5 ideas
| 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? |
| 20525 | Free markets lead to boom and bust, pointless middlemen, and alienated workers [Engels] |
| Full Idea: Free markets inevitably lead to unemployment and ruined businesses, when the capitalist market is punctuated by a 'trade cycle' of boom and bust. .. There are speculating, swindling middlemen. ...and the nature of work is degrading and alienated. | |
| From: Friedrich Engels (Speeches in Elberfeld [1849]), quoted by Jonathan Wolff - An Introduction to Political Philosophy (Rev) 5 'Arguments' | |
| A reaction: [compression of Wolff's summary] Wolff observes that middlemen are heroes to lovers of the market. The idea of alienation seems to be that everyone should be in charge of their own work. That may approach anarchy. |
| 22254 | Economic capitalist liberty naturally leads to democratic political liberty [Novak] |
| Full Idea: The natural logic of capitalism leads to democracy. For economic liberties without political liberties are inherently unstable. | |
| From: Michael Novak (The Spirit of Democratic Capitalism [1982], p.15), quoted by David Conway - Capitalism and Community II | |
| A reaction: Not sure about 'inherently unstable'. Only in the sense that if you dish out economic liberties, people come to expect political liberties. China and Hong Kong are each currently facing this problem. Capitalist liberty can be highly restricted. |