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3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth

[theories of truth built from a set of axioms]

34 ideas
Ockham had an early axiomatic account of truth [Halbach on William of Ockham]
If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert]
We need an undefined term 'true' in the meta-language, specified by axioms [Tarski]
Tarski's had the first axiomatic theory of truth that was minimally adequate [Horsten on Tarski]
Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Halbach on Tarski]
Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Davidson on Tarski]
Certain three-valued languages can contain their own truth predicates [Gupta on Kripke]
The Tarskian move to a metalanguage may not be essential for truth theories [Gupta on Kripke]
We can get a substantive account of Tarski's truth by adding primitive 'true' to the object language [Etchemendy]
'Reflexive' truth theories allow iterations (it is T that it is T that p) [Horsten]
Axiomatic approaches to truth avoid the regress problem of semantic theories [Horsten]
The Naďve Theory takes the bi-conditionals as axioms, but it is inconsistent, and allows the Liar [Horsten]
Axiomatic theories take truth as primitive, and propose some laws of truth as axioms [Horsten]
A good theory of truth must be compositional (as well as deriving biconditionals) [Horsten]
By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content! [Horsten]
An axiomatic theory needs to be of maximal strength, while being natural and sound [Horsten]
Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models [Horsten]
Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach]
The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach]
Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach]
Truth axioms need a base theory, because that is where truth issues arise [Halbach]
We know a complete axiomatisation of truth is not feasible [Halbach]
To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach]
A theory is 'conservative' if it adds no new theorems to its base theory [PG on Halbach]
The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach]
Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach]
CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach]
Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach]
Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach]
Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach]
Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach]
If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach]
A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]
If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh]