Ideas from 'The Concept of Truth for Formalized Languages' by Alfred Tarski [1933], by Theme Structure
[found in 'Logic, Semantics, Meta-mathematics' by Tarski,Alfred [Hackett 1956,0-915144-76-x]].
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3. Truth / A. Truth Problems / 2. Defining Truth
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Tarski proved that truth cannot be defined from within a given theory [Halbach]
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15342
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Tarski proved that any reasonably expressive language suffers from the liar paradox [Horsten]
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19069
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'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless
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3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
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Tarski's Theorem renders any precise version of correspondence impossible [Halbach]
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3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
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Tarski gave up on the essence of truth, and asked how truth is used, or how it functions [Horsten]
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Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition [Halbach]
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Tarski enumerates cases of truth, so it can't be applied to new words or languages [Davidson]
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Tarski define truths by giving the extension of the predicate, rather than the meaning [Davidson]
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Tarski made truth relative, by only defining truth within some given artificial language [O'Grady]
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Tarski has to avoid stating how truths relate to states of affairs [Kirkham]
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Tarskian semantics says that a sentence is true iff it is satisfied by every sequence [Hossack]
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3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
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Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess]
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Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Rumfitt]
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We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Horsten]
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For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Kirkham]
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Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Kirkham]
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Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Davidson]
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3. Truth / F. Semantic Truth / 2. Semantic Truth
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Tarski made truth respectable, by proving that it could be defined [Halbach]
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Tarski defined truth for particular languages, but didn't define it across languages [Davidson]
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16304
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Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction [Halbach]
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10969
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Tarski had a theory of truth, and a theory of theories of truth [Read]
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Tarski's 'truth' is a precise relation between the language and its semantics [Walicki]
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Physicalists should explain reference nonsemantically, rather than getting rid of it [Field,H]
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10904
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Tarskian truth neglects the atomic sentences [Mulligan/Simons/Smith]
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Tarski says that his semantic theory of truth is completely neutral about all metaphysics [Haack]
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A physicalist account must add primitive reference to Tarski's theory [Field,H]
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3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
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16306
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Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses [Halbach]
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Tarski's had the first axiomatic theory of truth that was minimally adequate [Horsten]
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5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
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Identity is invariant under arbitrary permutations, so it seems to be a logical term [McGee]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
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10823
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A name denotes an object if the object satisfies a particular sentential function
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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Tarski built a compositional semantics for predicate logic, from dependent satisfactions [McGee]
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Tarksi invented the first semantics for predicate logic, using this conception of truth [Kirkham]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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The object language/ metalanguage distinction is the basis of model theory [Halbach]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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Tarski avoids the Liar Paradox, because truth cannot be asserted within the object language [Fisher]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman]
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21. Aesthetics / A. Aesthetic Experience / 3. Taste
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Taste is the capacity to judge an object or representation which is thought to be beautiful [Schellekens]
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