Combining Philosophers

All the ideas for Hesiod, Gavin Hesketh and Kenneth Kunen

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33 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]
8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation
18465 An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
20239 Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
21181 Relativity and Quantum theory give very different accounts of forces [Hesketh]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
21183 Thermodynamics introduced work and entropy, to understand steam engine efficiency [Hesketh]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / a. Electrodynamics
21199 Spinning electric charge produces magnetism, so all fermions are magnets [Hesketh]
21191 Photons are B and W° bosons, linked by the Higgs mechanism [Hesketh]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
21189 Electrons may have smaller components, bound by a new force [Hesketh]
21180 Electrons are fundamental and are not made of anything; they are properties without size [Hesketh]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
21182 Quantum mechanics is our only theory, and is very precise, and repeatedly confirmed [Hesketh]
21184 Physics was rewritten to explain stable electron orbits [Hesketh]
21187 Virtual particles can't be measured, and can ignore the laws of physics [Hesketh]
27. Natural Reality / B. Modern Physics / 3. Chromodynamics / a. Chromodynamics
21185 Colour charge is positive or negative, and also has red, green or blue direction [Hesketh]
27. Natural Reality / B. Modern Physics / 4. Standard Model / b. Standard model
21194 The Standard Model omits gravity, because there are no particles involved [Hesketh]
21195 In Supersymmetry the Standard Model simplifies at high energies [Hesketh]
21197 Standard Model forces are one- two- and three-dimensional [Hesketh]
27. Natural Reality / B. Modern Physics / 4. Standard Model / c. Particle properties
21188 Quarks and leptons have a weak charge, for the weak force [Hesketh]
27. Natural Reality / B. Modern Physics / 4. Standard Model / e. Protons
21186 Quarks rush wildly around in protons, restrained by the gluons [Hesketh]
27. Natural Reality / B. Modern Physics / 4. Standard Model / f. Neutrinos
21192 Neutrinos only interact with the weak force, but decays produce them in huge numbers [Hesketh]
27. Natural Reality / B. Modern Physics / 5. Unified Models / c. Supersymmetry
21196 To combine the forces, they must all be the same strength at some point [Hesketh]
27. Natural Reality / C. Space / 5. Relational Space
21190 'Space' in physics just means location [Hesketh]
27. Natural Reality / E. Cosmology / 8. Dark Matter
21193 The universe is 68% dark energy, 27% dark matter, 5% regular matter [Hesketh]
27. Natural Reality / E. Cosmology / 9. Fine-Tuned Universe
21198 If a cosmic theory relies a great deal on fine-tuning basic values, it is probably wrong [Hesketh]