Combining Philosophers

All the ideas for PG, John Haldane and George Cantor

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261 ideas

1. Philosophy / B. History of Ideas / 3. Greek-English Lexicon
Agathon: good [PG]
Aisthesis: perception, sensation, consciousness [PG]
Aitia / aition: cause, explanation [PG]
Akrasia: lack of control, weakness of will [PG]
Aletheia: truth [PG]
Anamnesis: recollection, remembrance [PG]
Ananke: necessity [PG]
Antikeimenon: object [PG]
Apatheia: unemotional [PG]
Apeiron: the unlimited, indefinite [PG]
Aphairesis: taking away, abstraction [PG]
Apodeixis: demonstration [PG]
Aporia: puzzle, question, anomaly [PG]
Arche: first principle, the basic [PG]
Arete: virtue, excellence [PG]
Chronismos: separation [PG]
Diairesis: division [PG]
Dialectic: dialectic, discussion [PG]
Dianoia: intellection [cf. Noesis] [PG]
Diaphora: difference [PG]
Dikaiosune: moral goodness, justice [PG]
Doxa: opinion, belief [PG]
Dunamis: faculty, potentiality, capacity [PG]
Eidos: form, idea [PG]
Elenchos: elenchus, interrogation [PG]
Empeiron: experience [PG]
Energeia: employment, actuality, power? [PG]
Enkrateia: control [PG]
Entelecheia: entelechy, having an end [PG]
Epagoge: induction, explanation [PG]
Episteme: knowledge, understanding [PG]
Epithumia: appetite [PG]
Ergon: function [PG]
Eristic: polemic, disputation [PG]
Eros: love [PG]
Eudaimonia: flourishing, happiness, fulfilment [PG]
Genos: type, genus [PG]
Hexis: state, habit [PG]
Horismos: definition [PG]
Hule: matter [PG]
Hupokeimenon: subject, underlying thing [cf. Tode ti] [PG]
Kalos / kalon: beauty, fineness, nobility [PG]
Kath' hauto: in virtue of itself, essentially [PG]
Kinesis: movement, process [PG]
Kosmos: order, universe [PG]
Logos: reason, account, word [PG]
Meson: the mean [PG]
Metechein: partaking, sharing [PG]
Mimesis: imitation, fine art [PG]
Morphe: form [PG]
Noesis: intellection, rational thought [cf. Dianoia] [PG]
Nomos: convention, law, custom [PG]
Nous: intuition, intellect, understanding [PG]
Orexis: desire [PG]
Ousia: substance, (primary) being, [see 'Prote ousia'] [PG]
Pathos: emotion, affection, property [PG]
Phantasia: imagination [PG]
Philia: friendship [PG]
Philosophia: philosophy, love of wisdom [PG]
Phronesis: prudence, practical reason, common sense [PG]
Physis: nature [PG]
Praxis: action, activity [PG]
Prote ousia: primary being [PG]
Psuche: mind, soul, life [PG]
Sophia: wisdom [PG]
Sophrosune: moderation, self-control [PG]
Stoicheia: elements [PG]
Sullogismos: deduction, syllogism [PG]
Techne: skill, practical knowledge [PG]
Telos: purpose, end [PG]
Theoria: contemplation [PG]
Theos: god [PG]
Ti esti: what-something-is, essence [PG]
Timoria: vengeance, punishment [PG]
To ti en einai: essence, what-it-is-to-be [PG]
To ti estin: essence [PG]
Tode ti: this-such, subject of predication [cf. hupokeimenon] [PG]
1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / a. Ancient chronology
323 (roughly): Euclid wrote 'Elements', summarising all of geometry [PG]
1000 (roughly): Upanishads written (in Sanskrit); religious and philosophical texts [PG]
750 (roughly): the Book of Genesis written by Hebrew writers [PG]
586: eclipse of the sun on the coast of modern Turkey was predicted by Thales of Miletus [PG]
570: Anaximander flourished in Miletus [PG]
563: the Buddha born in northern India [PG]
540: Lao Tzu wrote 'Tao Te Ching', the basis of Taoism [PG]
529: Pythagoras created his secretive community at Croton in Sicily [PG]
500: Heraclitus flourishes at Ephesus, in modern Turkey [PG]
496: Confucius travels widely, persuading rulers to be more moral [PG]
472: Empedocles persuades his city (Acragas in Sicily) to become a democracy [PG]
450 (roughly): Parmenides and Zeno visit Athens from Italy [PG]
445: Protagoras helps write laws for the new colony of Thurii [PG]
436 (roughly): Anaxagoras is tried for impiety, and expelled from Athens [PG]
170 (roughly): Marcus Aurelius wrote his private stoic meditations [PG]
-200 (roughly): Sextus Empiricus wrote a series of books on scepticism [PG]
263: Porphyry began to study with Plotinus in Rome [PG]
310: Christianity became the official religion of the Roman empire [PG]
387: Ambrose converts Augustine to Christianity [PG]
523: Boethius imprisoned at Pavia, and begins to write [PG]
529: the emperor Justinian closes all the philosophy schools in Athens [PG]
427: Gorgias visited Athens as ambassador for Leontini [PG]
399: Socrates executed (with Plato absent through ill health) [PG]
387 (roughly): Plato returned to Athens, and founded the Academy [PG]
387 (roughly): Aristippus the Elder founder a hedonist school at Cyrene [PG]
367: the teenaged Aristotle came to study at the Academy [PG]
360 (roughly): Diogenes of Sinope lives in a barrel in central Athens [PG]
347: death of Plato [PG]
343: Aristotle becomes tutor to 13 year old Alexander (the Great) [PG]
335: Arisotle founded his school at the Lyceum in Athens [PG]
330 (roughly): Chuang Tzu wrote his Taoist book [PG]
322: Aristotle retired to Chalcis, and died there [PG]
307 (roughly): Epicurus founded his school at the Garden in Athens [PG]
301 (roughly): Zeno of Citium founded Stoicism at the Stoa Poikile in Athens [PG]
261: Cleanthes replaced Zeno as head of the Stoa [PG]
229 (roughly): Chrysippus replaced Cleanthes has head of the Stoa [PG]
157 (roughly): Carneades became head of the Academy [PG]
85: most philosophical activity moves to Alexandria [PG]
78: Cicero visited the stoic school on Rhodes [PG]
60 (roughly): Lucretius wrote his Latin poem on epicureanism [PG]
65: Seneca forced to commit suicide by Nero [PG]
80: the discourses of the stoic Epictetus are written down [PG]
1. Philosophy / C. History of Philosophy / 3. Earlier European Philosophy / a. Earlier European chronology
1090: Anselm publishes his proof of the existence of God [PG]
622 (roughly): Mohammed writes the Koran [PG]
642: Arabs close the philosophy schools in Alexandria [PG]
910 (roughly): Al-Farabi wrote Arabic commentaries on Aristotle [PG]
1015 (roughly): Ibn Sina (Avicenna) writes a book on Aristotle [PG]
1115: Abelard is the chief logic teacher in Paris [PG]
1166: Ibn Rushd (Averroes) wrote extensive commentaries on Aristotle [PG]
1266: Aquinas began writing 'Summa Theologica' [PG]
1280: after his death, the teaching of Aquinas becomes official Dominican doctrine [PG]
1328: William of Ockham decides the Pope is a heretic, and moves to Munich [PG]
1347: the Church persecutes philosophical heresies [PG]
1470: Marsilio Ficino founds a Platonic Academy in Florence [PG]
1513: Machiavelli wrote 'The Prince' [PG]
1543: Copernicus publishes his heliocentric view of the solar system [PG]
1580: Montaigne publishes his essays [PG]
1600: Giordano Bruno was burned at the stake in Rome [PG]
1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / a. Later European chronology
1619: Descartes's famous day of meditation inside a stove [PG]
1620: Bacon publishes 'Novum Organum' [PG]
1633: Galileo convicted of heresy by the Inquisition [PG]
1641: Descartes publishes his 'Meditations' [PG]
1650: death of Descartes, in Stockholm [PG]
1651: Hobbes publishes 'Leviathan' [PG]
1662: the Port Royal Logic is published [PG]
1665: Spinoza writes his 'Ethics' [PG]
1676: Leibniz settled as librarian to the Duke of Brunswick [PG]
1687: Newton publishes his 'Principia Mathematica' [PG]
1690: Locke publishes his 'Essay' [PG]
1697: Bayle publishes his 'Dictionary' [PG]
1713: Berkeley publishes his 'Three Dialogues' [PG]
1734: Voltaire publishes his 'Philosophical Letters' [PG]
1739: Hume publishes his 'Treatise' [PG]
1762: Rousseau publishes his 'Social Contract' [PG]
1781: Kant publishes his 'Critique of Pure Reason' [PG]
1785: Reid publishes his essays defending common sense [PG]
1798: the French Revolution [PG]
1807: Hegel publishes his 'Phenomenology of Spirit' [PG]
1818: Schopenhauer publishes his 'World as Will and Idea' [PG]
1840: Kierkegaard is writing extensively in Copenhagen [PG]
1843: Mill publishes his 'System of Logic' [PG]
1848: Marx and Engels publis the Communist Manifesto [PG]
1859: Darwin publishes his 'Origin of the Species' [PG]
1861: Mill publishes 'Utilitarianism' [PG]
1867: Marx begins publishing 'Das Kapital' [PG]
1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / a. Modern philosophy chronology
1879: Peirce taught for five years at Johns Hopkins University [PG]
1879: Frege invents predicate logic [PG]
1892: Frege's essay 'Sense and Reference' [PG]
1884: Frege publishes his 'Foundations of Arithmetic' [PG]
1885: Nietzsche completed 'Thus Spake Zarathustra' [PG]
1888: Dedekind publishes axioms for arithmetic [PG]
1890: James published 'Principles of Psychology' [PG]
1895 (roughly): Freud developed theories of the unconscious [PG]
1900: Husserl began developing Phenomenology [PG]
1953: Wittgenstein's 'Philosophical Investigations' [PG]
1956: Place proposed mind-brain identity [PG]
1962: Kuhn's 'Structure of Scientific Revolutions' [PG]
1967: Putnam proposed functionalism of the mind [PG]
1971: Rawls's 'A Theory of Justice' [PG]
1972: Kripke publishes 'Naming and Necessity' [PG]
1975: Singer publishes 'Animal Rights' [PG]
1975: Putnam published his Twin Earth example [PG]
1986: David Lewis publishes 'On the Plurality of Worlds' [PG]
1903: Moore published 'Principia Ethica' [PG]
1904: Dewey became professor at Columbia University [PG]
1908: Zermelo publishes axioms for set theory [PG]
1910: Russell and Whitehead begin publishing 'Principia Mathematica' [PG]
1912: Russell meets Wittgenstein in Cambridge [PG]
1921: Wittgenstein's 'Tractatus' published [PG]
1927: Heidegger's 'Being and Time' published [PG]
1930: Frank Ramsey dies at 27 [PG]
1931: Gödel's Incompleteness Theorems [PG]
1933: Tarski's theory of truth [PG]
1942: Camus published 'The Myth of Sisyphus' [PG]
1943: Sartre's 'Being and Nothingness' [PG]
1945: Merleau-Ponty's 'Phenomenology of Perception' [PG]
1947: Carnap published 'Meaning and Necessity' [PG]
1950: Quine's essay 'Two Dogmas of Empiricism' [PG]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Note that "is" can assert existence, or predication, or identity, or classification [PG]
2. Reason / F. Fallacies / 1. Fallacy
Fallacies are errors in reasoning, 'formal' if a clear rule is breached, and 'informal' if more general [PG]
2. Reason / F. Fallacies / 3. Question Begging
Question-begging assumes the proposition which is being challenged [PG]
2. Reason / F. Fallacies / 6. Fallacy of Division
What is true of a set is also true of its members [PG]
2. Reason / F. Fallacies / 7. Ad Hominem
The Ad Hominem Fallacy criticises the speaker rather than the argument [PG]
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Minimal theories of truth avoid ontological commitment to such things as 'facts' or 'reality' [PG]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine]
Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine]
A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD]
Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg]
Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / b. Combinatorial sets
Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
There are infinite sets that are not enumerable [Cantor, by Smith,P]
5. Theory of Logic / L. Paradox / 1. Paradox
Monty Hall Dilemma: do you abandon your preference after Monty eliminates one of the rivals? [PG]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox
Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox
The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Cantor took the ordinal numbers to be primary [Cantor, by Tait]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait]
Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett]
Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine]
Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine]
Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine]
It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman]
Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner]
The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro]
Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD]
Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten]
Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS]
Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine]
Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Pure mathematics is pure set theory [Cantor]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Cantor says that maths originates only by abstraction from objects [Cantor, by Frege]
10. Modality / B. Possibility / 6. Probability
Everything has a probability, something will happen, and probabilities add up [PG]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / a. Naďve realism
If reality is just what we perceive, we would have no need for a sixth sense [PG]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
If my team is losing 3-1, I have synthetic a priori knowledge that they need two goals for a draw [PG]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
Maybe a mollusc's brain events for pain ARE of the same type (broadly) as a human's [PG]
Maybe a frog's brain events for fear are functionally like ours, but not phenomenally [PG]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor]
We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor]
23. Ethics / E. Utilitarianism / 4. Unfairness
Utilitarianism seems to justify the discreet murder of unhappy people [PG]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
Liberalism may fail because it neglects the shared nature of what we pursue and protect [Haldane]
27. Natural Reality / C. Space / 3. Points in Space
Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg]
27. Natural Reality / G. Biology / 2. Life
Life is Movement, Respiration, Sensation, Nutrition, Excretion, Reproduction, Growth (MRS NERG) [PG]
28. God / A. Divine Nature / 2. Divine Nature
Only God is absolutely infinite [Cantor, by Hart,WD]
28. God / A. Divine Nature / 4. Divine Contradictions
How could God know there wasn't an unknown force controlling his 'free' will? [PG]
An omniscient being couldn't know it was omniscient, as that requires information from beyond its scope of knowledge [PG]