Everything is Equally Interesting

William Seager
University of Toronto
Andre' Vellino,
Bell-Northern Research
Parrsboro, Nova Scotia, 16 August 1989

Theorem 1:
If everything is equally boring then everything is equally interesting.
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.*
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.
Nothing is boring.
Note that if something is interesting it is not boring. QED.

Theorem 3:

Everything is equally boring.
This follows immediately from the corollary to theorem 2. QED.

Theorem 4:

Everything is equally interesting.
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 {\em that} this thing is the least element in the set of uninteresting things. However, the fact that it is the least element {\em makes\/} it an interesting thing.