John Locke

“ This further is observable in number, that it is that which the mind makes use of in measuring all things that by us are measurable, which principally are expansion and duration ; and our idea of infinity, even when applied to those, seems to be nothing but the infinity of number. ”

“ That the mind distinguish carefully two ideas, which are different one from another only by the addition or subtraction of one unit : (2) That it retain in memory the names or marks of the several combinations, from an unit to that number ; and that not confusedly, and at random, but in that exact order that the numbers follow one another. In either of which, if it trips, the whole business of numbering will be disturbed, and there will remain only the confused idea of multitude, but the ideas necessary to distinct numeration will not be attained to. ”

“ For, the several simple modes of numbers being in our minds but so many combinations of units, which have no variety, nor are capable of any other difference but more or less, names or marks for each distinct combination seem more necessary than in any other sort of ideas. For, without such names or marks, we can hardly well make use of numbers in reckoning, especially where the combination is made up of any great multitude of units ”

“ The simple modes of number are of all other the most distinct ; every the least variation, which is an unit, making each combination as clearly different from that which approacheth nearest to it, as the most remote ”

“ Because the ideas of numbers are more precise and distinguishable than in extension ; where every equality and excess are not so easy to be observed or measured ; because our thoughts cannot in space arrive at any determined smallness beyond which it cannot go, as an unit ”

“ Amongst all the ideas we have, as there is none suggested to the mind by more ways, so there is none more simple, than that of unity, or one : it has no shadow of variety or composition in it : every object our senses are employed about ; every idea in our understandings ”

“ So that he that can add one to one, and so to two, and so go on with his tale, taking still with him the distinct names belonging to every progression ; and so again, by subtracting an unit from each collection, retreat and lessen them, is capable of all the ideas of numbers within the compass of his language, or for which he hath names, though not perhaps of more. ”

“ And some, through the default of their memories, who cannot retain the several combinations of numbers, with their names, annexed in their distinct orders, and the dependence of so long a train of numeral progressions, and their relation one to another, are not able all their lifetime to reckon, or regularly go over any moderate series of numbers. ”