164 ideas
| 11461 | 323 (roughly): Euclid wrote 'Elements', summarising all of geometry [PG] |
| Full Idea: Euclid: In around 323 BCE Euclid wrote his 'Elements', summarising all of known geometry. | |
| From: PG (Db (chronology) [2030]) |
| 11390 | 1000 (roughly): Upanishads written (in Sanskrit); religious and philosophical texts [PG] |
| Full Idea: In around 1000 BCE the Upanishads were written, the most philosophical of ancient Hindu texts | |
| From: PG (Db (chronology) [2030], 0001) |
| 11391 | 750 (roughly): the Book of Genesis written by Hebrew writers [PG] |
| Full Idea: In around 750 BCE the Book of Genesis was written by an anonymous jewish writer | |
| From: PG (Db (chronology) [2030], 0250) |
| 11392 | 586: eclipse of the sun on the coast of modern Turkey was predicted by Thales of Miletus [PG] |
| Full Idea: In 585 BCE there was an eclipse of the sun, which Thales of Miletus is said to have predicted | |
| From: PG (Db (chronology) [2030], 0415) |
| 11395 | 570: Anaximander flourished in Miletus [PG] |
| Full Idea: Anaximander: In around 570 BCE the philosopher and astronomer Anaximander flourished in Miletus | |
| From: PG (Db (chronology) [2030], 0430) |
| 11396 | 563: the Buddha born in northern India [PG] |
| Full Idea: In around 563 BCE Siddhartha Gautama, the Buddha, was born in northern India | |
| From: PG (Db (chronology) [2030], 0437) |
| 11398 | 540: Lao Tzu wrote 'Tao Te Ching', the basis of Taoism [PG] |
| Full Idea: In around 540 BCE Lao Tzu wrote the 'Tao Te Ching', the basis of Taoism | |
| From: PG (Db (chronology) [2030], 0460) |
| 11400 | 529: Pythagoras created his secretive community at Croton in Sicily [PG] |
| Full Idea: In around 529 BCE Pythagoras set up a community in Croton, with strict and secret rules and teachings | |
| From: PG (Db (chronology) [2030], 0471) |
| 11403 | 500: Heraclitus flourishes at Ephesus, in modern Turkey [PG] |
| Full Idea: In around 500 BCE Heraclitus flourished in the city of Ephesus in Ionia | |
| From: PG (Db (chronology) [2030], 0500) |
| 11404 | 496: Confucius travels widely, persuading rulers to be more moral [PG] |
| Full Idea: In 496 BCE Confucius began a period of wandering, to persuade rulers to be more moral | |
| From: PG (Db (chronology) [2030], 0504) |
| 11408 | 472: Empedocles persuades his city (Acragas in Sicily) to become a democracy [PG] |
| Full Idea: In 472 BCE Empedocles helped his city of Acragas change to democracy | |
| From: PG (Db (chronology) [2030], 0528) |
| 11412 | 450 (roughly): Parmenides and Zeno visit Athens from Italy [PG] |
| Full Idea: In around 450 BCE Parmenides and Zeno visited the festival in Athens | |
| From: PG (Db (chronology) [2030], 0550) |
| 11414 | 445: Protagoras helps write laws for the new colony of Thurii [PG] |
| Full Idea: In 443 BCE Protagoras helped write the laws for the new colony of Thurii | |
| From: PG (Db (chronology) [2030], 0557) |
| 11417 | 436 (roughly): Anaxagoras is tried for impiety, and expelled from Athens [PG] |
| Full Idea: In about 436 BCE Anaxagoras was tried on a charge of impiety and expelled from Athens | |
| From: PG (Db (chronology) [2030], 0564) |
| 11421 | 427: Gorgias visited Athens as ambassador for Leontini [PG] |
| Full Idea: In 427 BCE Gorgias of Leontini visited Athens as an ambassador for his city | |
| From: PG (Db (chronology) [2030], 0573) |
| 11425 | 399: Socrates executed (with Plato absent through ill health) [PG] |
| Full Idea: In 399 BCE Plato was unwell, and was not present at the death of Socrates | |
| From: PG (Db (chronology) [2030], 0601) |
| 11432 | 387 (roughly): Plato returned to Athens, and founded the Academy [PG] |
| Full Idea: In about 387 BCE Plato returned to Athens and founded his new school at the Academy | |
| From: PG (Db (chronology) [2030], 0613) |
| 11433 | 387 (roughly): Aristippus the Elder founder a hedonist school at Cyrene [PG] |
| Full Idea: In around 387 BCE a new school was founded at Cyrene by Aristippus the elder | |
| From: PG (Db (chronology) [2030], 0613) |
| 11440 | 367: the teenaged Aristotle came to study at the Academy [PG] |
| Full Idea: In 367 BCE the seventeen-year-old Aristotle came south to study at the Academy | |
| From: PG (Db (chronology) [2030], 0633) |
| 11443 | 360 (roughly): Diogenes of Sinope lives in a barrel in central Athens [PG] |
| Full Idea: In around 360 BCE Diogenes of Sinope was living in a barrel in the Agora in Athens | |
| From: PG (Db (chronology) [2030], 0640) |
| 11445 | 347: death of Plato [PG] |
| Full Idea: In 347 BCE Plato died | |
| From: PG (Db (chronology) [2030], 0653) |
| 11454 | 343: Aristotle becomes tutor to 13 year old Alexander (the Great) [PG] |
| Full Idea: In 343 BCE at Stagira Aristotle became personal tutor to the thirteen-year-old Alexander (the Great) | |
| From: PG (Db (chronology) [2030], 0657) |
| 11456 | 335: Arisotle founded his school at the Lyceum in Athens [PG] |
