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| 15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed |
| Full Idea: The platonist destroys the whole essence of infinity, which lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed. | |||
| From: Michael Dummett (Elements of Intuitionism [1977], p.57), quoted by Thomas J. McKay - Plural Predication | |||
| A reaction: I don't warm to intuitionism, but I warm to this conception of infinity. Completed infinities are convenient reifications for mathematicians. |
| 15939 | For intuitionists it is constructed proofs (which take time) which make statements true |
| 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. | |||
| From: Michael Dummett (Elements of Intuitionism [1977], p.336), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |||
| 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. |