nel (if any­one’s in­ter­ested) : https://​​www.youtube.com/​​chan­nel/​​UCAvRKtQNLKkAX0pOKUTOuzw/​​videos