[FOM] Falsify Platonism
Richard Pollack
pollack at cims.nyu.edu
Fri Apr 23 23:23:05 EDT 2010
I'm a bit puzzled by this conversation. I've always thought about
Platonism as a primarily emotional view of many Mathematicians
expressed by the remark 'All Mathematicians claim to be formalists
while in their heart they are all Platonists'. I've always understood
this as an expression of the belief (held by many Mathematicians)
that Mathematics has no content but is purely formal and consists
only in deriving (proving) consequences of postulates. Nevertheless,
many of the same Mathematicians (I count myself among these) believe
(feel) that the objects they study are real and have properties among
which they believe (hope) their postulates are "true" and thus they
are finding other "true" (and hopefully new) properties of these
objects. Given this, I don't see that a self contradiction in PA
would have any affect on the Mathematicians beliefs (feelings), The
Mathematician would give up his belief that PA is "true" (let alone
"characterizes") of the whole numbers. At best the Mathematician
will give up his belief that PA is true for the whole numbers and may
seek other postulates for them.
Ricky Pollack
Professor Emeritus Mathematics
Courant Institute of Mathematical Sciences/NYU
Office: Room 522, Warren Weaver Hall (Courant
Institute).
Phone (office): 212-998-3167
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Email: pollack at cims,<http://nyu.edu>nyu.edu
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