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3 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. |
| 2111 | Falsehood involves a contradiction, and truth is contradictory of falsehood [Leibniz] |
| Full Idea: We judge to be false that which involves a contradiction, and true that which is opposed or contradictory to the false. | |
| From: Gottfried Leibniz (Monadology [1716], §31) |
| 16416 | The quantifier in logic is not like the ordinary English one (which has empty names, non-denoting terms etc) [Hofweber] |
| Full Idea: The inferential role of the existential quantifier in first order logic does not carry over to the existential quantifier in English (we have empty names, singular terms that are not even in the business of denoting, and so on). | |
| From: Thomas Hofweber (Ambitious, yet modest, Metaphysics [2009], 2) |