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Single Idea 10217

[from 'Philosophy of Mathematics' by Stewart Shapiro, in 18. Thought / E. Abstraction / 3. Abstracta by Ignoring ]

Full Idea

One way to apprehend a particular structure is through a process of pattern recognition, or abstraction. One observes systems in a structure, and focuses attention on the relations among the objects - ignoring features irrelevant to their relations.

Gist of Idea

We can apprehend structures by focusing on or ignoring features of patterns

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 3.1)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.74


A Reaction

A lovely statement of the classic Aristotelian abstractionist approach of focusing-and-ignoring. But this is made in 1997, long after Frege and Geach ridiculed it. It just won't go away - not if you want a full and unified account of what is going on.