ONE:Lawrence smiled as he flicked off the end of his cigarette.Perhaps the processes of logic and mathematics may be adduced as an exception. It may be contended that the genus is prior to the species, the premise to the conclusion,321 the unit to the multiple, the line to the figure, in reason though not in time. And Plotinus avails himself to the fullest extent of mathematical and logical analogies in his transcendental constructions. His One is the starting-point of numeration, the centre of a circle, the identity involved in difference; and under each relation it claims an absolute priority, of which causal power is only the most general expression. We have already seen how a multitude of archetypal Ideas spring from the supreme Nous as from their fountain-head. Their production is explained, on the lines of Platos Sophist, as a process of dialectical derivation. By logically analysing the conception of self-consciousness, we obtain, first of all, Nous itself, or Reason, as the subject, and Existence as the object of thought. Subject and object, considered as the same with one another, give us Identity; considered as distinct, they give us Difference. The passage from one to the other gives Motion; the limitation of thought to itself gives Rest. The plurality of determinations so obtained gives number and quantity, their specific difference gives quality, and from these principles everything else is derived.473 It might seem as if, here at least, we had something which could be called a process of eternal generationa causal order independent of time. But, in reality, the assumed sequence exists only in our minds, and there it takes place under the form of time, not less inevitably than do the external re-arrangements of matter and motion. Thus in logic and mathematics, such terms as priority, antecedence, and evolution can only be used to signify the order in which our knowledge is acquired; they do not answer to causal relations existing among things in themselves. And apart from these two ordersthe objective order of dynamical production in space and time, and the subjective order of intelligibility in thoughtthere is no kind of succession that we can conceive. Eternal relations, if they exist at all, must322 be relations of co-existence, of resemblance, or of difference, continued through infinite time. Wherever there is antecedence, the consequent can only have existed for a finite time.
TWO:207It is not intended to claim that this platen-reversing motion cannot, like any other mechanical movement, be resolved mathematically, but that the mechanical conditions are so obscure and the invention made at a time that warrants the supposition of accidental discovery.
