Combining Texts

All the ideas for 'Why Reason Can't be Naturalized', 'First-Order Logic' and 'Frege on Apriority (with ps)'

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12 ideas

3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
8828 Truth is rational acceptability [Putnam]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
10284 There are three different standard presentations of semantics [Hodges,W]
10285 I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
16901 The equivalent algebra model of geometry loses some essential spatial meaning [Burge]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
16902 Peano arithmetic requires grasping 0 as a primitive number [Burge]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
16892 Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge]