more on this theme     |     more from this thinker

Single Idea 9923

[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers ]

Full Idea

The modal strategy for numbers is to replace assumptions about the actual existence of numbers by assumptions about the possible existence of numbers

Gist of Idea

We should talk about possible existence, rather than actual existence, of numbers

Source

JP Burgess / G Rosen (A Subject with No Object [1997], II.B.3.a)

Book Ref

Burgess,J/Rosen,G: 'A Subject with No Object' [OUP 1997], p.137

A Reaction

This seems to be quite a good way of dealing with very large numbers and infinities. It is not clear whether 5 is so regularly actualised that we must consider it as permanent, or whether it is just a prominent permanent possibility.

The 15 ideas from 'A Subject with No Object'

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]