Combining Texts
Ideas for
'Meaning and the Moral Sciences', 'To be is to be the value of a variable..' and 'Which Logic is the Right Logic?'
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23 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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10766
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Logic is either for demonstration, or for characterizing structures [Tharp]
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5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
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10767
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Elementary logic is complete, but cannot capture mathematics [Tharp]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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10769
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Second-order logic isn't provable, but will express set-theory and classic problems [Tharp]
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10225
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Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro]
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10736
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Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo]
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10780
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Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo]
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5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
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10697
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Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
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10762
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In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp]
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5. Theory of Logic / G. Quantification / 2. Domain of Quantification
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10776
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The main quantifiers extend 'and' and 'or' to infinite domains [Tharp]
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
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13671
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Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro]
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5. Theory of Logic / G. Quantification / 6. Plural Quantification
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10267
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We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro]
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10698
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Plural forms have no more ontological commitment than to first-order objects [Boolos]
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5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
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7806
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Boolos invented plural quantification [Boolos, by Benardete,JA]
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10774
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There are at least five unorthodox quantifiers that could be used [Tharp]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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10773
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The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
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10777
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Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp]
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5. Theory of Logic / K. Features of Logics / 3. Soundness
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10765
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Soundness would seem to be an essential requirement of a proof procedure [Tharp]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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10763
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Completeness and compactness together give axiomatizability [Tharp]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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10770
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If completeness fails there is no algorithm to list the valid formulas [Tharp]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
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10771
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Compactness is important for major theories which have infinitely many axioms [Tharp]
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10772
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Compactness blocks infinite expansion, and admits non-standard models [Tharp]
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5. Theory of Logic / K. Features of Logics / 8. Enumerability
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10764
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A complete logic has an effective enumeration of the valid formulas [Tharp]
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10768
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Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp]
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