Maximal consistent sets of instances of Tarski's schema (T)

McGee, Vann

doi:10.1007/bf00260929

Cited by 88 publications

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“…The theory, which is an abstract object whatever we say about it, may still exist. 4 A similar thing can be said of McGee's (1992) criticism that the concessions Horwich needs to make to the Liar paradox make it so that we cannot construct the set of axioms. Even if this conclusion can be shown to apply to a propositional axiomatic theory, rather than (as McGee does) a formal theory, it does not have the bite it would have applied to Horwich's account of the meaning of the truth predicate.…”

Section: How To Axiomatize Truthmentioning

confidence: 82%

“…David (2002) and Raatikainen (2005) argue that Horwich's defense fails, and in Section 5, I consider a special case of this. McGee (1992) used the Gödel self-referential lemma in a different proof against the Naïve Theory. Because of the differences between Horwich's theory and the Naïve Theory, McGee's argument does not apply directly to the former, but in Section 4 I argue that an argument similar to Gödel's does hold against theories like Horwich's.…”

Section: Introductionmentioning

confidence: 99%

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Theories and Theories of Truth

Christensen

2011

Int Ontology Metaphysics

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Formal theories, as in logic and mathematics, are sets of sentences closed under logical consequence. Philosophical theories, like scientific theories, are often far less formal. There are many axiomatic theories of the truth predicate for certain formal languages; on analogy with these, some philosophers (most notably Paul Horwich) have proposed axiomatic theories of the property of truth. Though in many ways similar to logical theories, axiomatic theories of truth must be different in several nontrivial ways. I explore what an axiomatic theory of truth would look like. Because Horwich's is the most prominent, I examine his theory and argue that it fails as a theory of truth. Such a theory is adequate if, given a suitable base theory, every fact about truth is a consequence of the axioms of the theory. I show, using an argument analogous to Gödel's incompleteness proofs, that no axiomatic theory of truth could ever be adequate. I also argue that a certain class of generalizations cannot be consequences of the theory.

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Section: How To Axiomatize Truthmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Theories and Theories of Truth

Christensen

2011

Int Ontology Metaphysics

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“…Much of what is said about MT ignores this point and assumes that it is a formal theory, that it is, in fact, the same theory (sentence-MT) that Tarski (1956, p. 257) long ago rejected-or that it is a theory so similar that, at most, we need make only a few slight adjustments to account for the differences. Sentence-MT is clearly unsatisfactory, for the reasons pointed out by Tarski (and frequently rehearsed), and also for the reasons pointed out by McGee (1992). 2 MT may be unsatisfactory as well.…”

Section: Theories and Theories Of Truthmentioning

confidence: 91%

“…difficult problem to determine which propositions are the ones that lead to paradox, but he says an adequate solution to the paradox will have three properties: (a) it will guarantee that MT entail no contradictions, (b) it will leave as much of the theory intact as possible, and (c) it will be constructive (Horwich 1998, p. 42). McGee (1992) claims, without argument, that (c) is inconsistent with minimalism, and examines the result of constructing a theory with just (a) and (b). Horwich is unpersuaded that (c) is inconsistent with minimalism, and proposes a constructive solution (see Horwich 2005).…”

Section: Mcgee's Proofmentioning

confidence: 96%

“…These theories develop predicates that are more or less close to truth, but are never materially adequate-they never give us all the T sentences. McGee (1992) shows that there are serious problems for a theory operating on the sole requirement that it be as materially adequate as possible. He develops his argument, at least in part, as a response to Horwich's theory of truth.…”

Section: Mcgee's Proofmentioning

confidence: 98%

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McGee on Horwich

Christensen

2015

Synthese

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Vann McGee has argued against solutions to the liar paradox that simply restrict the scope of the T sentences as little as possible. This argument is often taken to disprove Paul Horwich's preferred solution to the liar paradox for his Minimal Theory of truth (MT). I argue that Horwich's theory is different enough from the theory McGee criticized that these criticisms do not apply to Horwich's theory. On the basis of this, I argue that propositional theories, like MT, cannot be evaluated using the same methods as sentential theories.Keywords Theories of truth · Mimimalism · Paul Horwich · Vann McGee Theories and Theories of TruthPhilosophers have long been interesting in truth, and logicians have developed interesting and sophisticated formal theories of the truth predicate. The theories of the logicians obviously have something to do with the property the philosophers are interested in, but it's not always clear what the relationship is. I offer a negative result.Better said, I offer a corrective to a tendency to conflate the philosophical investigation with the logical investigation. The logical investigation has given us beautiful logical theories like Friedman-Sheard (FS) and Kripke-Feferman (KF) (see Halbach and Horsten (2002) for a good overview of such theories). Partly on analogy with such theories, Paul Horwich has developed a theory of the property of truth for propositions, which he calls the Minimal Theory (MT). MT is a theory, like the formal theories FS and KF, in the sense of a set of axioms and theorems. MT is unlike those formal the-B Ryan Christensen

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From Paradox to Truth

Leigh

2022

Lecture Notes in Computer Science

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Maximal consistent sets of instances of Tarski's schema (T)

Cited by 88 publications

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Theories and Theories of Truth

Theories and Theories of Truth

McGee on Horwich

From Paradox to Truth

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