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'fragments/reports', 'What is Logic?' and 'Philosophy of Logic'
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21 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
9020
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My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine]
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5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
9028
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Maybe logical truth reflects reality, but in different ways in different languages [Quine]
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5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13845
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The various logics are abstractions made from terms like 'if...then' in English [Hacking]
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5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13840
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First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
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13844
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A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10014
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Quine rejects second-order logic, saying that predicates refer to multiple objects [Quine, by Hodes]
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10828
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Quantifying over predicates is treating them as names of entities [Quine]
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13842
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Second-order completeness seems to need intensional entities and possible worlds [Hacking]
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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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9024
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Excluded middle has three different definitions [Quine]
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5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10012
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Quantification theory can still be proved complete if we add identity [Quine]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13837
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With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
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5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13839
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Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
9016
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Names are not essential, because naming can be turned into predication [Quine]
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5. Theory of Logic / G. Quantification / 1. Quantification
9015
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Universal quantification is widespread, but it is definable in terms of existential quantification [Quine]
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5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9025
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You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine]
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9026
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Some quantifications could be false substitutionally and true objectually, because of nameless objects [Quine]
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10705
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Putting a predicate letter in a quantifier is to make it the name of an entity [Quine]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9027
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A sentence is logically true if all sentences with that grammatical structure are true [Quine]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843
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If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
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