Combining Texts

All the ideas for 'Conditional Assertion and Restricted Quantification', 'Logical Consequence' and 'Whitehead and the Rise of Modern Logic'

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11 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Validity is explained as truth in all models, because that relies on the logical terms [McGee]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Natural language includes connectives like 'because' which are not truth-functional [McGee]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Second-order variables need to range over more than collections of first-order objects [McGee]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
An ontologically secure semantics for predicate calculus relies on sets [McGee]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logically valid sentences are analytic truths which are just true because of their logical words [McGee]
5. Theory of Logic / K. Features of Logics / 3. Soundness
Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Russell confused use and mention, and reduced classes to properties, not to language [Quine, by Lackey]
14. Science / C. Induction / 5. Paradoxes of Induction / b. Raven paradox
Read 'all ravens are black' as about ravens, not as about an implication [Belnap]
19. Language / F. Communication / 2. Assertion
A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee]