OT Re: Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]

[Paul Rubin]

Steven D'Aprano <steve at pearwood.info> writes:
> That's wrong. If we had such a reason, we could state it: "the reason
> we expect natural numbers are irreducible is ..." and fill in the
> blank. But I don't believe that such a reason exists (or at least, as
> far as we know).
>
> However, neither do we have any reason to think that they are *not*
> irreducible. Hence, we have no reason to think that they are anything
> but irreducible.

But by the same reasoning, we have no reason to think they are anything
but non-irreducible (reducible, I guess).  What the heck does it mean
for a natural number to be irreducible anyway?  I know what it means for
a polynomial to be irreducable, but the natural number analogy would be
a composite number, and there are plenty of those.

You might like this:

https://web.archive.org/web/20110806055104/http://www.math.princeton.edu/~nelson/papers/hm.pdf

Remember also that "in ultrafinitism, Peano Arithmetic goes from 1 to
88" (due to Shachaf on irc #haskell).  ;-)