If classification does not imply understanding things and assigning to them their value, neither does enumeration imply intelligence and comprehension, because it consists of a manipulation, which is altogether extrinsic and indifferent to the quality of the things enumerated. That given objects are capable of enumeration or measurable as ioo, or iooo, or 10,000 reveals nothing as to their character. It is only as the result of gross illusion that value is sometimes believed to be a function of number, and that value increases or diminishes with the increase or diminution of number. The common saying that number is not quality is a good answer to that illusion. [Sidenote: _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. [Sidenote: _Mathematical space and time and their abstraction._]