FOM: 'constructivism' as 'minimalistic platonism'
V. Sazonov
V.Sazonov at doc.mmu.ac.uk
Mon Jun 5 14:53:50 EDT 2000
Stephen G Simpson wrote:
> Schuster Thu, 1 Jun 2000 18:55:11 +0200 (MET DST):
>
> > The reason why to choose intuitionistic logic is then the insight
> > due to Brouwer that tertium non datur can hardly be applied in
> > infinite contexts: who is legitimated to decide whether there is
> > any odd perfect number?
>
> Let me play devil's advocate for a moment.
>
> >From the realist point of view, there is nothing wrong with tertium
> non datur. If P states something unambiguous about something real,
> then necessarily P is either so or not so, i.e., we can confidently
> assert ``P or not P'', even if we don't know which of the two is the
> case. And this reasoning would seem to apply across the board, even
> if P involves an (actually or potentially) infinite sequence of
> natural numbers, provided the number sequence is real, as your
> ``minimalist Platonism'' assumes.
<snip>
> Thus classical logic seems to be the logic of what really exists,
<snip>
> However, a conflict arises if you deny that ``P'' has meaning apart
> from ``we know P''. In other words, a conflict arises if you insist
> on subjectivism, i.e., if you deny the objective principle, that
> reality exists independently of our knowledge of it.
I read this as follows:
First, quite reasonable "objective principle" was
identified (related) with so called "realist point
of view" on mathematics (whose relation to our real
world is at least very doubtful). Then this was used
to conclude that (actually) denying the "realist
point of view" is considered as subjectivism.
I do not understand this kind of reasoning.
I personally reject "realist point of view"
on mathematics, but I consider that our reality
exists independently of our knowledge of it.
Here is probably some shift of meanings of words.
I think this is also due to this realist point of
view and/or due to the very term "realist point of view"
Vladimir Sazonov
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