[FOM] Fictionalism About Mathematics

[Richard Heck]

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

Check out my book Frege's Theorem:
	http://tinyurl.com/fregestheorem
Visit my website:
	http://frege.brown.edu/heck/