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10242 | I apply structuralism to concrete and abstract objects indiscriminately |
Full Idea: My own line is a yet more sweeping structuralism (than David Lewis's account of classes), applying to concrete and abstract objects indiscriminately. | |||
From: Willard Quine (Structure and Nature [1992], p.6), quoted by Stewart Shapiro - Philosophy of Mathematics 4.9 | |||
A reaction: Shapiro calls this 'breathtaking', and retreats from it, but it is something like my own view, starting from Mill's pebbles and working up. |
10243 | My ontology is quarks etc., classes of such things, classes of such classes etc. |
Full Idea: My tentative ontology continues to consist of quarks and their compounds, also classes of such things, classes of such classes, and so on. | |||
From: Willard Quine (Structure and Nature [1992], p.9), quoted by Stewart Shapiro - Philosophy of Mathematics 4.9 | |||
A reaction: I would call this the Hierarchy of Abstraction (just coined it - what do you think?). Unlike Quine, I don't see why its ontology should include things called 'sets' in addition to the things that make them up. |