281 ideas
| 11300 | Agathon: good [PG] |
| Full Idea: Agathon: good, the highest good | |
| From: PG (Db (lexicon) [c.1001 BCE], 01) |
| 11301 | Aisthesis: perception, sensation, consciousness [PG] |
| Full Idea: Aisthesis: perception, sensation, consciousness | |
| From: PG (Db (lexicon) [c.1001 BCE], 02) |
| 11302 | Aitia / aition: cause, explanation [PG] |
| Full Idea: Aitia / aition: cause, explanation | |
| From: PG (Db (lexicon) [c.1001 BCE], 03) | |
| A reaction: The consensus is that 'explanation' is the better translation, and hence that the famous Four Causes (in 'Physics') must really be understood as the Four Modes of Explanation. They then make far more sense. |
| 11303 | Akrasia: lack of control, weakness of will [PG] |
| Full Idea: Akrasia: lack of control, weakness of will | |
| From: PG (Db (lexicon) [c.1001 BCE], 04) | |
| A reaction: The whole Greek debate (and modern debate, I would say) makes much more sense if we stick to 'lack of control' as the translation, and forget about weakness of will - and certainly give up 'incontinence' as a translation. |
| 11304 | Aletheia: truth [PG] |
| Full Idea: Aletheia: truth | |
| From: PG (Db (lexicon) [c.1001 BCE], 05) |
| 11305 | Anamnesis: recollection, remembrance [PG] |
| Full Idea: Anamnesis: recollection, remembrance | |
| From: PG (Db (lexicon) [c.1001 BCE], 06) | |
| A reaction: This is used for Plato's doctrine that we recollect past lives. |
| 11306 | Ananke: necessity [PG] |
| Full Idea: Ananke: necessity | |
| From: PG (Db (lexicon) [c.1001 BCE], 07) |
| 11307 | Antikeimenon: object [PG] |
| Full Idea: Antikeimenon: object | |
| From: PG (Db (lexicon) [c.1001 BCE], 08) |
| 11375 | Apatheia: unemotional [PG] |
| Full Idea: Apatheia: lack of involvement, unemotional | |
| From: PG (Db (lexicon) [c.1001 BCE], 09) |
| 11308 | Apeiron: the unlimited, indefinite [PG] |
| Full Idea: Apeiron: the unlimited, indefinite | |
| From: PG (Db (lexicon) [c.1001 BCE], 10) | |
| A reaction: Key term in the philosophy of Anaximander, the one unknowable underlying element. |
| 11376 | Aphairesis: taking away, abstraction [PG] |
| Full Idea: Aphairesis: taking away, abstraction | |
| From: PG (Db (lexicon) [c.1001 BCE], 11) |
| 11309 | Apodeixis: demonstration [PG] |
| Full Idea: Apodeixis: demonstration, proof | |
| From: PG (Db (lexicon) [c.1001 BCE], 12) |
| 11310 | Aporia: puzzle, question, anomaly [PG] |
| Full Idea: Aporia: puzzle, question, anomaly | |
| From: PG (Db (lexicon) [c.1001 BCE], 13) |
| 11311 | Arche: first principle, the basic [PG] |
| Full Idea: Arché: first principle, the basic | |
| From: PG (Db (lexicon) [c.1001 BCE], 14) | |
| A reaction: Interchangeable with 'aitia' by Aristotle. The first principle and the cause are almost identical. |
| 11312 | Arete: virtue, excellence [PG] |
| Full Idea: Areté: virtue, excellence | |
| From: PG (Db (lexicon) [c.1001 BCE], 15) | |
| A reaction: The word hovers between moral excellence and being good at what you do. Annas defends the older translation as 'virtue', rather than the modern 'excellence'. |
| 11313 | Chronismos: separation [PG] |
| Full Idea: Chronismos: separation | |
| From: PG (Db (lexicon) [c.1001 BCE], 16) |
| 11314 | Diairesis: division [PG] |
| Full Idea: Diairesis: division, distinction | |
| From: PG (Db (lexicon) [c.1001 BCE], 17) |
| 11315 | Dialectic: dialectic, discussion [PG] |
| Full Idea: Dialectic: dialectic, discussion | |
| From: PG (Db (lexicon) [c.1001 BCE], 18) |
| 11316 | Dianoia: intellection [cf. Noesis] [PG] |
| Full Idea: Dianoia: intellection, understanding [cf. Noesis] | |
| From: PG (Db (lexicon) [c.1001 BCE], 21) |
| 11317 | Diaphora: difference [PG] |
| Full Idea: Diaphora: difference | |
| From: PG (Db (lexicon) [c.1001 BCE], 22) |
| 11318 | Dikaiosune: moral goodness, justice [PG] |
| Full Idea: Dikaiosune: moral goodness, justice | |
| From: PG (Db (lexicon) [c.1001 BCE], 23) | |
| A reaction: Usually translated as 'justice' in 'Republic', but it is a general term of moral approbation, not like the modern political and legal notion of 'justice'. 'Justice' actually seems to be bad translation. |
| 11319 | Doxa: opinion, belief [PG] |
| Full Idea: Doxa: opinion, belief, judgement | |
| From: PG (Db (lexicon) [c.1001 BCE], 24) |
| 11320 | Dunamis: faculty, potentiality, capacity [PG] |
| Full Idea: Dunamis: faculty, potentiality, capacity | |
| From: PG (Db (lexicon) [c.1001 BCE], 25) |
| 11321 | Eidos: form, idea [PG] |
| Full Idea: Eidos: form, idea | |
| From: PG (Db (lexicon) [c.1001 BCE], 26) | |
| A reaction: In Plato it is the word best translated as 'Form' (Theory of...); in Aritotle's 'Categories' it designates the species, and in 'Metaphysics' it ends up naming the structural form of the species (and hence the essence) [Wedin p.120] |
| 11322 | Elenchos: elenchus, interrogation [PG] |
| Full Idea: Elenchos: elenchus, interrogation | |
| From: PG (Db (lexicon) [c.1001 BCE], 27) |
| 11323 | Empeiron: experience [PG] |
| Full Idea: Empeiron: experience | |
| From: PG (Db (lexicon) [c.1001 BCE], 28) |
| 11324 | Energeia: employment, actuality, power? [PG] |
| Full Idea: Energeia: employment, actuality, power? | |
| From: PG (Db (lexicon) [c.1001 BCE], 31) |
| 11325 | Enkrateia: control [PG] |
| Full Idea: Enkrateia: control | |
| From: PG (Db (lexicon) [c.1001 BCE], 32) | |
| A reaction: See 'akrasia', of which this is the opposite. The enkratic person is controlled. |
| 11326 | Entelecheia: entelechy, having an end [PG] |
| Full Idea: Entelecheia: entelechy, having an end | |
| From: PG (Db (lexicon) [c.1001 BCE], 33) |
| 11327 | Epagoge: induction, explanation [PG] |
| Full Idea: Epagoge: induction, explanation, leading on | |
| From: PG (Db (lexicon) [c.1001 BCE], 34) |
| 11328 | Episteme: knowledge, understanding [PG] |
| Full Idea: Episteme: knowledge, understanding | |
| From: PG (Db (lexicon) [c.1001 BCE], 35) | |
| A reaction: Note that 'episteme' can form a plural in Greek, but we can't say 'knowledges', so we have to say 'branches of knowledge', or 'sciences'. |
| 11329 | Epithumia: appetite [PG] |
| Full Idea: Epithumia: appetite | |
| From: PG (Db (lexicon) [c.1001 BCE], 36) |
| 11330 | Ergon: function [PG] |
| Full Idea: Ergon: function, work | |
| From: PG (Db (lexicon) [c.1001 BCE], 37) |
| 11331 | Eristic: polemic, disputation [PG] |
| Full Idea: Eristic: polemic, disputation | |
| From: PG (Db (lexicon) [c.1001 BCE], 38) | |
| A reaction: This is confrontational argument, rather than the subtle co-operative dialogue of dialectic. British law courts and the House of Commons are founded on eristic, rather than on dialectic. Could there be a dialectical elected assembly? |
| 11332 | Eros: love [PG] |
| Full Idea: Eros: love, desire | |
| From: PG (Db (lexicon) [c.1001 BCE], 41) |
| 11333 | Eudaimonia: flourishing, happiness, fulfilment [PG] |
| Full Idea: Eudaimonia: flourishing, happiness, fulfilment | |
| From: PG (Db (lexicon) [c.1001 BCE], 42) | |
| A reaction: Some people defend 'happiness' as the translation, but that seems to me wildly misleading, since eudaimonia is something like life going well, and certainly isn't a psychological state - and definitely not pleasure. |
| 11334 | Genos: type, genus [PG] |
| Full Idea: Genos: type, genus, kind | |
| From: PG (Db (lexicon) [c.1001 BCE], 43) |
| 11335 | Hexis: state, habit [PG] |
| Full Idea: Hexis: state, habit | |
| From: PG (Db (lexicon) [c.1001 BCE], 44) |
| 11336 | Horismos: definition [PG] |
| Full Idea: Horismos: definition | |
| From: PG (Db (lexicon) [c.1001 BCE], 45) |
| 11337 | Hule: matter [PG] |
| Full Idea: Hule: matter | |
| From: PG (Db (lexicon) [c.1001 BCE], 46) | |
| A reaction: The first half of the 'hylomorphism' of Aristotle. See 'morphe'! |
| 11338 | Hupokeimenon: subject, underlying thing [cf. Tode ti] [PG] |
| Full Idea: Hupokeimenon: subject, underlying thing, substratum [cf. Tode ti] | |
| From: PG (Db (lexicon) [c.1001 BCE], 47) | |
| A reaction: Literally 'that which lies under'. Latin version is 'substratum'. In Aristotle it is the problem, of explaining what lies under. It is not the theory that there is some entity called a 'substratum'. |
| 11339 | Kalos / kalon: beauty, fineness, nobility [PG] |
| Full Idea: Kalos / kalon: beauty, fineness, nobility | |
| From: PG (Db (lexicon) [c.1001 BCE], 48) | |
| A reaction: A revealing Greek word, which is not only our rather pure notion of 'beauty', but also seems to mean something like wow!, and (very suggestive, this) applies as much to actions as to objects. |
| 11340 | Kath' hauto: in virtue of itself, essentially [PG] |
| Full Idea: Kath' hauto: in virtue of itself, essentially | |
| From: PG (Db (lexicon) [c.1001 BCE], 51) |
| 11341 | Kinesis: movement, process [PG] |
| Full Idea: Kinesis: movement, process, change | |
| From: PG (Db (lexicon) [c.1001 BCE], 52) |
| 11342 | Kosmos: order, universe [PG] |
| Full Idea: Kosmos: order, universe | |
| From: PG (Db (lexicon) [c.1001 BCE], 53) |
| 11343 | Logos: reason, account, word [PG] |
| Full Idea: Logos: reason, account, word | |
| From: PG (Db (lexicon) [c.1001 BCE], 54) |
| 11344 | Meson: the mean [PG] |
| Full Idea: Meson: the mean | |
| From: PG (Db (lexicon) [c.1001 BCE], 55) | |
| A reaction: This is not the 'average', and hence not some theoretical mid-point. I would call it the 'appropriate compromise', remembering that an extreme may be appropriate in certain circumstances. |
| 11345 | Metechein: partaking, sharing [PG] |
| Full Idea: Metechein: partaking, sharing | |
| From: PG (Db (lexicon) [c.1001 BCE], 56) | |
| A reaction: The key word in Plato for the difficult question of the relationships between the Forms and the particulars. The latter 'partake' of the former. Hm. Compare modern 'instantiation', which strikes me as being equally problematic. |
| 11377 | Mimesis: imitation, fine art [PG] |
| Full Idea: Mimesis: imitation, fine art | |
| From: PG (Db (lexicon) [c.1001 BCE], 57) |
| 11346 | Morphe: form [PG] |
| Full Idea: Morphe: form | |
| From: PG (Db (lexicon) [c.1001 BCE], 58) |
| 11347 | Noesis: intellection, rational thought [cf. Dianoia] [PG] |
| Full Idea: Noesis: intellection, rational thought [cf. Dianoia] | |
| From: PG (Db (lexicon) [c.1001 BCE], 59) |
| 11348 | Nomos: convention, law, custom [PG] |
| Full Idea: Nomos: convention, law, custom | |
| From: PG (Db (lexicon) [c.1001 BCE], 61) |
| 11349 | Nous: intuition, intellect, understanding [PG] |
| Full Idea: Nous: intuition, intellect | |
| From: PG (Db (lexicon) [c.1001 BCE], 62) | |
| A reaction: There is a condensed discussion of 'nous' in Aristotle's Posterior Analytics B.19 |
| 11350 | Orexis: desire [PG] |
| Full Idea: Orexis: desire | |
| From: PG (Db (lexicon) [c.1001 BCE], 63) |
| 11351 | Ousia: substance, (primary) being, [see 'Prote ousia'] [PG] |
| Full Idea: Ousia: substance, (primary) being [see 'Prote ousia'] | |
| From: PG (Db (lexicon) [c.1001 BCE], 64) | |
| A reaction: It is based on the verb 'to be'. Latin therefore translated it as 'essentia' (esse: to be), and we have ended up translating it as 'essence', but this is wrong! 'Being' is the best translation, and 'substance' is OK. It is the problem, not the answer. |
| 11352 | Pathos: emotion, affection, property [PG] |
| Full Idea: Pathos: emotion, affection, property | |
| From: PG (Db (lexicon) [c.1001 BCE], 65) |
| 11353 | Phantasia: imagination [PG] |
| Full Idea: Phantasia: imagination | |
| From: PG (Db (lexicon) [c.1001 BCE], 66) |
| 11354 | Philia: friendship [PG] |
| Full Idea: Philia: friendship | |
| From: PG (Db (lexicon) [c.1001 BCE], 67) |
| 11355 | Philosophia: philosophy, love of wisdom [PG] |
| Full Idea: Philosophia: philosophy, love of wisdom | |
| From: PG (Db (lexicon) [c.1001 BCE], 68) | |
| A reaction: The point of the word is its claim only to love wisdom, and not actually to be wise. |
| 11356 | Phronesis: prudence, practical reason, common sense [PG] |
| Full Idea: Phronesis: prudence, practical reason, common sense | |
| From: PG (Db (lexicon) [c.1001 BCE], 71) | |
| A reaction: None of the experts use my own translation, which is 'common sense', but that seems to me to perfectly fit all of Aristotle's discussions of the word in 'Ethics'. 'Prudence' seems a daft translation in modern English. |
| 11357 | Physis: nature [PG] |
| Full Idea: Physis: nature | |
| From: PG (Db (lexicon) [c.1001 BCE], 72) |
| 11358 | Praxis: action, activity [PG] |
| Full Idea: Praxis: action, activity | |
| From: PG (Db (lexicon) [c.1001 BCE], 73) |
| 11359 | Prote ousia: primary being [PG] |
| Full Idea: Prote ousia: primary being | |
| From: PG (Db (lexicon) [c.1001 BCE], 74) | |
| A reaction: The main topic of investigation in Aristotle's 'Metaphysics'. 'Ousia' is the central problem of the text, NOT the answer to the problem. |
| 11360 | Psuche: mind, soul, life [PG] |
| Full Idea: Psuche: mind, soul, life | |
| From: PG (Db (lexicon) [c.1001 BCE], 75) | |
| A reaction: The interesting thing about this is that we have tended to translate it as 'soul', but Aristotle says plants have it, and not merely conscious beings. It is something like the 'form' of a living thing, but then 'form' is a misleading translation too. |
| 11361 | Sophia: wisdom [PG] |
| Full Idea: Sophia: wisdom | |
| From: PG (Db (lexicon) [c.1001 BCE], 76) |
| 11362 | Sophrosune: moderation, self-control [PG] |
| Full Idea: Sophrosune: moderation, self-control | |
| From: PG (Db (lexicon) [c.1001 BCE], 77) |
| 11363 | Stoicheia: elements [PG] |
| Full Idea: Stoicheia: elements | |
| From: PG (Db (lexicon) [c.1001 BCE], 78) |
| 11364 | Sullogismos: deduction, syllogism [PG] |
| Full Idea: Sullogismos: deduction, syllogism | |
| From: PG (Db (lexicon) [c.1001 BCE], 81) |
| 11365 | Techne: skill, practical knowledge [PG] |
| Full Idea: Techne: skill, practical knowledge | |
| From: PG (Db (lexicon) [c.1001 BCE], 82) |
| 11366 | Telos: purpose, end [PG] |
| Full Idea: Telos: purpose, end | |
| From: PG (Db (lexicon) [c.1001 BCE], 83) |
| 11367 | Theoria: contemplation [PG] |
| Full Idea: Theoria: contemplation | |
| From: PG (Db (lexicon) [c.1001 BCE], 84) |
| 11368 | Theos: god [PG] |
| Full Idea: Theos: god | |
| From: PG (Db (lexicon) [c.1001 BCE], 85) |
| 11369 | Ti esti: what-something-is, essence [PG] |
| Full Idea: Ti esti: the what-something-is, essence, whatness | |
| From: PG (Db (lexicon) [c.1001 BCE], 86) |
| 11370 | Timoria: vengeance, punishment [PG] |
| Full Idea: Timoria: vengeance, punishment | |
| From: PG (Db (lexicon) [c.1001 BCE], 87) |
| 11371 | To ti en einai: essence, what-it-is-to-be [PG] |
| Full Idea: To ti en einai: essence, what-it-is-to-be | |
| From: PG (Db (lexicon) [c.1001 BCE], 88) | |
| A reaction: This is Aristotle's main term for what we would now call the 'essence'. It is still not a theory of essence, merely an identification of the target. 'Form' is the nearest we get to his actual theory. |
| 11372 | To ti estin: essence [PG] |
| Full Idea: To ti estin: essence | |
| From: PG (Db (lexicon) [c.1001 BCE], 91) |
| 11373 | Tode ti: this-such, subject of predication [cf. hupokeimenon] [PG] |
| Full Idea: Tode ti: this-something, subject of predication, thisness [cf. hupokeimenon] | |
| From: PG (Db (lexicon) [c.1001 BCE], 92) |
| 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) |
| 4465 | Note that "is" can assert existence, or predication, or identity, or classification [PG] |
| Full Idea: There are four uses of the word "is" in English: as existence ('he is at home'), as predication ('he is tall'), as identity ('he is the man I saw'), and as classification ('he is British'). | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: This seems a nice instance of the sort of point made by analytical philosophy, which can lead to horrible confusion in other breeds of philosophy when it is overlooked. |
| 8721 | An 'impredicative' definition seems circular, because it uses the term being defined [Friend] |
| Full Idea: An 'impredicative' definition is one that uses the terms being defined in order to give the definition; in some way the definition is then circular. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], Glossary) | |
| A reaction: There has been a big controversy in the philosophy of mathematics over these. Shapiro gives the definition of 'village idiot' (which probably mentions 'village') as an example. |
| 8680 | Classical definitions attempt to refer, but intuitionist/constructivist definitions actually create objects [Friend] |
| Full Idea: In classical logic definitions are thought of as revealing our attempts to refer to objects, ...but for intuitionist or constructivist logics, if our definitions do not uniquely characterize an object, we are not entitled to discuss the object. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.4) | |
| A reaction: In defining a chess piece we are obviously creating. In defining a 'tree' we are trying to respond to fact, but the borderlines are vague. Philosophical life would be easier if we were allowed a mixture of creation and fact - so let's have that. |
| 3678 | Reductio ad absurdum proves an idea by showing that its denial produces contradiction [Friend] |
| Full Idea: Reductio ad absurdum arguments are ones that start by denying what one wants to prove. We then prove a contradiction from this 'denied' idea and more reasonable ideas in one's theory, showing that we were wrong in denying what we wanted to prove. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is a mathematical definition, which rests on logical contradiction, but in ordinary life (and philosophy) it would be enough to show that denial led to absurdity, rather than actual contradiction. |
| 4686 | Fallacies are errors in reasoning, 'formal' if a clear rule is breached, and 'informal' if more general [PG] |
| Full Idea: Fallacies are errors in reasoning, labelled as 'formal' if a clear rule has been breached, and 'informal' if some less precise error has been made. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: Presumably there can be a grey area between the two. |
| 7415 | Question-begging assumes the proposition which is being challenged [PG] |
| Full Idea: To beg the question is to take for granted in your argument that very proposition which is being challenged | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: An undoubted fallacy, and a simple failure to engage in the rational enterprise. I suppose one might give a reason for something, under the mistaken apprehension that it didn't beg the question; analysis of logical form is then needed. |
| 7414 | What is true of a set is also true of its members [PG] |
| Full Idea: The fallacy of division is the claim that what is true of a set must therefore be true of its members. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: Clearly a fallacy, but if you only accept sets which are rational, then there is always a reason why a particular is a member of a set, and you can infer facts about particulars from the nature of the set |
| 6696 | The Ad Hominem Fallacy criticises the speaker rather than the argument [PG] |
| Full Idea: The Ad Hominem Fallacy is to criticise the person proposing an argument rather than the argument itself, as when you say "You would say that", or "Your behaviour contradicts what you just said". | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: Nietzsche is very keen on ad hominem arguments, and cheerfully insults great philosophers, but then he doesn't believe there is such a thing as 'pure argument', and he is a relativist. |
| 8705 | Anti-realists see truth as our servant, and epistemically contrained [Friend] |
| Full Idea: For the anti-realist, truth belongs to us, it is our servant, and as such, it must be 'epistemically constrained'. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.1) | |
| A reaction: Put as clearly as this, it strikes me as being utterly and spectacularly wrong, a complete failure to grasp the elementary meaning of a concept etc. etc. If we aren't the servants of truth then we jolly we ought to be. Truth is above us. |
| 4687 | Minimal theories of truth avoid ontological commitment to such things as 'facts' or 'reality' [PG] |
| Full Idea: Minimalist theories of truth are those which involve minimum ontological commitment, avoiding references to 'reality' or 'facts' or 'what works', preferring to refer to formal relationships within language. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: Personally I am suspicious of minimal theories, which seem to be designed by and for anti-realists. They seem too focused on language, when animals can obviously formulate correct propositions. I'm quite happy with the 'facts', even if that is vague. |
| 8713 | In classical/realist logic the connectives are defined by truth-tables [Friend] |
| Full Idea: In the classical or realist view of logic the meaning of abstract symbols for logical connectives is given by the truth-tables for the symbol. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007]) | |
| A reaction: Presumably this is realist because it connects them to 'truth', but only if that involves a fairly 'realist' view of truth. You could, of course, translate 'true' and 'false' in the table to empty (formalist) symbols such a 0 and 1. Logic is electronics. |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| Full Idea: In intuitionist logic, if we do not know that we do not know A, it does not follow that we know A, so the inference (and, in general, double negation elimination) is not intuitionistically valid. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: That inference had better not be valid in any logic! I am unaware of not knowing the birthday of someone I have never heard of. Propositional attitudes such as 'know' are notoriously difficult to explain in formal logic. |
| 8694 | Free logic was developed for fictional or non-existent objects [Friend] |
| Full Idea: Free logic is especially designed to help regiment our reasoning about fictional objects, or nonexistent objects of some sort. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.7) | |
| A reaction: This makes it sound marginal, but I wonder whether existential commitment shouldn't be eliminated from all logic. Why do fictional objects need a different logic? What logic should we use for Robin Hood, if we aren't sure whether or not he is real? |
