Combining Texts

All the ideas for 'fragments/reports', 'Machine Man' and 'Higher-Order Logic'

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22 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
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]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
5996 Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA]
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]
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]