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Single Idea 8727

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

Full Idea

Geometers talk as if they were actually doing something, and the point of their theorems is to have some effect (like 'squaring'). ...But the sole purpose is knowledge, of things which exist forever, not coming into existence and passing away.

Gist of Idea

Geometry is not an activity, but the study of unchanging knowledge

Source

Plato (The Republic [c.374 BCE], 527a)

Book Ref

Plato: 'Republic', ed/tr. Waterfield,Robin [OUP 1993], p.258


A Reaction

Modern Constructivism defends the view which Plato is attacking. The existence of real infinities can be doubted simply because we have not got enough time to construct them.