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Ideas for 'Parmenides', 'A New Kind of Science' and 'works'

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3 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Anti-realism needs an intuitionist logic with no law of excluded middle [Dummett, by Miller,A]
     Full Idea: Dummett argues that antirealism implies that classical logic must be given up in favour of some form of intuitionistic logic that does not have the law of excluded middle as a theorem.
     From: report of Michael Dummett (works [1970]) by Alexander Miller - Philosophy of Language 9.4
     A reaction: Only realists can think every proposition is either true or false, even if it is beyond the bounds of our possible knowledge (e.g. tiny details from remote history). Personally I think "Plato had brown eyes" is either true or false.
5. Theory of Logic / L. Paradox / 3. Antinomies
Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle]
     Full Idea: Plato (in 'Parmenides') shows that the theory that 'Eide' are substances, and Kant that space and time are substances, and Bradley that relations are substances, all lead to aninomies.
     From: report of Plato (Parmenides [c.364 BCE]) by Gilbert Ryle - Are there propositions? 'Objections'
Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato]
     Full Idea: Plato's 'Parmenides' is perhaps the best collection of antinomies ever made.
     From: comment on Plato (Parmenides [c.364 BCE]) by Bertrand Russell - The Principles of Mathematics §337