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Full Idea
The most popular approach of nominalistically inclined philosophers is to try to reinterpret mathematics, so that its terms and quantifiers only make reference to, say, physical objects, or linguistic expressions, or mental constructions.
Gist of Idea
Nominalists try to only refer to physical objects, or language, or mental constructions
Source
Hartry Field (Science without Numbers [1980], Prelim)
Book Ref
Field,Hartry: 'Science without Number' [Blackwell 1980], p.1
A Reaction
I am keen on naturalism and empiricism, but only referring to physical objects is a non-starter. I think I favour constructions, derived from the experience of patterns, and abstracted, idealised and generalised. Field says application is the problem.
| 21696 | Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine] |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| 18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
| 19002 | A nominalist can assert statements about mathematical objects, as being partly true [Yablo] |