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Single Idea 9934

[filed under theme 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism ]

Full Idea

The transition from using number words purely as adjectives to using them extensively as nouns has been traced to 'around the time of Plato'.

Gist of Idea

Number words became nouns around the time of Plato

Source

JP Burgess / G Rosen (A Subject with No Object [1997], III.C.2.a)

Book Ref

Burgess,J/Rosen,G: 'A Subject with No Object' [OUP 1997], p.228

A Reaction

[The cite Kneale and Kneale VI,§2 for this] It is just too tempting to think that in fact Plato (and early Platonists) were totally responsible for this shift, since the whole reification of numbers seems to be inherently platonist.

The 15 ideas from JP Burgess / G Rosen

9918 Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen]
9919 The old debate classified representations as abstract, not entities [Burgess/Rosen]
9921 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen]
9922 If space is really just a force-field, then it is a physical entity [Burgess/Rosen]
9923 We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen]
9924 Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen]
9925 Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen]
9926 A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen]
9928 Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen]
9927 Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen]
9929 Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen]
9930 Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen]
9933 The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen]
9932 The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen]
9934 Number words became nouns around the time of Plato [Burgess/Rosen]