11 ideas
| 20110 | Hegel, Fichte and Schelling wanted to know Kant's thing-in-itself, as ego, or nature, or spirit [Safranski] |
| Full Idea: The 'thing in iself' acted on Kant's successors like a hole in the closed world of knowledge...Hegel, Fichte and Schelling wanted to penetrate into what they presumed to be the heart of things, by the invention of means of 'ego', or 'nature', or 'spirit., | |
| From: Rüdiger Safranski (Nietzsche: a philosophical biography [2000], 07) | |
| A reaction: [a bit compressed] Although no scientist claims to know the ultimate essence of matter, the authority of science largely comes from persuasively moving us several steps closer to the thing in itself (more persuasively than these three). |
| 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. |
| 8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
| Full Idea: Chihara's programme is to replace talk of sets with talk of open sentences. Instead of speaking of the set of all cats, we talk about the open sentence 'x is a cat'. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2 | |
| A reaction: As Shapiro points out, this is following up Russell's view that sets should be replaced with talk of properties. Chihara is expressing it more linguistically. I'm in favour of any attempt to get rid of sets. |
| 10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
| Full Idea: Chihara's system is a version of type theory. Translate thus: replace variables of sets of type n with level n variables over open sentences, replace membership/predication with satisfaction, and high quantifiers with constructability quantifiers. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4 |
| 8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
| Full Idea: Chihara's system is similar to simple type theory; he replaces each type with variables over open sentences, replaces membership (or predication) with satisfaction, and replaces quantifiers over level 1+ variables with constructability quantifiers. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2 | |
| A reaction: This is interesting for showing that type theory may not be dead. The revival of supposedly dead theories is the bread-and-butter of modern philosophy. |
| 10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
| Full Idea: Chihara has proposal a modal primitive, a 'constructability quantifier'. Syntactically it behaves like an ordinary quantifier: Φ is a formula, and x a variable. Then (Cx)Φ is a formula, read as 'it is possible to construct an x such that Φ'. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4 | |
| A reaction: We only think natural numbers are infinite because we see no barrier to continuing to count, i.e. to construct new numbers. We accept reals when we know how to construct them. Etc. Sounds promising to me (though not to Shapiro). |
| 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. |