Combining Texts

All the ideas for 'Confessions of a Philosopher', 'Set Theory' and 'Physics and Philosophy'

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29 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]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
17536 If it can't be expressed mathematically, it can't occur in nature? [Heisenberg]
7. Existence / D. Theories of Reality / 2. Realism
17545 Quantum theory shows that exact science does not need dogmatic realism [Heisenberg]
7. Existence / D. Theories of Reality / 4. Anti-realism
17538 Quantum theory does not introduce minds into atomic events [Heisenberg]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
17534 A 'probability wave' is a quantitative version of Aristotle's potential, a mid-way type of reality [Heisenberg]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
17553 We can retain the idea of 'substance', as indestructible mass or energy [Heisenberg]
9. Objects / C. Structure of Objects / 2. Hylomorphism / b. Form as principle
17544 Basic particles have a mathematical form, which is more important than their substance [Heisenberg]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
17550 We give a mathematical account of a system of natural connections in order to clarify them [Heisenberg]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
3102 Why don't we experience or remember going to sleep at night? [Magee]
26. Natural Theory / D. Laws of Nature / 2. Types of Laws
17549 Seven theories in science: mechanics, heat, electricity, quantum, particles, relativity, life [Heisenberg, by PG]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
17540 Energy is that which moves, and is the substance from which everything is made [Heisenberg]
17541 Energy is an unchanging substance, having many forms, and causing all change [Heisenberg]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
17548 Maxwell introduced real fields, which transferred forces from point to point [Heisenberg]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
17533 Radiation interference needs waves, but radiation photoelectric effects needs particles [Heisenberg]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
17532 An atom's stability after collisions needs explaining (which Newton's mechanics can't do) [Heisenberg]
17537 Position is complementary to velocity or momentum, so the whole system is indeterminate [Heisenberg]
17551 It was formerly assumed that electromagnetic waves could not be a reality in themselves [Heisenberg]
27. Natural Reality / C. Space / 4. Substantival Space
17543 So-called 'empty' space is the carrier of geometry and kinematics [Heisenberg]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
17552 In relativity the length of the 'present moment' is relative to distance from the observer [Heisenberg]