True and False? Dialethism and the Liar Paradox | Attic Philosophy

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?

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.

Links:

Get in touch on Social media!

#logic #philosophy

[markuspfeifer]

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]

[donatolisio]

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?

[oldmanSturzl]

True or false:

A) This sentence is true.
B) This sentence is false.
C) This sentence is dialethism.
D) All of the above.

[neopalm]

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.

[patrickwithee]

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?

[jawojciechdrzymala]

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?

[animefurry]

Do you think Hegels Dialectical Logic was Dialetheism?

...

Would Lacan be a Dialetheist?

[ABC-ytnq]

This purported paradox proceeds on the false premise that the evaluation of some thing can be contained within the very thing sought to be evaluated. 

It appears to be impossible for the evaluation of something - let's call it X - to also be contained in that X. The evaluation of X changes the value of X from X to X + [Evaluation of X]. Prima facie these values are not and can never be equal. 

Imagine X can only be either True or False. We know some things about X, but not whether or not it is T or F. To learn that will add information to and expand our definition of X, changing it from X to either X+T or X+F.

This appears to be similar to the observer effect, which alters the results of the double slit experiment by the act of observation of sub-atomic particles, which previously were waves, by collapsing the wave function. 

Thus, in order to evaluate X, and not X + [Evaluation of X], the evaluator of X must be completely separate from and independent of X and must not affect the value of X by the act of evaluation. This is impossible when observing sub-atomic particles because of the workings of quantum mechanics, but it is possible in larger, grosser information systems. Symbology - specifically written language - is such a system.

The sentence that is the target of evaluation for Truth or Falsity is an essential part of the communication but is missing. This appears similar to asking someone to calculate the square root of ... and then not telling them the number you want them to calculate the square root of. Without the separate sentence to be evaluated being set out, the word combination "This sentence is false" is gibberish with zero information value.

The sentence "This sentence is false" must by necessity be an evaluation of a separate and independent sentence which was communicated, in full, at some point in time prior to the evaluation.

The only proper answer to the Liar's Paradox of "Is this sentence false?" is, "Which specific sentence are you referring to?"

[derpnerpwerp]

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

[polcott]

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.

[BelegaerTheGreat]

(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.

[dominiks]

great video! not a fan of dialetheism myself, but it's fun to read about it