7 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? |
| 2599 | Either intentionality causes things, or epiphenomenalism is true [Fodor] |
| Full Idea: The avoidance of epiphenomenalism requires making it plausible that intentional properties can meet sufficient conditions for causal responsibility. | |
| From: Jerry A. Fodor (Making Mind Matter More [1989], p.154) | |
| A reaction: A wordy way of saying we either have epiphenomenalism, or the mind had better do something - and a good theory will show how. The biggest problem of the mind may not be Chalmer's Hard Question (qualia), but how thought-contents cause things. |
| 2597 | Contrary to the 'anomalous monist' view, there may well be intentional causal laws [Fodor] |
| Full Idea: I argue that (contrary to the doctrine called "anomalous monism") there is no good reason to doubt that there are intentional causal laws. | |
| From: Jerry A. Fodor (Making Mind Matter More [1989], p.151) | |
| A reaction: I certainly can't see a good argument, in Davidson or anywhere else, to demonstrate their impossibility. Give the complexity of the brain, they would be like the 'laws' for weather or geology. |
| 2598 | Lots of physical properties are multiply realisable, so why shouldn't beliefs be? [Fodor] |
| Full Idea: If one of your reasons for doubting that believing-that-P is a physical property is that believing is multiply realizable, then you have the same reason for doubting that being an airfoil (or a mountain) counts as a physical property. | |
| From: Jerry A. Fodor (Making Mind Matter More [1989], p.153) | |
| A reaction: This merely points out that functionalism is not incompatible with physicalism, which must be right. |
| 23873 | Dividing history books into separate chapters is disastrous [Weil] |
| Full Idea: The division of history textbooks into chapters will cost us many disastrous mistakes. | |
| From: Simone Weil (Fragments [1936], p.131) | |
| A reaction: Nice observation. The point is that we fail to grasp what really happened if we draw sharp lines across history. |