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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. |
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) |