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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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13745
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Supervenience is not a dependence relation, on the lines of causal, mereological or semantic dependence [Kim]
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Full Idea:
It is a mistake, or at least misleading, to think of supervenience itself as a special and distinctive type of dependence relation, alongside causal dependence, mereological dependence, semantic dependence, and others.
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From:
Jaegwon Kim (Postscripts on supervenience [1993], 2)
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A reaction:
The point, I take it, is that supervenience is something which requires explanation, rather than being a conclusion to the debate. Why are statues beautiful? Why do brains generate minds?
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7388
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McGinn invites surrender, by saying it is hopeless trying to imagine conscious machines [Dennett on McGinn]
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Full Idea:
McGinn invites his readers to join him in surrender: It's just impossible to imagine how software could make a conscious robot. Don't even try, he says. Other philosophical experiments (involving China) "work" by dissuading readers from imagining.
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From:
comment on Colin McGinn (The Problem of Consciousness [1991]) by Daniel C. Dennett - Consciousness Explained 14.1
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A reaction:
I agree with Dennett. If you don't try to imagine how robots might do it, you are also denied the right to try to imagine how brains might manage it. Admittedly this is hard, but good imagination needs study, effort, discussion, time, information...
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