Combining Texts
Ideas for
'Thinking About Mathematics', '25: Third Epistle of John' and 'Grundlagen der Arithmetik (Foundations)'
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7 ideas
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
8729
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Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
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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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Despite Gödel, Frege's epistemic ordering of all the truths is still plausible [Frege, by Burge]
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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 / 6. Plural Quantification
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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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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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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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To understand axioms you must grasp their logical power and priority [Frege, by Burge]
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