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3 ideas
| 6653 | Syntactical methods of proof need only structure, where semantic methods (truth-tables) need truth [Lowe] |
| Full Idea: Syntactical methods of proof (e.g.'natural deduction') have regard only to the formal structure of premises and conclusions, whereas semantic methods (e.g. truth-tables) consider their possible interpretations as expressing true or false propositions. | |
| From: E.J. Lowe (Introduction to the Philosophy of Mind [2000], Ch. 8) | |
| A reaction: This is highly significant, because the first method of reasoning could be mechanical, whereas the second requires truth, and hence meaning, and hence (presumably) consciousness. Is full rationality possible with 'natural deduction'? |
| 13986 | 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' |
| 14150 | 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 |