9 ideas
| 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). |
| 17722 | The concept 'red' is tied to what actually individuates red things [Peacocke] |
| Full Idea: The possession conditions for the concept 'red' of the colour red are tied to those very conditions which individuate the colour red. | |
| From: Christopher Peacocke (Explaining the A Priori [2000], p.267), quoted by Carrie Jenkins - Grounding Concepts 2.5 | |
| A reaction: Jenkins reports that he therefore argues that we can learn something about the word 'red' from thinking about the concept 'red', which is his new theory of the a priori. I find 'possession conditions' and 'individuation' to be very woolly concepts. |
| 22330 | Grice said patterns of use are often semantically irrelevant, because it is a pragmatic matter [Grice, by Glock] |
| Full Idea: The slogan that meaning is use came under scrutiny by Grice's theory of conversational implicature. He said patterns of use shown in analysis were often semantically irrelevant, snce they are due not meanings of expressions but to pragmatic principles. | |
| From: report of H. Paul Grice (Some Models for Implicature [1967]) by Hans-Johann Glock - What is Analytic Philosophy? 2.8 | |
| A reaction: I think the simplest objection is that words only have use because they have a meaning; The most interesting part of pragmatics is what you DON'T say in conversation. |
| 18045 | Grice's maxim of quality says do not assert what you believe to be false [Grice, by Magidor] |
| Full Idea: Grice's maxim of quality says one ought not to assert what one believes to be false. | |
| From: report of H. Paul Grice (Some Models for Implicature [1967]) by Ofra Magidor - Category Mistakes 5.2 | |
| A reaction: The obvious exception is irony, where are truth is asserted, but the listener is supposed to spot that you are not really asserting it. |
| 18044 | Grice's maxim of manner requires one to be as brief as possible [Grice, by Magidor] |
| Full Idea: Grice's maxim of manner requires one to be as brief as possible. | |
| From: report of H. Paul Grice (Some Models for Implicature [1967]) by Ofra Magidor - Category Mistakes 5.2 | |
| A reaction: An alternative maxim of conversation is that there should not be long silences between contributions - which would probably result if the contributions are all curtly abbreviated. |
| 18046 | Grice's maxim of quantity says be sufficiently informative [Grice, by Magidor] |
| Full Idea: Grice's maxim of quantity says 'make your contributions as informative as required'. | |
| From: report of H. Paul Grice (Some Models for Implicature [1967]) by Ofra Magidor - Category Mistakes 5.2 | |
| A reaction: Is the 'requirement' of informative for the speaker or for the listener? It is easy to image situations where, one way or the other, the two people don't agree about informativenss. |