True and False? Dialethism and the Liar Paradox | Attic Philosophy
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- เผยแพร่เมื่อ 24 ก.ค. 2024
- Can sentences be both true and false at the same time? Dialethism is the view that says yes, they can. Truth and falsity are compatible, according to Dialethism. So how does the view work, what kind of logic does it use, and can it really help up out with difficult paradoxes, like the Liar?
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00:00 - Intro
01:07 - Dialethism
01:29 - Paraconsistent logic
02:36 - Logic of Paradox
03:47 - Why ‘both’ is better than ‘neither’
05:21 - Does Dialethism really solve the Liar?
05:45 - Just true
06:27 - A Dialethist response
07:25 - Does that response work?
08:44 - The best Dialethist response
10:48 - What’s my take?
11:14 - The Curry paradox
11:39 - Wrap-Up
If there’s a topic you’d like to see covered, leave me a comment below.
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Congratulations on your video and your channel. I have one doubt. From the point of view of classic logic natural deduction, are the explosion principle and the contradiction elimination rule the same thing? If they are the same thing, since the rule of elimination of contradiction is an abbreviation of the rule of introduction of negation, does Dialethism by rejecting the explosion principle also reject the introduction of negation?
It depends on the system, classically we might have rules A, ~A / F and F / A (where F is the falsum or absurdity consistent). Dialethists usually reject the former. In natural deduction, dialethists won’t have a single rule for negation, but rather, will consider separate rules for ~(A&B), ~(AvB) etc. classically, those rules are redundant, but a nice feature is you can drop A,~A/F to get LP, drop /Av~A to get K3, and drop both to get FDE.
My favorite paradox is „you will never know for a fact that this sentence is true!“
[if you believe it, you believe a falsehood, but if you don’t believe it, it becomes true and there’s a true statement in the world that you don’t believe]
You definitely can’t know it, but why’s it a problem if you don’t believe it? There’s lots of truths out there we don’t believe - no one knows everything! Maybe the problem is that there’s a *proof* that it’s true (you can’t know it) and yet you can’t know that it’s true.
Hi there! I'm quite new here and a lot of this nomenclature is new to me as well, but what I would truly appreciate is if you could talk for a second about, let's say, a simple down-to-earth example of a logical problem that could be approached from a dialethistic point of view and how something that comes to my mind naturally as a paradox, could be seen as totally fine to be both true and false.
See, this is where I struggle a lot in all the talks about different kinds of logic - I feel like they exist in this weird speculative bubble and outside of that there's really no use for them in real world. And I'm most probably wrong here, I just struggle to see their potential since, I guess, I've been stuck with classical logic for so long
Let's say a "round square". This triggers a red light in my head. How could one approach this and say something can be a square AND be round at the same time? My head screams: No, it couldn't - one would literally deny the definition of the other, that's the end of discussion for me and I simply can't imagine any other way to discuss that.
How would you approach, let's say, the round square example with a dialethistic mindset?
Hi! Often, dialethism is discussed in theoretical contexts, like the Liar paradox. A slightly more practical example might be in-between colours, like a box that's somewhere between definite red and definite orange. Asked whether it's red, someone might say, 'well, it is and it isn't'. Classical logicians must re-interpret them, whereas a dialethist can take their words at face value! It's both red and not-red at the same time. A much more real-world example of paraconsistent logic (but maybe not specifically dialethism) comes from cases like inconsistent rules. If two rules conflict, does that entail that anything goes? No! We have to somehow work around the contradiction. That's what paraconsistent logics do. Dialethism is one (but not the only) way of setting up a paraconsistent logic. Hope that helps!
@@AtticPhilosophy thank you, it does help, yes :)
The reason I initially went to learn more about dialethism and the non-classical logics, is because I faced this sort of logic in an argument and it got me very confused. The conversation I had was, I believe, about the existence of supernatural or god - and regardless of the nature of the conversation, I remember that my interlocutor claimed that "we both could be right", hence the "god" could exist and not exist at the same time. Apparently, for them, this was a possible option and this was the main point where we couldn't agree to move on in the conversation.
I remember struggling with this, and I argued that anything in the world can either exist or not exist, there couldn't be a state in between or neither both could be valid. Either the sun is or isn't, either god is or isn't. And then they jumped out at me saying "oh, but this is only in classical logic", I think they even called it "western logic" or something like that. And they started some mumbo-jumbo about some eastern wisdom that allows for things to exist and not exist at the same time.
I must admit that this stood in such a strong contradiction to my fundamental understanding of the nature of universe, that out of curiosity I started looking up into it, but didn't find anything that sounds any reasonable so far. Actually you talking about this Dialethistic logic are the one to make the most sense so far, but I still can't understand how this logic could be applied to something existing or not. I respect that approach on paper, I respect it in, e.g. colors, as you brought up, but in a discussion on where something exists or not, I just can't see the possibility of duality or gray-scaling such matter. :) My brain just totally collapses
@@jawojciechdrzymala 99.9% (as a rough guess!) of philosophers agree with you: nothing can both exist and not exist; no statement can be both true and false. Genuine card-carrying dialethists are very few in number. Arguments in its favour tend to focus on confusing, unusual cases: vagueness, paradox, and so on. It is, however, an interesting view, which is hard to reject decisively (due to the work of Graham Priest & others, which is worth reading if you're interested in this).
Interesting 🤔🤔
How about undecidable?
That’s not a good contrast term to true/false, since some sentences are true/false but also undecidable. “Undetermined” would be better.
Do you think Hegels Dialectical Logic was Dialetheism?
...
Would Lacan be a Dialetheist?
I don't think Hegel had a logic in the modern sense. It's possible to extrapolate his ideas into a dialethist theory, but I doubt that's an accurate interpretation. (I think Franz Berto has interesting stuff on this.)
Isn’t the liar paradox just a category error or a sign that we don’t have a truth predicate definable by our system for our system?
What’s the category error? We can clearly say of a sentence that it’s true/false.
@@AtticPhilosophy I don’t see how you can say it in the same level of language. Of course, per Kripke we can say things like “for every sentence A in a level of language there is a sentence B in the next level that denies A,” but I’m not too worried about that. I think it is just a lesson that if we are thinking in absolutely general terms, we need to only talk about true things. I think that if there is an absolute meta-language that can define its own truth predicate, then that language would have to contain neither negation nor falsum. This language would still be explosive, but it seems the only consistent conclusion to draw from trying to talk about truth in an absolute sense.
@@patrickwithee7625 Dialethists aren't aiming for consistency - they allow sentences to be both true and false. You can say it in the same language like this: TL & ~TL.
@@AtticPhilosophy I see that. I guess my argument is that dialetheism is a major overreaction when “sentences” like the Liar can be sacrificed without self-reference or meta-level reasoning being sacrificed. I also think giving up consistency is too high of a cost for expressivity, especially since it is controversial that “sentences” like the Liar are even saying anything at all.
True or false:
A) This sentence is true.
B) This sentence is false.
C) This sentence is dialethism.
D) All of the above.
Well, it depends on whether you're a dialethist or not! Dialethists will treat A & B as both true and false. C depends on detail. Eg ''this sentence is both true and false" will be true, hence both true and false, like A & B.
great video! not a fan of dialetheism myself, but it's fun to read about it
Same. It's become something we should all learn about.
About "Just true": there is always the fallback solution of no longer disallowing "true = false" just to allow a logical system in which this sentence takes its single value of true.
Yes, the sentence is _not_ just true because the sentence is just true. _not_ true is true. No contradiction here. At least you may accept that if you weren't me. I would say that whenever we say "contradiction" we mean something that leads to T->F, which allows you to take any two propositions A and B and say A->T->F->B, which means all implications are valid. It completely trivializes the logic system and makes it no longer useful. The idea solves every version of the liar paradox, but it costs you the entire universe to do so.
But true = false is disastrous for the definition of entailment. Since T is a designated value, then F too would be designated, and so you’d get some very dodgy entailments, e.g. A |= ~A !
@@AtticPhilosophy That's what I meant when I said it "completely trivializes the logic system and makes it no longer useful" and it "costs you the entire universe to do so". It forces every entailment to hold in the logic system.
