FOM: Definition of Platonism

[Ed Mares]

Michael Hardy wrote

>
>	In the posting numbered 9801.53 in the archive,
>Stephen G Simpson <simpson at math.psu.edu> wrote:
>
>> (i.e. Platonism, the view that mathematical truth exists independently
>> of, and reveals itself to, passive consciousness).
>
>	I think this gets the definition of Platonism wrong, in just
>the way mathematicians often get it wrong.  Platonism is the proposition
>that the existence and nature of _universals_ is independent of
>_particulars_.  The fact that mathematics deals _only_ with universals
>is perhaps why mathematicians often fail to realize that Platonism
>says something about universals that it doesn't say about particulars.
>Note also what Platonism holds things to be independent of: They are
>held to be independent, not of consciousness, but of particulars.
>

Actually, Simpson's characterisation of Platonism isn't any worse than
Hardy's. Both accept elements of what has been added to Plato's doctrine
rather than "original" Platonism. Sorry for being pedantic, but Plato didn't
have universals, in the sense that his forms were copied by (or participated
in) but not shared by more than one individual (a universal, as the term was
defined in the middle ages, is something that is in more than one thing at a
time). What he did have was a realm of elements that do not change over time
and things that are independent of spatio-temporal individuals. Simpson's
characterisation, on the other hand, concentrates on the epistemological
independence of "Platonic objects" which surely is an important part of
Platonism.

Also, it is far from clear that maths is about universals, rather than
individuals like sets or functions. (If this comment is too PhoM and not
enough FoM, then please ignore it.)

Ed Mares


Ed Mares
Department of Philosophy
Victoria University of Wellington
P.O. Box 600 
Wellington, New Zealand
Edwin.Mares at vuw.ac.nz