Combining Texts
Ideas for
'Logical Consequence', 'Posterior Analytics' and 'The Nature of Musical Expression'
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10 ideas
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 / A. Overview of Logic / 6. Classical Logic
12376
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Demonstrations by reductio assume excluded middle [Aristotle]
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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
12373
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Something holds universally when it is proved of an arbitrary and primitive case [Aristotle]
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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 / 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
12363
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Everything is either asserted or denied truly [Aristotle]
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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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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
13004
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Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof [Aristotle, by Leibniz]
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