more from Philip Kitcher

Single Idea 18072

[catalogued under 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism]

Full Idea

The constructivist ontological thesis is that mathematics owes its truth to the activity of an actual or ideal subject. The epistemological thesis is that we can have a priori knowledge of this activity, and so recognise its limits.

Gist of Idea

Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori)

Source

Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5)

Book Reference

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.142


A Reaction

The mention of an 'ideal' is Kitcher's personal view. Kitcher embraces the first view, and rejects the second.