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We now proceed to determine clearly our notion of a synthesis which can never be complete. 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.
Other similarities, such as they are, may without impropriety, perhaps, be attributed to the ideals progressus. Hindu and Chaldean beliefs constitute the two primal inspirational faiths. From the one, Buddhism and Zoroasterism developed. From the other the creed of Israel and possibly that of Egypt came. Religions that followed were afterthoughts of the divine.
Inde partim asper, partimnavigia patiens; mox pracipiti cursu progressus, inter occursantes scopulos non fluere immenso fragore creditur, sed ruere. Bis in anno, certis diebus auctu magno per totam spatiatus Agyptum, foecundus innatat terris.
According to the idea of reason, the whole past time, as the condition of the given moment, is necessarily cogitated as given. But, as regards space, there exists in it no distinction between progressus and regressus; for it is an aggregate and not a series its parts existing together at the same time.
It differs, however, in this respect from that of time, that the side of the conditioned is not in itself distinguishable from the side of the condition; and, consequently, regressus and progressus in space seem to be identical.
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.
And so he went to the Latin School at Freising. The first three years were all right. Nothing brilliant, but good enough so he could show his reports at the parsonage when he came home for vacations. And when the priest read that Matthew Fottner was of moderate talent and industry and was making sufficient progress, he would say each time in his fat voice: magnos progressus fecisti, discipule!
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.
One must appeal to immense opposing forces, in order to thwart this natural, all-too-natural PROGRESSUS IN SIMILE, the evolution of man to the similar, the ordinary, the average, the gregarious to the IGNOBLE !
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.