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12 ideas
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10048
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There is no clear boundary between the logical and the non-logical [Tarski]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10479
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Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W]
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10694
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Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by 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 / 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 / 4. Identity in Logic
6051
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In 'x is F and x is G' we must assume the identity of x in the two statements [McGinn]
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6055
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Both non-contradiction and excluded middle need identity in their formulation [McGinn]
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6059
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Identity is unitary, indefinable, fundamental and a genuine relation [McGinn]
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5. Theory of Logic / G. Quantification / 1. Quantification
6042
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The quantifier is overrated as an analytical tool [McGinn]
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6067
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Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists' [McGinn]
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5. Theory of Logic / G. Quantification / 3. Objectual Quantification
6069
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'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn]
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5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
6068
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We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn]
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