- Alexander the Commentator defined synthesis as a progress from principles to consequences, analysis as a regress from consequences to principles; and Latin logicians preserved the same distinction between the progressus a principiis ad principiata, and the regressus a principiatis ad principia.
If we reject the infinite regress and the circle in proof (circulus in probando) which resolves itself ultimately into proving A by B and B by A, 7 we are confronted by the need for principles of two kinds, those which condition all search scientific for truth, and those which are the peculiar or proper principles.
Even so the inference to the a priori ground of its necessity is, it has been often pointed out, subject to the limitation inherent in any process of reduction, in any regress, that is, from conditionate to condition, viz.
If, then, there is objective truth at all, the existence of real facts must be made known to us otherwise than through the logical faculty of thought; and, as the regress from conclusion to premises must depend upon something not itself capable of logical grounding, mediate thought implies the consciousness of immediate truth.
Once applied to the facts at all, it would drive us beyond the first antecedent or term of antecedents of volition to a still further cause or ground - in fact, land us in an infinite regress of causes.
The former should be regarded as asserting that the whole is, not temporally, but logically, subsequent to the part, and that therefore there is an infinite regress in the notion of a whole which is infinitely divisible - a view which at any rate demands a serious refutation.