Combining Texts
Ideas for
'', 'Philosophies of Mathematics' and 'Grundlagen (Foundations of Theory of Manifolds)'
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10 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211
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If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
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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 / 2. Logical Connectives / a. Logical connectives
11212
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The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
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11210
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Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
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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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