Combining Philosophers

Ideas for Peter B. Lewis, Halbach,V/Leigh,G.E and Volker Halbach

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42 ideas

3. Truth / A. Truth Problems / 1. Truth
Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach]
Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach]
3. Truth / A. Truth Problems / 2. Defining Truth
Traditional definitions of truth often make it more obscure, rather than less [Halbach]
Any definition of truth requires a metalanguage [Halbach]
If we define truth, we can eliminate it [Halbach/Leigh]
If people have big doubts about truth, a definition might give it more credibility [Halbach]
Truth definitions don't produce a good theory, because they go beyond your current language [Halbach]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach]
Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach]
Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh]
3. Truth / F. Semantic Truth / 2. Semantic Truth
The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh]
Disquotational truth theories are short of deductive power [Halbach]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [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]
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]
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]
A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG]
The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach]
Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [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]
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach]
The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach]
The KF is much stronger deductively that FS, which relies on classical truth [Halbach]
KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh]
The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
The main problem for deflationists is they can express generalisations, but not prove them [Halbach]
Some say deflationism is axioms which are conservative over the base theory [Halbach]
Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach]
Deflationists say truth merely serves to express infinite conjunctions [Halbach]
Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach]
Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach]