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Description: |
I'll discuss how Gödel's paradox "This statement is
false/unprovable" yields his famous result on the limits of axiomatic
reasoning.
I'll contrast that with my work, which is based on the paradox of "The
first uninteresting positive whole number", which is itself a rather
interesting number, since it is precisely the first uninteresting number.
This leads to my first result on the limits of axiomatic reasoning, namely
that most numbers are uninteresting or random, but we can never be sure, we
can never prove it, in individual cases. And these ideas culminate in my
discovery that some mathematical facts are true for no reason, they are
true by accident, or at random. In other words, God not only plays dice in
physics, but even
in pure mathematics, in logic, in the world of pure reason. Sometimes
mathematical truth is completely random and has no structure or pattern
that we will ever be able to understand. It is not the case that simple
clear questions have simple clear answers, not even in the world of pure
ideas, and much less so in the messy real world of everyday life.
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