Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'First-Order Logic' and 'Mathematical Logic (revised)'

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11 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 / E. Structures of Logic / 4. Variables in Logic

12221

'Corner quotes' (quasi-quotation) designate 'whatever these terms designate' [Quine]

5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated

19321

We might do without names, by converting them into predicates [Quine, by Kirkham]

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 / 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]

23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues

7903	The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]