# 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.

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 {\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.