Combining Texts
Ideas for
'Parmenides', 'Philosophies of Mathematics' and 'Thought and Responsibility'
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9 ideas
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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10111
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Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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10129
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A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman]
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5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
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10105
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Differences between isomorphic structures seem unimportant [George/Velleman]
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5. Theory of Logic / K. Features of Logics / 2. Consistency
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10119
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Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman]
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10126
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A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman]
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5. Theory of Logic / K. Features of Logics / 3. Soundness
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10120
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Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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10127
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A 'complete' theory contains either any sentence or its negation [George/Velleman]
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5. Theory of Logic / L. Paradox / 3. Antinomies
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13986
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Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle]
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14150
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Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato]
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