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)

Showing 3 of 5 replies (Click to show all)

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)

Copyright Pete Olcott 2016 ,2017

http://LiarParadox.org/

0[anonymous]9yHelpful links. As stated though this doesn't dissolve the strengthened liars paradox.
0Jack9yDoes holding the view that meaningful questions have to be phrased in terms of finite computational processes imply the other tenets of formalism?

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

by Kevin 1 min read30th Nov 2010142 comments

4


Graham Priest discusses The Liar's Paradox for a NY Times blog. It seems that one way of solving the Liar's Paradox is defining dialethei, a true contradiction. Less Wrong, can you do what modern philosophers have failed to do and solve or successfully dissolve the Liar's Paradox? This doesn't seem nearly as hard as solving free will.

This post is a practice problem for what may become a sequence on unsolved problems in philosophy.