One of the surprises in the recently unveiled results of the PhilPapers Survey of philosophers is the popularity of nominalism:
Target responses
Abstract objects: Platonism or nominalism?
Accept or lean toward: Platonism 366 / 931 (39.3%)
Accept or lean toward: nominalism 351 / 931 (37.7%)
Other 214 / 931 (22.9%)
All responses
Abstract objects: Platonism or nominalism?
Accept or lean toward: nominalism 1454 / 3226 (45%)
Accept or lean toward: Platonism 1016 / 3226 (31.4%)
Other 756 / 3226 (23.4%)
That is, 45% of all the respondents tend towards nominalism. But when we look at people who list an AOS as philosophy of mathematics, the numbers switch:
AOS: Philosophy of mathematics
Abstract objects: Platonism or nominalism?
Accept or lean toward: Platonism 50 / 102 (49%)
Accept or lean toward: nominalism 30 / 102 (29.4%)
Other 22 / 102 (21.5%)
AOS: Logic or Philosophy of Logic
Abstract objects: Platonism or nominalism?
Accept or lean toward: Platonism 112 / 264 (42.4%)
Accept or lean toward: nominalism 96 / 264 (36.3%)
Other 56 / 264 (21.2%)
Does this mean that people outside of philosophy of mathematics don't care what we think, or is it just that our arguments for platonism aren't very good?
8 comments:
Or is it that your arguments are just too universal...
I was pretty surprised by this result too. I wondered whether a lot of respondents were perhaps thinking of other, more standardly philosophical, abstracta besides the natural numbers. I'm thinking of properties or propositions, for example.
Greg, yes, it's possible that people were thinking of these standard abstract objects. Still, this explanation would fit will my overall worry that most philosophers don't think enough about mathematics!
Those following this post might also want to chime in on the logic part discussed here.
That's interesting, I had thought that nominalism was far more common among philosophers of mathematics than in general.
I generally expect "weird" views to be oversubscribed among specialists, but in this case maybe it's not clear which view counts as "weird". I am definitely surprised that nominalism is so popular though - I had always gotten the impression that very few non-specialists believe it. But maybe that's because the "non-specialists" I'm thinking of are in M&E, rather than philosophy of science or something.
Kenny, my impression is that most philosophers of science don't want to believe in platonic entities -- they sometimes fall back on the idea that mathematics is "just a language", whatever that is supposed to come to.
It would be interesting to try to use the PhilPapers data to see how views vary across specializations. Presumably somebody over there is going to put out an analysis of their results at some point ...
Hi Chris,
I had Kenny's same reaction. I thought most people would be nominalist. My impression (and I am one of those who chose "leaning for platonism") is that nominalism is often a view you need to be argued out of. This is why, if I remember correctly, in the meta-survey I had nominalism winning by a bunch. So I was surprised in the opposite direction!
Fabrizio, thanks for the comment. I haven't delved into the metasurvey data, but it would be interesting to see how systematic these misperceptions are about the popularity of this or that view ...
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