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? |
| 23222 | A soul with physical extension is more likely than an immaterial soul that moves bodies [Elizabeth] |
| Full Idea: I would find it easier to concede matter and extension to the soul than to concede that an immaterial thing could move and be moved by a body. | |
| From: Elizabeth, Princess of Bohemia (Letters to Descartes [1643], p.42), quoted by Matthew Cobb - The Idea of the Brain 2 | |
| A reaction: Very nicely expressed! I'm trying to imagine a ghost which finds itself stuck with a physical body which it has to drag around like a reluctant dog. She is stating the classic interaction problem which plagues all mind-body dualism. |
| 18681 | The base for values has grounds, catalysts and intensifiers [Dancy,J, by Orsi] |
| Full Idea: Dancy distinguishes three parts of the supervenience base of values: 1) those which ground the value ('resultance base'); 2) those which enable the ground to make something good ('enabling conditions'); 3) those which intensify or diminish value. | |
| From: report of Jonathan Dancy (Ethics without Principles [2004], p. 170-181) by Francesco Orsi - Value Theory 5.2 | |
| A reaction: I really like and admire this. Dancy has focused on what really matters about values (and hence about the whole of ethics), and begun the work of getting a bit of clarity and increased understanding. |