Combining Philosophers
Ideas for Monroe Beardsley, Volker Halbach and Gregory Vlastos
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19 ideas
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
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15654
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If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach]
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16294
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Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach]
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16326
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The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach]
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16311
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To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach]
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16318
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Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach]
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16299
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Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach]
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16340
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Truth axioms need a base theory, because that is where truth issues arise [Halbach]
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16305
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We know a complete axiomatisation of truth is not feasible [Halbach]
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16313
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A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG]
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16315
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The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach]
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16314
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Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach]
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15650
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Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach]
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16322
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CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach]
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15648
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Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach]
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15655
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Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach]
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3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
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16327
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Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach]
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3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
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16331
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The KF is much stronger deductively than FS, which relies on classical truth [Halbach]
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16329
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Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach]
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16332
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The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach]
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