| Full Idea: In 335 BCE Aristotle founded the Lyceum in Athens | |
| From: PG (Db (chronology) [2030], 0665) |
| 11459 | 330 (roughly): Chuang Tzu wrote his Taoist book [PG] |
| Full Idea: In around 330 BCE Chuang Tzu wrote a key work in the Taoist tradition | |
| From: PG (Db (chronology) [2030], 0670) |
| 11465 | 322: Aristotle retired to Chalcis, and died there [PG] |
| Full Idea: In 322 BCE Aristotle retired to Chalcis in Euboea, where he died | |
| From: PG (Db (chronology) [2030], 0678) |
| 11468 | 307 (roughly): Epicurus founded his school at the Garden in Athens [PG] |
| Full Idea: In about 307 BCE Epicurus founded his school at the Garden in Athens | |
| From: PG (Db (chronology) [2030], 0693) |
| 11470 | 301 (roughly): Zeno of Citium founded Stoicism at the Stoa Poikile in Athens [PG] |
| Full Idea: In about 301 BCE the Stoic school was founded by Zeno of Citium in the Stoa Poikile in Athens | |
| From: PG (Db (chronology) [2030], 0699) |
| 11483 | 261: Cleanthes replaced Zeno as head of the Stoa [PG] |
| Full Idea: In 261 BCE Cleanthes took over from Zeno as head of the Stoa. | |
| From: PG (Db (chronology) [2030], 0739) |
| 11486 | 229 (roughly): Chrysippus replaced Cleanthes has head of the Stoa [PG] |
| Full Idea: In about 229 BCE Chrysippus took over from Cleanthes as the head of the Stoic school | |
| From: PG (Db (chronology) [2030], 0771) |
| 11492 | 157 (roughly): Carneades became head of the Academy [PG] |
| Full Idea: In around 157 BCE Carneades took over as head of the Academy from Hegesinus | |
| From: PG (Db (chronology) [2030], 0843) |
| 11509 | 85: most philosophical activity moves to Alexandria [PG] |
| Full Idea: In around 85 BCE Athens went into philosophical decline, and leadership moved to Alexandria | |
| From: PG (Db (chronology) [2030], 0915) |
| 11513 | 78: Cicero visited the stoic school on Rhodes [PG] |
| Full Idea: In around 78 BCE Cicero visited the school of Posidonius in Rhodes. | |
| From: PG (Db (chronology) [2030], 0922) |
| 11516 | 60 (roughly): Lucretius wrote his Latin poem on epicureanism [PG] |
| Full Idea: In around 60 BCE Lucretius wrote his Latin poem on Epicureanism | |
| From: PG (Db (chronology) [2030], 0940) |
| 11528 | 65: Seneca forced to commit suicide by Nero [PG] |
| Full Idea: In 65 CE Seneca was forced to commit suicide by the Emperor Nero. | |
| From: PG (Db (chronology) [2030], 1065) |
| 11531 | 80: the discourses of the stoic Epictetus are written down [PG] |
| Full Idea: In around 80 CE the 'Discourses' of the freed slave Epictetus were written down in Rome. | |
| From: PG (Db (chronology) [2030], 1080) |
| 11535 | 170 (roughly): Marcus Aurelius wrote his private stoic meditations [PG] |
| Full Idea: In around 170 CE the Emperor Marcus Aurelius wrote his 'Meditations' for private reading. | |
| From: PG (Db (chronology) [2030], 1170) |
| 11537 | -200 (roughly): Sextus Empiricus wrote a series of books on scepticism [PG] |
| Full Idea: In around 200 CE Sextus Empiricus wrote a series of books (which survive) defending scepticism | |
| From: PG (Db (chronology) [2030], 1200) |
| 11541 | 263: Porphyry began to study with Plotinus in Rome [PG] |
| Full Idea: In 263 CE Porphyry joined Plotinus' classes in Rome | |
| From: PG (Db (chronology) [2030], 1263) |
| 11545 | 310: Christianity became the official religion of the Roman empire [PG] |
| Full Idea: In 310 CE Christianity became the official religion of the Roman Empire | |
| From: PG (Db (chronology) [2030], 1310) |
| 11549 | 387: Ambrose converts Augustine to Christianity [PG] |
| Full Idea: In 387 CE Augustine converted to Christianity in Milan, guided by St Ambrose | |
| From: PG (Db (chronology) [2030], 1387) |
| 11555 | 523: Boethius imprisoned at Pavia, and begins to write [PG] |
| Full Idea: In 523 CE Boethius was imprisoned in exile at Pavia, and wrote 'Consolations of Philosophy' | |
| From: PG (Db (chronology) [2030], 1523) |
| 11557 | 529: the emperor Justinian closes all the philosophy schools in Athens [PG] |
| Full Idea: In 529 CE the Emperor Justinian closed all the philosophy schools in Athens | |
| From: PG (Db (chronology) [2030], 1529) |
| 11558 | 622 (roughly): Mohammed writes the Koran [PG] |
| Full Idea: Mohammed: In about 622 CE Muhammed wrote the basic text of Islam, the Koran. | |
| From: PG (Db (chronology) [2030], 1622) |
| 11559 | 642: Arabs close the philosophy schools in Alexandria [PG] |
| Full Idea: In 642 CE Alexandria was captured by the Arabs, and the philosophy schools were closed | |
| From: PG (Db (chronology) [2030], 1642) |
| 11560 | 910 (roughly): Al-Farabi wrote Arabic commentaries on Aristotle [PG] |
| Full Idea: Alfarabi: In around 910 CE Al-Farabi explained and expanded Aristotle for the Islamic world. | |
| From: PG (Db (chronology) [2030], 1910) |
| 11562 | 1015 (roughly): Ibn Sina (Avicenna) writes a book on Aristotle [PG] |
