Combining Texts

All the ideas for 'works', 'A Problem about Substitutional Quantification?' and 'First-Order Logic'

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10 ideas

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 / G. Quantification / 4. Substitutional Quantification

10792

The substitutional quantifier is not in competition with the standard interpretation [Kripke, by Marcus (Barcan)]

5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic

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]

10283

A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

10289

Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]

10288

Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [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 / 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]

22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature

7667	There are two sides to men - the pleasantly social, and the violent and creative [Diderot, by Berlin]