3 ideas
| 15927 | Definition just needs negation, known variables, conjunction, disjunction, substitution and quantification [Weyl, by Lavine] |
| Full Idea: For mathematics, Weyl arrived (by 1917) at a satisfactory list of definition principles: negation, identification of variables, conjunction, disjunction, substitution of constants, and existential quantification over the domain. | |
| From: report of Hermann Weyl (works [1917]) by Shaughan Lavine - Understanding the Infinite V.3 | |
| A reaction: Lavine summarises this as 'first-order logic with parameters'. |
| 18946 | Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer] |
| Full Idea: As speakers of the language, we unreflectively assume that there are nonexistents, and that reference to them is possible. | |
| From: Marga Reimer (The Problem of Empty Names [2001], p.499), quoted by Sarah Sawyer - Empty Names 4 | |
| A reaction: Sarah Swoyer quotes this as a good solution to the problem of empty names, and I like it. It introduces a two-tier picture of our understanding of the world, as 'unreflective' and 'reflective', but that seems good. We accept numbers 'unreflectively'. |
| 19284 | Asserting a necessity just expresses our inability to imagine it is false [Blackburn] |
| Full Idea: To say that we dignify a truth as necessary we are expressing our own mental attitudes - our own inability to make anything of a possible way of thinking which denies it. It is this blank unimaginability which we voice when we use the modal vocabulary. | |
| From: Simon Blackburn (Spreading the Word [1984], 6.5) | |
| A reaction: Yes, but why are we unable to imagine it? I accept that the truth or falsity of Goldbach's Conjecture may well be necessary, but I have no imagination one way or the other about it. Philosophers like Blackburn are very alien to me! |