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2 ideas
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 18736 | Contradiction is between two rules, not between rule and reality [Wittgenstein] |
| Full Idea: Contradiction is between one rule and another, not between rule and reality. | |
| From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], C XIII) | |
| A reaction: If I say 'he is sitting' and 'he is standing', it seems to be reality which produces the contradiction. What 'rule' could possibly do it? The rule which says sitting and standing are incompatible? But what makes that so? |