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Single Idea 10881

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory ]

Full Idea

The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept.

Gist of Idea

The concept of 'ordinal number' is set-theoretic, not arithmetical

Source

Leon Horsten (Philosophy of Mathematics [2007], §2.3)

Book Ref

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.7

The 4 ideas from 'Philosophy of Mathematics'

10881 The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
10882 Predicative definitions only refer to entities outside the defined collection [Horsten]
10884 A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
10885 Computer proofs don't provide explanations [Horsten]