The Liar's Paradox

In this video, possible truth values for a variety of liar's statement are evaluated using actual/potential tables, which compare the statement's actual truth value (what it is) with its potential truth value (what it says it can be).

In addition to the familiar truth values that can be assigned to the liar's statement, a new possibility is considered: true or false.

Below are links to corresponding sections of the video:
Intro: 0:00
true / false : 1:10
neither true nor false: 1:45
true and false: 3:58
true or false: 5:18

#LiarsParadox

[keystoneperspectives]

In this video I suggest that asking whether the truth predicate applies is equivalent to asking whether the statement is determinately true or not. This is not correct. I should have said that it is equivalent to asking whether the statement is determinate. "Determinately true" means that a truth value of true can be determined whereas "determinate" means that a truth value (either true or false) can be determined. This subtle difference does not affect the arguments or conclusions presented, but I thought it was worth clarifying.

[ganrimmonim]

Reminds me of the wave-particle problem in physic that said it is going to keep me awake at night.

[thisismyname]

You left out the correct answer. It's truth value is undefined, like the arithmetic value for 7/0 is undefined, because any method of evaluating the liar will never halt.. Undefined =/= other. The value of 7/0 is not other. It is undefined. The truth value of the statement "this statement is true" is also undefined.

[alanbunyan]

One approach to solving this issue is to take the view that the supposed self-referentiality of the proposition in question is impossible, for the simple reason that the sentence apparently referenced by the word 'this' does not yet exist: it is IN THE PROCESS of being formed: that is to say, it consists at the moment of reference of nothing more than a grammatical subject ("this") but, as yet lacking any predicate, it has not been formed, i.e. it does not yet exist AS A SENTENCE. It could refer to another sentence which has already been formed, but never to itself. It's a bit like my trying to sell you a car that has not yet been built and asserting '"This car never breaks down", to which you would be entitled to retort that I cannot reasonably make any such claim of something that does not actually exist!

[Google_Censored_Commenter]

What is meant by the statement "It can potentially be true or false" if there's no actual truth value? What is meant in the word "potential" if it isn't "actually" potential in the first place?

[jamestagge]

Interesting to watch all these supposed experts go all around the houses to try to resolve paradoxes like the Liar paradox as per Quine. Kripke’s ideas on groundedness are sensible but only as a qualifier of the proper resolution which no one seems to recognize. Consider…………the very famous W. V. Quine created three categories of paradoxes (not necessary to go into here, but for the third, antimony), an example of the third of which he claimed to present a “crisis of thought”, he apparently believing it to be unresolvable. He could not have been more wrong and transparently so. His representative example of the problem was the statement, ”this statement (or sentence) is false”. If you consider that if it is true, it is false for it claims to be so…then how could it be true that it is false?…thus the paradox. However, it is in fact not a paradox at all and certainly no crisis of anything. The deceptive self-referencing statement is the only means by which to facilitate such a paradoxical function, making it on that basis alone, in this case, invalid. In order for it to be paradoxical, the subject noun “statement” (which is also a set definition but devoid of members) must be devoid of content or meaning. By this only can the term statement be free of any connection to a reference object which would then be that to which it referred and that by which it might be judged true or false. For clarity, consider the modification, “this statement that the sky is green, is false”. Here no paradox arises because “that the sky is green” is the reference object (of the content) of the term “statement”, a possible member of the set of which it (statement) is the definition. There is information which can be judged as to whether it is true or false. Absent such a construction, there is nothing to judge. Additionally, the paradox violates the law of non-contradiction, that it cannot be true and false at the same time and that the object of the statement, “this statement is false”, or false (or the adjective linked to the subject noun, statement), be at once the cause and effect of the paradoxical function.

Consider, for the paradox to be stated at all and that its paradoxical function might be conveyed and understood for consideration, deference to the (formal) logic of the structure of language must be made and maintained. Logically then, we are obliged to assume that the statement, “this statement is false”, is true or what is the point of the exercise?

This “paradox” is an assault on logic and the language itself, including that by which the paradox was defined in the first place and cannot truly be considered legitimate by anyone, the sophistry applied by the “experts” to facilitate the escape from such a conclusion, notwithstanding. I believe Wittgenstein, Frege and Russell would have agreed, a notion easily understood in their works on language and meaning. The error allowing the paradox is in the application of the language used, i.e., as mentioned above, that the term “statement” in “this statement is false” is a set definition absent members and by that the error is grammatical.

The liar paradox is sophomoric and that it is claimed to have challenged many philosophers for hundreds of years is hardly high praise. Sad formulations such as dialethism as a means of validation of this kind of sophistry only make my point when examined. There are no paradoxes in the material or abstract realm. None. There are no conceptual contradictions which material reality permits. That a rock cannot be both here and there at once is self-evident. That one cannot appeal to truths to formulate a position which denies the existence of truth is equally so. It is all piffle.

[Lilly_Israel]

Me thinking about the statement: If it's false it's true if it's true it's false HELP.MY BRAIN IT HURTS

[stephenmorgan]

He nailed it. This statement is ambiguous

[uprola]

Didn't Goedel prove that it makes no sense even to try solving liar's paradox? As any powerful enough logic will have non-derivable self-referential statements similar to this one?

[StrapMerf]

How about the liars paradox is a paradox

[abdulchoudhury]

The answer: Right now he is saying the truth but usually he tells lies

[theodriggers]

This statement has a 0% chance of being true

[ambernectar]

There is no solution. It is true and false.

[theodriggers]

This statement is only not determinately true

[amithachandima]

"This statment is false." It seems like quantum super possition.
It may be 1
It may be 0
It may be 1 or 0
It may be 1 and 0
It may be neither 1or 0
Any posibility can happen. 😂😂😂