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Full Idea
The intuitionist account of the meaning of mathematical statements does not employ the notion of a statement's being true, but only that of something's being a proof of the statement.
Gist of Idea
Intuitionists rely on the proof of mathematical statements, not their truth
Source
Michael Dummett (Truth and the Past [2001], 2)
Book Ref
Dummett,Michael: 'Truth and the Past (Dewey Lectures)' [Columbia 2004], p.30
A Reaction
I remain unconvinced that anyone could give an account of proof that didn't discreetly employ the notion of truth. What are we to make of "we suspect this is true, but no one knows how to prove it?" (e.g. Goldbach's Conjecture).
| 8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
| 8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
| 8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
| 8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
| 8193 | Verification is not an individual but a collective activity [Dummett] |
| 8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
| 8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
| 8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
| 8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
| 8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |
| 8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |