9 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. |
| 6455 | Maybe 'sense-data' just help us to talk about unusual perceptual situations [Lacey] |
| Full Idea: One possibility is that talk of sense-data is a mere linguistic convenience, providing a noun for talking about appearances, as when seeing a red object in sodium light (when it looks grey). | |
| From: A.R. Lacey (A Dictionary of Philosophy [1976], p.196) | |
| A reaction: The term seems to have been coined to deal with situations where there is a gap between appearance and presumed reality, as in illusions. Maybe illusions prove the existence of sense-data, rather than it being a 'convenient' term. |
| 6454 | Where do sense-data begin or end? Can they change? What sort of thing are they? [Lacey] |
| Full Idea: It is hard to individuate sense-data, saying where one ends and the next begins, and hard to say whether they can change; are they substances, qualities, events, or what? | |
| From: A.R. Lacey (A Dictionary of Philosophy [1976], p.196) | |
| A reaction: The problem is not that these questions are unanswerable. The answer seems to be either that they are physical and external, or that they are mental and internal, and that there is no ontological space for them between the two. |
| 6453 | Some claim sense-data are public, and are parts of objects [Lacey] |
| Full Idea: Sometimes it is said that sense-data are public, and parts either of objects or of the surfaces of objects. | |
| From: A.R. Lacey (A Dictionary of Philosophy [1976], p.196) | |
| A reaction: This suggests two drastically different theories, one making sense-data into mental events, the other placing them in the 'external' world. The latter theory can dovetail them with the physics, but then why would we need them? |
| 4051 | People will volunteer for euthanasia because they think other people want them dead [Kamisar] |
| Full Idea: In the process of voluntary euthanasia we will sweep up some who are not really tired of life, but think others are tired of them. | |
| From: Yale Kamisar (Against Euthanasia [1958], p.78) | |
| A reaction: We could permit such choices. Or set up systems to eliminate such cases. |
| 4050 | We only allow voluntary euthanasia to someone who is both sane and crazed by pain [Kamisar] |
| Full Idea: It seems that voluntary euthanasia can only be carried out by someone who is both sane, and crazed by pain. | |
| From: Yale Kamisar (Against Euthanasia [1958], p.77) | |
| A reaction: A fair point, despite its obvious exaggeration. How much pain must someone experience before we permit them to choose euthanasia? |