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'fragments/reports', 'Logical Consequence' and 'The Laws of Thought'
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10 ideas
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
8686
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Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10690
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Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10691
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Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10695
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Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
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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 / B. Logical Consequence / 8. Material Implication
10689
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A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
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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 / H. Proof Systems / 2. Axiomatic Proof
22277
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Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10696
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A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10693
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Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
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