FOM: 'constructivism' as 'minimalistic platonism'

[Fred Richman]

"V. Sazonov" wrote (in response to Fred Richman):

>> If I believe in the objective existence of the natural number series,
>> am I committed to the proposition "either there exists an odd perfect
>> number, or all perfect numbers are even"?
 
> And what does it mean at all "to believe in the
> objective existence of the natural number series"
> if it is not just a play with words?

If there is no defensible realist position, then, of course, it is
pointless for me to wonder whether the law of excluded middle follows
from it. I had thought that there was a defensible realist position,
and that believing in the objective existence of the natural number
series was more or less the minimal part of it.

> And also, why such unrealistic way of thinking
> to believe in the *objective* existence of evidently
> *unrealistic* things is called "realism"?

I can sympathize with this attitude. Bishop called such a way of
thinking "idealism". Mycielski has said that idealism in mathematics
is the belief that mathematical objects are real, and realism in
mathematics is the belief that mathematical objects are ideal. But I
didn't think that the terms were being used in that way in the
discussions here.

--Fred