Note 160 — Chapter XVI · DISPLACEMENT OF THE SYNTACTICAL DISTRIBUTION.

It is altogether unimportant that, in the case of such a sentence as the one which we took for our example, the ultimate result, as far as the understanding of the meaning goes, makes practically very little, if any, difference. Thus, we teach a child that three times five and five times three are the same, because the ultimate result of bringing together three fives or five groups of three each is identical. Still, no one will deny that, for correct conception of the operation, there is an important difference between—

..... ..... ..... and— ... ... ... ... ...

or maintain that the understanding of this difference is of no importance for the theory. Nay, even in practical life there would be a great difference between going thrice, e.g., to fetch five apples at a time, and making five journeys for three apples each time. Yet every one admits that 3 × 5 = 5 × 3 is a ‘truth’ generally quite ‘true enough.’