6 ideas
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought. | |
| From: report of David Hilbert (works [1900], 6.7) by Michčle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault. |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign. | |
| From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience. |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1). | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application. |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning. | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem. |
| 16640 | Form is the principle that connects a thing's constitution (rather than being operative) [Hill,N] |
| Full Idea: Form is the state and condition of a thing, a result of the connection among its material principles; it is a constituting principle, not an operative one. | |
| From: Nicholas Hill (Philosophia Epicurea [1610], n 35) | |
| A reaction: Pasnau presents this as a denial of form, but it looks to me like someone fishing for what form could be in a more scientific context. Aristotle would have approved of 'principles'. Hill seems to defend the categorical against the dispositional. |
| 20751 | As a young girl assumes her status as feminine, she acts in a more fragile immobile way [Young,IM] |
| Full Idea: The young girl acquires many subject habits of feminine body comportment - walking, tilting her head, standing and sitting like a girl, and so on ….The more a girl assumes her status as feminine, the more she takes herself to be fragile and immobile. | |
| From: Iris Marion Young (On Female Body Experience [2005], p.43), quoted by Kevin Aho - Existentialism: an introduction 3 'Aspects' | |
| A reaction: This strikes me as true of young women, but it largely wears off as they get older, at least among modern women. A whole book could be written about women and smiling. |