Combining Texts
Ideas for
'To be is to be the value of a variable..', 'Paradox without Self-Reference' and 'Grundlagen der Arithmetik (Foundations)'
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15 ideas
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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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 / 1. Logical Form
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8645
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Convert "Jupiter has four moons" into "the number of Jupiter's moons is four" [Frege]
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5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
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16891
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Despite Gödel, Frege's epistemic ordering of all the truths is still plausible [Frege, by Burge]
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16906
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The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Frege, by Jeshion]
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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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14236
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Each horse doesn't fall under the concept 'horse that draws the carriage', because all four are needed [Oliver/Smiley on Frege]
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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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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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22294
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We can show that a concept is consistent by producing something which falls under it [Frege]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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17624
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To understand axioms you must grasp their logical power and priority [Frege, by Burge]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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9138
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An infinite series of sentences asserting falsehood produces the paradox without self-reference [Yablo, by Sorensen]
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