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Ideas for 'Parmenides', 'Causal and Metaphysical Necessity' and 'The Nature of Mathematical Knowledge'

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3 ideas

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Restrict 'logical truth' to formal logic, rather than including analytic and metaphysical truths [Shoemaker]
     Full Idea: I favour restricting the term 'logical truth' to what logicians would count as such, excluding both analytic truths like 'Bachelors are unmarried' and Kripkean necessities like 'Gold is an element'.
     From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], I)
     A reaction: I agree. There is a tendency to splash the phrases 'logical truth' and 'logical necessity around in vague ways. I take them to strictly arise out of the requirements of formal systems of 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