You seem not to have read the linked post. It offers four distinct ways of dealing with the liar, not one.
But also, at least since Frege, logicians differentiate between the use of a sentence and what renders it true. Asserting that P is performing an act with words, and is distinct from what does or does not render P true.
The Liar concerns truth conditions, not speech acts. Your move is too fast.
What counts here is that we cannot construct a coherent bivalent truth theory that assigns stable truth conditions to such sentences.
I didnât know I had to click the link in blue. I read it now. Iâm close to some of the âsolutionsâ but no explicit mention of Habermasâ performative contradiction. Itâs quite interesting to see logicians/philosophers trying to solve the paradox in so many different ways.
Habermas borrowed the notion of a performative contradiction from Austin, Strawson and others. Strawson is probably closest to your approach. Heâd say âthe present King of France is baldâ (Are you familiar with that example?) is not false, but does not amount to an assertion and so is without a truth value. Roughly, an exampel of the first approach.
A valid approach, but not the only one and not without issues.
I see, but no explicit mention of a performative contradiction.
Thereâs a plethora of approaches. I first discovered your, not all statements are âŚ, a few years ago. It wouldâve been a nice dodge if not implied was abdicating the LEM. I donât understand LEM or bivalence all that well though. LEM to me is p \vee \neg p and bivalence means 2 truth values, true and false.
Thereâs a difference between saying that there are sentences with a third truth value, and that there are sentences with no truth value at all.
And there is the other view that allows for sentences that are both truthful and false.
There are logics that conserve some form of consistency in each case.
There is no need to choose one logic amongst these and elevate it to the level of being the âone, true logicâ. Indeed, doing so implies that we already have a, presumably logical, basis for making that very decision, and so involves some form of auto-aggrandising circularity - âItâs the one true logic because it says itâs the one true logicâŚâ.
A better approach is to choose logics and models to suit our discussions. Thatâs not relativism. The consequence relations logic studies capture differing notions of validity and consistency that we can acknowledge and discuss.
What is clear is that paradoxes such as the Liar do not threaten the basis of logic, so much as show us the edges of what can and canât be said clearly. They show us why we need logic as well as natural languages.
Yes, paraconsistent logic and dialetheism. How does that work? The Liar is true and false.
âSome form of consistencyâ??
I want to disagree, but I donât think my vote counts. So you mean I should adopt dialetheism/paraconsistent logic with the Liar? Ok, so I do and then the Liar is both true and false. Thatâs like saying snow is white and not white to me. Can we make sense of snow being white and note white?
Thatâs the crux of the matter. Even with my limited understanding I can see Gottlob Frege working on predicate logic and making decisions. Why is predicate logic the way it is? Why doesnât it possess structural features, linguistically-informed structural features, that help solve the Liar? In fact I donât know how to express the Liar in predicate logic? Is it just L = This sentence is false?
In Kleen logic, âunknownâ. Look in to it. As for the rest, Iâm happy to answer specific questions, but reading up on nonclassical logic might better suit your needs.
See the SEP article. Generally, given a sentence L in the language and a truth predicate Tr, the Liar is expressed as L â ÂŹTr(âLâ)
Thanks for the suggestion. Very helpful. Chatted up an AI, have made notes for future reference.
I have a problem with the term, designated. With regard to \implies (implication), given both the antecedent and consequent is U, it evaluates to U in Kleene logic but in Lukaseiwicz logic it evaluates to T. What does this mean?
A can of worms. Think of Kleene logic as formalising what we know, while Ĺukasiewicz formalises what might be the case.
Take a murder trial. The Jury is deliberating. Now the defendant either committed the murder or didnât, but we donât as yet know which - so we assign a âUâ to âThe defendant is guiltyâ.
What truth value might we assign to âIf the defendant is guilty, then the defendant is guiltyâ?
Kleene logic formalises what we know, and since we donât know if the defendant is guilty, it assigns âUnknownâ to âIf the defendant is guilty, then the defendant is guiltyâ, since we donât know what the Jury will decide.
Ĺukasiewicz logic formalises structure, and to be sure, if the defendant is guilty, than it is true that the defendant is indeed guilty. So it assigns âTrueâ to âIf the defendant is guilty, then the defendant is guiltyâ.
In Kleene logic, if we donât know the defendant is guilty, we donât pretend to know the truth of âIf he is guilty, he is guiltyâ. In Ĺukasiewiczâs logic, regardless of whether he is guilty or no, if he is guilty, then he is guilty.
Both are consistent three-valued logics. Neither is âwrong.â They simply have different motivations and different domains of application.