Combining Philosophers

All the ideas for Herodotus, John von Neumann and Brian R. Martin

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25 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
3340 Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
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]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
3355 Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13489 Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
22716 Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
12336 A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
18179 For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
18180 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
15925 Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
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]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
21202 The strong force has a considerably greater range than the weak force [Martin,BR]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / c. Conservation of energy
21211 If an expected reaction does not occur, that implies a conservation law [Martin,BR]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / a. Electrodynamics
21209 Electron emit and reabsorb photons, which create and reabsorb virtual electrons and positrons [Martin,BR]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
21201 A 'field' is just a region to which points can be assigned in space and time [Martin,BR]
21212 The Higgs field, unlike others, has a nozero value in a state without particles [Martin,BR]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
21205 Many physicists believe particles have further structure, if only we could see it [Martin,BR]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
21203 Uncertainty allows very brief violations of energy conservation - even shorter with higher energies [Martin,BR]
21207 The Exclusion Principle says no two fermions occupy the same state, with the same numbers [Martin,BR]
27. Natural Reality / B. Modern Physics / 4. Standard Model / b. Standard model
21204 The standard model combines theories of strong interaction, and electromagnetic and weak interaction [Martin,BR]
27. Natural Reality / B. Modern Physics / 4. Standard Model / c. Particle properties
21208 Eletrons don't literally 'spin', because they are point-like [Martin,BR]
21210 Virtual particles surround any charged particle [Martin,BR]
21206 The properties of a particle are determined by its quantum numbers and its mass [Martin,BR]
27. Natural Reality / B. Modern Physics / 5. Unified Models / b. String theory
21213 String theory only has one free parameter (tension) - unlike the standard model with 19 [Martin,BR]
27. Natural Reality / F. Chemistry / 2. Modern Elements
21200 An 'element' is what cannot be decomposed by chemistry [Martin,BR]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
1513 The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]