Combining Philosophers
Ideas for Peter B. Lewis, Halbach,V/Leigh,G.E and Volker Halbach
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23 ideas
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
15648

Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach]

15650

Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach]

16294

Axiomatic truth doesn't presuppose a truthdefinition, though it could admit it at a later stage [Halbach]

15655

Should axiomatic truth be 'conservative'  not proving anything apart from implications of the axioms? [Halbach]

15654

If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach]

16326

The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach]

16299

Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach]

16340

Truth axioms need a base theory, because that is where truth issues arise [Halbach]

16305

We know a complete axiomatisation of truth is not feasible [Halbach]

16311

To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach]

16318

Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach]

16322

CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach]

16313

A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG]

16315

The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski biconditionals [Halbach]

16314

Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'typefree' [Halbach]

19124

A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]

19126

If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh]

3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
16327

FriedmanSheard is typefree Compositional Truth, with two inference rules for truth [Halbach]

19129

The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh]

3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
16329

KripkeFeferman theory KF axiomatises Kripke fixedpoints, with Strong Kleene logic with gluts [Halbach]

16331

The KF is much stronger deductively that FS, which relies on classical truth [Halbach]

19130

KF is formulated in classical logic, but describes nonclassical truth, which allows truthvalue gluts [Halbach/Leigh]

16332

The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach]
