| There are two terms commonly employed for this purpose. |
| These terms are regarded as expressions of different and distinguishable notions, although the ground of the distinction has never been clearly exposed. |
| The term employed by the mathematicians is progressus in infinitum. |
| The philosophers prefer the expression progressus in indefinitum. |
| Without detaining the reader with an examination of the reasons for such a distinction, or with remarks on the right or wrong use of the terms, I shall endeavour clearly to determine these conceptions, so far as is necessary for the purpose in this Critique. |
| We may, with propriety, say of a straight line, that it may be produced to infinity. |
| In this case the distinction between a progressus in infinitum and a progressus in indefinitum is a mere piece of subtlety. |
| For, although when we say, "Produce a straight line," it is more correct to say in indefinitum than in infinitum; because the former means, "Produce it as far as you please," the second, "You must not cease to produce it"; the expression in infinitum is, when we are speaking of the power to do it, perfectly correct, for we can always make it longer if we please--on to infinity. |
| And this remark holds good in all cases, when we speak of a progressus, that is, an advancement from the condition to the conditioned; this possible advancement always proceeds to infinity. |
| We may proceed from a given pair in the descending line of generation from father to son, and cogitate a never-ending line of descendants from it. |
| For in such a case reason does not demand absolute totality in the series, because it does not presuppose it as a condition and as given (datum), but merely as conditioned, and as capable of being given (dabile). |
| Very different is the case with the problem; "How far the regress, which ascends from the given conditioned to the conditions, must extend"; whether I can say; "It is a regress in infinitum," or only "in indefinitum"; and whether, for example, setting out from the human beings at present alive in the world, I may ascend in the series of their ancestors, in infinitum--mr whether all that can be said is, that so far as I have proceeded, I have discovered no empirical ground for considering the series limited, so that I am justified, and indeed, compelled to search for ancestors still further back, although I am not obliged by the idea of reason to presuppose them. |
| My answer to this question is; "If the series is given in empirical intuition as a whole, the regress in the series of its internal conditions proceeds in infinitum; but, if only one member of the series is given, from which the regress is to proceed to absolute totality, the regress is possible only in indefinitum." For example, the division of a portion of matter given within certain limits--of a body, that is--proceeds in infinitum. |
| For, as the condition of this whole is its part, and the condition of the part a part of the part, and so on, and as in this regress of decomposition an unconditioned indivisible member of the series of conditions is not to be found; there are no reasons or grounds in experience for stopping in the division, but, on the contrary, the more remote members of the division are actually and empirically given prior to this division. |
| That is to say, the division proceeds to infinity. |
| On the other hand, the series of ancestors of any given human being is not given, in its absolute totality, in any experience, and yet the regress proceeds from every genealogical member of this series to one still higher, and does not meet with any empirical limit presenting an absolutely unconditioned member of the series. |
| But as the members of such a series are not contained in the empirical intuition of the whole, prior to the regress, this regress does not proceed to infinity, but only in indefinitum, that is, we are called upon to discover other and higher members, which are themselves always conditioned. |
| In neither case--the regressus in infinitum, nor the regressus in indefinitum, is the series of conditions to be considered as actually infinite in the object itself. |
| This might be true of things in themselves, but it cannot be asserted of phenomena, which, as conditions of each other, are only given in the empirical regress itself. |
| Hence, the question no longer is, "What is the quantity of this series of conditions in itself--is it finite or infinite?" for it is nothing in itself; but, "How is the empirical regress to be commenced, and how far ought we to proceed with it?" And here a signal distinction in the application of this rule becomes apparent. |
| If the whole is given empirically, it is possible to recede in the series of its internal conditions to infinity. |