Truth2 Tarski's theory of truth |
(論理学の標準的な意味論)
Convention T:
An adequate theory of truth for L must imply, for each sentence φ of L
⌈ φ ⌉ is true if and only if φ .
Base clauses
reference and satisfaction:
‘Snow’ refers to snow.
‘Grass’ refers to grass.
a satisfies ‘is white’ if and only if a is white.
a satisfies ‘is green’ if and only if a is green.
For any atomic sentence ⌈ t is P ⌉ : ⌈ t is P ⌉ is true if and only if the referent of t satisfies the referent of P.
Recursion clauses
For any sentences φ and ψ of L:
⌈ φ ∨ ψ ⌉ is true if and only if ⌈ φ ⌉ is true or ⌈ ψ ⌉ is true.
⌈ ¬φ ⌉ is true if and only if it is not the case that ⌈ φ ⌉ is true.
This theory satisfies Convention T.
Tarskiは(propositionsではなく)sentencesを bearers of truthとしている (こう考えた最初の人というわけではない)
Tarski, Alfred, 1935, “Der Wahrheitsbegriff in den formalisierten Sprachen”, Studia Philosophica, 1: 261–405. References are to the translation by J. H. Woodger as “The concept of truth in formalized languages” in Tarski (1983).
Tarski, Alfred, 1944, “The semantic conception of truth”, Philosophy and Phenomenological Research, 4: 341–375.