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Ideas for 'Parmenides', 'fragments/reports' and 'Virtues of the Mind'

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3 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus]
     Full Idea: The remark of Heraclitus that all things are and are not effectively renders all assertions true, and that of Anaxagoras that there is an intermediary between assertion and negation makes all assertions false.
     From: comment on Heraclitus (fragments/reports [c.500 BCE]) by Aristotle - Metaphysics 1012a
     A reaction: Compare Idea 416. Heraclitus is discussing truth-value 'gluts', as in paraconsistent logic, and Anaxagoras is discussing truth-value 'gaps', as in three-valued Kleene logic.
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