[FOM] Fictionalism About Mathematics

Harry Deutsch hdeutsch at ilstu.edu
Sat Mar 10 18:36:58 EST 2012

I didn't mean to imply that fictionalism is dominant.  But it is a respectable doctrine--or so it is supposed by many philosophers of mathematics, including those who are not engaged in the debate.  A survey of prominent views in current philosophy of mathematics would have to include fictionalism.  What Richard says about the debate on fictionalism--that some defend it, some oppose it, some ignore it, and so on,-- could be said about any controversial doctrine in philosophy.
On Mar 10, 2012, at 4:30 PM, Richard Heck wrote:

> On 03/10/2012 03:29 PM, Harry Deutsch wrote:
>> 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 addres!
>>  s 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.
> For what it's worth, I don't know how true this characterization is. There are philosophers of mathematics, some of them quite prominent, who defend fictionalist views, and there are others, also quite prominent, who oppose them. Then there are others who ignore the whole debate, who find the fictionalist line sufficiently implausible, or what have you, to be bothered with it. And among those, you will likely find many who would agree with Lewis's famously funny rebuttal of fictionalism and its kin in *Parts of Classes*.
> One would obviously have to take some kind of formal poll to find out what the percentages are, but I'm not convinced myself that fictionalism is taken seriously by anything like the majority of philosophers of mathematics.
> Richard
> -- 
> -----------------------
> Richard G Heck Jr
> Romeo Elton Professor of Natural Theology
> Brown University
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