I am a programmer.. and I don't work on quantum computers.. I feel like dialetheism is pointless.. to me it seems much better to just accept some statements are nonsensical even if they are grammatically correct in natural language.
Also:
x = true & false..
Therefore x = false
This example actually demonstrates the inherent ambiguity of natural language.. in a programming language this would have a well defined meaning.. however if you say "x is true and false".. maybe you are a programmer/classical logician taking a roundabout way to say something is false.. or maybe you are a dialethic saying something that has no resolvable meaning in the human mind.. its ambiguous.. just like a paradoxical statement is.
Seems to me that dialetheism just takes the chaos/ambiguity out of the language and embeds it into itself
Saying the liar is nonsensical is one option, but it's problematic. Don't you understand what it's saying?
@@AtticPhilosophy I don't see why it is any more problematic than saying something is both true and false at the same time. But I understand the paradox, of course. Honestly calling a statement nonsensical is probably the inverse of saying it is true and false at the same time.. its essentially calling it neither. Which to me, is a more agreeable resolution, but either way it kinda seems like a waste of time.. since at the end of the day all you've done is to say something about a statement that isn't really saying anything at all (at least nothing useful).
@@AtticPhilosophy also I read up on this a little more to try to look into actually useful applications.. and I think its interesting that my initial response kinda hints at Arthur Prior's resolution.. which to me makes a lot of sense. The statement is false because it is asserting itself as both true (implicitly) and false at the same time.
(This video repeats footage from an earlier one, but later is unique again.)
00:30 Dialethism - "The view that sentences can be both true and false at the same time."
01:15 "Dialethism requires a Paraconsistent Logic, which is any logic denying the Explosion Principle." (Which in my opinion makes the Para.Logic almost always Dialethist.) (Also Jago used ⊨ instead of ⊢ describing the Explosion Principle, which I am 90% sure is wrong.)
02:30 Paradox Logic: A Logic in which there is a third Truth Value, "O". Most of the confusion in this video stems from the lack of ¬'s definition in Paradox Logic. There are 2 approaches:
1.The Set-theoretic one - ¬T=O∨F; ¬F=O∨T; ¬O=T∨F.
2.The one Jago presents - ¬T=F; ¬F=T; ¬O=O, in which set theory gets a stroke.
03:45 "Why 'both' true and false, instead of 'neither' true nor false?" Assuming option 2, "because unintelligent people do not realize that ¬T∧¬F=T∧F". Assuming option 1, "'both' means ¬O, and 'neither' means O".
05:30 Credit to Jago for seeing the problem himself, the Strengthened Liar. But all his skulduggery is needless. All we have to construct is:
"This sentence is False or Other, and not True." If it is T, then it cannot be T. If it is F or O, then it must be T.
06:15 The Dialethist's response is wrong. It says "This sentence is not just T." ⇔
"This sentence is not (T∧¬¬T)" which means it is just the regular Liar.
But really "This sentence is not just T." ⇔
"This sentence is F∨O." which can be refuted the same way Dialect's Naive Solution was!
07:45 "To capture the meaning of 'This sentence is just T.' we need metalanguage."
No we do not. As I wrote above.
09:00 The last Dialethist response:
We are in the Paradox Logic here, so our Liar sentence can both be just-true and ¬just-true. After all, the Dialethist allows all contradictions! Yay! (Obviously when we build a Logic in which we just ignore contradictions our system will be paradox-free.)
Of course, in the process, ¬ lost all its meaning, and bivalency is out the window. 👍
It was a nice explanation of Dialethism, though not the simplest to follow.
T, F, O are truth-values, so sentences like '~T' (really, shorthand for '~Tp' for a given proposition p) belong to the metalanguage. Properties like this can't be expressed in a propositional object language.
en.wikipedia.org/wiki/Principle_of_explosion
When we encode the principle of explosion as a syllogism:
Socrates is a man.
Socrates is not a man.
Therefore, Socrates is a butterfly.
The conclusion does not follow from the premises, thus the non-sequitur error.