6 ideas
| 2764 | Full coherence might involve consistency and mutual entailment of all propositions [Blanshard, by Dancy,J] |
| Full Idea: Blanshard says that in a fully coherent system there would not only be consistency, but every proposition would be entailed by the others, and no proposition would stand outside the system. | |
| From: report of Brand Blanshard (The Nature of Thought [1939], 2:265) by Jonathan Dancy - Intro to Contemporary Epistemology 8.1 | |
| A reaction: Hm. If a proposition is entailed by the others, then it is a necessary truth (given the others) which sounds deterministic. You could predict all the truths you had never encountered. See 1578:178 for quote. |
| 19080 | Coherence tests for truth without implying correspondence, so truth is not correspondence [Blanshard, by Young,JO] |
| Full Idea: Blanshard said that coherent justification leads to coherence truth. It might be said that coherence is a test for truth, but truth is correspondence. But coherence doesn't guarantee correspondence, and coherence is a test, so truth is not correspondence. | |
| From: report of Brand Blanshard (The Nature of Thought [1939], Ch.26) by James O. Young - The Coherence Theory of Truth §2.2 | |
| A reaction: [compression of Young's summary] Rescher (1973) says that Blanshard's argument depends on coherence being an infallible test for truth, which it isn't. |
| 10670 | A 'singulariser' converts a plural like 'number of' to a syntactically neutral form [Cartwright,H, by Hossack] |
| Full Idea: Helen Cartwright calls 'a number of' a 'singulariser', an expression whose linguistic function is to convert to a syntactically neutral form an expression whose semantic value remains plural. It is a great convenience grammatically. | |
| From: report of Helen Cartwright (On Plural Reference and Set Theory [1993]) by Keith Hossack - Plurals and Complexes 2 | |
| A reaction: Compare Hofweber's Idea 10004, suggesting it is a crucial psychological convenience for reasoning, as well as a 'grammatical' convenience. |
| 17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
| Full Idea: Usually Gödel's incompleteness theorems are taken as showing a limitation on the syntactic approach to an understanding of the concept of infinity. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 05) |
| 17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
| Full Idea: It is necessary to use non-mathematical concepts, i.e. concepts lacking the precision which permit mathematical manipulation, for a significant approach to foundations. We currently have no concepts of this kind which we can take seriously. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 06) | |
| A reaction: Music to the ears of any philosopher of mathematics, because it means they are not yet out of a job. |
| 17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |
| Full Idea: In analysis, the most natural conception of a point ignores the matter of naming the point, i.e. how the real number is represented or by what constructions the point is reached from given points. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 13) | |
| A reaction: This problem has bothered me. There are formal ways of constructing real numbers, but they don't seem to result in a name for each one. |