9 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? |
| 19508 | Contextualism needs a semantics for knowledge sentences that are partly indexical [Schiffer,S] |
| Full Idea: Contextualist semantics must capture the 'indexical' nature of knowledge claims, the fact that different utterances of a knowledge sentence with no apparent indexical terms can express different propositions. | |
| From: Stephen Schiffer (Contextualist Solutions to Scepticism [1996], p.325), quoted by Keith DeRose - The Case for Contextualism 1.5 | |
| A reaction: Schiffer tries to show that this is too difficult, and DeRose defends contextualism against the charge. |
| 19509 | The indexical aspect of contextual knowledge might be hidden, or it might be in what 'know' means [Schiffer,S] |
| Full Idea: One might have a 'hidden-indexical' theory of knowledge sentences: they contain constituents that are not the semantic values of any terms; ...or 'to know' itself might be indexical, as in 'I know[easy] I have hands' or 'I know[tough] I have hands'. | |
| From: Stephen Schiffer (Contextualist Solutions to Scepticism [1996], p.326-7), quoted by Keith DeRose - The Case for Contextualism 1.5 | |
| A reaction: [very compressed] Given the choice, I would have thought it was in 'know', since to say 'either you know p or you don't' sounds silly to me. |
| 20582 | World government needs a shared global identity [Oksala] |
| Full Idea: Critics have argued that a global 'demos' would require a shared global identity. | |
| From: Johanna Oksala (Political Philosophy: all that matters [2013], Ch.9 'Epi') | |
| A reaction: The great divisions are religion and language. The great unifiers are sport, arts and entertainment, plus basic human needs like food, health and housing. The reply is that there cannot be identity without differences, so global democracy is out. |
| 20568 | The principles Rawls arrives at do not just conform to benevolence, but also result from choices [Oksala] |
| Full Idea: The advantage of Rawls's method is that the principles the individual chooses are not only fair according to some abstract principle of benevolence, but also the result of rational choice. | |
| From: Johanna Oksala (Political Philosophy: all that matters [2013], Ch.5) | |
| A reaction: That is a very nice way of putting the beauty of Rawls's idea. In modern political philosophy you hear far more criticisms of Rawls than praise. If a philosopher is criticised a lot, it is probably because they have stated their views clearly. |
| 20578 | Anarchists prefer local and communal government [Oksala] |
| Full Idea: Anarchists advocate forms of governance such as communes and associations that are as local and close to the direct control of the people as possible. | |
| From: Johanna Oksala (Political Philosophy: all that matters [2013], Ch.8) | |
| A reaction: Which might explain why recent conservative governments have steadily eliminated local government in Britain. |
| 20574 | Utilitarianism neglects responsibility, duties and rights [Oksala] |
| Full Idea: A focus solely on utility excludes considerations of personal responsibility and duty, as well as considerations of the basic rights of individuals. | |
| From: Johanna Oksala (Political Philosophy: all that matters [2013], Ch.7) | |
| A reaction: [He cites these as the common modern criticisms] The defence is to explain the value of each of these in utilitarian terms. There is a general problem (conceded by Mill) of motivation in utilitarianism. There's not much in it for me! |