Combining Texts

All the ideas for 'Set Theory', 'Introduction to the Philosophy of Mind' and 'Cosmic Apprentice'

expand these ideas     |    start again     |     specify just one area for these texts

22 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
16567 Scientists know everything about nothing, philosophers nothing about everything [Sagan,D]
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 / 5. Supervenience / c. Significance of supervenience
3523 Shadows are supervenient on their objects, but not reducible [Maslin]
7. Existence / D. Theories of Reality / 1. Ontologies
3517 'Ontology' means 'study of things which exist' [Maslin]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / d. Other minds by analogy
3538 Analogy to other minds is uncheckable, over-confident and chauvinistic [Maslin]
16. Persons / B. Nature of the Self / 7. Self and Body / b. Self as brain
3540 If we are brains then we never meet each other [Maslin]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
3518 I'm not the final authority on my understanding of maths [Maslin]
17. Mind and Body / D. Property Dualism / 2. Anomalous Monism
3530 Denial of purely mental causation will lead to epiphenomenalism [Maslin]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
3520 Token-identity removes the explanatory role of the physical [Maslin]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
3528 Causality may require that a law is being followed [Maslin]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
3525 Strict laws make causation logically necessary [Maslin]
3527 Strict laws allow no exceptions and are part of a closed system [Maslin]