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expression of a [511] progressus in indefinitum only. Without losing any time in the examination of the reasons which may have suggested such a distinction, and of its useful or useless application, I shall at once endeavour to define these concepts accurately for my own purpose. Of a straight line it can be said correctly that it may be [416] produced to infinity; and here the distinction between an infinite and an indefinite progress (progressus in indefinitum) would be mere subtilty. No doubt, if we are told to carry on a line, it would be more correct to add in indefinitum, than in infinitum, because the former means no more than, produce it as far as you wish, but the second, you shall never cease producing it (which can never be intended). Nevertheless, if we speak only of what is possible, the former expression is quite correct, because we can always make it longer, if we like, without end. The same applies in all cases where we speak only of the progressus, that is, of our proceeding from the condition to the conditioned, for such progress proceeds in the series of phenomena without end. From a given pair of parents we may, in the descending line of generation, proceed without end, and conceive quite well that that line should so continue in the world. For here reason never requires an absolute totality of the series, [512] because it is not presupposed as a condition, and as it were given (datum), but only as something conditioned, that is, capable only of being given (dabile), and can be added to without end. The case is totally different with the problem, how far the regressus from something given as conditioned may ascend in a series to its conditions; whether I may call it a regressus into the infinite, or only into the indefinite (in indefinitum; and whether I may ascend, for instance, from the men now living, through the series of their ancestors, in infinitum; or whether I may onlysay that, so far as I have gone back, I have nevermet with an empirical ground for considering the series limited anywhere, so that i hil justified, and at the same time obliged [417] to search for an ancestor of every one of these ancestors, though not to presuppose them. I say, therefore, that where the whole is given in empirical intuition, the regressus in the series of its internal conditions proceeds in infinitum, while if a member only of a series is given, from which the regressus to the absolute totality has first to be carried out, the regressus is only in indefinitum. Thus we must [513] saythat the division of matter, as given between its limits(a body), goes on in infinitum, because that matter is complete and therefore, with all its possible parts, given in empirical intuition. As the condition of that whole consists in its part, and the condition of that part in the part of that part, and so on, and as in this regressus of decomposition we never meet with an unconditioned (indivisible) member of that series of conditions, there is nowhere an empirical ground for stopping the division; nay, the further members of that continued division are themselves empirically given before the continuation of the division, and therefore the division goes on in infinitum. The series of ancestors, on the contrary, of any given man, exists nowhere in its absolute totality, in any possible experience, while the regressus goes on from every link in the generation to a higher one, so that no empirical limit can be found which should represent a link as .