[FOM] Falsify Platonism

[Richard Pollack]

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
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