Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'First-Order Logic' and 'The soul's dependence on the body'

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16 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
23269 Philosophy must start from clearly observed facts [Galen]
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 / B. Unity of Objects / 2. Substance / d. Substance defined
19347 Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
23266 The spirit in the soul wants freedom, power and honour [Galen]
15. Nature of Minds / A. Nature of Mind / 8. Brain
23219 Stopping the heart doesn't terminate activity; pressing the brain does that [Galen, by Cobb]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
23264 Philosophers think faculties are in substances, and invent a faculty for every activity [Galen]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
23220 The brain contains memory and reason, and is the source of sensation and decision [Galen]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
23265 The rational part of the soul is the desire for truth, understanding and recollection [Galen]
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
23268 We execute irredeemable people, to protect ourselves, as a deterrent, and ending a bad life [Galen]