Combining Philosophers

All the ideas for Anaxarchus, Brian Clegg and Penelope Mackie

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39 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]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
11897 A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P]
11898 Individuation may include counterfactual possibilities, as well as identity and persistence [Mackie,P]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
11883 A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P]
9. Objects / D. Essence of Objects / 1. Essences of Objects
11889 Essentialism must avoid both reduplication of essences, and multiple occupancy by essences [Mackie,P]
9. Objects / D. Essence of Objects / 3. Individual Essences
11877 An individual essence is the properties the object could not exist without [Mackie,P]
11882 No other object can possibly have the same individual essence as some object [Mackie,P]
11886 There are problems both with individual essences and without them [Mackie,P]
9. Objects / D. Essence of Objects / 5. Essence as Kind
11909 Unlike Hesperus=Phosophorus, water=H2O needs further premisses before it is necessary [Mackie,P]
11899 Why are any sortals essential, and why are only some of them essential? [Mackie,P]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
11906 The Kripke and Putnam view of kinds makes them explanatorily basic, but has modal implications [Mackie,P]
9. Objects / E. Objects over Time / 12. Origin as Essential
11894 Origin is not a necessity, it is just 'tenacious'; we keep it fixed in counterfactual discussions [Mackie,P]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
11887 Transworld identity without individual essences leads to 'bare identities' [Mackie,P]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
11890 De re modality without bare identities or individual essence needs counterparts [Mackie,P]
11892 Things may only be counterparts under some particular relation [Mackie,P]
11893 Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
11884 The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
11905 Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P]
26. Natural Theory / B. Natural Kinds / 6. Necessity of Kinds
11907 Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P]