So-called conversion of quantity into quality.
A mental fact, afterwards called the transition from quantity to quality, or the conversion of quantity into quality, has certainly been known since ancient times. This transition finds a parallel in those logical diversions, in which, granted the admission, apparently as legitimate as it is slight, that by the removal of a single hair from the head of a luxuriantly haired individual, that individual does not become bald, or that by the removal of a single grain from a heap, the heap does not disappear, one hair or one grain after another is removed, and he of the luxuriant locks becomes bald and for the heap is substituted the bare ground. But the error is in reality contained entirely in the first admission. A man with a head of hair or a heap of grain are what they are, so long as nothing in them is changed. The change of quantity is translated into change of quality, not because the first concept is constitutive of the second, but, on the contrary, because the second is constitutive of the first. Quantity has been obtained, measurement has been effected, by starting from quality, determined in the pure individual judgment and made homogeneous in the empirical judgment, which is the basis of the judgment of enumeration and of measurement. Thus quality constitutes the only real content of the abstract quantitative concept. By the taking away of the hair or the grain, quality itself is changed through the quantitative formula. That is to say, quantity does not pass into quality, but one quality passes into another quality. Quantity, taken by itself, as an abstract determination, is impotent in presence of the real.
Mathematical space and time and their abstraction.
A final observation, suggested by the difference between pure individual judgments (or judgments of reality and value, if it please you so to call them), and quantitative or empirico-abstract judgments, is that the entire conception of things as occupying various portions of space and following one another in a discontinuous manner, separated from one another in time, is derived from the last type of pseudojudgments, namely the quantitative. It is an alteration effected for practical ends from the ingenuous view offered by pure perception. To show, as we have shown, the genesis of quantitative judgments and so of mathematical space and time, amounts to describing their nature and giving their definition. It amounts to revealing them as thoughts of abstractions, which are not to be confounded with real thought, or with genuine thought of reality. The Kantian concept of the ideality of time and space gives the same result. This doctrine is among the greatest discoveries of history, and should be accepted by every philosophy worthy of the name. In accepting it ourselves, we make but one reservation (justified by the proofs given above), namely, that the character of mathematical space and time should be called not ideality (because ideality is true reality), but rather unreality or abstract ideality, or, as we prefer to call it, abstractness.