Monday, March 21, 2011
Phenomenology of Spirit, Preface, paragraph 46
Nor does immanent, so-called pure mathematics, oppose time as time to space, as a second material for its consideration. Applied mathematics, no doubt, treats of time, as also of motion, and other actual things as well; but it picks up from experience synthetic propositions – i.e. statements of their relations, which are determined by their concept – and merely applies its formulae to these conditions. That the so-called proofs of propositions such as those concerning the equilibrium of the lever, the relation of space and time in gravitation, etc., which applied mathematics frequently gives, should be taken and given as proofs, is itself merely a proof of how great the need is for cognition to have a process of proof, seeing that, even where it has no proof, it yet esteems the mere semblance of it, and thereby gains a certain satisfaction. A criticism of those proofs would be as instructive as it would be significant, if the criticism could purify mathematics of this false finery, partly to indicate its limits, and thence the necessity for another type of knowledge. As to time, which, one is to believe, is to constitute, as counterpart to space, the material of the other division of pure mathematics, this is the concept-in-existence itself. The principle of quantity, the concept-less distinction, and the principle of equality, of abstract lifeless unity, are incapable of dealing with that sheer restlessness of life and absolute distinction. This negativity only becomes the second material of this cognition, then, as paralyzed, namely, as the unit, which, it being an external operation, degrades what is self-moving to the level of mere matter, in order thus to get an indifferent, external, lifeless content.