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Full Idea
Nominalism has two main versions, one which tries to 'reduce' the objects of mathematics to something simpler (Russell and Wittgenstein), and another which claims that such objects are mere 'fictions' which have no reality (Field).
Gist of Idea
Nominalism about mathematics is either reductionist, or fictionalist
Source
David Bostock (Philosophy of Mathematics [2009], 9)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.262
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] |