Combining Texts

All the ideas for 'The Internalist Conception of Justification', 'First-Order Logic' and 'Life of Theseus'

expand these ideas     |    start again     |     specify just one area for these texts

---

10 ideas

2. Reason / A. Nature of Reason / 6. Coherence

4262	If the only aim was consistent beliefs then new evidence and experiments would be irrelevant [Goldman]

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 / 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]

9. Objects / E. Objects over Time / 9. Ship of Theseus

1212	Replacing timbers on Theseus' ship was the classic illustration of the problem of growth and change [Plutarch]