Ideas of Halbach,V/Leigh,G.E., by Theme

[, fl. 2013, At Oxford University.]

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3. Truth / A. Truth Problems / 2. Defining Truth
If we define truth, we can eliminate it
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
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
Semantic theories need a powerful metalanguage, typically including set theory
3. Truth / F. Semantic Truth / 2. Semantic Truth
The T-sentences are deductively weak, and also not deductively conservative
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness
If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
The FS axioms use classical logical, but are not fully consistent
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts
5. Theory of Logic / K. Features of Logics / 3. Soundness
If soundness cannot be proved internally, 'reflection principles' be added which assert soundness
8. Modes of Existence / B. Properties / 12. Denial of Properties
We can reduce properties to true formulas
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories