[FOM] Fictionalism About Mathematics
Kevin Scharp
scharp.1 at osu.edu
Sat Mar 10 19:13:42 EST 2012
The results of a recent poll of philosophers on prominent philosophical
issues is here: http://philpapers.org/surveys/results.pl
The second question is on abstract objects, and "Platonism" is the most
popular answer with 39.3%. The question isn't directly on fictionalism in
philosophy of mathematics, but mathematical entities are surely one of the
most familiar purportedly abstract objects and one would think that
Platonism is incompatible with fictionalism.
Kevin
On Sat, Mar 10, 2012 at 5:30 PM, Richard Heck <rgheck at brown.edu> 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 addr!
>>
> es!
>
>> 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<http://tinyurl.com/fregestheorem>
> Visit my website:
> http://frege.brown.edu/heck/
>
>
>
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