Full Idea
The arithmetic of the many computes sums of unequal units, such as two armies, or two herds, ..but philosopher's arithmetic computes when it is guaranteed that none of those infinitely many units differed in the least from any of the others.
Gist of Idea
Daily arithmetic counts unequal things, but pure arithmetic equalises them
Source
Plato (Philebus [c.354 BCE], 56d)
Book Reference
Plato: 'Complete Works', ed/tr. Cooper,John M. [Hackett 1997], p.446
A Reaction
But of course 'the many' are ironing out the differences too, when they say there are 'three armies'. Shocking snob, Plato. Even philosophers are interested in the difference between three armies and three platoons.