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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22306
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To explain false belief we should take belief as relating to a proposition's parts, not to the whole thing [Russell]
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Full Idea:
To explain belief in what is false we shall have to regard what is called belief in a proposition as not a thought related to the proposition, but rather as a thought related to the constituents of the proposition.
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From:
Bertrand Russell (Papers of 1906 [1906], V.321), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 40 '1906'
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A reaction:
Russell proposed a new theory of judgement, in order to explain erroneous judgements, given that true propositions are identical with facts. Of course there might be errors about the constituents, as well as about their structure. Othello is his example.
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