Combining Texts

All the ideas for 'Set Theory', 'The Mystery of Consciousness' and 'Commentary on Euclid's 'Elements''

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26 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13040 Constructibility: V = L (all sets are constructible) [Kunen]
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]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
13165 Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus]
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]
18. Thought / E. Abstraction / 1. Abstract Thought
9569 The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus]