Saul Kripke's Theory of Truth (Semantic Type-Free)

[@maiku20]

In the language Lz, why couldn't U(p)be defined as ( T(p) iff not T(p) ), or as ( T(p) iff T(not p) ) ? (EDIT: Never mind, i just realized that U iff U means U and not T!) By the way, what an awesome channel you have created! I am impressed to the border of astonishment at the quality and voluminousness of your videos.

[@CarneadesOfCyrene]

Thanks! And thanks for watching. I'm glad you enjoy the videos!

[@sagebias2251]

Does this have any relationship to why philosophers debate the definition of truth in common parlance.

[@thisismyname9569]

p > q where p is false should be U=undefined. If p is false, then the IF statement is inapplicable. "IF a THEN b" only says that b is true if a is true. It says nothing about what is the case if a is false. "This sentence is false" should be U because any evaluation mechanism has to first evaluate "this sentence" which is the sentence itself and will therefore go into an infinite recursive loop and never halt. Thus any evaluation mechanism evaluating an expression containing the liar paradox will also never halt and therefore should also be U. A different case is p="The present King of France is bald", which is also U. This case is more debatable, but I would argue any expression containing a U sentence should also be U.

[@CarneadesOfCyrene]

+This IS my name That sounds like a different version of non classical logic which questions the rules of the conditional. It is certainly a debate as to which logic we should use, but this one tries to be faithful to classical logic where any conditional with a false antecedant is true.

[@thisismyname9569]

Carneades.org - Yes, it is a different version of non-classical logic designed to better reflect people's actual understanding of if statements. Literally everyone disagrees when first told that 'if a then b' is true if a is false. None of the usual explanations why - 'if a is false all bets are off', 'if a is false I wasn't lying', 'it's the principle of explosion' ( as if naming what you are doing is an explanation) work. I think my first paragraph above explains why they disagree and also explains many well known issues in logic, including for example the liar's revenge, which is undefined. [ edit: because any evaluating mechanism would go into an infinite recursive loop.] To clarify, the value U belongs to the meta-language, not the logic itself. There the sentences have no truth values at all. Great videos BTW. Keep em coming.

[@eammonful]

Does type in these contexts mean essentially the same thing as type in Math or Computer Science?

[@CarneadesOfCyrene]

+eammonful Yes, basically, all steming from Russell and Whitehead's type theory.

[@zacn654]

Please do Stirner for halloween