[FOM] Fictionalism About Mathematics
hdeutsch at ilstu.edu
Sat Mar 10 15:29:29 EST 2012
The view that mathematical objects are fictitious and that "strictly speaking" seemingly true mathematical statements such as 5 + 6 = 11 are false, though they are true in the "story" of mathematics, is currently a very popular philosophy of mathematics among philosophers. The claim is that such fictionalism solves the epistemological problem of how mathematical knowledge is possible, and it solves the semantical problem of providing a uniform semantics for both mathematical and non-mathematical discourse. Fictionalist have also tried to address the obvious question of how, if mathematics is pure fiction, it nonetheless manages to be so useful in the sciences and in daily life. But I won't go into that here. My question is this: How do mathematical logicians and mathematicians in general react to this fictionalist doctrine? I realize that it may not be clear whether or how the doctrine might affect foundations or one's view of foundations. But I thought I would address this question to the FOM group since work in foundations and work in the philosophy of mathematics are intertwined. Let me put it this way: This fictionalism about mathematics is taken very seriously by philosophers of mathematics, but I doubt that mathematicians would find it at all appealing.
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