Combining Texts

All the ideas for 'The Mystery of Consciousness', 'An Axiomatization of Set Theory' and 'On Second-Order Logic'

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22 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
15943 Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13672 All the axioms for mathematics presuppose set theory [Neumann]
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]
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]