Combining Texts

All the ideas for 'On Freedom', 'First-Order Logic' and 'Machine Man'

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21 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]
10. Modality / B. Possibility / 5. Contingency
5040 Necessary truths can be analysed into original truths; contingent truths are infinitely analysable [Leibniz]
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
13159 Only God sees contingent truths a priori [Leibniz]
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
5039 If non-existents are possible, their existence would replace what now exists, which cannot therefore be necessary [Leibniz]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
7647 The imagination alone perceives all objects; it is the soul, playing all its roles [La Mettrie]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
7645 When falling asleep, the soul becomes paralysed and weak, just like the body [La Mettrie]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
23225 The soul's faculties depend on the brain, and are simply the brain's organisation [La Mettrie]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
7652 Man is a machine, and there exists only one substance, diversely modified [La Mettrie]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
7650 All thought is feeling, and rationality is the sensitive soul contemplating reasoning [La Mettrie]
18. Thought / B. Mechanics of Thought / 6. Artificial Thought / a. Artificial Intelligence
7651 With wonderful new machines being made, a speaking machine no longer seems impossible [La Mettrie]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
7648 The sun and rain weren't made for us; they sometimes burn us, or spoil our seeds [La Mettrie]
27. Natural Reality / G. Biology / 3. Evolution
7646 There is no abrupt transition from man to animal; only language has opened a gap [La Mettrie]
28. God / A. Divine Nature / 3. Divine Perfections
5041 God does everything in a perfect way, and never acts contrary to reason [Leibniz]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
7649 There is no clear idea of the soul, which should only refer to our thinking part [La Mettrie]