15 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. |
| 17945 | Forms are not a theory of universals, but an attempt to explain how predication is possible [Nehamas] |
| Full Idea: The theory of Forms is not a theory of universals but a first attempt to explain how predication, the application of a single term to many objects - now considered one of the most elementary operations of language - is possible. | |
| From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxvii) |
| 17946 | Only Tallness really is tall, and other inferior tall things merely participate in the tallness [Nehamas] |
| Full Idea: Only Tallness and nothing else really is tall; everything else merely participates in the Forms and, being excluded from the realm of Being, belongs to the inferior world of Becoming. | |
| From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxviii) | |
| A reaction: This is just as weird as the normal view (and puzzle of participation), but at least it makes more sense of 'metachein' (partaking). |
| 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! |
| 17944 | 'Episteme' is better translated as 'understanding' than as 'knowledge' [Nehamas] |
| Full Idea: The Greek 'episteme' is usually translated as 'knowledge' but, I argue, closer to our notion of understanding. | |
| From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xvi) | |
| A reaction: He agrees with Julia Annas on this. I take it to be crucial. See the first sentence of Aristotle's 'Metaphysics'. It is explanation which leads to understanding. |
| 3488 | Freud treats the unconscious as intentional and hence mental [Freud, by Searle] |
| Full Idea: Freud thinks that our unconscious mental states exist as occurrent intrinsic intentional states even when unconscious. Their ontology is that of the mental, even when they are unconscious. | |
| From: report of Sigmund Freud (works [1900]) by John Searle - The Rediscovery of the Mind Ch. 7.V | |
| A reaction: Searle states this view in order to attack it. Whether such states are labelled as 'mental' seems uninteresting. Whether unconscious states can be intentional is crucial, and modern scientific understanding of the brain strongly suggest they can. |
| 5689 | Freud and others have shown that we don't know our own beliefs, feelings, motive and attitudes [Freud, by Shoemaker] |
| Full Idea: Freud persuaded many that beliefs, wishes and feelings are sometimes unconscious, and even sceptics about Freud acknowledge that there is self-deception about motive and attitudes. | |
| From: report of Sigmund Freud (works [1900]) by Sydney Shoemaker - Introspection p.396 | |
| A reaction: This seems to me obviously correct. The traditional notion is that the consciousness is the mind, but now it seems obvious that consciousness is only one part of the mind, and maybe even a peripheral (epiphenomenal) part of it. |
| 23950 | Freud said passions are pressures of some flowing hydraulic quantity [Freud, by Solomon] |
| Full Idea: Freud argued that the passions in general …were the pressures of a yet unknown 'quantity' (which he simply designated 'Q'). He first thought this flowed through neurones, …and always couched the idea in the language of hydraulics. | |
| From: report of Sigmund Freud (works [1900]) by Robert C. Solomon - The Passions 3.4 | |
| A reaction: This is the main target of Solomon's criticism, because its imagery has become so widespread. It leads to talk of suppressing emotions, or sublimating them. However, it is not too different from Nietzsche's 'drives' or 'will to power'. |
| 22344 | Freud is pessimistic about human nature; it is ambivalent motive and fantasy, rather than reason [Freud, by Murdoch] |
| Full Idea: Freud takes a thoroughly pessimistic view of human nature. ...Introspection reveals only the deep tissue of ambivalent motive, and fantasy is a stronger force than reason. Objectivity and unselfishness are not natural to human beings. | |
| From: report of Sigmund Freud (works [1900], II) by Iris Murdoch - The Sovereignty of Good II | |
| A reaction: Interesting. His view seems to have coloured the whole of modern culture, reinforced by the hideous irrationality of the Nazis. Adorno and Horkheimer attacking the Enlightenment was the last step in that process. |