Argument
Liar paradox
Overview
In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In "this sentence is a lie", the paradox is strengthened in order to make it amenable to more rigorous logical analysis. It is still generally called the "liar paradox" although abstraction is made precisely from the liar making the statement. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction.
Assume that "this sentence is false" is true, then we can trust its content, which states the opposite and thus causes a contradiction. Similarly, we get a contradiction when we assume the opposite.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
Thus although truth and falsehood are properties of beliefs, yet they are in a sense extrinsic properties, for the condition of the truth of a belief is something not involving beliefs, or (in general) any mind at all, but only the _objects_ of the belief. A mind, which believes, believes truly when there is a _corresponding_ complex not involving the mind, but only its objects. This correspondence ensures truth…
Bertrand Russell, The Problems of Philosophy
States what Liar paradox is.
173.] This negation of a particular quality, which is the first negation, still leaves the connexion of the subject with the predicate subsisting. The predicate is in that manner a sort of relative universal, of which a special phase only has been negatived.
Georg Wilhelm Friedrich Hegel, The Logic of Hegel
States what Liar paradox is.
[Sidenote: According to reason, against reason.] 12. Now when a man _reasoneth_ from _principles_ that are _found_ indubitable by experience, all deceptions of sense and equivocation of words avoided, the conclusion he maketh is said to be _according to right reason_: but when from his conclusion a man may, by good ratiocination, derive that which is _contradictory_ to any evident truth whatsoever, then he is said…
Thomas Hobbes, The English works of Thomas Hobbes of Malmesbury, Volume 04
States what Liar paradox is.
Philosophers who discussed Liar paradox
- Carneades
- Heraclitus
- Susanne Bobzien
- Graham Priest
- Chrysippus
- Saul Kripke
- Epimenides
- Andrew David Irvine
- Stephen Yablo
- Benson Mates
- Eubulides
Related ideas
- Bhartṛhari
- Grammar
- Philosophy
- Ancient Greek
- Truth value
- Kurt Gödel
- Jean Buridan
- Law of excluded middle
- Mathematical logic
- Principle of bivalence
- Paradox
- Semantics
- Truth
- Arthur Prior
- George Boolos
- Graham Priest
- Boolean domain
- Logic
- Saul Kripke
- Oxford University Press
- Fuzzy logic
- Boolean algebra
- Gödel's incompleteness theorems
- Dialetheism
Place in the tradition
Part of Analytic philosophy.