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

What about this:

The predicate "is true" usually gets applied to a sentence with a subject and predicate. The classic example is "Snow is white". As Tarski says, "'Snow is white' is true if and only if snow is white".

English allows us to pretend we're applying the words "is true" to a noun, for example "Islam is true". But this confuses Tarski: "Islam is true if and only if Islam" is nonsense. So we should properly understand "Islam" in this sentence as a stand-in for various sentences lu... (read more)

Showing 3 of 4 replies (Click to show all)

What about

'all sentances are either true or false'.

This sounds like the sort of sentance we'd want to assign a truth value to. Yet we can instanciate it into

'this sentance is either true or false'

Which is problematic - and yet it seems that it must have a truth value if the first sentance did.

1shokwave9yI really like this. It's an intuitive model of reference in the language, and most importantly it rules out self-reference for an actual reason (never unpacks). EDIT: I wonder if you couldn't do something with that infinite regress. Maybe that's something interesting in a formal language - doing calculus on infinite recursion? If that's even possible.
1komponisto9yMy knowledge of the Arabic language is only good enough to recognize that this is a tautology. ...and now that I think about it, it doesn't appear that the first part of is actually an existence claim!

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

by Kevin 1 min read30th Nov 2010142 comments


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.