Tarski's Undefinability Theorem
Updated 2026-08-01
INTRODUCTION
English translation pending.
CORE DEFINITION
Proved by Alfred Tarski. The theorem states that in any consistent formal system strong enough to express arithmetic, the set of true sentences of that system cannot be defined within the system itself. Any attempt to build such a truth predicate lets the liar sentence be constructed, producing a contradiction. Truth must therefore be defined in a richer metalanguage, which makes the theorem the semantic counterpart of Godel's incompleteness theorem.
SCAFFOLDING EFFECT
Reduce cognitive load
- Mark the boundary: identify which claims a system can evaluate using only its own rules - Step up a level: move truth judgments into a metalanguage when self-reference produces paradox - Avoid circularity: refuse definitions that use the very term being defined
Anchor fast decisions
If a system could define truth for its own sentences, the definition could be applied to a sentence asserting its own untruth. That sentence would then be true exactly when it is not true, which is a contradiction. Because the construction is unavoidable once arithmetic is expressible, the truth predicate must lie outside the system, at a higher level of language.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Tarski's_undefinability_theoremverified
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