Combining Texts

All the ideas for 'Scientific Thought', 'On the Necessity of Origin' and 'First-Order Logic'

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15 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 / 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 / 4. Four-Dimensionalism

14759

A thing is simply a long event, linked by qualities, and spatio-temporal unity [Broad]

11842

If short-lived happenings like car crashes are 'events', why not long-lived events like Dover Cliffs? [Broad]

9. Objects / E. Objects over Time / 10. Beginning of an Object

18892

Suppose a world where I'm from different gametes; add my gametes; which one is more me? [McGinn]

9. Objects / E. Objects over Time / 12. Origin as Essential

12019

McGinn falsely claims necessity of origin is a special case of the necessity of identity [Forbes,G on McGinn]

27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block

8160	The present and past exist, but the future does not [Broad, by Dummett]

14609

We could say present and past exist, but not future, so that each event adds to the total history [Broad]

27. Natural Reality / D. Time / 2. Passage of Time / d. Time series

22933

We imagine the present as a spotlight, moving across events from past to future [Broad]