Combining Philosophers
Ideas for Hermarchus, Roger Penrose and Stewart Shapiro
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17 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
13642
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Logic is the ideal for learning new propositions on the basis of others [Shapiro]
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13627
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There is no 'correct' logic for natural languages [Shapiro]
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5. Theory of Logic / A. Overview of Logic / 2. History of Logic
13668
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Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro]
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13669
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Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro]
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13667
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Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro]
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5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13624
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The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro]
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13660
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Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro]
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13662
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First-order logic was an afterthought in the development of modern logic [Shapiro]
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13673
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The notion of finitude is actually built into first-order languages [Shapiro]
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10588
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First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13650
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Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro]
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15944
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Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine]
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13645
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In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro]
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13649
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Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro]
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10298
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Some say that second-order logic is mathematics, not logic [Shapiro]
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10299
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If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
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13629
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Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro]
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