11 ideas
| 21563 | The 'no classes' theory says the propositions just refer to the members [Russell] |
| Full Idea: The contention of the 'no classes' theory is that all significant propositions concerning classes can be regarded as propositions about all or some of their members. | |
| From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.200) | |
| A reaction: Apparently this theory has not found favour with later generations of theorists. I see it in terms of Russell trying to get ontology down to the minimum, in the spirit of Goodman and Quine. |
| 9406 | A class is natural when everybody can spot further members of it [Quinton] |
| Full Idea: To say that a class is natural is to say that when some of its members are shown to people they pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: He concedes a number of problems with his view, but I admire his attempt to at least begin to distinguish the natural (real!) classes from the ersatz ones. A mention of causal powers would greatly improve his story. |
| 21565 | Richard's puzzle uses the notion of 'definition' - but that cannot be defined [Russell] |
| Full Idea: In Richard's puzzle, we use the notion of 'definition', and this, oddly enough, is not definable, and is indeed not a definite notion at all. | |
| From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.209) | |
| A reaction: The background for this claim is his type theory, which renders certain forms of circular reference meaningless. |
| 21564 | Vicious Circle: what involves ALL must not be one of those ALL [Russell] |
| Full Idea: The 'vicious-circle principle' says 'whatever involves an apparent variable must not be among the possible values of that variable', or (less exactly) 'whatever involves ALL must not be one of ALL which it involves. | |
| From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.204) | |
| A reaction: He offers this as a parallel to his 'no classes' principle. That referred to classes, but this refers to propositions, and specifically the Liar Paradox (which he calls the 'Epimenedes'). |
| 10242 | I apply structuralism to concrete and abstract objects indiscriminately [Quine] |
| Full Idea: My own line is a yet more sweeping structuralism (than David Lewis's account of classes), applying to concrete and abstract objects indiscriminately. | |
| From: Willard Quine (Structure and Nature [1992], p.6), quoted by Stewart Shapiro - Philosophy of Mathematics 4.9 | |
| A reaction: Shapiro calls this 'breathtaking', and retreats from it, but it is something like my own view, starting from Mill's pebbles and working up. |
| 10243 | My ontology is quarks etc., classes of such things, classes of such classes etc. [Quine] |
| Full Idea: My tentative ontology continues to consist of quarks and their compounds, also classes of such things, classes of such classes, and so on. | |
| From: Willard Quine (Structure and Nature [1992], p.9), quoted by Stewart Shapiro - Philosophy of Mathematics 4.9 | |
| A reaction: I would call this the Hierarchy of Abstraction (just coined it - what do you think?). Unlike Quine, I don't see why its ontology should include things called 'sets' in addition to the things that make them up. |
| 15730 | Extreme nominalists say all classification is arbitrary convention [Quinton] |
| Full Idea: Pure, extreme nominalism sees all classification as the product of arbitrary convention. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I'm not sure what the word 'arbitrary' is doing there. Nominalists are not daft, and if they can classify any way they like, they are not likely to choose an 'arbitrary' system. Pragmatism tells the right story here. |
| 15728 | The naturalness of a class depends as much on the observers as on the objects [Quinton] |
| Full Idea: The naturalness of a class depends as essentially on the nature of the observers who classify as it does on the nature of the objects that they classify. ...It depends on our perceptual apparatus, and on our relatively mutable needs and interests. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: This seems to translate 'natural' as 'natural for us', which is not much use to scientists, who spend quite a lot of effort combating folk wisdom. Do desirable sports cars constitute a natural class? |
| 9407 | Properties imply natural classes which can be picked out by everybody [Quinton] |
| Full Idea: To say there are properties is to say there are natural classes, classes introduction to some of whose members enables people to pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: Aristotle would like this approach, but it doesn't find many friends among modern logician/philosophers. We should go on to ask why people agree on these things. Causal powers will then come into it. |
| 15729 | Uninstantiated properties must be defined using the instantiated ones [Quinton] |
| Full Idea: Properties that have no concrete instances must be defined in terms of those that have. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I wonder what the dodo used to smell like? |
| 8520 | An individual is a union of a group of qualities and a position [Quinton, by Campbell,K] |
| Full Idea: Quinton proposes that an individual is a union of a group of qualities and a position. | |
| From: report of Anthony Quinton (The Nature of Things [1973], Pt I) by Keith Campbell - The Metaphysic of Abstract Particulars §5 | |
| A reaction: This seems the obvious defence of a bundle account of objects against the charge that indiscernibles would have to be identical. It introduces, however, 'positions' into the ontology, but maybe that price must be paid. Materialism needs space. |