"Those numbers... independent of the particular things which happen to undergo counting—of what are these... ? To pose this question means to raise the problem of "scientific" arithmetic or logistic. ...we are no longer interested in the requirements of daily life ...now our concern is rather with understanding the very possibility of this activity, with understanding... that knowing is involved and that there must... be a corresponding being which possesses that permanence of condition which first makes it capable of being "known." But the soul's turning away from the things of daily life, the changing of the direction... the "conversion" and "turning about"... leads to a further question... What is required is an object which has a purely noetic character and which exhibits at the same time... the countable... This requirement is exactly fulfilled by the "pure" units, which are "nonsensual," accessible only to the understanding, indistinguishable from one another, and resistant to all participation. The "scientific" arithmetician and logistician deals with numbers of pure monads. And... Plato stresses emphatically that there is "no mean difference" between these and the ordinary numbers. ...Only a careful consideration of the fact... forces us into the further supposition that there must indeed be a special "nonsensual" material to which these numbers refer. The immense propaedeutic importance... within Platonic doctrine is immediately clear, for is not a continual effort made in this doctrine to exhibit as the true object of knowing that which is not accessible to the senses? Here we have indeed a "learning matter"... "capable of hauling [us] toward being". It forces the soul to study, by thought alone, the truth as it shows itself by itself. ...ability to count and to calculate presupposes the existence of "nonsensual" units. Thus an unlimited field of "pure" units presents itself to the view of the "scientific" arithemetician and logistician."