Bruno Marchal wrote:

> I did not have problem with the expression "platonic object" but be
> careful because it makes some people believe (cf Peter Jones) that we
> are reifying numbers and mathematical objects.

That is exactly what mathematical Platonism has always meant [*]

But "reifying" doesn't mean treating as material. Platonic objects are
to immaterial, somehow. Well, you beleive the UD exists,
and you believe matter doesn't so you belive in
immaterial entitities, so you are a Platonist.


There were three major points of view in the debate about the nature of
mathematics. The formalists argued (roughly: the short
summaries that follow are really caricatures) that mathematics was
really simply the formal manipulation of symbols based on
arbitrarily-chosen axioms. The Platonists saw mathematics as almost an
experimental science, studying objects that really exist
(in some sense), though they clearly don't exist in a physical or
material sense. The intuitionists had the most radical point of
view; essentially, they saw all mathematics as a human creation and
therefore as essentially finite.


Platonism is the view that there exist abstract objects, and again, an
object is abstract just in case it is non-spatiotemporal, i.e.,
does not exist in space or time. [ ... ] Three examples of things that
are often taken to be abstract are (a) mathematical objects
(most notably, numbers), (b) properties, and (c) propositions.

Platonists about mathematical objects claim that the theorems of our
mathematical theories - sentences like '3 is prime'
(a theorem of arithmetic) and 'There are infinitely many transfinite
cardinal numbers' (a theorem of set theory) -
are literally true and that the only plausible view of such sentences
is that they are about abstract objects
(i.e., that their singular terms denote abstract objects and their
existential quantifiers range over abstract objects).


The philosophy of Plato, or an approach to philosophy resembling his.
For example, someone who asserts that numbers exist
independently of the things they number could be called a Platonist.


The view that mathematical concepts could exist in such a
timeless,ethereal sense was put forward in ancient times
(c.360 BC) by the great Greek philosopher  Plato.Consequently,this view
is frequently referred to as mathematical Platonism

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