## LESSWRONGLW

Unsolved Problems in Philosophy Part 1: The Liar's Paradox

The formalist) school of math philosophy thinks that meaningful questions have to be phrased in terms of finite computational processes. But if you try to write a program for determining the truth value of "this statement is false", you'll see it recurses and never terminates:

``````def f():
return (not f())
``````

See also Kleene-Rosser paradox. This may or may not dissolve the original question for you, but it works for me.

There's more to be said about the paradox because it keeps turning up in many contexts. For example, see Terry Tao's posts about &qu... (read more)

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The above comment is the closest that I have ever found to the following Predicate Logic formalization:

“This sentence is not true.” ∃x ∈ finite strings from the alphabet of predicate logic ∃T ∈ Predicates ∃hasProperty ∈ Predicates | x = hasProperty(x, ~T(x))

Finite string x asserts that it has the property of the negation of the Boolean value result of evaluating predicate T with itself as T’s only argument.

The above is based on Tarski formal correctness of True: For all x, True(x) if and only if φ(x)