Ideas from 'Structure and Nature' by Willard Quine [1992], by Theme Structure

[found in 'Journal of Philosophy' (ed/tr -) [- ,]].

green numbers give full details    |     back to texts     |     unexpand these ideas


6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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.
7. Existence / D. Theories of Reality / 6. Physicalism
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.