Ideas from 'The Semantic Conception of Truth' by Alfred Tarski [1944], by Theme Structure

[found in 'Semantics and the Philosophy of Language' (ed/tr Linsky,Leonard) [University of Illinois 1972,0-252-00093-5]].

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1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics beyond Science
Some say metaphysics is a highly generalised empirical study of objects
1. Philosophy / F. Analytic Philosophy / 1. Analysis
Disputes that fail to use precise scientific terminology are all meaningless
2. Reason / D. Definition / 1. Definitions
For a definition we need the words or concepts used, the rules, and the structure of the language
3. Truth / A. Truth Problems / 2. Defining Truth
Definitions of truth should not introduce a new version of the concept, but capture the old one
A definition of truth should be materially adequate and formally correct
A rigorous definition of truth is only possible in an exactly specified language
We may eventually need to split the word 'true' into several less ambiguous terms
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
It is convenient to attach 'true' to sentences, and hence the language must be specified
In the classical concept of truth, 'snow is white' is true if snow is white
Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction
Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate'
We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true
Scheme (T) is not a definition of truth
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
The best truth definition involves other semantic notions, like satisfaction (relating terms and objects)
Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
We can't use a semantically closed language, or ditch our logic, so a meta-language is needed
The metalanguage must contain the object language, logic, and defined semantics
3. Truth / F. Semantic Truth / 2. Semantic Truth
If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
We need an undefined term 'true' in the meta-language, specified by axioms
3. Truth / H. Deflationary Truth / 1. Redundant Truth
Truth can't be eliminated from universal claims, or from particular unspecified claims
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Semantics is a very modest discipline which solves no real problems
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth tables give prior conditions for logic, but are outside the system, and not definitions
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
The truth definition proves semantic contradiction and excluded middle laws (not the logic laws)
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The Liar makes us assert a false sentence, so it must be taken seriously