Single Idea 10248

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism]

Full Idea

According to 'in re' structuralism, a statement that appears to be about numbers is a disguised generalization about all natural-number sequences; the numbers are bound variables, not singular terms.

Clarification

'In re' means the structures are in the entities, rather than preceding them

Gist of Idea

Number statements are generalizations about number sequences, and are bound variables

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 5.3.4)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.166


A Reaction

Any theory of anything which comes out with the thought that 'really it is a variable, not a ...' has my immediate attention and sympathy.