##  [Liar Paradox](/liar-paradox-0) 

 Definition

A semantic paradox arising from sentences that assert their own falsehood, typically exemplified by 'This sentence is false', which forces a contradiction under naive truth-attribution rules.

 

 

 

 

 

 





## Principle

Principle

If a language permits a sentence to refer to the truth value of itself and if one assumes classical bivalence and a naive truth predicate that satisfies 'S is true iff what S says is the case', then self-reference produces inconsistency.

 

 

 

 

 





## Demonstration

Demonstration

Let L be the sentence 'L is false'. If L is true then what it says holds and so L is false; if L is false then it is not the case that L is false, hence L is true. Both options conflict with naive truth rules.

 

 

 

 

## Misapplication

Misapplication

Treating the paradox as merely a linguistic trick without modifying the underlying logic, or trying to block every form of self-reference as a cure rather than refining the conception of truth or the logic used.

 

 

 

 

 





## Consequence

Consequence

Motivates refined semantic frameworks: hierarchical truth predicates, paracomplete/paraconsistent logics, or formal distinctions between object language and metalanguage to avoid paradoxical assignments.

 

 

 

 

## Reversal

Reversal

Contrast with a self-asserting sentence like 'This sentence is true', which does not create the same contradiction and instead produces stable fixed points under naive truth or may be handled differently in non-classical logics.

 

 

 

 

 





## Boundary

Boundary

Pertains to sentences that self-reference their truth or falsity; it does not arise for ordinary declarative sentences lacking self-referential truth claims or for contradictions that are syntactically external.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Tension between preserving classical truth principles (bivalence, excluded middle) and accommodating self-referential sentences without collapse; different resolutions trade off classicality for expressive convenience.

 

 

 

 

 





## Synthesis

Synthesis

The liar paradox exposes a clash between naive truth principles and self-reference: resolving it requires either altering the logic (rejecting bivalence or explosion) or stratifying truth and separating object language from the level where truth is asserted.