| 8665 | A 'proper subset' of A contains only members of A, but not all of them [Friend] |
| Full Idea: A 'subset' of A is a set containing only members of A, and a 'proper subset' is one that does not contain all the members of A. Note that the empty set is a subset of every set, but it is not a member of every set. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Is it the same empty set in each case? 'No pens' is a subset of 'pens', but is it a subset of 'paper'? Idea 8219 should be borne in mind when discussing such things, though I am not saying I agree with it. |
| 8672 | A 'powerset' is all the subsets of a set [Friend] |
| Full Idea: The 'powerset' of a set is a set made up of all the subsets of a set. For example, the powerset of {3,7,9} is {null, {3}, {7}, {9}, {3,7}, {3,9}, {7,9}, {3,7,9}}. Taking the powerset of an infinite set gets us from one infinite cardinality to the next. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Note that the null (empty) set occurs once, but not in the combinations. I begin to have queasy sympathies with the constructivist view of mathematics at this point, since no one has the time, space or energy to 'take' an infinite powerset. |
| 8677 | Set theory makes a minimum ontological claim, that the empty set exists [Friend] |
| Full Idea: As a realist choice of what is basic in mathematics, set theory is rather clever, because it only makes a very simple ontological claim: that, independent of us, there exists the empty set. The whole hierarchy of finite and infinite sets then follows. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: Even so, for non-logicians the existence of the empty set is rather counterintuitive. "There was nobody on the road, so I overtook him". See Ideas 7035 and 8322. You might work back to the empty set, but how do you start from it? |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |
| Full Idea: Two sets are the same size if they can be placed in one-to-one correspondence. But even numbers have one-to-one correspondence with the natural numbers. So a set is infinite if it has one-one correspondence with a proper subset. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Dedekind's definition. We can match 1 with 2, 2 with 4, 3 with 6, 4 with 8, etc. Logicians seem happy to give as a definition anything which fixes the target uniquely, even if it doesn't give the essence. See Frege on 0 and 1, Ideas 8653/4. |
| 8682 | Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend] |
| Full Idea: Zermelo-Fraenkel and Gödel-Bernays set theory differ over the notions of ordinal construction and over the notion of class, among other things. Then there are optional axioms which can be attached, such as the axiom of choice and the axiom of infinity. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.6) | |
| A reaction: This summarises the reasons why we cannot just talk about 'set theory' as if it was a single concept. The philosophical interest I would take to be found in disentangling the ontological commitments of each version. |
| 10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
| Full Idea: The Axiom of Choice seems better treated as a non-logical principle of set-theory. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4 n8) | |
| A reaction: This reinforces the idea that set theory is not part of logic (and so pure logicism had better not depend on set theory). |
| 10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |
| Full Idea: We cannot explicitly define one-one correspondence from the sets to the ordinals (because there is no explicit well-ordering of R). Nevertheless, the Axiom of Choice guarantees that a one-one correspondence does exist, even if we cannot define it. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) |
| 23623 | Predicativism says only predicated sets exist [Hossack] |
| Full Idea: Predicativists doubt the existence of sets with no predicative definition. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 02.3) | |
| A reaction: This would imply that sets which encounter paradoxes when they try to be predicative do not therefore exist. Surely you can have a set of random objects which don't fall under a single predicate? |
| 23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
| Full Idea: The iterative conception justifies Power Set, but cannot justify a satisfactory theory of von Neumann ordinals, so ZFC appropriates Replacement from NBG set theory. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
| A reaction: The modern approach to axioms, where we want to prove something so we just add an axiom that does the job. |
| 23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
| Full Idea: The limitation of size conception of sets justifies the axiom of Replacement, but cannot justify Power Set, so NBG set theory appropriates the Power Set axiom from ZFC. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
| A reaction: Which suggests that the Power Set axiom is not as indispensable as it at first appears to be. |
| 10687 | Maybe we reduce sets to ordinals, rather than the other way round [Hossack] |
| Full Idea: We might reduce sets to ordinal numbers, thereby reversing the standard set-theoretical reduction of ordinals to sets. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) | |
| A reaction: He has demonstrated that there are as many ordinals as there are sets. |
| 10677 | Extensional mereology needs two definitions and two axioms [Hossack] |
| Full Idea: Extensional mereology defs: 'distinct' things have no parts in common; a 'fusion' has some things all of which are parts, with no further parts. Axioms: (transitivity) a part of a part is part of the whole; (sums) any things have a unique fusion. | |
| From: Keith Hossack (Plurals and Complexes [2000], 5) |
| 8709 | The law of excluded middle is syntactic; it just says A or not-A, not whether they are true or false [Friend] |
| Full Idea: The law of excluded middle is purely syntactic: it says for any well-formed formula A, either A or not-A. It is not a semantic law; it does not say that either A is true or A is false. The semantic version (true or false) is the law of bivalence. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: No wonder these two are confusing, sufficiently so for a lot of professional philosophers to blur the distinction. Presumably the 'or' is exclusive. So A-and-not-A is a contradiction; but how do you explain a contradiction without mentioning truth? |
| 23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
| Full Idea: The sentence connective 'and' also has an order-sensitive meaning, when it means something like 'and then'. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.4) | |
| A reaction: This is support the idea that orders are a feature of reality, just as much as possible concatenation. Relational predicates, he says, refer to series rather than to individuals. Nice point. |
| 23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
| Full Idea: The reason the two predicates 'before' and 'after' are needed is not to express different relations, but to indicate its order. Since there can be difference of order without difference of relation, the nature of relations is not the source of order. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.3) | |
| A reaction: This point is to refute Russell's 1903 claim that order arises from the nature of relations. Hossack claims that it is ordered series which are basic. I'm inclined to agree with him. |
