16 ideas
| 9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
| Full Idea: Any set with a concrete member is 'impure'. 'Pure' sets are those that are not impure, and are paradigm cases of abstract entities, such as the sort of sets apparently dealt with in Zermelo-Fraenkel (ZF) set theory. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.116) | |
| A reaction: [I am unclear whether Jubien is introducing this distinction] This seems crucial in accounts of mathematics. On the one had arithmetic can be built from Millian pebbles, giving impure sets, while logicists build it from pure sets. |
| 9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
| Full Idea: A first-order model can be viewed as a kind of ordered set, and if the domain of the model contains only concrete entities then it is a 'fundamental' model. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.117) | |
| A reaction: An important idea. Fundamental models are where the world of logic connects with the physical world. Any account of relationship between fundamental models and more abstract ones tells us how thought links to world. |
| 9965 | There couldn't just be one number, such as 17 [Jubien] |
| Full Idea: It makes no sense to suppose there might be just one natural number, say seventeen. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.113) | |
| A reaction: Hm. Not convinced. If numbers are essentially patterns, we might only have the number 'twelve', because we had built our religion around anything which exhibited that form (in any of its various arrangements). Nice point, though. |
| 9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
| Full Idea: The subject-matter of (pure) mathematics is abstract structure per se. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.115) | |
| A reaction: This is the Structuralist idea beginning to take shape after Benacerraf's launching of it. Note that Jubien gets there by his rejection of platonism, whereas some structuralist have given a platonist interpretation of structure. |
| 9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
| Full Idea: If the intuition of mathematical objects were general, there would be no real debate over platonism. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.111) | |
| A reaction: It is particularly perplexing when Gödel says that his perception of them is just like sight or smell, since I have no such perception. How do you individuate very large numbers, or irrational numbers, apart from writing down numerals? |
| 9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
| Full Idea: I am unable to see how the mere existence of pure abstract entities enables us to concoct appropriate models to serve as interpretations. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.111) | |
| A reaction: Nice question. It is always assumed that once we have platonic realm, that everything else follows. Even if we are able to grasp the objects, despite their causal inertness, we still have to discern innumerable relations between them. |
| 9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
| Full Idea: The essential properties of mathematical entities seem to be relational, ...so we make no progress unless we can pick out some mathematical entities wihout presupposing other entities already picked out. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.112) | |
| A reaction: [compressed] Jubien is a good critic of platonism. He has identified the problem with Frege's metaphor of a 'borehole', where we discover delightful new properties of numbers simply by reaching them. |
| 9969 | The empty set is the purest abstract object [Jubien] |
| Full Idea: The empty set is the pure abstract object par excellence. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.118 n8) | |
| A reaction: So a really good PhD on the empty set could crack the whole nature of reality. Get to work, whoever you are! |
| 20725 | The idea of duty in one's calling haunts us, like a lost religion [Weber] |
| Full Idea: The idea of duty in one's calling prowls about in our lives like the ghost of dead religious beliefs. | |
| From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], 5) | |
| A reaction: Great sentence! Vast scholarship boiled down to a simple and disturbing truth. I recognise this in me. Having been 'Head of Philosophy' once is partly what motivates me to compile these ideas. |
| 20722 | Acquisition and low consumption lead to saving, investment, and increased wealth [Weber] |
| Full Idea: If people are acquisitive but consumption is limited, the inevitable result is the accumulation of capital through the compulsion to save. The restraints on consumption naturally served to increase wealth by enabling the productive investment of capital. | |
| From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], 5) | |
| A reaction: [compressed. He also quotes John Wesley saying this] In a nutshell, this is how the protestant ethic (esp. if puritan) drives capitalism. It also needs everyone to have a 'calling', and a rebellion against monasticism in favour of worldly work. |
| 20724 | When asceticism emerged from the monasteries, it helped to drive the modern economy [Weber] |
| Full Idea: When asceticism was carried out of the monastic cells into everyday life, and began to dominate worldly morality, it did its part in building the tremendous cosmos of the modern economic order. | |
| From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], 5) | |
| A reaction: Since Max Weber's time I should think this is less and less true. If you hunt for ascetics in the modern world, they are probably dropped out, and pursuing green politics. Industrialists are obsessed with property and wine. |
| 20717 | Capitalism is not unlimited greed, and may even be opposed to greed [Weber] |
| Full Idea: Unlimited greed for gain is not in the least identical with capitalism, and is still less in its spirit. Capitalism may even be identical with the restraint, or at least a rational tempering, of this irrational impulse. | |
| From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], Author's Intro) | |
| A reaction: The point is that profits have to be re-invested, rather than spent on pleasure. If we are stuck with capitalism we need a theory of Ethical Capitalism. |
| 20718 | Modern western capitalism has free labour, business separate from household, and book-keeping [Weber] |
| Full Idea: The modern Occident has developed a very different form of capitalism: the rational capitalist organisation of free labour …which needed two other factors: the separation of the business from the household, and the closely connected rational book-keeping. | |
| From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], Author's Intro) | |
| A reaction: For small businesses the separation has to be maintained by a ruthless effort of imagination. Book-keeping is because the measure of loss and profit is the engine of the whole game. Labour had to be dragged free of family and community. |
| 20719 | Punish the heretic, but be indulgent to the sinner [Weber] |
| Full Idea: The rule of the Catholic church is 'punishing the heretic, but indulgent of the sinner'. | |
| From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], 1) | |
| A reaction: Weber cites this as if it is a folklore saying. It seems to fit the teachings of Jesus, who is intensely keen on unwavering faith, but very kind to those who stray morally. Hence Graham Greene novels, all about sinners. |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |