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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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19509
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The indexical aspect of contextual knowledge might be hidden, or it might be in what 'know' means [Schiffer,S]
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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'.
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From:
Stephen Schiffer (Contextualist Solutions to Scepticism [1996], p.326-7), quoted by Keith DeRose - The Case for Contextualism 1.5
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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.
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8404
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Explain single events by general rules, or vice versa, or probability explains both, or they are unconnected [Field,H]
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Full Idea:
Some think singular causal claims should be explained in terms of general causal claims; some think the order should be reversed; some think a third thing (e.g. objective probability) will explain both; and some think they are only loosely connected.
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From:
Hartry Field (Causation in a Physical World [2003], 2)
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A reaction:
I think Ducasse gives the best account, which is the second option, of giving singular causal claims priority. Probability (Mellor) strikes me as a non-starter, and the idea that they are fairly independent seems rather implausible.
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8401
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Physical laws are largely time-symmetric, so they make a poor basis for directional causation [Field,H]
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Full Idea:
It is sometimes pointed out that (perhaps with a few minor exceptions) the fundamental physical laws are completely time-symmetric. If so, then if one is inclined to found causation on fundamental physical law, it isn't evident how directionality gets in.
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From:
Hartry Field (Causation in a Physical World [2003], 1)
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A reaction:
All my instincts tell me that causation is more fundamental than laws, and that directionality is there at the start. That, though, raises the nice question of how, if causation explains laws, the direction eventually gets left OUT!
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8402
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The only reason for adding the notion of 'cause' to fundamental physics is directionality [Field,H]
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Full Idea:
Although it is true that the notion of 'cause' is not needed in fundamental physics, even statistical physics, still directionality considerations don't preclude this notion from being consistently added to fundamental physics.
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From:
Hartry Field (Causation in a Physical World [2003], 1)
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A reaction:
This only makes sense if the notion of cause already has directionality built into it, which I think is correct. The physicist might reply that they don't care about directionality, but the whole idea of an experiment seems to depend on it (Idea 8363).
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