[FOM] Lewis on Fictionalism About Mathematics

Richard Heck rgheck at brown.edu
Tue Mar 13 12:45:12 EDT 2012

On 03/13/2012 08:10 AM, Staffan Angere wrote:
> There is one version of the quote in his "Mathematics in Megethology", Philosophia Mathematica, vol. 1, 1993, pp. 3-23. That paper was included in some edition of Parts of Classes. Apolpgies for posting it in (almost) full, but I think that it definitely has affected a lot of philosophers to not take fictionalism and other forms of anti-realism about mathematics seriously, in a misguided attempt to be "naturalistic":
Thanks for posting this. I'll not copy it....

> I think, personally, that Lewis is misunderstanding what it means to be a naturalist here: mathematicians are definitely more reliable than philosophers when it comes to questions of mathematics. However, "external" questions such as the existence of sets (as apart from the existence of certain specific sets in, say, ZFC) are not obviously mathematical questions at all, so there may be no reason to believe mathematicians to have a better understanding of them than anyone else. A different way to put it is that even if a philosopher is in no position to question what a mathematician says, she may very well discuss its interpretation.
As I see it, Lewis is insisting on a form of naturalism that rejects 
"first philosophy". It isn't fictionalism's answer to the "external" 
question with which Lewis disagrees. It's the idea that there is such a 
question in the first place. So Lewis is insisting that there are no 
such things as "external" questions, just as Quine had before him.


Richard G Heck Jr
Romeo Elton Professor of Natural Theology
Brown University

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