Combining Texts
Ideas for
'fragments/reports', 'Philosophies of Mathematics' and 'Axiomatic Theories of Truth (2013 ver)'
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9 ideas
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
8078
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Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
6023
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Every proposition is either true or false [Chrysippus, by Cicero]
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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
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
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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