Combining Philosophers
Ideas for Saunders MacLane, Timothy Williamson and George Engelbretsen
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13 ideas
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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18912
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Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen]
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5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
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6858
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Formal logic struck me as exactly the language I wanted to think in [Williamson]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
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21611
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Formal semantics defines validity as truth preserved in every model [Williamson]
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5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
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21606
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'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false [Williamson]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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21605
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Excluded Middle is 'A or not A' in the object language [Williamson]
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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
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18922
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Logical syntax is actually close to surface linguistic form [Engelbretsen]
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18905
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Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
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18908
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Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen]
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5. Theory of Logic / G. Quantification / 1. Quantification
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18492
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Not all quantification is either objectual or substitutional [Williamson]
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5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
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15136
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Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson]
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5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
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15138
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Not all quantification is objectual or substitutional [Williamson]
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5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
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21612
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Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B' [Williamson]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
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21599
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A sorites stops when it collides with an opposite sorites [Williamson]
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