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'fragments/reports', 'Logical Necessity' and 'Inverted Earth'
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7 ideas
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
12195
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Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
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12199
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There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
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12201
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We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]
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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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5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
12194
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Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt]
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5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
12198
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Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]
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