Combining Texts
Ideas for
'works', 'Philosophies of Mathematics' and 'Reason, Truth and History'
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10 ideas
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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 / E. Structures of Logic / 1. Logical Form
4730
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For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
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5. Theory of Logic / I. Semantics of Logic / 6. Intensionalism
14203
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Intension is not meaning, as 'cube' and 'square-faced polyhedron' are intensionally the same [Putnam]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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
14207
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If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth [Putnam]
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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
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
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
10127
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A 'complete' theory contains either any sentence or its negation [George/Velleman]
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