Combining Texts
Ideas for
'Writing the Book of the World', 'Philosophy of Logic' and 'Science of Logic'
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18 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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9020
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My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine]
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14980
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There is a real issue over what is the 'correct' logic [Sider]
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15000
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'It is raining' and 'it is not raining' can't be legislated, so we can't legislate 'p or ¬p' [Sider]
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5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
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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 / 6. Classical Logic
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15020
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Classical logic is good for mathematics and science, but less good for natural language [Sider]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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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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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
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15029
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Modal accounts of logical consequence are simple necessity, or essential use of logical words [Sider]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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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
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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
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15019
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Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral [Sider]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
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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
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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
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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
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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 / H. Proof Systems / 4. Natural Deduction
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15001
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'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted [Sider]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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9027
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A sentence is logically true if all sentences with that grammatical structure are true [Quine]
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