Everything is equally interesting

(by William Seager)

Theorem 1

If everything is equally boring then everything is equally interesting.

Proof:

Assume everything is equally boring but suppose that there exist an X such that X is less interesting than some Y, Y <> X. Clearly X is more boring than Y, which contradicts our assumption. QED.

Theorem 2

Everything is interesting.*

Proof:

Suppose not. Then there are uninteresting things. Assuming the axiom of choice, the set of uninteresting things can be well ordered. Then there is a least element: a least uninteresting thing**. But this would be interesting.*** QED.

Corollary

Nothing is boring.

Proof:

Note that if something is interesting it is not boring. QED.

Theorem 3

Everything is equally boring.

Proof:

This follows immediately from the corollary to theorem 2. QED.

Theorem 4

Everything is equally interesting.

Proof:

By modus ponens from theorems 1 and 3. QED.

* This result is well known generalization of the famous proof by van Fraassen that every integer is interesting.

** We are not claiming, of course, that the ordering relation is that of being more interesting, simply that there is a least element in the set of uninteresting things.

*** This claim should not be confused with the meta-theoretical claim that it would be interesting that this thing is the least element in the set of uninteresting things. However, the fact that it is the least element makes it an interesting thing.