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Single Idea 18141

[filed under theme 6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism ]

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

The 5 ideas with the same theme [denial of the real existence of mathematical objects]:

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]