more from Charles Chihara

Single Idea 9568

[catalogued under 18. Thought / E. Abstraction / 7. Abstracta by Equivalence]

Full Idea

What I refer to as an 'equivalence class' (of line segments of a particular length) is an open sentence in my Constructibility Theory. I just use this terminology of the Platonist for didactic purposes.

Gist of Idea

I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes'


Charles Chihara (A Structural Account of Mathematics [2004], 09.10)

Book Reference

Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.277

A Reaction

This is because 'equivalence classes' is committed to the existence of classes, which is Quinean Platonism. I am with Chihara in wanting a story that avoids such things. Kit Fine is investigating similar notions of rules of construction.