| 10671 | Plural definite descriptions pick out the largest class of things that fit the description [Hossack] |
| Full Idea: If we extend the power of language with plural definite descriptions, these would pick out the largest class of things that fit the description. | |
| From: Keith Hossack (Plurals and Complexes [2000], 3) |
| 10666 | Plural reference will refer to complex facts without postulating complex things [Hossack] |
| Full Idea: It may be that plural reference gives atomism the resources to state complex facts without needing to refer to complex things. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: This seems the most interesting metaphysical implication of the possibility of plural quantification. |
| 10669 | Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack] |
| Full Idea: If all properties are distributive, plural reference is just a handy abbreviation to avoid repetition (as in 'A and B are hungry', to avoid 'A is hungry and B is hungry'), but not all properties are distributive (as in 'some people surround a table'). | |
| From: Keith Hossack (Plurals and Complexes [2000], 2) | |
| A reaction: The characteristic examples to support plural quantification involve collective activity and relations, which might be weeded out of our basic ontology, thus leaving singular quantification as sufficient. |
| 10675 | A plural comprehension principle says there are some things one of which meets some condition [Hossack] |
| Full Idea: Singular comprehension principles have a bad reputation, but the plural comprehension principle says that given a condition on individuals, there are some things such that something is one of them iff it meets the condition. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| Full Idea: In the intuitionist version of quantification, the universal quantifier (normally read as "all") is understood as "we have a procedure for checking every" or "we have checked every". | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.5) | |
| A reaction: It seems better to describe this as 'verificationist' (or, as Dummett prefers, 'justificationist'). Intuition suggests an ability to 'see' beyond the evidence. It strikes me as bizarre to say that you can't discuss things you can't check. |
| 6516 | Monty Hall Dilemma: do you abandon your preference after Monty eliminates one of the rivals? [PG] |
| Full Idea: The Monty Hall Dilemma: Three boxes, one with a big prize; pick one to open. Monty Hall then opens one of the other two, which is empty. You may, if you wish, switch from your box to the other unopened box. Should you? | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: The other two boxes, as a pair, are more likely contain the prize than your box. Monty Hall has eliminated one of them for you, so you should choose the other one. Your intuition that the two remaining boxes are equal is incorrect! |
| 8675 | Paradoxes can be solved by talking more loosely of 'classes' instead of 'sets' [Friend] |
| Full Idea: The realist meets the Burali-Forti paradox by saying that all the ordinals are a 'class', not a set. A proper class is what we discuss when we say "all" the so-and-sos when they cannot be reached by normal set-construction. Grammar is their only limit. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This strategy would be useful for Class Nominalism, which tries to define properties in terms of classes, but gets tangled in paradoxes. But why bother with strict sets if easy-going classes will do just as well? Descartes's Dream: everything is rational. |
| 8674 | The Burali-Forti paradox asks whether the set of all ordinals is itself an ordinal [Friend] |
| Full Idea: The Burali-Forti paradox says that if ordinals are defined by 'gathering' all their predecessors with the empty set, then is the set of all ordinals an ordinal? It is created the same way, so it should be a further member of this 'complete' set! | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is an example (along with Russell's more famous paradox) of the problems that began to appear in set theory in the early twentieth century. See Idea 8675 for a modern solution. |
| 10673 | Plural language can discuss without inconsistency things that are not members of themselves [Hossack] |
| Full Idea: In a plural language we can discuss without fear of inconsistency the things that are not members of themselves. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) | |
| A reaction: [see Hossack for details] |
| 8667 | The 'integers' are the positive and negative natural numbers, plus zero [Friend] |
| Full Idea: The set of 'integers' is all of the negative natural numbers, and zero, together with the positive natural numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Zero always looks like a misfit at this party. Credit and debit explain positive and negative nicely, but what is the difference between having no money, and money being irrelevant? I can be 'broke', but can the North Pole be broke? |
| 8668 | The 'rational' numbers are those representable as fractions [Friend] |
| Full Idea: The 'rational' numbers are all those that can be represented in the form m/n (i.e. as fractions), where m and n are natural numbers different from zero. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: Pythagoreans needed numbers to stop there, in order to represent the whole of reality numerically. See irrational numbers for the ensuing disaster. How can a universe with a finite number of particles contain numbers that are not 'rational'? |
| 8670 | A number is 'irrational' if it cannot be represented as a fraction [Friend] |
| Full Idea: A number is 'irrational' just in case it cannot be represented as a fraction. An irrational number has an infinite non-repeating decimal expansion. Famous examples are pi and e. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: There must be an infinite number of irrational numbers. You could, for example, take the expansion of pi, and change just one digit to produce a new irrational number, and pi has an infinity of digits to tinker with. |
| 8661 | The natural numbers are primitive, and the ordinals are up one level of abstraction [Friend] |
| Full Idea: The natural numbers are quite primitive, and are what we first learn about. The order of objects (the 'ordinals') is one level of abstraction up from the natural numbers: we impose an order on objects. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: Note the talk of 'levels of abstraction'. So is there a first level of abstraction? Dedekind disagrees with Friend (Idea 7524). I would say that natural numbers are abstracted from something, but I'm not sure what. See Structuralism in maths. |
| 10680 | The theory of the transfinite needs the ordinal numbers [Hossack] |
| Full Idea: The theory of the transfinite needs the ordinal numbers. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 8664 | Cardinal numbers answer 'how many?', with the order being irrelevant [Friend] |
| Full Idea: The 'cardinal' numbers answer the question 'How many?'; the order of presentation of the objects being counted as immaterial. Def: the cardinality of a set is the number of members of the set. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: If one asks whether cardinals or ordinals are logically prior (see Ideas 7524 and 8661), I am inclined to answer 'neither'. Presenting them as answers to the questions 'how many?' and 'which comes first?' is illuminating. |
| 10684 | I take the real numbers to be just lengths [Hossack] |
| Full Idea: I take the real numbers to be just lengths. | |
| From: Keith Hossack (Plurals and Complexes [2000], 9) | |
| A reaction: I love it. Real numbers are beginning to get on my nerves. They turn up to the party with no invitation and improperly dressed, and then refuse to give their names when challenged. |
| 8671 | The 'real' numbers (rationals and irrationals combined) is the Continuum, which has no gaps [Friend] |
| Full Idea: The set of 'real' numbers, which consists of the rational numbers and the irrational numbers together, represents "the continuum", since it is like a smooth line which has no gaps (unlike the rational numbers, which have the irrationals missing). | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: The Continuum is the perfect abstract object, because a series of abstractions has arrived at a vast limit in its nature. It still has dizzying infinities contained within it, and at either end of the line. It makes you feel humble. |
| 8663 | Raising omega to successive powers of omega reveal an infinity of infinities [Friend] |
| Full Idea: After the multiples of omega, we can successively raise omega to powers of omega, and after that is done an infinite number of times we arrive at a new limit ordinal, which is called 'epsilon'. We have an infinite number of infinite ordinals. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: When most people are dumbstruck by the idea of a single infinity, Cantor unleashes an infinity of infinities, which must be the highest into the stratosphere of abstract thought that any human being has ever gone. |
| 8662 | The first limit ordinal is omega (greater, but without predecessor), and the second is twice-omega [Friend] |
| Full Idea: The first 'limit ordinal' is called 'omega', which is ordinal because it is greater than other numbers, but it has no immediate predecessor. But it has successors, and after all of those we come to twice-omega, which is the next limit ordinal. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.4) | |
| A reaction: This is the gateway to Cantor's paradise of infinities, which Hilbert loved and defended. Who could resist the pleasure of being totally boggled (like Aristotle) by a concept such as infinity, only to have someone draw a map of it? See 8663 for sequel. |
| 23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
| Full Idea: The transfinite ordinal numbers are important in the theory of proofs, and essential in the theory of recursive functions and computability. Mathematics would be incomplete without them. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.1) | |
| A reaction: Hossack offers this as proof that the numbers are not human conceptual creations, but must exist beyond the range of our intellects. Hm. |
| 8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
| Full Idea: Since between any two rational numbers there is an infinite number of rational numbers, we could consider that we have infinity in three dimensions: positive numbers, negative numbers, and the 'depth' of infinite numbers between any rational numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 1.5) | |
| A reaction: This is before we even reach Cantor's staggering infinities (Ideas 8662 and 8663), which presumably reside at the outer reaches of all three of these dimensions of infinity. The 'deep' infinities come from fractions with huge denominators. |
| 8676 | Is mathematics based on sets, types, categories, models or topology? [Friend] |
| Full Idea: Successful competing founding disciplines in mathematics include: the various set theories, type theory, category theory, model theory and topology. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: Or none of the above? Set theories are very popular. Type theory is, apparently, discredited. Shapiro has a version of structuralism based on model theory (which sound promising). Topology is the one that intrigues me... |
| 10674 | A plural language gives a single comprehensive induction axiom for arithmetic [Hossack] |
| Full Idea: A language with plurals is better for arithmetic. Instead of a first-order fragment expressible by an induction schema, we have the complete truth with a plural induction axiom, beginning 'If there are some numbers...'. | |
| From: Keith Hossack (Plurals and Complexes [2000], 4) |
| 10681 | In arithmetic singularists need sets as the instantiator of numeric properties [Hossack] |
| Full Idea: In arithmetic singularists need sets as the instantiator of numeric properties. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 8678 | Most mathematical theories can be translated into the language of set theory [Friend] |
| Full Idea: Most of mathematics can be faithfully redescribed by classical (realist) set theory. More precisely, we can translate other mathematical theories - such as group theory, analysis, calculus, arithmetic, geometry and so on - into the language of set theory. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3) | |
| A reaction: This is why most mathematicians seem to regard set theory as foundational. We could also translate football matches into the language of atomic physics. |
| 10685 | Set theory is the science of infinity [Hossack] |
| Full Idea: Set theory is the science of infinity. | |
| From: Keith Hossack (Plurals and Complexes [2000], 10) |
| 23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
| Full Idea: I propose that numbers are properties, not sets. Magnitudes are a kind of property, and numbers are magnitudes. …Natural numbers are properties of pluralities, positive reals of continua, and ordinals of series. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro) | |
| A reaction: Interesting! Since time can have a magnitude (three weeks) just as liquids can (three litres), it is not clear that there is a single natural property we can label 'magnitude'. Anything we can manage to measure has a magnitude. |
| 8701 | The number 8 in isolation from the other numbers is of no interest [Friend] |
| Full Idea: There is no interest for the mathematician in studying the number 8 in isolation from the other numbers. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: This is a crucial and simple point (arising during a discussion of Shapiro's structuralism). Most things are interesting in themselves, as well as for their relationships, but mathematical 'objects' just are relationships. |
| 8702 | In structuralism the number 8 is not quite the same in different structures, only equivalent [Friend] |
| Full Idea: Structuralists give a historical account of why the 'same' number occupies different structures. Numbers are equivalent rather than identical. 8 is the immediate predecessor of 9 in the whole numbers, but in the rationals 9 has no predecessor. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: I don't become a different person if I move from a detached house to a terraced house. This suggests that 8 can't be entirely defined by its relations, and yet it is hard to see what its intrinsic nature could be, apart from the units which compose it. |
| 8699 | Are structures 'ante rem' (before reality), or are they 'in re' (grounded in physics)? [Friend] |
| Full Idea: Structuralists disagree over whether objects in structures are 'ante rem' (before reality, existing independently of whether the objects exist) or 'in re' (in reality, grounded in the real world, usually in our theories of physics). | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: Shapiro holds the first view, Hellman and Resnik the second. The first view sounds too platonist and ontologically extravagant; the second sounds too contingent and limited. The correct account is somewhere in abstractions from the real. |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| Full Idea: According to the structuralist, mathematicians study the concepts (objects of study) such as variable, greater, real, add, similar, infinite set, which are one level of abstraction up from prima facie base objects such as numbers, shapes and lines. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.1) | |
| A reaction: This still seems to imply an ontology in which numbers, shapes and lines exist. I would have thought you could eliminate the 'base objects', and just say that the concepts are one level of abstraction up from the physical world. |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |
| Full Idea: Structuralism says we study whole structures: objects together with their predicates, relations that bear between them, and functions that take us from one domain of objects to a range of other objects. The objects can even be eliminated. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.1) | |
| A reaction: The unity of object and predicate is a Quinean idea. The idea that objects are inessential is the dramatic move. To me the proposal has very strong intuitive appeal. 'Eight' is meaningless out of context. Ordinality precedes cardinality? Ideas 7524/8661. |
| 8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |
| Full Idea: In the 'in re' version of mathematical structuralism, pattern-spotting is the process of abstraction. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4) | |
| A reaction: This might work for non-mathematical abstraction as well, if we are allowed to spot patterns within sensual experience, and patterns within abstractions. Properties are causal patterns in the world? No - properties cause patterns. |
| 23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
| Full Idea: Numbers cannot be mental objects constructed by our own minds: there exists at most a potential infinity of mental constructions, whereas the axioms of mathematics require an actual infinity of numbers. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro 2) | |
| A reaction: Doubt this, but don't know enough to refute it. Actual infinities were a fairly late addition to maths, I think. I would think treating fictional complete infinities as real would be sufficient for the job. Like journeys which include imagined roads. |
| 8681 | The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts? [Friend] |
| Full Idea: The main philosophical problem with the position of platonism or realism is the epistemic problem: of explaining what perception or intuition consists in; how it is possible that we should accurately detect whatever it is we are realists about. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.5) | |
| A reaction: The best bet, I suppose, is that the mind directly perceives concepts just as eyes perceive the physical (see Idea 8679), but it strikes me as implausible. If we have to come up with a special mental faculty for an area of knowledge, we are in trouble. |
| 8712 | Mathematics should be treated as true whenever it is indispensable to our best physical theory [Friend] |
| Full Idea: Central to naturalism about mathematics are 'indispensability arguments', to the effect that some part of mathematics is indispensable to our best physical theory, and therefore we ought to take that part of mathematics to be true. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 6.1) | |
| A reaction: Quine and Putnam hold this view; Field challenges it. It has the odd consequence that the dispensable parts (if they can be identified!) do not need to be treated as true (even though they might follow logically from the dispensable parts!). Wrong! |
| 8716 | Formalism is unconstrained, so cannot indicate importance, or directions for research [Friend] |
| Full Idea: There are not enough constraints in the Formalist view of mathematics, so there is no way to select a direction for trying to develop mathematics. There is no part of mathematics that is more important than another. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 6.6) | |
| A reaction: One might reply that an area of maths could be 'important' if lots of other areas depended on it, and big developments would ripple big changes through the interior of the subject. Formalism does, though, seem to reduce maths to a game. |
| 8706 | Constructivism rejects too much mathematics [Friend] |
| Full Idea: Too much of mathematics is rejected by the constructivist. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.1) | |
| A reaction: This was Hilbert's view. This seems to be generally true of verificationism. My favourite example is that legitimate speculations can be labelled as meaningless. |
| 8707 | Intuitionists typically retain bivalence but reject the law of excluded middle [Friend] |
| Full Idea: An intuitionist typically retains bivalence, but rejects the law of excluded middle. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.2) | |
| A reaction: The idea would be to say that only T and F are available as truth-values, but failing to be T does not ensure being F, but merely not-T. 'Unproven' is not-T, but may not be F. |
| 10668 | We are committed to a 'group' of children, if they are sitting in a circle [Hossack] |
| Full Idea: By Quine's test of ontological commitment, if some children are sitting in a circle, no individual child can sit in a circle, so a singular paraphrase will have us committed to a 'group' of children. | |
| From: Keith Hossack (Plurals and Complexes [2000], 2) | |
| A reaction: Nice of why Quine is committed to the existence of sets. Hossack offers plural quantification as a way of avoiding commitment to sets. But is 'sitting in a circle' a real property (in the Shoemaker sense)? I can sit in a circle without realising it. |
| 8704 | Structuralists call a mathematical 'object' simply a 'place in a structure' [Friend] |
| Full Idea: What the mathematician labels an 'object' in her discipline, is called 'a place in a structure' by the structuralist. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.5) | |
| A reaction: This is a strategy for dispersing the idea of an object in the world of thought, parallel to attempts to eliminate them from physical ontology (e.g. Idea 614). |
| 10664 | Complex particulars are either masses, or composites, or sets [Hossack] |
| Full Idea: Complex particulars are of at least three types: masses (which sum, of which we do not ask 'how many?' but 'how much?'); composite individuals (how many?, and summing usually fails); and sets (only divisible one way, unlike composites). | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: A composite pile of grains of sand gradually becomes a mass, and drops of water become 'water everywhere'. A set of people divides into individual humans, but redescribe the elements as the union of males and females? |
| 10678 | The relation of composition is indispensable to the part-whole relation for individuals [Hossack] |
| Full Idea: The relation of composition seems to be indispensable in a correct account of the part-whole relation for individuals. | |
| From: Keith Hossack (Plurals and Complexes [2000], 7) | |
| A reaction: This is the culmination of a critical discussion of mereology and ontological atomism. At first blush it doesn't look as if 'composition' has much chance of being a precise notion, and it will be plagued with vagueness. |
| 10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack] |
| Full Idea: We can employ Leibniz's Law against mereological atomism. Water is wet, but no water molecule is wet. The set of infinite numbers is infinite, but no finite number is infinite. ..But with plural reference the atomist can resist this argument. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: The idea of plural reference is to state plural facts without referring to complex things, which is interesting. The general idea is that we have atomism, and then all the relations, unities, identities etc. are in the facts, not in the things. I like it. |
| 10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack] |
| Full Idea: The fusion of five rectangles may have a decomposition into more than five parts that are rectangles. | |
| From: Keith Hossack (Plurals and Complexes [2000], 8) |
| 24054 | Everything has a probability, something will happen, and probabilities add up [PG] |
| Full Idea: The three Kolgorov axioms of probability: the probability of an event is a non-negative real number; it is certain that one of the 'elementary events' will occur; and the unity of probabilities is the sum of probability of parts ('additivity'). | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: [My attempt to verbalise them; they are normally expressed in terms of set theory]. Got this from a talk handout, and Wikipedia. |
| 3875 | If reality is just what we perceive, we would have no need for a sixth sense [PG] |
| Full Idea: Reality must be more than merely what we perceive, because a sixth sense would enhance our current knowledge, and a seventh, and so on. | |
| From: PG (Db (ideas) [2031]) |
| 3876 | If my team is losing 3-1, I have synthetic a priori knowledge that they need two goals for a draw [PG] |
| Full Idea: If my football team is losing 3-1, I seem to have synthetic a priori knowledge that they need two goals to achieve a draw | |
| From: PG (Db (ideas) [2031]) |
| 8685 | Studying biology presumes the laws of chemistry, and it could never contradict them [Friend] |
| Full Idea: In the hierarchy of reduction, when we investigate questions in biology, we have to assume the laws of chemistry but not of economics. We could never find a law of biology that contradicted something in physics or in chemistry. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.1) | |
| A reaction: This spells out the idea that there is a direction of dependence between aspects of the world, though we should be cautious of talking about 'levels' (see Idea 7003). We cannot choose the direction in which reduction must go. |
| 7734 | Maybe a mollusc's brain events for pain ARE of the same type (broadly) as a human's [PG] |
| Full Idea: To defend type-type identity against the multiple realisability objection, we might say that a molluscs's brain events that register pain ARE of the same type as humans, given that being 'of the same type' is a fairly flexible concept. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: But this reduces 'of the same type' to such vagueness that it may become vacuous. You would be left with token-token identity, where the mental event is just identical to some brain event, with its 'type' being irrelevant. |
| 7735 | Maybe a frog's brain events for fear are functionally like ours, but not phenomenally [PG] |
| Full Idea: To defend type-type identity against the multiple realisability objection, we might (also) say that while a frog's brain events for fear are functionally identical to a human's (it runs away), that doesn't mean they are phenomenally identical. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: I take this to be the key reply to the multiple realisability problem. If a frog flees from a loud noise, it is 'frightened' in a functional sense, but that still leaves the question 'What's it like to be a frightened frog?', which may differ from humans. |
| 10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
| Full Idea: A thought can refer to a particular or a universal or a state of affairs, but it can predicate only a universal and it can affirm only a state of affairs. | |
| From: Keith Hossack (Plurals and Complexes [2000], 1) | |
| A reaction: Hossack is summarising Armstrong's view, which he is accepting. To me, 'thought' must allow for animals, unlike language. I think Hossack's picture is much too clear-cut. Do animals grasp universals? Doubtful. Can they predicate? Yes. |
| 8688 | Concepts can be presented extensionally (as objects) or intensionally (as a characterization) [Friend] |
| Full Idea: The extensional presentation of a concept is just a list of the objects falling under the concept. In contrast, an intensional presentation of a concept gives a characterization of the concept, which allows us to pick out which objects fall under it. | |
| From: Michèle Friend (Introducing the Philosophy of Mathematics [2007], 3.4) | |
| A reaction: Logicians seem to favour the extensional view, because (in the standard view) sets are defined simply by their members, so concepts can be explained using sets. I take this to be a mistake. The intensional view seems obviously prior. |
| 3877 | Utilitarianism seems to justify the discreet murder of unhappy people [PG] |
| Full Idea: If I discreetly murdered a gloomy and solitary tramp who was upsetting people in my village, if is hard to see how utilitarianism could demonstrate that I had done something wrong. | |
| From: PG (Db (ideas) [2031]) |
| 10683 | We could ignore space, and just talk of the shape of matter [Hossack] |
| Full Idea: We might dispense with substantival space, and say that if the distribution of matter in space could have been different, that just means the matter of the Universe could have been shaped differently (with geometry as the science of shapes). | |
| From: Keith Hossack (Plurals and Complexes [2000], 9) |
| 6126 | Life is Movement, Respiration, Sensation, Nutrition, Excretion, Reproduction, Growth (MRS NERG) [PG] |
| Full Idea: The biologists' acronym for the necessary conditions of life is MRS NERG: that is, Movement, Respiration, Sensation, Nutrition, Excretion, Reproduction, Growth. | |
| From: PG (Db (ideas) [2031]) | |
| A reaction: How strictly necessary are each of these is a point for discussion. A notorious problem case is fire, which (at a stretch) may pass all seven tests. |
| 3873 | An omniscient being couldn't know it was omniscient, as that requires information from beyond its scope of knowledge [PG] |
| Full Idea: God seems to be in the paradoxical situation that He may be omniscient, but can never know that He is, because that involves knowing that there is nothing outside his scope of knowledge (e.g. another God) | |
| From: PG (Db (ideas) [2031]) |
| 3874 | How could God know there wasn't an unknown force controlling his 'free' will? [PG] |
| Full Idea: How could God be certain that he has free will (if He has), if He couldn't be sure that there wasn't an unknown force controlling his will? | |
| From: PG (Db (ideas) [2031]) |