Combining Texts
Ideas for
'In Defense of Essentialism', 'Posterior Analytics' and 'Negation'
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12 ideas
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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18793
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Material implication (and classical logic) considers nothing but truth values for implications [Mares]
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18784
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In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares]
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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 / D. Assumptions for Logic / 1. Bivalence
18786
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Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares]
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18780
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Standard disjunction and negation force us to accept the principle of bivalence [Mares]
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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 / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
18782
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The connectives are studied either through model theory or through proof theory [Mares]
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5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
18783
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Many-valued logics lack a natural deduction system [Mares]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
18792
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Situation semantics for logics: not possible worlds, but information in situations [Mares]
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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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5. Theory of Logic / K. Features of Logics / 2. Consistency
18785
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Consistency is semantic, but non-contradiction is syntactic [Mares]
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