Combining Texts

Ideas for 'Thinking About Mathematics', 'Rationality and Goodness' and 'Categories'

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2 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
11033 Predications of predicates are predications of their subjects [Aristotle]
     Full Idea: Whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject also.
     From: Aristotle (Categories [c.331 BCE], 01b10)
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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.