11 ideas
| 13365 | Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell] |
| Full Idea: Russell's Paradox is a stripped-down version of Cantor's Paradox. | |
| From: comment on Bertrand Russell (Letters to Frege [1902]) by Graham Priest - The Structure of Paradoxes of Self-Reference §2 |
| 10711 | Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell] |
| Full Idea: Russell's paradox showed that we cannot consistently assume what is sometimes called the 'naïve comprehension principle', namely that every property is collectivizing. | |
| From: comment on Bertrand Russell (Letters to Frege [1902]) by Michael Potter - Set Theory and Its Philosophy 03.6 |
| 9127 | Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen] |
| Full Idea: Russell refuted Frege's principle that there is a set for each property. | |
| From: report of Bertrand Russell (Letters to Frege [1902], 1904.12.12) by Roy Sorensen - Vagueness and Contradiction 6.1 | |
| A reaction: This is the principle stumbling block to any attempt to explain properties purely in terms of sets. I would say that Russell proved there couldn't be a set for each predicate. You can't glibly equate proper properties with predicates. |
| 4483 | If abstract terms are sets of tropes, 'being a unicorn' and 'being a griffin' turn out identical [Loux] |
| Full Idea: If trope theorists say abstract singular terms name sets of tropes, what is the referent of 'is a unicorn'? The only candidate is the null set (with no members), but there is just one null set, so 'being a unicorn' and 'being a griffin' will be identical. | |
| From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.86) | |
| A reaction: Not crucial, I would think, given that a unicorn is just a horse with a horn. Hume explains how we do that, combining ideas which arose from actual tropes. |
| 4481 | Austere nominalists insist that the realist's universals lack the requisite independent identifiability [Loux] |
| Full Idea: Austere nominalists insist that the realist's universals lack the requisite independent identifiability. | |
| From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.60) | |
| A reaction: Plato's view seems to be that we don't identify universals independently. We ascend The Line, or think about the shadows in The Cave, and infer the universals from an array of particulars (by dialectic). |
| 4477 | Universals come in hierarchies of generality [Loux] |
| Full Idea: Universals come in hierarchies of generality. | |
| From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.24) | |
| A reaction: If it is possible to state facts about universals, this obviously encourages a rather Platonic approach to them, as existent things with properties. But maybe the hierarchies are conventional, not natural. |
| 4482 | Austere nominalism has to take a host of things (like being red, or human) as primitive [Loux] |
| Full Idea: In return for a one-category ontology (with particulars but no universals), the austere nominalist is forced to take a whole host of things (like being red, or triangular, or human) as unanalysable or primitive. | |
| From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.68) | |
| A reaction: I see that 'red' might have to be primitive, but being human can just be a collection of particulars. It is no ontologically worse to call them 'primitive' than to say they exist. |
| 4478 | Nominalism needs to account for abstract singular terms like 'circularity'. [Loux] |
| Full Idea: Nominalists have been very concerned to provide an account of the role of abstract singular terms (such as 'circularity'). | |
| From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.34) | |
| A reaction: Whether this is a big problem depends on our view of abstraction. If it only consists of selecting one property of an object and reifying it, then we can give a nominalist account of properties, and the problem is solved. |
| 4480 | Times and places are identified by objects, so cannot be used in a theory of object-identity [Loux] |
| Full Idea: Any account of the identity of material objects which turns on the identity of places and times must face the objection that the identity of places and times depends, in turn, on the identities of the objects located at them. | |
| From: Michael J. Loux (Metaphysics: contemporary introduction [1998], p.56) | |
| A reaction: This may be a benign circle, in which we concede that there are two basic interdependent concepts of objects and space-time. If you want to define identity - in terms of what? |
| 7531 | We don't assert private thoughts; the objects are part of what we assert [Russell] |
| Full Idea: I believe Mont Blanc itself is a component part of what is actually asserted in the proposition 'Mont Blanc is more than 4000 metres high'; we do not assert the thought, which is a private psychological matter, but the object of the thought. | |
| From: Bertrand Russell (Letters to Frege [1902], 1904.12.12), quoted by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
| A reaction: This would appear to be pretty much externalism about concepts, given that Russell would accept that other people know much more about Mont Blanc than he does, and their knowledge is included in what he asserts. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |