more from this thinker     |     more from this text

Single Idea 10613

[filed under theme 5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth ]

Full Idea

No nice theory can define truth for its own language.

Clarification

[an extensive discussion of 'nice' precedes this theorem]

Gist of Idea

No nice theory can define truth for its own language

Source

Peter Smith (Intro to Gödel's Theorems [2007], 21.5)

Book Ref

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.180

A Reaction

This leads on to Tarski's account of truth.

The 6 ideas with the same theme [role of truth in various systems of formal logic]:

5542 There must be a general content-free account of truth in the rules of logic [Kant]
10620 Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]
10613 No nice theory can define truth for its own language [Smith,P]
10819 Tarski gives us the account of truth needed to build a group of true sentences in a model [Field,H]
9375 Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian]
10892 We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]