more from John Stuart Mill

Single Idea 9799

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

Full Idea

'Three is two and one' presupposes that collections of objects exist, which while they impress the senses thus, ¶¶¶, may be separated into two parts, thus, ¶¶ ¶. This being granted, we term all such parcels Threes.

Gist of Idea

3=2+1 presupposes collections of objects ('Threes'), which may be divided thus

Source

John Stuart Mill (System of Logic [1843], 2.6.2)

Book Reference

Mill,John Stuart: 'System of Logic (9th ed, 2 vols)' [Longmans, Green etc 1875], p.296


A Reaction

Mill is clearly in trouble here because he sticks to simple arithmetic. He must deal with parcels too big for humans to count, and parcels so big that they could not naturally exist, and that is before you even reach infinite parcels.