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. |
| 8499 | Nominalists cannot translate 'red resembles pink more than blue' into particulars [Jackson] |
| Full Idea: It is not always possible for nominalists to translate all statements putatively about universals as statements about particulars. It is not possible for 'red is a colour' and 'red resembles pink more than blue' | |
| From: Frank Jackson (Statements about Universals [1977], p.89) | |
| A reaction: His second example strikes me as the biggest challenge facing nominalism. I wish they wouldn't use secondary qualities as examples. I am unconvinced that the existence of universals will improve the explanation. It's a mystery. |
| 8500 | Colour resemblance isn't just resemblance between things; 'colour' must be mentioned [Jackson] |
| Full Idea: Some red things resemble some blue things more than some pink things because of factors other than colour. Nominalists must offer 'anything red colour-resembles anything pink', but that may contain a universal in disguise. | |
| From: Frank Jackson (Statements about Universals [1977], p.90) | |
| A reaction: Hume and Quine are probably right that we spot resemblances instantly, and only articulate the respect of the resemblance at a later stage. |
| 20420 | The emotion expressed is non-conscious, but feels oppressive until expression relieves it [Collingwood] |
| Full Idea: The emotion expressed is one of whose nature the person feeling it is no longer conscious. As unexpressed, he feels it in a helpless and oppressed way; as expressed, the oppression has vanished. His mind is somehow lightened and eased. | |
| From: R.G. Collingwood (The Principles of Art [1938], p.110), quoted by Gary Kemp - Croce and Collingwood 1 | |
| A reaction: It sounds like the regular smoking of cigarettes. This is Collingwood answer the doubts I felt about Idea 20419. I would have thought the desire of Picasso was to create another painting, but not to express yet another new oppressive feeling. |
| 20421 | Art exists ideally, purely as experiences in the mind of the perceiver [Collingwood, by Kemp] |
| Full Idea: For Collingwood (and Croce) the work of art is an ideal object; …they are things that exist only in the mind, that is, only when one perceives. …The physical work exists to make this experience available. | |
| From: report of R.G. Collingwood (The Principles of Art [1938]) by Gary Kemp - Croce and Collingwood 2 | |
| A reaction: This means that the paintings in a gallery cease to be works of art when the gallery is shut, which sounds odd. I suppose 'work of art' is ambiguous, between the experience (right) and the facilitator of the experience (wrong). |
| 20406 | Art clarifies the artist's mind and feelings, thus leading to self-knowledge [Collingwood, by Davies,S] |
| Full Idea: Collingwood suggests art should be thought of not as product or artifact but as an act or process of expression through which the artist clarifies her initially vague emotions and states of mind. As such, it is a source of self-knowledge. | |
| From: report of R.G. Collingwood (The Principles of Art [1938], Ch.6) by Stephen Davies - The Philosophy of Art (2nd ed) 8.4 | |
| A reaction: I might believe this of writing novels, but not much else. |