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Single Idea 15939

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

Full Idea

For an intuitionist a mathematical statement is rendered true or false by a proof or disproof, that is, by a construction, and constructions are effected in time.

Gist of Idea

For intuitionists it is constructed proofs (which take time) which make statements true

Source

Michael Dummett (Elements of Intuitionism [1977], p.336), quoted by Shaughan Lavine - Understanding the Infinite VI.2

Book Ref

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.168

A Reaction

Lavine is quoting this to draw attention to the difficulties of thinking of it as all taking place 'in time', especially when dealing with infinities.

The 2 ideas from 'Elements of Intuitionism'

15939 For intuitionists it is constructed proofs (which take time) which make statements true [Dummett]
15938 Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett]