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
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Truth definitions don't produce a good theory, because they go beyond your current language
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3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
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In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage
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3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
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Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms?
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If truth is defined it can be eliminated, whereas axiomatic truth has various commitments
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Instead of a truth definition, add a primitive truth predicate, and axioms for how it works
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Axiomatic theories of truth need a weak logical framework, and not a strong metatheory
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3. Truth / H. Deflationary Truth / 2. Deflationary Truth
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Deflationists say truth merely serves to express infinite conjunctions
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
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To prove the consistency of set theory, we must go beyond set theory
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
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We can use truth instead of ontologically loaded second-order comprehension assumptions about properties
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5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
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Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true'
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