| Full Idea: In around 1015 Avicenna produced his Platonised version of Aristotle in 'The Healing' | |
| From: PG (Db (chronology) [2030], 2015) |
| 11564 | 1090: Anselm publishes his proof of the existence of God [PG] |
| Full Idea: Anselm: In about 1090 St Anselm of Canterbury publishes his Ontological Proof of God's existence | |
| From: PG (Db (chronology) [2030], 2090) |
| 11566 | 1115: Abelard is the chief logic teacher in Paris [PG] |
| Full Idea: In around 1115 Abelard became established as the chief logic teacher in Paris | |
| From: PG (Db (chronology) [2030], 2115) |
| 11573 | 1166: Ibn Rushd (Averroes) wrote extensive commentaries on Aristotle [PG] |
| Full Idea: In around 1166 Averroes (Ibn Rushd), in Seville, wrote extensive commentaries on Aristotle | |
| From: PG (Db (chronology) [2030], 2166) |
| 11581 | 1266: Aquinas began writing 'Summa Theologica' [PG] |
| Full Idea: In 1266 Aquinas began writing his great theological work, the 'Summa Theologica' | |
| From: PG (Db (chronology) [2030], 2266) |
| 11586 | 1280: after his death, the teaching of Aquinas becomes official Dominican doctrine [PG] |
| Full Idea: In around 1280 Aquinas's teaching became the official theology of the Dominican order | |
| From: PG (Db (chronology) [2030], 2280) |
| 11591 | 1328: William of Ockham decides the Pope is a heretic, and moves to Munich [PG] |
| Full Idea: In 1328 William of Ockham decided the Pope was a heretic, and moved to Munich | |
| From: PG (Db (chronology) [2030], 2328) |
| 17916 | 1347: the Church persecutes philosophical heresies [PG] |
| Full Idea: In 1347 the Church began extensive persecution of unorthodox philosophical thought | |
| From: PG (Db (chronology) [2030], 2347) |
| 11593 | 1470: Marsilio Ficino founds a Platonic Academy in Florence [PG] |
| Full Idea: In around 1470 Marsilio Ficino founded a Platonic Academy in Florence | |
| From: PG (Db (chronology) [2030], 2470) |
| 11596 | 1513: Machiavelli wrote 'The Prince' [PG] |
| Full Idea: In 1513 Machiavelli wrote 'The Prince', a tough view of political theory. | |
| From: PG (Db (chronology) [2030], 2513) |
| 11599 | 1543: Copernicus publishes his heliocentric view of the solar system [PG] |
| Full Idea: In 1543 Nicholas Copernicus, a Polish monk, publishes his new theory of the solar system. | |
| From: PG (Db (chronology) [2030], 2543) |
| 11601 | 1580: Montaigne publishes his essays [PG] |
| Full Idea: In 1580 Montaigne published a volume of his 'Essays' | |
| From: PG (Db (chronology) [2030], 2580) |
| 11607 | 1600: Giordano Bruno was burned at the stake in Rome [PG] |
| Full Idea: In 1600 Giordano Bruno was burnt at the stake in Rome, largely for endorsing Copernicus | |
| From: PG (Db (chronology) [2030], 2600) |
| 11613 | 1619: Descartes's famous day of meditation inside a stove [PG] |
| Full Idea: In 1619 Descartes had a famous day of meditation in a heated stove at Ulm | |
| From: PG (Db (chronology) [2030], 2619) |
| 11614 | 1620: Bacon publishes 'Novum Organum' [PG] |
| Full Idea: Francis Bacon: In 1620 Bacon published his 'Novum Organon', urging the rise of experimental science | |
| From: PG (Db (chronology) [2030], 2620) |
| 11619 | 1633: Galileo convicted of heresy by the Inquisition [PG] |
| Full Idea: In 1633 Galileo was condemned to life emprisonment for contradicting church teachings. | |
| From: PG (Db (chronology) [2030], 2633) |
| 11623 | 1641: Descartes publishes his 'Meditations' [PG] |
| Full Idea: In 1641 Descartes published his well-known 'Meditations', complete with Objections and Replies | |
| From: PG (Db (chronology) [2030], 2641) |
| 11626 | 1650: death of Descartes, in Stockholm [PG] |
| Full Idea: In 1650 Descartes died in Stockholm, after stressful work for Queen Christina | |
| From: PG (Db (chronology) [2030], 2650) |
| 11627 | 1651: Hobbes publishes 'Leviathan' [PG] |
| Full Idea: In 1651 Hobbes published his great work on politics and contract morality, 'Leviathan' | |
| From: PG (Db (chronology) [2030], 2651) |
| 11633 | 1662: the Port Royal Logic is published [PG] |
| Full Idea: Antoine Arnauld: In 1662 Arnauld and Nicole published their famous text, the 'Port-Royal Logic' | |
| From: PG (Db (chronology) [2030], 2662) |
| 11634 | 1665: Spinoza writes his 'Ethics' [PG] |
| Full Idea: In 1665 the first draft of Spinoza's 'Ethics', his major work, was finished, and published posthumously | |
| From: PG (Db (chronology) [2030], 2665) |
| 11643 | 1676: Leibniz settled as librarian to the Duke of Brunswick [PG] |
| Full Idea: In 1676 Leibniz became librarian to the Duke of Brunswick, staying for the rest of his life | |
| From: PG (Db (chronology) [2030], 2676) |
| 11649 | 1687: Newton publishes his 'Principia Mathematica' [PG] |
| Full Idea: In 1687 Newton published his 'Principia', containing his theory of gravity. | |
| From: PG (Db (chronology) [2030], 2687) |
| 11652 | 1690: Locke publishes his 'Essay' [PG] |
| Full Idea: In 1690 Locke published his 'Essay', his major work on empiricism | |
| From: PG (Db (chronology) [2030], 2690) |
| 11654 | 1697: Bayle publishes his 'Dictionary' [PG] |
| Full Idea: Pierre Bayle: In about 1697 Pierre Bayle published his 'Historical and Critical Dictionary' | |
| From: PG (Db (chronology) [2030], 2697) |
| 11659 | 1713: Berkeley publishes his 'Three Dialogues' [PG] |
| Full Idea: In 1713 Berkeley published a popular account of his empiricist idealism in 'Three Dialogues' | |
| From: PG (Db (chronology) [2030], 2713) |
| 11666 | 1734: Voltaire publishes his 'Philosophical Letters' [PG] |
| Full Idea: Francois-Marie Voltaire: In 1734 Voltaire's 'Lettres Philosophiques' praised liberalism and empiricism | |
| From: PG (Db (chronology) [2030], 2734) |
| 11667 | 1739: Hume publishes his 'Treatise' [PG] |
| Full Idea: In 1739 Hume returned to Edinburgh and published his 'Treatise', but it sold very few copies | |
| From: PG (Db (chronology) [2030], 2739) |
| 11675 | 1762: Rousseau publishes his 'Social Contract' [PG] |
| Full Idea: In 1762 Rousseau published his 'Social Contract', basing politics on the popular will | |
| From: PG (Db (chronology) [2030], 2762) |
| 11682 | 1781: Kant publishes his 'Critique of Pure Reason' [PG] |
| Full Idea: In 1781 Kant published his first great work, the 'Critique of Pure Reason' | |
| From: PG (Db (chronology) [2030], 2781) |
| 11683 | 1785: Reid publishes his essays defending common sense [PG] |
| Full Idea: In 1785 Thomas Reid, based in Glasgow, published essays defending common sense. | |
| From: PG (Db (chronology) [2030], 2785) |
| 11687 | 1798: the French Revolution [PG] |
| Full Idea: In 1789 the French Revolution gave strong impetus to the anti-rational 'Romantic' movement | |
| From: PG (Db (chronology) [2030], 2789) |
| 11694 | 1807: Hegel publishes his 'Phenomenology of Spirit' [PG] |
| Full Idea: In 1807 Hegel published his first major work, the 'Phenomenology of Spirit' | |
| From: PG (Db (chronology) [2030], 2807) |
| 11701 | 1818: Schopenhauer publishes his 'World as Will and Idea' [PG] |
| Full Idea: In 1818 Schopenhauer published 'The World as Will and Idea', his major work | |
| From: PG (Db (chronology) [2030], 2818) |
| 11710 | 1840: Kierkegaard is writing extensively in Copenhagen [PG] |
| Full Idea: In around 1840 Kierkegaard lived a quiet life as a writer in Copenhagen | |
| From: PG (Db (chronology) [2030], 2840) |
| 11713 | 1843: Mill publishes his 'System of Logic' [PG] |
| Full Idea: In 1843 Mill published his 'System of Logic' | |
| From: PG (Db (chronology) [2030], 2843) |
| 11715 | 1848: Marx and Engels publis the Communist Manifesto [PG] |
| Full Idea: Karl Marx: In 1848 Marx and Engels published their 'Communist Manifesto' | |
| From: PG (Db (chronology) [2030], 2848) |
| 11717 | 1859: Darwin publishes his 'Origin of the Species' [PG] |
| Full Idea: Charles Darwin: In 1859 Charles Darwin published his theory of natural selection in 'Origin of the Species'. | |
| From: PG (Db (chronology) [2030], 2859) |
| 11721 | 1861: Mill publishes 'Utilitarianism' [PG] |
| Full Idea: In 1861 Mill published his book 'Utilitarianism' | |
| From: PG (Db (chronology) [2030], 2861) |
| 11724 | 1867: Marx begins publishing 'Das Kapital' [PG] |
| Full Idea: Karl Marx: In 1867 Karl Marx began publishing his political work 'Das Kapital' | |
| From: PG (Db (chronology) [2030], 2867) |
| 11733 | 1879: Peirce taught for five years at Johns Hopkins University [PG] |
| Full Idea: In 1879 Peirce began five years of teaching at Johns Hopkins University | |
| From: PG (Db (chronology) [2030], 2879) |
| 17907 | 1879: Frege invents predicate logic [PG] |
| Full Idea: In 1879 Frege published his 'Concept Script', which created predicate logic | |
| From: PG (Db (chronology) [2030], 2879) |
| 17909 | 1892: Frege's essay 'Sense and Reference' [PG] |
| Full Idea: In 1892 Frege published his famous essay 'Sense and Reference' (Sinn und Bedeutung) | |
| From: PG (Db (chronology) [2030], 2882) |
| 17908 | 1884: Frege publishes his 'Foundations of Arithmetic' [PG] |
| Full Idea: In 1884 Frege published his 'Foundations of Arithmetic', the beginning of logicism | |
| From: PG (Db (chronology) [2030], 2884) |
| 11735 | 1885: Nietzsche completed 'Thus Spake Zarathustra' [PG] |
| Full Idea: In about 1885 Nietzsche completed his book 'Also Sprach Zarathustra' | |
| From: PG (Db (chronology) [2030], 2885) |
| 17911 | 1888: Dedekind publishes axioms for arithmetic [PG] |
| Full Idea: In 1888 Dedekind created simple axioms for arithmetic (the Peano Axioms) | |
| From: PG (Db (chronology) [2030], 2888) |
| 11740 | 1890: James published 'Principles of Psychology' [PG] |
| Full Idea: In 1890 James published his 'Principles of Psychology' | |
| From: PG (Db (chronology) [2030], 2890) |
| 11742 | 1895 (roughly): Freud developed theories of the unconscious [PG] |
| Full Idea: In around 1895 Sigmund Freud developed his theories of the unconscious mind | |
| From: PG (Db (chronology) [2030], 2895) |
| 11745 | 1900: Husserl began developing Phenomenology [PG] |
| Full Idea: In 1900 Edmund Husserl began presenting his new philosophy of Phenomenology | |
| From: PG (Db (chronology) [2030], 2900) |
| 11746 | 1903: Moore published 'Principia Ethica' [PG] |
| Full Idea: In 1903 G.E. Moore published his 'Principia Ethica', attacking naturalistic ethics. | |
| From: PG (Db (chronology) [2030], 2903) |
| 11747 | 1904: Dewey became professor at Columbia University [PG] |
| Full Idea: In 1904 Dewey moved to Columbia University in New York. | |
| From: PG (Db (chronology) [2030], 2904) |
| 17910 | 1908: Zermelo publishes axioms for set theory [PG] |
| Full Idea: In 1908 Zermelo published an axiomatisation of the new set theory | |
| From: PG (Db (chronology) [2030], 2908) |
| 11752 | 1910: Russell and Whitehead begin publishing 'Principia Mathematica' [PG] |
| Full Idea: In 1910 Russell began publication of 'Principia Mathematica', with Whitehead | |
| From: PG (Db (chronology) [2030], 2910) |
| 11756 | 1912: Russell meets Wittgenstein in Cambridge [PG] |
| Full Idea: In 1912 Russell met Wittgenstein at Cambridge | |
| From: PG (Db (chronology) [2030], 2912) |
| 11762 | 1921: Wittgenstein's 'Tractatus' published [PG] |
| Full Idea: In 1921 Wittgenstein's 'Tractatus' was published | |
| From: PG (Db (chronology) [2030], 2921) |
| 11765 | 1927: Heidegger's 'Being and Time' published [PG] |
| Full Idea: In 1927 Heidegger's major work, 'Being and Time', was published | |
| From: PG (Db (chronology) [2030], 2927) |
| 11768 | 1930: Frank Ramsey dies at 27 [PG] |
| Full Idea: In 1930 Frank Ramsey died at the age of 27. | |
| From: PG (Db (chronology) [2030], 2930) |
| 11770 | 1931: Gödel's Incompleteness Theorems [PG] |
| Full Idea: Kurt Gödel: In 1931 the mathematician Kurt Gödel publishes his Incompleteness Theorems. | |
| From: PG (Db (chronology) [2030], 2931) |
| 11773 | 1933: Tarski's theory of truth [PG] |
| Full Idea: Alfred Tarski: In 1933 Alfred Tarski wrote a famous paper presenting a semantic theory of truth. | |
| From: PG (Db (chronology) [2030], 2933) |
| 11783 | 1942: Camus published 'The Myth of Sisyphus' [PG] |
| Full Idea: In 1942 Camus published 'The Myth of Sisyphus', exploring suicide and the absurd | |
| From: PG (Db (chronology) [2030], 2942) |
| 11784 | 1943: Sartre's 'Being and Nothingness' [PG] |
| Full Idea: In 1943 Jean-Paul Sartre published his major work, 'Being and Nothingness' | |
| From: PG (Db (chronology) [2030], 2943) |
| 11787 | 1945: Merleau-Ponty's 'Phenomenology of Perception' [PG] |
| Full Idea: Maurice Merleau-Ponty: In 1945 Maurice Merleau-Pont published 'The Phenomenology of Perception' | |
| From: PG (Db (chronology) [2030], 2945) |
| 17918 | 1947: Carnap published 'Meaning and Necessity' [PG] |
| Full Idea: In 1947 Carnap published 'Meaning and Necessity' | |
| From: PG (Db (chronology) [2030], 2947) |
| 11794 | 1950: Quine's essay 'Two Dogmas of Empiricism' [PG] |
| Full Idea: In 1950 Willard Quine published 'Two Dogmas of Empiricism', attacking analytic truth | |
| From: PG (Db (chronology) [2030], 2950) |
| 17917 | 1953: Wittgenstein's 'Philosophical Investigations' [PG] |
| Full Idea: In 1953 Wittgenstein's posthumous work 'Philosophical Investigations' is published | |
| From: PG (Db (chronology) [2030], 2953) |
| 17919 | 1956: Place proposed mind-brain identity [PG] |
| Full Idea: In 1956 U.T. Place proposed that the mind is identical to the brain | |
| From: PG (Db (chronology) [2030], 2956) |
| 11804 | 1962: Kuhn's 'Structure of Scientific Revolutions' [PG] |
| Full Idea: In 1962 Thomas Kuhn's 'Structure of Scientific Revolutions' questioned the authority of science | |
| From: PG (Db (chronology) [2030], 2962) |
| 17921 | 1967: Putnam proposed functionalism of the mind [PG] |
| Full Idea: In 1967 Putname proposed the functionalist view of the mind | |
| From: PG (Db (chronology) [2030], 2967) |
| 11808 | 1971: Rawls's 'A Theory of Justice' [PG] |
| Full Idea: In 1971 John Rawls published his famous defence of liberalism in 'A Theory of Justice' | |
| From: PG (Db (chronology) [2030], 2971) |
| 11810 | 1972: Kripke publishes 'Naming and Necessity' [PG] |
| Full Idea: In 1972 Saul Kripke's 'Naming and Necessity' revised theories about language and reality | |
| From: PG (Db (chronology) [2030], 2972) |
| 11813 | 1975: Singer publishes 'Animal Rights' [PG] |
| Full Idea: Peter Singer: In 1975 Peter Singer's 'Animal Rights' turned the attention of philosophers to applied ethics. | |
| From: PG (Db (chronology) [2030], 2975) |
| 17920 | 1975: Putnam published his Twin Earth example [PG] |
| Full Idea: In 1975 Putnam published 'The Meaning of 'Meaning'', containing his Twin Earth example | |
| From: PG (Db (chronology) [2030], 2975) |
| 11820 | 1986: David Lewis publishes 'On the Plurality of Worlds' [PG] |
| Full Idea: In 1986 David Lewis published 'On the Plurality of Worlds', about possible worlds. | |
| From: PG (Db (chronology) [2030], 2986) |
| 10073 | There cannot be a set theory which is complete [Smith,P] |
| Full Idea: By Gödel's First Incompleteness Theorem, there cannot be a negation-complete set theory. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.3) | |
| A reaction: This means that we can never prove all the truths of a system of set theory. |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| Full Idea: Going second-order in arithmetic enables us to prove new first-order arithmetical sentences that we couldn't prove before. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.4) | |
| A reaction: The wages of Satan, perhaps. We can prove things about objects by proving things about their properties and sets and functions. Smith says this fact goes all the way up the hierarchy. |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| Full Idea: A 'partial function' is one which maps only some elements of a domain to elements in another set. For example, the reciprocal function 1/x is not defined for x=0. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1 n1) |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| Full Idea: A 'total function' is one which maps every element of a domain to exactly one corresponding value in another set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| Full Idea: If a function f maps the argument a back to a itself, so that f(a) = a, then a is said to be a 'fixed point' for f. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 20.5) |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| Full Idea: The 'range' of a function is the set of elements in the output set that are values of the function for elements in the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: In other words, the range is the set of values that were created by the function. |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| Full Idea: We count two functions as being the same if they have the same extension, i.e. if they pair up arguments with values in the same way. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 11.3) | |
| A reaction: So there's only one way to skin a cat in mathematical logic. |
| 10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
| Full Idea: The so-called Comprehension Schema ∃X∀x(Xx ↔ φ(x)) says that there is a property which is had by just those things which satisfy the condition φ. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 22.3) |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| Full Idea: 'Theorem': given a derivation of the sentence φ from the axioms of the theory T using the background logical proof system, we will say that φ is a 'theorem' of the theory. Standard abbreviation is T |- φ. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
| Full Idea: A 'natural deduction system' will have no logical axioms but may rules of inference. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 09.1) | |
| A reaction: He contrasts this with 'Hilbert-style systems', which have many axioms but few rules. Natural deduction uses many assumptions which are then discharged, and so tree-systems are good for representing it. |
| 10613 | No nice theory can define truth for its own language [Smith,P] |
| Full Idea: No nice theory can define truth for its own language. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 21.5) | |
| A reaction: This leads on to Tarski's account of truth. |
| 10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
| Full Idea: An 'injective' function is 'one-to-one' - each element of the output set results from a different element of the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: That is, two different original elements cannot lead to the same output element. |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| Full Idea: A 'surjective' function is 'onto' - the whole of the output set results from the function being applied to elements of the original set. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
| Full Idea: A 'bijective' function has 'one-to-one correspondence' - it is both surjective and injective, so that every element in each of the original and the output sets has a matching element in the other. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.1) | |
| A reaction: Note that 'injective' is also one-to-one, but only in the one direction. |
| 10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
| Full Idea: If everything that a theory proves must be true, then it is a 'sound' theory. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) |
| 10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
| Full Idea: Soundness is normally a matter of having true axioms and a truth-preserving proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) | |
| A reaction: The only exception I can think of is if a theory consisted of nothing but the axioms. |
| 10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
| Full Idea: A theory is 'sound' iff every theorem of it is true (i.e. true on the interpretation built into its language). Soundness is normally a matter of having true axioms and a truth-preserving proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
| Full Idea: A theory is 'negation complete' if it decides every sentence of its language (either the sentence, or its negation). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
| Full Idea: There is an annoying double-use of 'complete': a logic may be semantically complete, but there may be an incomplete theory expressed in it. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) |
| 10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
| Full Idea: Logicians say that a theory T is '(negation) complete' if, for every sentence φ in the language of the theory, either φ or ¬φ is deducible in T's proof system. If this were the case, then truth could be equated with provability. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) | |
| A reaction: The word 'negation' seems to be a recent addition to the concept. Presumable it might be the case that φ can always be proved, but not ¬φ. |
| 10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
| Full Idea: There are two routes to Incompleteness results. One goes via the semantic assumption that we are dealing with sound theories, using a result about what they can express. The other uses the syntactic notion of consistency, with stronger notions of proof. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 18.1) |
| 10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
| Full Idea: An 'effectively decidable' (or 'computable') algorithm will be step-by-small-step, with no need for intuition, or for independent sources, with no random methods, possible for a dumb computer, and terminates in finite steps. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.2) | |
| A reaction: [a compressed paragraph] |
| 10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
| Full Idea: A theory is 'decidable' iff there is a mechanical procedure for determining whether any sentence of its language can be proved. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.4) | |
| A reaction: Note that it doesn't actually have to be proved. The theorems of the theory are all effectively decidable. |
| 10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
| Full Idea: Any consistent, axiomatized, negation-complete formal theory is decidable. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 03.6) |
| 10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
| Full Idea: A set is 'enumerable' iff either the set is empty, or there is a surjective function to the set from the set of natural numbers, so that the set is in the range of that function. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.3) |
| 10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
| Full Idea: A set is 'effectively enumerable' if an (idealised) computer could be programmed to generate a list of its members such that any member will eventually be mentioned (even if the list is empty, or without end, or contains repetitions). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.4) |
| 10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
| Full Idea: A finite set of finitely specifiable objects is always effectively enumerable (for example, the prime numbers). | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.4) |
| 10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
| Full Idea: The set of ordered pairs of natural numbers (i,j) is effectively enumerable, as proven by listing them in an array (across: <0,0>, <0,1>, <0,2> ..., and down: <0,0>, <1,0>, <2,0>...), and then zig-zagging. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 02.5) |
| 10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
| Full Idea: The theorems of any properly axiomatized theory can be effectively enumerated. However, the truths of any sufficiently expressive arithmetic can't be effectively enumerated. Hence the theorems and truths of arithmetic cannot be the same. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 05 Intro) |
| 10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
| Full Idea: Whether a property is 'expressible' in a given theory depends on the richness of the theory's language. Whether the property can be 'captured' (or 'represented') by the theory depends on the richness of the axioms and proof system. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 04.7) |
| 10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
| Full Idea: For prime numbers we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))). That is, the only way to multiply two numbers and a get a prime is if one of them is 1. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 04.5) |
| 10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
| Full Idea: It has been proved (by Tarski) that the real numbers R is a complete theory. But this means that while the real numbers contain the natural numbers, the pure theory of real numbers doesn't contain the theory of natural numbers. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 18.2) |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| Full Idea: The truths of arithmetic are just the true equations involving particular numbers, and universally quantified versions of such equations. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 27.7) | |
| A reaction: Must each equation be universally quantified? Why can't we just universally quantify over the whole system? |
| 10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
| Full Idea: All numbers are related to zero by the ancestral of the successor relation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.5) | |
| A reaction: The successor relation only ties a number to the previous one, not to the whole series. Ancestrals are a higher level of abstraction. |
| 10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
| Full Idea: The number of Fs is the 'successor' of the number of Gs if there is an object which is an F, and the remaining things that are F but not identical to the object are equinumerous with the Gs. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 14.1) |
| 10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
| Full Idea: Baby Arithmetic 'knows' the addition of particular numbers and multiplication, but can't express general facts about numbers, because it lacks quantification. It has a constant '0', a function 'S', and functions '+' and 'x', and identity and negation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.1) |
| 10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
| Full Idea: Baby Arithmetic is negation complete, so it can prove every claim (or its negation) that it can express, but it is expressively extremely impoverished. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.3) |
| 10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
| Full Idea: Robinson Arithmetic (Q) is not negation complete | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.4) |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| Full Idea: We can beef up Baby Arithmetic into Robinson Arithmetic (referred to as 'Q'), by restoring quantifiers and variables. It has seven generalised axioms, plus standard first-order logic. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 08.3) |
| 10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
| Full Idea: The sequence of natural numbers starts from zero, and each number has just one immediate successor; the sequence continues without end, never circling back on itself, and there are no 'stray' numbers, lurking outside the sequence. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 01.1) | |
| A reaction: These are the characteristics of the natural numbers which have to be pinned down by any axiom system, such as Peano's, or any more modern axiomatic structures. We are in the territory of Gödel's theorems. |
| 10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
| Full Idea: If the logic of arithmetic doesn't have second-order quantifiers to range over properties of numbers, how can it handle induction? | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.1) |
| 10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
| Full Idea: Multiplication in itself isn't is intractable. In 1929 Skolem showed a complete theory for a first-order language with multiplication but lacking addition (or successor). Multiplication together with addition and successor produces incompleteness. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.7 n8) |
| 10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
| Full Idea: Putting multiplication together with addition and successor in the language of arithmetic produces incompleteness. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 10.7) | |
| A reaction: His 'Baby Arithmetic' has all three and is complete, but lacks quantification (p.51) |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| Full Idea: The 'ancestral' of a relation is that relation which holds when there is an indefinitely long chain of things having the initial relation. | |
| From: Peter Smith (Intro to Gödel's Theorems [2007], 23.5) | |
| A reaction: The standard example is spotting the relation 'ancestor' from the receding relation 'parent'. This is a sort of abstraction derived from a relation which is not equivalent (parenthood being transitive but not reflexive). The idea originated with Frege. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |