Ideas from 'Axiomatic Theories of Truth (2005 ver)' by Volker Halbach [2005], by Theme Structure

[found in 'Stanford Online Encyclopaedia of Philosophy' (ed/tr Stanford University) [ ,-]].

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3. Truth / A. Truth Problems / 2. Defining Truth
Truth definitions don't produce a good theory, because they go beyond your current language
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
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Instead of a truth definition, add a primitive truth predicate, and axioms for how it works
Axiomatic theories of truth need a weak logical framework, and not a strong metatheory
If truth is defined it can be eliminated, whereas axiomatic truth has various commitments
Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms?
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationists say truth merely serves to express infinite conjunctions
4. Formal Logic / F. Set Theory ST / 1. Set Theory
To prove the consistency of set theory, we must go beyond set theory
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
We can use truth instead of ontologically loaded second-order comprehension assumptions about properties
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true'
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / g. Incompleteness of Arithmetic
We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness