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Article 3509 of comp.ai.philosophy:
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>From: gudeman@cs.arizona.edu (David Gudeman)
Newsgroups: comp.ai.philosophy,sci.philosophy.meta
Subject: Re: Intelligence Testing
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Date: 5 Feb 92 20:17:25 GMT
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In article  <1992Feb5.180356.25845@javelin.sim.es.com> Heiner Biesel writes:
]gudeman@cs.arizona.edu (David Gudeman) writes:
]
]....[ ]...
]>Formalism, as I used it in the above quoted sentence, is a philosophy,
]>not a method.  Specifically, it is the philosophy that mathematical
]>objects are nothing more than meaningless symbols and that mathematics
]>is nothing more than a game played with meaningless symbols.  The
]>formalist theory fails in that it cannot explain how our manipulations
]>of these meaningless symbols manage to give us information about the
]>real world.
]
]I take it that you assert that mathematics, as distiguished from mathematical
]physics, provides us information about the real world.

How do you distinguish mathematics from mathematical physics?  I
caution you that if you try to say that mathematical physics is
_about_ things in the real world, then you are immediately
contradicting the formalist theory. For the theory applies to any use
of mathematical methods, regardless of the application.  It is
uninteresting to say that it is _possible_ to do mathematics with
meaningless symbols, so much is obvious.  The point of contention is
what the 1, 3, and 4 _mean_ in the expression "1 + 3 = 6" (not to
mention the + and =), regardless of how it is used.

There have been several popular answers to this question, of which a
few are:

(1) formalist: they don't mean anything, they are just meaningless
marks on paper.

(2) psychologist: they refer to personal mental objects in the mind of
the reader.

(3) logicist: (as I understand it) they are place-holders in a logical
proposition with no meaning outside of the proposition in which they
occur.

(4) Platonist: they refer to objects that really exist in some
abstract, non-material sense.  And furthermore these objects are not
dependent on the existence of minds.

]Unless you mean to
]include mathematical objects and constructs in your definition of the "real"
]world, I would dispute your assertion.

By assuming the existence of mathematical objects you become a
Platonist, whether or not you say they are part of the real world.

]Mathematics per se speaks of nothing
]but mathematics;

That statement could be true in any of the 4 theories I mentioned
above, depending of what you mean by the second "mathematics".

] the association between mathematics and certain perceived
]regularities in the physical world is fortunate, and useful, but says nothing
]about the meaning of mathematics.

Saying that there is a "fortunate" association is unsatisfactory;
especially when the association seems to be necessary.  It does not
seem to be possible for 2 apples + 2 oranges to be anything else but 4
pieces of fruit.
--
					David Gudeman
gudeman@cs.arizona.edu
noao!arizona!gudeman


