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

[Steven D'Aprano]

On Thursday 23 July 2015 03:48, Paul Rubin wrote:

> 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?  

Reducible in the sense that we can define the natural numbers in terms of a 
simpler concept. E.g. the rationals can be reduced to the quotient of 
integers. One might argue that defining them in terms of sets is precisely 
that, but then we get into an argument as to which is simpler, natural 
numbers or sets?



-- 
Steve