Re: Platonism

From: Stephen Harris (cyberguard1048-usenet_at_yahoo.com)
Date: 12/02/04 

Date: Thu, 02 Dec 2004 00:23:27 GMT

>>
>> "Mitch Harris" <harrisq@tcs.inf.tu-dresden.de> wrote in message
>> news:316843F36l732U1@news.dfncis.de...
>>> Eray Ozkural exa wrote:
>>>> Mitch Harris <harrisq@tcs.inf.tu-dresden.de> wrote in message
>>>> news:<315dr5F34rsgmU1@news.dfncis.de>...
>>>>>Eray Ozkural exa wrote:
>>>>>
>>>>>>Arithmetic does occur physically. It's not something we make up in our
>>>>>> >>>>>>heads.
>>>> Precisely. That is the realist portion of my theory that Godel has
>>>> dubbed "Aristotelian Realism". It is realist without the extra baggage
>>>> of Platonism.
>>>>

http://en.wikipedia.org/wiki/Philosophy_of_mathematics
"Mathematical realism holds that mathematical entities exist independently
of the human mind. Thus humans do not invent mathematics, but rather
discover it, and any other intelligent beings in the universe would
presumably do the same. The term Platonism is used because such a view is
seen to parallel Plato's belief in a "heaven of ideas", an unchanging
ultimate reality that the everyday world can only imperfectly approximate.
Plato's view probably derives from Pythagoras, and his followers the
Pythagoreans, who believed that the world was, quite literally, built up by
the numbers. This idea may have even older origins that are unknown to us."
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Embodied mind theories:
"These theories hold that mathematical thought is a natural outgrowth of the
human cognitive apparatus which finds itself in our physical universe. For
example, the abstract concept of number springs from the experience of
counting discrete objects. It is held that mathematics is not universal and
does not exist in any real sense, other than in human brains. Humans
construct, but do not discover, mathematics.

The physical universe can thus be seen as the ultimate foundation of
mathematics: it guided the evolution of the brain and later determined which
questions this brain would find worthy of investigation. However, the human
mind has no special claim on "reality" or approaches to it built out of
math; If such constructs as Euler's Identity are "true" then they are true
as a map of the human mind and cognition, not as a map of anything it
"sees".

The effectiveness of mathematics is thus easily explained: mathematics was
constructed by the brain in order to be effective in this universe."

SH: This is the mathematical perspective philosophy which is in accord with
physicalism. Not Platonism which posits an abstract realm which is not at
all physical. Aristotelian realism is not as close to physicalism as
'embodied minds'.

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Aristotelean realism

"Similar to idealism, realism is also one of the oldest philosophies in
western culture and its origin began with the Greek philosopher Aristotle
(384-322 B.C.E.) in ancient Greece. Being a longtime star student of Plato,
he elaborated on the idealist view of reality being based on ideas and not
matter. He thought that a proper study of matter could lead to better and
more distinct ideas."

"The exaggerated Realism of Plato, investing the real being with the
attributes
of the being in thought, is the principal doctrine of his metaphysics. ..

Aristotle broke away from these exaggerated views of his master and
formulated the main doctrines of Moderate Realism. The real is not, as Plato
says, some vague entity of which the sensible world is only the shadow; it
dwells in the midst of the sensible world. Individual substance (this man,
that
horse) alone has reality; it alone can exist. The universal is not a thing
in
itself; it is immanent in individuals and is multiplied in all the
representatives
of a class. As to the form of universality of our concepts (man, just), it
is a
product of our subjective consideration. The objects of our generic and
specific representations can certainly be called substances (ousíai), when
they designate
the fundamental reality (man) with the accidental determinations (just,
big);
but these are deúterai ousíai (second substances), and by that Aristotle
means
precisely that this attribute of universality which affects the substance as
in
thought does not belong to the substance (thing in itself); it is the
outcome of
our subjective elaboration. This theorem of Aristotle, which completes the
metaphysics of Heraclitus (denial of permanent) by means of that of
Parmenides (denial of change), is the antithesis of Platonism, and may be
considered one of
the finest pronouncements of Peripateticism. It was through this wise
doctrine
that the Stagyrite exercised his ascendency over all later thought."

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