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 didnāt know I had to click the link in blue. I read it now. Iām close to some of the āsolutionsā but no explicit mention of Habermasā performative contradiction. Itās 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. Heād say āthe present King of France is baldā (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.
Thereās a plethora of approaches. I first discovered your, not all statements are ā¦, a few years ago. It wouldāve been a nice dodge if not implied was abdicating the LEM. I donāt 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.
Thereās 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 āone, true logicā. 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 - āItās the one true logic because it says itās the one true logicā¦ā.
A better approach is to choose logics and models to suit our discussions. Thatās 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 canāt 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.
āSome form of consistencyā??
I want to disagree, but I donāt 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. Thatās like saying snow is white and not white to me. Can we make sense of snow being white and note white?
Thatās 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 doesnāt it possess structural features, linguistically-informed structural features, that help solve the Liar? In fact I donāt know how to express the Liar in predicate logic? Is it just L = This sentence is false?
In Kleen logic, āunknownā. Look in to it. As for the rest, Iām 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 ā Ā¬Tr(āLā)
