FOM: Re: Definition of Platonism

Karlis Podnieks podnieks at
Thu Jan 15 02:16:58 EST 1998

-----Original Message-----
From: Michael Hardy <hardy at>
Date: 1998, January  15
Subject: FOM: Definition of Platonism

Forwarded message:
> From news Mon Dec  9 10:45:13 1996
> From: owl at (Michael Huemer)


> greg at (Greg Kuperberg) writes:
> > Platonism: The habit among mathematicians, especially
geometers, of
> > pretending that mathematical objects actually exist.
> This doesn't seem like a very fair definition.
> Platonism is a position on the problem of universals, and
> derivatively a position in philosophy of mathematics.
Platonism is
> the view that universals exist, and their existence is
independent of
> the existence of particulars.
>  Michael Huemer <owl at>        / O   O \

So, let's define two character strings:

platonism#1 = "universals exist, and their existence is
independent of the existence of particulars";
platonism#2 = " mathematical objects actually exist,  and their
existence is independent of the existence of any axioms";

As a mathematician, I cannot imagine how platonism#1 could be
used in FOM. My favorite platonism is platonism#2, no matter, is
it "true" or not. For me, this sort of platonism is an essential
aspect of the mathematical method. During my everyday work I am
used to treat numbers, points, lines, groups, algebras, sets,
cardinals etc. as the "last reality" (i.e. not as a model of
something "more real"), as a specific "world".  It seems to me
that platonism#2 is (for me as a human being) the only way to
work with mathematical (i.e. by definition - self-contained)
models effectively. Working with self-contained models
mathematicians have learned to draw maximum of conclusions from
a minimum of premises. This is why mathematical modelling is so
surprisingly efficient.

But, of course, platonism#2 is "false", because mathematical
objects do not actually exist,  their existence depends of the
existence of the axioms used  - explicitly or implicitly - by

Best wishes,
podnieks at
University of Latvia
Institute of Mathematics and Computer Science
Rainis boulevard 29, Riga, LV-1459, Latvia

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