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) [plato.stanford.edu ,]].
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3. Truth / A. Truth Problems / 2. Defining Truth
15647

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. Metalanguage for truth
15649

In semantic theories of truth, the predicate is in an objectlanguage, and the definition in a metalanguage

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

15650

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

15655

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

15654

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

3. Truth / H. Deflationary Truth / 2. Deflationary Truth
15656

Deflationists say truth merely serves to express infinite conjunctions

4. Formal Logic / F. Set Theory ST / 1. Set Theory
15657

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
15652

We can use truth instead of ontologically loaded secondorder comprehension assumptions about properties

5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
15651

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
15653

We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness
