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

Kevin

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.

Well, we here agree that beliefs should pay rent. So you see the sentence "this sentence is false" or similar. What new things do you expect now?

This feels like the wrong step in the dance to me. Haven't you just thrown away all of mathematics? What new things do you expect after solving a quadratic equation?

User:Tiiba is correct. Math (after mapping to real-world predicates) allows me to more quickly form reliable expectations about the world. The claim that "this sentence is false" does not. Therefore, I can leave beliefs about the latter unassigned without epistemic or instrumental penalty.

1magfrump15y

To echo Tiiba but more formally: given a specific physical circumstance (transistors designed to do a computation) you can predict the result of the computation exactly and arbitrarily quickly (or as fast as you can look it up), because you have already done that computation. For more abstract theorems, proving two things are equivalent leads me to expect one in the presence of the other. For example, before proving Fermat's Last Theorem, I might expect there to be a right triangle whose three sides were squares of integers. Now I expect not to.

6wedrifid15y

Omega places a series of 50 boxes in front of you, labelled numerically. Two of them contain explosive boobytraps while each of the remaining 48 contain $200,000. The sum of the labels on the trapped boxes is 55 while the product is 714. Which boxes would you not choose to open?