5 ideas
| 21355 | The Pre-Socratics are not simple naturalists, because they do not always 'leave the gods out' [Leroi] |
| Full Idea: The problem with making naturalism the hallmark of Pre-Socratic thought ...is that they do not always 'leave the gods out'; the Divine can usually be found lurking somewhere is their cosmologies. | |
| From: Armand Marie LeRoi (The Lagoon: how Aristotle invented science [2014], 007) | |
| A reaction: An important observation. I've been guilty of this simplistic view. We tend to ignore the religious fragments, or we possess so little that we have no idea where religion figured in their accounts. |
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 5271 | Prejudice apart, push-pin has equal value with music and poetry [Bentham] |
| Full Idea: Prejudice apart, the game of push-pin is of equal value with the arts and science of music and poetry. | |
| From: Jeremy Bentham (Constitutional Code I [1827], p.139), quoted by J.R. Dinwiddy - Bentham p.114 | |
| A reaction: Mill quoted this with implied outrage, but Bentham was attacking public subsidies to the arts when he said it. It is a basic idea in the debate on pleasure - that pleasures are only distinguished by their intensity, not some other value. |