See, this thread is cool, because if the Chicago adcomms see it, they will realize how awesome we are and admit us all. Please.

I have two books just about paradoxes. My favorite paradox of all time is called "The Heap". It goes like this (taken from

*Paradoxes from A to Z* by Michael Clark):

A pile of 10,000 grains is a heap.

For any number

*n*>1, if a pile of

*n* grains is a heap, then so is a pile of

*n* - 1 grains.

So one grain is a heap.

This form of argument (p->q; p; therefore, q) is known as

*modus ponens*. It works fine with pure logic, but not with how we define a heap. The paradox lies in the definition of words. A "heap" is not a sharply defined word, so we don't have a specific point that we'd call the pile of grains a heap, or stop calling it a heap.

My favorite resolution of this argument comes about by using "degrees of truth". Let's say that we're at the borderline of a heap when we reach 70 grains, and consider the following:

If 71 grains makes a heap, then so do 70.

The "if" part of the statement (71 grains) is more true than the "then" part (70 grains). So, if one part of the if-then statement is more true than the other, then it's reasonable to say that the statement isn't strictly true. It may be only by a small degree, but if we keep making these inferences down the chain, the small errors propagate and make it impossible to say that only one grain is a heap.

There are other approaches (fuzzy logic, supervaluations), but they're not as interesting, I think.