Combining Texts
Ideas for
'Carnap and Logical Truth', 'Introduction to the Philosophy of Mathematics' and 'An Axiomatization of Set Theory'
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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
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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 / D. Assumptions for Logic / 2. Excluded Middle
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Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
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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 / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17929
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Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17930
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Axioms are 'categorical' if all of their models are isomorphic [Colyvan]
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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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