6 ideas
| 22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
| Full Idea: Hilbert proposed to circuvent the paradoxes by means of the doctrine (already proposed by Poincaré) that in mathematics consistency entails existence. | |
| From: report of David Hilbert (On the Concept of Number [1900], p.183) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Exist' | |
| A reaction: Interesting. Hilbert's idea has struck me as weird, but it makes sense if its main motive is to block the paradoxes. Roughly, the idea is 'it exists if it isn't paradoxical'. A low bar for existence (but then it is only in mathematics!). |
| 16045 | General facts supervene on particular facts, but cannot be inferred from them [Russell, by Bennett,K] |
| Full Idea: Russell noted that you cannot arrive at general facts by inference from numerous particular facts, ..but general facts logically supervene on particular ones. So the general facts supervene, but are not entailed. | |
| From: report of Bertrand Russell (On Relations of Universals and Particulars [1911]) by Karen Bennett - Supervenience §3.2 | |
| A reaction: The belief that the general facts supervene on the particular ones then seems to be more a matter of faith than of fact. Or maybe it is analytic, depending on what we understand by 'general'. Universal, or generalised? |
| 14327 | Trope theorists cannot explain how tropes resemble each other [Russell, by Mumford] |
| Full Idea: The trope theorist cannot explain how a number of tropes resemble each other. | |
| From: report of Bertrand Russell (On Relations of Universals and Particulars [1911]) by Stephen Mumford - Dispositions 07.6 | |
| A reaction: [My 13,000th Idea: 31/10/11] Every theory is left with something it cannot explain. Is it likely that we could come up with an explanation of resemblance? It seems like a combination of identity in the physics, and identity in the brain mechanisms. |
| 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). |
| 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. |