Single Idea 9805

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism]

Full Idea

When we say 12 is the cube of 1728, we affirm that if we had sufficient pebbles, we put them into parcels or aggregates called twelves, and put those twelves into similar collections, and make twelve of these largests parcels, we have the aggregate 1728.

Gist of Idea

12 is the cube of 1728 means pebbles can be aggregated a certain way

Source

John Stuart Mill (System of Logic [1843], 3.24.5)

Book Reference

Mill,John Stuart: 'System of Logic (9th ed, 2 vols)' [Longmans, Green etc 1875], p.152


A Reaction

There is always hidden modal thinking in Mill's proposals, despite his longing to stick to actual experience. Imagination actually plays a much bigger role in his theory than sense experience does.