13 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! |
| 4316 | Either all action is rational, or reason dominates, or reason is only concerned with means [Cottingham] |
| Full Idea: We can distinguish rational exclusivism (all activity is guided by reason - Plato and Spinoza), rational hegemonism (all action is dominated by reason), and rational instrumentalism (reason assesses means rather than ends - Hume). | |
| From: John Cottingham (Reason, Emotions and Good Life [2000]) | |
| A reaction: The idea that reason is the only cause of actions seems deeply implausible, but I strongly resist Hume's instrumental approach. Action without desire is not a contradiction. |
| 8108 | Aesthetics presupposes a distinctive sort of experience, and a unified essence for art [Gardner] |
| Full Idea: Aesthetics traditionally has two presuppositions: the first is that there is a distinctive form of experience which is common to the appreciation of art and natural beauty; the second is that art has an essence or some sort of underlying unity. | |
| From: Sebastian Gardner (Aesthetics [1995], Intro) | |
| A reaction: Both must come up for discussion. I think the biggest problem for the first one is the place of sexual attraction, or even fancying a prawn sandwich. The second has been weakened by Marcel Duchamp's urinal, and modern fringe arts. |
| 8112 | Art works originate in the artist's mind, and appreciation is re-creating this mental object [Gardner] |
| Full Idea: A strong tradition in aesthetics (the 'idealist' view) regards works of art as existing originally in the artist's mind, and the appreciation of art as a matter of re-creating the artist's mental object. | |
| From: Sebastian Gardner (Aesthetics [1995], 2.2) | |
| A reaction: He mentions Collingwood and Croce. Against this is the view (Idea 7268) that what goes on in the artist's mind is just irrelevant. Freud is important here, suggesting that the artist doesn't quite know what he or she is doing. |
| 8111 | Aesthetic objectivists must explain pleasure being essential, but not in the object [Gardner] |
| Full Idea: The aesthetic objectivist faces the difficulty of accounting for the fact that pleasure is not in the object, and is necessary for, and not just a contingent accompaniment to, aesthetic response. | |
| From: Sebastian Gardner (Aesthetics [1995], 1.2.3) | |
| A reaction: The objectivist has to claim, not utterly implausibly, that if you don't get pleasure from certain works, then you 'ought' to. You can ignore a good work, but to deny that it gives pleasure is a failing in you. |
| 8109 | Aesthetic judgements necessarily require first-hand experience, unlike moral judgements [Gardner] |
| Full Idea: I am not within my rights to declare an object beautiful until I have seen it myself, ..unlike moral judgement, which (arguably) does not presuppose either a felt response or personal acquaintance. | |
| From: Sebastian Gardner (Aesthetics [1995], 1.1) | |
| A reaction: Particularists might argue that moral judgements also require exposure to the actual situation, if they are to be authentic and authoritative. We can also discuss principles of aesthetics in the absence of examples. |