Combining Texts

All the ideas for 'The Evolution of Modern Metaphysics', 'Pref to new 'Materialist Theory'' and 'Higher-Order Logic'

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22 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
21959 Metaphysics is the most general attempt to make sense of things [Moore,AW]
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
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [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]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
21958 Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
7440 Secondary qualities are microscopic primary qualities of physical things [Armstrong]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
7437 Consciousness and experience of qualities are not the same [Armstrong]
17. Mind and Body / B. Behaviourism / 1. Behaviourism
7434 Behaviourism is false, but mind is definable as the cause of behaviour [Armstrong]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
7436 The manifestations of a disposition need never actually exist [Armstrong]
17. Mind and Body / C. Functionalism / 4. Causal Functionalism
7429 Causal Functionalism says mental states are apt for producing behaviour [Armstrong]
17. Mind and Body / C. Functionalism / 5. Teleological Functionalism
7438 A causal theory of mentality would be improved by a teleological element [Armstrong]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
7431 The identity of mental states with physical properties is contingent, because the laws of nature are contingent [Armstrong]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
7432 One mental role might be filled by a variety of physical types [Armstrong]