Single Idea 5105

[catalogued under 7. Existence / A. Nature of Existence / 4. Abstract Existence]

Full Idea

The incommensurability of the diagonal always exists, and so it is not in time.

Clarification

A diagonal cannot be expressed as a fraction of whole numbers (e.g. square root of 2)

Gist of Idea

The incommensurability of the diagonal always exists, and so it is not in time

Source

Aristotle (Physics [c.337 BCE], 221b36)

Book Reference

Aristotle: 'Physics', ed/tr. Waterfield,Robin [OUP 1996], p.112


A Reaction

This must make Aristotle sympathetic to Platonism in mathematics, even though he rejects the full theory of Forms. Such a view is not uncommon among modern philosophers. Presumably the incommensurability is true in all possible worlds? 'In'?