8 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? |
| 15432 | Structural universals might serve as possible worlds [Forrest, by Lewis] |
| Full Idea: Forrest proposed that structural universals should serve as ersatz possible worlds. | |
| From: report of Peter Forrest (Ways Worlds Could Be [1986]) by David Lewis - Against Structural Universals 'Intro' | |
| A reaction: I prefer powers to property universals. Perhaps a possible world is a maximal set of co-existing dispositions? |
| 23169 | Democratic institutions become impossible in a fanatical democracy [Russell] |
| Full Idea: Even democracy, when it becomes fanatical, as it did …in the French Revolution, ceases to be Liberal. Indeed, a fanatical belief in democracy makes democratic institutions impossible. | |
| From: Bertrand Russell (Philosophy and Politics [1950], p.26) | |
| A reaction: Presumably this is because the supposed 'will of the people' is continually placed in opposition to the institutions. For example, there is a problem if a referendum is held, which produces a result in conflict with the institutions. |
| 23170 | Liberal opinions are tentative rather than dogmatic, and are always responsive to new evidence [Russell] |
| Full Idea: The essence of the Liberal outlook lies ...in how opinions are held: instead of being held dogmatically, they are held tentatively (as they are in science), and with a consciousness that new evidence may at any moment lead to their abandonment. | |
| From: Bertrand Russell (Philosophy and Politics [1950], p.26) | |
| A reaction: A nice assessment. Russell shows himself finally to be a Liberal. This flexible approach to opinions is what infuriates dogmatists from both the left and the right. It might be said that the basic evidence rarely changes. |
| 23172 | Empiricist Liberalism is the only view for someone who favours scientific evidence and happiness [Russell] |
| Full Idea: Empiricist Liberalism (not incompatible with democratic socialism) is, as in Locke's time, the only philosophy that can be adopted by a man who demands some scientific evidence for beliefs, and also desires human happiness more than some party or creed. | |
| From: Bertrand Russell (Philosophy and Politics [1950], p.31) | |
| A reaction: I like this way of presenting liberalism. In the modern world we are sunk if we don't pay attention to experts, so we all need a critical understanding of what counts as good evidence. Tricky in a world of lying media. |
| 23171 | Empiricism is ethically superior, because dogmatism favours persecution and hatred [Russell] |
| Full Idea: Empiricism is to be commended not only on the grounds of its greater truth, but also on ethical grounds. Dogma demands authority rather than intelligent thought; it requires persecution of heretics and unbelievers, and favours systematic hatred. | |
| From: Bertrand Russell (Philosophy and Politics [1950], p.31) | |
| A reaction: He links empiricism with the liberal outlook. At its best, the respect by empiricists for evidence is a sort of humility. |