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13737
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The empiricist says that metaphysics is meaningless, rather than false [Schlick]
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Full Idea:
The empiricist does not say to the metaphysician 'what you say is false', but 'what you say asserts nothing at all!' He does not contradict him, but says 'I don't understand you'.
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From:
Moritz Schlick (Positivism and Realism [1934], p.107), quoted by Jonathan Schaffer - On What Grounds What 1.1
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A reaction:
I take metaphysics to be meaningful, but at such a high level of abstraction that it is easy to drift into vague nonsense, and incredibly hard to assess what is meant, and whether it is correct. The truths of metaphysics are not recursive.
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22028
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Unity emerges from understanding particulars, so understanding is prior to seeing unity [Schleiermacher]
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Full Idea:
We only gradually arrive at the knowledge of the inner unity via the understanding of individual utterances, and therefore the art of explication is also presupposed if the inner unity is to be found....The task is infinite, and can never be accomplished.
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From:
Friedrich Schleiermacher (works [1825], p.235), quoted by Terry Pinkard - German Philosophy 1760-1860 06
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A reaction:
[p.235 in ed Bowie 1998] This is the first statement of the hermeneutic circle, which needs whole to grasp parts, and parts to grasp whole. Personally I think the dangers of circles in philosophy are greatly exaggerated.
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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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