Combining Texts

All the ideas for 'The Mystery of Consciousness', 'Higher-Order Logic' and 'The Theory of Relativity and A Priori Knowledge'

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26 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]
7. Existence / C. Structure of Existence / 2. Reduction
5791 Reduction is either by elimination, or by explanation [Searle]
5799 Eliminative reduction needs a gap between appearance and reality, as in sunsets [Searle]
8. Modes of Existence / B. Properties / 3. Types of Properties
5790 A property is 'emergent' if it is caused by elements of a system, when the elements lack the property [Searle]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
12. Knowledge Sources / B. Perception / 5. Interpretation
18278 Kant showed that our perceptions are partly constructed from our concepts [Reichenbach]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
5792 Explanation of how we unify our mental stimuli into a single experience is the 'binding problem' [Searle]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
5786 A system is either conscious or it isn't, though the intensity varies a lot [Searle]
5794 Consciousness has a first-person ontology, which only exists from a subjective viewpoint [Searle]
5795 There isn't one consciousness (information-processing) which can be investigated, and another (phenomenal) which can't [Searle]
15. Nature of Minds / B. Features of Minds / 5. Qualia / a. Nature of qualia
5788 The use of 'qualia' seems to imply that consciousness and qualia are separate [Searle]
17. Mind and Body / C. Functionalism / 7. Chinese Room
5789 I now think syntax is not in the physics, but in the eye of the beholder [Searle]
17. Mind and Body / D. Property Dualism / 1. Reductionism critique
5798 Consciousness has a first-person ontology, so it cannot be reduced without omitting something [Searle]
17. Mind and Body / D. Property Dualism / 4. Emergentism
5787 There is non-event causation between mind and brain, as between a table and its solidity [Searle]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
5797 The pattern of molecules in the sea is much more complex than the complexity of brain neurons [Searle]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / a. Physicalism critique
5796 If tree rings contain information about age, then age contains information about rings [Searle]