36 ideas
| 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. |
| 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. |
| 15105 | F(x) walked into a bar. The barman said.. [Sommers,W] |
| Full Idea: F(x) walked into a bar. The barman said, 'Sorry, we don't cater for functions'. | |
| From: Will Sommers (talk [2019]) |
| 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. |
| 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. |
| 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. |
| 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. |
| 12408 | Sartre to Waitress: Coffee with no cream, please... [Sommers,W] |
| Full Idea: Sartre to Waitress: Coffee with no cream, please. Waitress: Sorry, we're out of cream; would no milk do? | |
| From: Will Sommers (talk [2019]) |
| 12397 | Said Plato: 'The things that we feel... [Sommers,W] |
| Full Idea: Said Plato: 'The things that we feel/ Are not ontologically real,/ But just the excrescence/ Of numinous essence/ Our senses can never reveal.' [Basil Ransome-Davis] | |
| From: Will Sommers (talk [2019]) |
| 12399 | There was a young student called Fred... [Sommers,W] |
| Full Idea: There was a young student called Fred,/ Who was questioned on Descartes and said:/ 'It's perfectly clear/ That I'm not really here,/ For I haven't a thought in my head.' [V.R. Ormerod] | |
| From: Will Sommers (talk [2019]) |
| 12407 | Barman to Descartes: Would you like another drink?... [Sommers,W] |
| Full Idea: Barman to Descartes: Would you like another drink? Descartes: I think not (...and promptly vanishes) | |
| From: Will Sommers (talk [2019]) |
| 20963 | A philosopher and his wife are out for a drive... [Sommers,W] |
| Full Idea: A philosopher and his wife are out for a drive in the country. 'Oh look!' she says, 'Those sheep have been shorn.' 'Yes', says the philosopher, 'on this side'. | |
| From: Will Sommers (talk [2019]) |
| 12404 | Dear Sir, Your astonishment's odd.... [Sommers,W] |
| Full Idea: (reply to 12403) Dear Sir, Your astonishment's odd:/ I am always about in the Quad./ And that's why the tree/ Will continue to be,/ Since observed by Yours faithfully, God.' [anon] | |
| From: Will Sommers (talk [2019]) |
| 12403 | There once was a man who said: 'God... [Sommers,W] |
| Full Idea: There once was a man who said: 'God/ Must think it exceedingly odd/ If he finds that this tree/ Continues to be,/ When there's no-one about in the Quad.' [Ronald Knox] (reply in 12404) | |
| From: Will Sommers (talk [2019]) |
| 12402 | ..But if he's a student of Berkeley... [Sommers,W] |
| Full Idea: (continued from 12401) ..But if he's a student of Berkeley,/ One thing will emerge, rather starkly,/ That he ought to believe/ What his senses perceive,/ No matter how dimly or darkly. [Leslie Johnson] | |
| From: Will Sommers (talk [2019]) |
| 12409 | The philosopher Berkeley once said.. [Sommers,W] |
| Full Idea: The philosopher Berkeley once said/ In the dark to a maid in his bed:/ 'No perception, my dear,/ Means I'm not really here,/ But only a thought in your head.' [P.W.R. Foot] | |
| From: Will Sommers (talk [2019]) |
| 14694 | "My dog's got synaesthesia." How does he smell? ..... [Sommers,W] |
| Full Idea: "My dog's got synaesthesia." How does he smell? "Purple." | |
| From: Will Sommers (talk [2019]) |
| 12401 | A toper who spies in the distance... [Sommers,W] |
| Full Idea: A toper who spies in the distance,/ Striped tigers, will get some assistance/ From reading Descartes,/ Who holds that it's part/ Of his duty to doubt their existence. ... [Leslie Johnson] - (continued in 12402) | |
| From: Will Sommers (talk [2019]) |
| 12410 | There once was a man who said 'Damn!... [Sommers,W] |
| Full Idea: There once was a man who said 'Damn!/ It is borne in upon me I am/ An engine that moves/ In predestinate grooves:/ I'm not even a bus, I'm a tram.' [M.E. Hare] | |
| From: Will Sommers (talk [2019]) |
| 9392 | How do behaviourists greet each other? [Sommers,W] |
| Full Idea: How do behaviourists greet each other? Hi - you're fine, how am I? | |
| From: Will Sommers (talk [2019]) |
| 7357 | People who control others with fluent language often end up being hated [Kongzi (Confucius)] |
| Full Idea: Of what use is eloquence? He who engages in fluency of words to control men often finds himself hated by them. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], V.5) | |
| A reaction: I don't recall Socrates making this very good point to any of the sophists (such as Gorgias). The idea that if you battle or connive your way to dominance over others then you are successful is false. Life is a much longer game than that. |
| 7358 | All men prefer outward appearance to true excellence [Kongzi (Confucius)] |
| Full Idea: I have yet to meet a man as fond of excellence as he is of outward appearances. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], IX.18) | |
| A reaction: Interestingly, this cynical view of the love of virtue is put by Plato into the mouths of Glaucon and Adeimantus (in Bk II of 'Republic', e.g. Idea 12), and not into the mouth of Socrates, who goes on to defend the possibility of true virtue. |
| 7362 | Humans are similar, but social conventions drive us apart (sages and idiots being the exceptions) [Kongzi (Confucius)] |
| Full Idea: In our natures we approximate one another; habits put us further and further apart. The only ones who do not change are sages and idiots. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XVII.2) | |
| A reaction: I find most of Confucius rather uninteresting, but this is a splendid remark about the influence of social conventions on human nature. Sages can achieve universal morality if they rise above social convention, and seek the true virtues of human nature. |
| 7360 | Do not do to others what you would not desire yourself [Kongzi (Confucius)] |
| Full Idea: Do not do to others what you would not desire yourself. Then you will have no enemies, either in the state or in your home. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XII.2) | |
| A reaction: The Golden Rule, but note the second sentence. Logically, it leads to the absurdity of not giving someone an Elvis record for Christmas because you yourself don't like Elvis. Kant (Idea 3733) and Nietzsche (Idea 4560) offer good criticisms. |
| 7359 | Excess and deficiency are equally at fault [Kongzi (Confucius)] |
| Full Idea: Excess and deficiency are equally at fault. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XI.16) | |
| A reaction: This is the sort of wisdom we admire in Aristotle (and in any sensible person), but it may also be the deepest motto of conservatism, and it is a long way from romantic philosophy, and the clarion call of Nietzsche to greater excitement in life. |
| 7363 | The virtues of the best people are humility, maganimity, sincerity, diligence, and graciousness [Kongzi (Confucius)] |
| Full Idea: He who in this world can practise five things may indeed be considered Man-at-his-best: humility, maganimity, sincerity, diligence, and graciousness. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XVII.5) | |
| A reaction: A very nice list. Who could resist working with a colleague who had such virtues? Who could go wrong if they married a person who had them? I can't think of anything important that is missing. |
| 7361 | Men of the highest calibre avoid political life completely [Kongzi (Confucius)] |
| Full Idea: Men of the highest calibre avoid political life completely. | |
| From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XIV.37) | |
| A reaction: Plato notes that such people tend to avoid political life (and a left sheltering, as if from a wild storm!), but he thinks they should be dragged into the political arena for the common good. Confucius seems to approve of the avoidance. Plato is right. |
| 12405 | 'If you're aristocratic,' said Nietzsche... [Sommers,W] |
| Full Idea: 'If you're aristocratic,' said Nietzsche,/ 'It's thumbs up, you're OK. Pleased to mietzsche./ If you're working-class bores,/ It's thumbs down and up yours!/ If you don't know your place, then I'll tietzsche.' [Gerry Hamill] | |
| From: Will Sommers (talk [2019]) |
| 9391 | Why do anarchists drink herbal tea? [Sommers,W] |
| Full Idea: Why do anarchists drink herbal tea? Because proper tea is theft. | |
| From: Will Sommers (talk [2019]) |
| 23393 | Confucianism assumes that all good developments have happened, and there is only one Way [Norden on Kongzi (Confucius)] |
| Full Idea: The two major limitations of Confucianism are that it assumes that all worthwhile cultural, social and ethical innovation has already occurred, and that it does not recognise the plurality of worthwhile ways of life. | |
| From: comment on Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE]) by Bryan van Norden - Intro to Classical Chinese Philosophy 3.III | |
| A reaction: In modern liberal terms that is about as conservative as it is possible to get. We think of it as the state of mind of an old person who can only long for the way things were when they were young. But 'hold fast to that which is good'! |
| 12400 | Cries the maid: 'You must marry me Hume!'... [Sommers,W] |
| Full Idea: Cries the maid: 'You must marry me Hume!'/ A statement that made David fume./ He said: 'In cause and effect,/ There is a defect;/ That it's mine you can only assume.' [P.W.R. Foot] | |
| From: Will Sommers (talk [2019]) |
| 16527 | Causation - we all thought we knew it/ Till Hume came along and saw through it/…. [Sommers,W] |
| Full Idea: Causation - we all thought we knew it / Till Hume came along and saw through it / We notice that A / Follows B every day / And frankly that's all there is to it. | |
| From: Will Sommers (talk [2019]) |
| 17592 | The barman called 'Time!', and Augustine said..... [Sommers,W] |
| Full Idea: The barman called 'Time!'. Augustine: 'I don't know what you mean, though I did before you said that'. | |
| From: Will Sommers (talk [2019]) |
| 15208 | The past, present and future walked into a bar.... [Sommers,W] |
| Full Idea: The past, present and future walked into a bar. It was tense. | |
| From: Will Sommers (talk [2019]) |