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21595 | Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel] |
Full Idea: The law of excluded middle is ...the maxim of the definite understanding, which would fain avoid contradiction, but in doing so falls into it. | |
From: Georg W.F.Hegel (Logic (Encyclopedia I) [1817], p.172), quoted by Timothy Williamson - Vagueness 1.5 | |
A reaction: Not sure how this works, but he would say this, wouldn't he? |
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. |