more from Keith Hossack

### Single Idea 23626

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity]

Full Idea

The transfinite ordinal numbers are important in the theory of proofs, and essential in the theory of recursive functions and computability. Mathematics would be incomplete without them.

Gist of Idea

Transfinite ordinals are needed in proof theory, and for recursive functions and computability

Source

Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.1)

Book Reference

Hossack, Keith: 'Knowledge and the Philosophy of Number' [Routledge 2021], p.152

A Reaction

Hossack offers this as proof that the numbers are not human conceptual creations, but must exist beyond the range of our intellects. Hm.

Related Idea

Idea 23622
We can only mentally construct potential infinities, but maths needs actual infinities **[Hossack]**