Combining Philosophers

All the ideas for Anaxarchus, Brian Clegg and Brian R. Martin

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

35 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10859 A set is 'well-ordered' if every subset has a first element [Clegg]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10857 Set theory made a closer study of infinity possible [Clegg]
10864 Any set can always generate a larger set - its powerset, of subsets [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10872 Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10875 Pairing: For any two sets there exists a set to which they both belong [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
10876 Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10878 Infinity: There exists a set of the empty set and the successor of each element [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
10877 Powers: All the subsets of a given set form their own new powerset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10879 Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
10871 Axiom of Existence: there exists at least one set [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10874 Specification: a condition applied to a set will always produce a new set [Clegg]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10880 Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10860 An ordinal number is defined by the set that comes before it [Clegg]
10861 Beyond infinity cardinals and ordinals can come apart [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10854 Transcendental numbers can't be fitted to finite equations [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
10858 By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10853 Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10866 Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10869 The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
10862 The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
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
21212 The Higgs field, unlike others, has a nozero value in a state without particles [Martin,BR]
21201 A 'field' is just a region to which points can be assigned in space and time [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]