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
Tarski proved that truth cannot be defined from within a given theory
'True sentence' has no use consistent with logic and ordinary language, so definition seems hopeless
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Tarski did not just aim at a definition; he also offered an adequacy criterion for any truth definition
Tarski gave up on the essence of truth, and asked how truth is used, or how it functions
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them
We can define the truth predicate using 'true of' (satisfaction) for variables and some objects
3. Truth / F. Semantic Truth / 2. Semantic Truth
Tarskian truth neglects the atomic sentences
Tarski made truth respectable, by proving that it could be defined
Tarski didn't capture the notion of an adequate truth definition, as Convention T won't prove non-contradiction
Tarski's 'truth' is a precise relation between the language and its semantics
A physicalist account must add primitive reference to Tarski's theory
Tarski had a theory of truth, and a theory of theories of truth
Physicalists should explain reference nonsemantically, rather than getting rid of it
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Tarski's had the first axiomatic theory of truth that was minimally adequate
Tarski defined truth, but an axiomatisation can be extracted from his inductive clauses
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
A name denotes an object if the object satisfies a particular sentential function
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Tarski built a compositional semantics for predicate logic, from dependent satisfactions
Tarksi invented the first semantics for predicate logic, using this conception of truth