more from Keith Hossack

Single Idea 23622

[catalogued under 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism]

Full Idea

Numbers cannot be mental objects constructed by our own minds: there exists at most a potential infinity of mental constructions, whereas the axioms of mathematics require an actual infinity of numbers.

Gist of Idea

We can only mentally construct potential infinities, but maths needs actual infinities


Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro 2)

Book Reference

Hossack, Keith: 'Knowledge and the Philosophy of Number' [Routledge 2021], p.3

A Reaction

Doubt this, but don't know enough to refute it. Actual infinities were a fairly late addition to maths, I think. I would think treating fictional complete infinities as real would be sufficient for the job. Like journeys which include imagined roads.

Related Idea

Idea 23626 Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]