Combining Philosophers

All the ideas for Paul M. Pietroski, Michael Frede and Brian Clegg

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31 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / e. Late classical philosophy
23326 In the third century Stoicism died out, replaced by Platonism, with Aristotelian ethics [Frede,M]
23335 In late antiquity nearly all philosophers were monotheists [Frede,M]
1. Philosophy / C. History of Philosophy / 3. Earlier European Philosophy / b. Early medieval philosophy
16137 Earlier views of Aristotle were dominated by 'Categories' [Frede,M]
2. Reason / A. Nature of Reason / 1. On Reason
23249 The early philosophers thought that reason has its own needs and desires [Frede,M]
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 / E. Objects over Time / 9. Ship of Theseus
16157 Insurance on the original ship would hardly be paid out if the plank version was wrecked! [Frede,M]
16. Persons / F. Free Will / 2. Sources of Free Will
23334 For Christians man has free will by creation in God's image (as in Genesis) [Frede,M]
23337 The Stoics needed free will, to allow human choices in a divinely providential cosmos [Frede,M]
23333 The idea of free will achieved universal acceptance because of Christianity [Frede,M]
19. Language / B. Reference / 5. Speaker's Reference
21650 No language is semantically referential; it all occurs at the level of thought or utterance [Pietroski, by Hofweber]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
23336 There is no will for Plato or Aristotle, because actions come directly from perception of what is good [Frede,M]
29. Religion / A. Polytheistic Religion / 4. Dualist Religion
23313 The Gnostic demiurge (creator) is deluded, and doesn't care about us [Frede,M]