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

[Steven D'Aprano]

On Thu, 23 Jul 2015 02:58 am, Steven D'Aprano wrote:

>> 1. We have reason to expect that the natural numbers are absolutely
>> fundamental and irreducible
> 
> 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).

Sorry, that's not as clear as I intended. By "a reason", I mean a direct
reason for that choice, rather than some reason for the opposite choice. I
hope that's clear? Perhaps an example will help.

"Are tomatoes red?"

We can have direct reasons for believing that tomatoes are red, e.g. "the
light reflecting off these tomatoes peaks at frequency X, which is within
the range of red light". 

Alternatively, we might not have any such reason, and be reduced to arguing
against the alternatives. Only if all the alternatives are false could we
then believe that tomatoes are red.

"If tomatoes were blue, they would appear green when viewed under yellow
light; since these tomatoes fail to appear green, they might be red."

I'm suggesting that we have no direct reason for believing that the natural
numbers are irreducible concepts, only indirect ones, namely that all the
attempts to reduce them are unsatisfactory in some fashion or another. But
neither do we have direct reasons for expecting them to be reducible.


-- 
Steven