FOM: constructivist philosophy

[V. Sazonov]

Fred Richman wrote:

> > The moon exists, yet we did not construct it, and no fraud is
> > involved.  Why and how does Bishop think mathematics is different
> > from the rest of science?
>
> I have always been a little mystified by the inclusion of mathematics
> with the sciences. It seems bizarre to me to draw a parallel between
> the existence of the moon and the existence of an odd perfect number,
> while the question of the existence of the number 5 strikes me as
> almost meaningless.

This seems to be an objection to the so called realist(??)
(= Platonist?) point of view on mathematics (5, Aleph_17,
square root of -1, etc. exit *like* the moon). This objection
seems normal for constructivists, but, I believe, also
quite reasonable for any mathematician. On the other hand,
if to take that mathematics is science on (meaningful,
whatever this mean) formal systems, then mathematics is
really a science (as these formal systems are quite real
things which can be physically imitated, say, by computer).
Simultaneously, it is a kind of engineering, because it
constructs these formalisms (like any other devices)
to make human thought and intuition more powerful.


Vladimir Sazonov