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'fragments/reports', 'Remarks on the definition and nature of mathematics' and 'Carnap and Logical Truth'
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8 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
13010
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In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine]
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5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
9002
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Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine]
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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13681
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Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
8078
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Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
6023
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Every proposition is either true or false [Chrysippus, by Cicero]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13829
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If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine]
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5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
17807
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To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
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5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
9003
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Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine]
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