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Single Idea 10280

[from 'Philosophy of Mathematics' by Stewart Shapiro, in 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism ]

Full Idea

For each stone, there is at least one pattern such that the stone is a position in that pattern. The stone can be treated in terms of places-are-objects, or places-are-offices, to be filled with objects drawn from another ontology.

Clarification

His 'offices' are like offices of government, which can be held by varied persons

Gist of Idea

A stone is a position in some pattern, and can be viewed as an object, or as a location

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 8.4)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.259


A Reaction

I believe this is the story J.S. Mill had in mind. His view was that the structures move off into abstraction, but it is only at the empirical and physical level that we can possibly learn the structures.