8698
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Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
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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.
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From:
report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3
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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'?
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10263
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Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
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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.
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From:
comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3
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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?
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23684
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Morality gives everyone reasons to act, irrespective of their desires [Foot, by Hacker-Wright]
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Full Idea:
In her early work she also defends moral rationalism, which is the idea that morality gives reasons for action to everyone, even those who lack the desire to do what is right.
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From:
report of Philippa Foot (Moral Beliefs [1959]) by John Hacker-Wright - Philippa Foot's Moral Thought Intro
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A reaction:
Evidently a rejection of the Humean view that only a desire can motivate action, including moral action. There is an ongoing debate about whether reasons can cause anything, or motivate anything. I think the contents of reasons pull us towards action.
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23690
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We all have reason to cultivate the virtues, even when we lack the desire [Foot, by Hacker-Wright]
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Full Idea:
Foot advocates the view that anyone has reason to cultivate the virtues, even if they lack the desire to do so at a given moment.
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From:
report of Philippa Foot (Moral Beliefs [1959], Pt II) by John Hacker-Wright - Philippa Foot's Moral Thought 2 'Concepts'
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A reaction:
The view which she soon abandoned, but then returned to later. It specifically repudiates the view of Hume, that only desires can motivate. I'm unsure, because the concept of 'reason' strikes me as too imprecise. She sees self-interest as a reason.
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22379
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The meaning of 'good' and other evaluations must include the object to which they attach [Foot]
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Full Idea:
There is no describing the evaluative meaning of 'good', evaluation, commending, or anything of the sort, without fixing the object to which they are supposed to be attached.
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From:
Philippa Foot (Moral Beliefs [1959], p.112)
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A reaction:
I go further, and say that a specification of the feature(s) of the object that produce the value must also be available (if requested). 'That's a good car, but I've no idea why' makes no sense. 'Apparently that's a good car', if other people know why.
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