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2 ideas
| 12238 | The Aristotelian view is that numbers depend on (and are abstracted from) other things [Oderberg] |
| Full Idea: The Aristotelian account of numbers is that their existence depends on the existence of things that are not numbers, ..since numbers are abstractions from the existence of things. | |
| From: David S. Oderberg (Real Essentialism [2007], 1.2) | |
| A reaction: This is the deeply unfashionable view to which I am attached. The problem is the status of transfinite, complex etc numbers. They look like fictions to me. |
| 8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
| 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. | |
| From: Michael Dummett (Truth and the Past [2001], 2) | |
| 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). |