14 ideas
| 19048 | Contextual definition shifted the emphasis from words to whole sentences [Quine] |
| Full Idea: Contextual definition precipitated a revolution in semantics. The primary vehicle of meaning is seen no longer as the word, but as the sentence. | |
| From: Willard Quine (Five Milestones of Empiricism [1975], p.69) | |
| A reaction: I think the idea is that the term is now supported entirely by its surrounding language, and not by its denotation of something in the world. |
| 19047 | Bentham's contextual definitions preserved terms after their denotation became doubtful [Quine] |
| Full Idea: If Bentham found some term convenient but ontologically embarrassing, contextual definition enabled him in some cases to continue to enjoy the services of the term while disclaiming its denotation. | |
| From: Willard Quine (Five Milestones of Empiricism [1975], p.68) | |
| A reaction: In Quine's terms this would be to withdraw the term from the periphery of the theory, where it has to meet the world, and make it part of the inner connections of the theory. He suggests that Bentham invented this technique. |
| 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! |
| 19049 | In scientific theories sentences are too brief to be independent vehicles of empirical meaning [Quine] |
| Full Idea: We have come to recognise that in a scientific theory even a whole sentence is ordinarily too short a text to serve as an independent vehicle of empirical meaning. | |
| From: Willard Quine (Five Milestones of Empiricism [1975], p.70) |
| 19046 | Empiricism improvements: words for ideas, then sentences, then systems, then no analytic, then naturalism [Quine] |
| Full Idea: Since 1750 empiricism shows five turns for the better. First was a shift from ideas to words. Second a shift from terms to sentences. Third the shift to systems of sentences. Fourth the abandonment of analytic-synthetic dualism. Fifth was naturalism. | |
| From: Willard Quine (Five Milestones of Empiricism [1975], p.67) | |
| A reaction: [compressed] Quine must be largely credited with the last two. The first four are almost entirely linguistic in character, which is characteristic of mid-twentieth-century empiricism. I would offer the recognition of explanation as central for the sixth. |
| 19050 | Holism in language blurs empirical synthetic and empty analytic sentences [Quine] |
| Full Idea: Holism blurs the supposed contrast beween the synthetic sentence, with its empirical content, and the analytic sentence, with its null content. | |
| From: Willard Quine (Five Milestones of Empiricism [1975], p.71) | |
| A reaction: This spells out nicely that Quine's rejection of the distinction is completely tied to his holistic view of language. The obvious phenomenon of compositionality (building sentence meaning in steps) counts against holism. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |