Ideas from 'Logical Consequence' by Vann McGee [2014], by Theme Structure
[found in 'Bloomsbury Companion to Philosophical Logic' (ed/tr Horsten,L/Pettigrew,R) [Bloomsbury 2014,978-1-4725-2303-0]].
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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
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Validity is explained as truth in all models, because that relies on the logical terms
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
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Natural language includes connectives like 'because' which are not truth-functional
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
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Second-order variables need to range over more than collections of first-order objects
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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An ontologically secure semantics for predicate calculus relies on sets
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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Logically valid sentences are analytic truths which are just true because of their logical words
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5. Theory of Logic / K. Features of Logics / 3. Soundness
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Soundness theorems are uninformative, because they rely on soundness in their proofs
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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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The culmination of Euclidean geometry was axioms that made all models isomorphic
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19. Language / F. Communication / 2. Assertion
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A maxim claims that if we are allowed to assert a sentence, that means it must be true
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