[G] Not, of course, in human experience, which is incapable of containing the heart of a flea, much less what may be endured in remoter spheres. But if an intelligence were constructed ad hoc there is nothing real that might not fall within the scope of experience. The difference between existence and truth on the one side and knowledge or representation on the other may be reduced to this: that knowledge brings what exists or what is true under apperception, while being diffuses what is understood into an impartial subsistence. As truth is indistinguishable from an absolute motionless intellect, which should no longer be a function of life but merely a static order, so existence is indistinguishable from an absolute motionless experience, which should no longer be a foreshortening or representation of anything. This existence would be motionless in the sense that it would “mark time,” for of course every fact in it might be a fact of transition. The whole system, however, would have a static ideal constitution, since the fact that things change in a certain way or stand in a certain order is as much a fact as any other; and it is not a logical necessity, either, but a brute matter of fact that might well have been otherwise.
CHAPTER VII
DIALECTIC
Dialectic elaborates given forms.
The advantage which the mechanical sciences have over history is drawn from their mathematical form. Mathematics has somewhat the same place in physics that conscience has in action; it seems to be a directive principle in natural operations where it is only a formal harmony. The formalistic school, which treats grammar in all departments as if it were the ground of import rather than a means of expressing it, takes mathematics also for an oracular deliverance, springing full-armed out of the brain, and setting up a canon which all concrete things must conform to. Thus mathematical science has become a mystery which a myth must be constructed to solve. For how can it happen, people ask, that pure intuition, retreating into its cell, can evolve there a prodigious system of relations which it carries like a measuring-rod into the world and lo! everything in experience submits to be measured by it? What pre-established harmony is this between the spinning cerebral silkworm and nature’s satins and brocades?
If we but knew, so the myth runs, that experience can show no patterns but those which the prolific Mind has woven, we should not wonder at this necessary correspondence. The Mind having decreed of its own motion, while it sat alone before the creation of the world, that it would take to dreaming mathematically, it evoked out of nothing all formal necessities; and later, when it felt some solicitation to play with things, it imposed those forms upon all its toys, admitting none of any other sort into the nursery. In other words, perception perfected its grammar before perceiving any of its objects, and having imputed that grammar to the materials of sense, it was able to perceive objects for the first time and to legislate further about their relations.
The most obvious artifices of language are often the most deceptive and bring on epidemic prejudices. What is this Mind, this machine existing prior to existence? The mind that exists is only a particular department or focus of existence; its principles cannot be its own source, much less the source of anything in other beings. Mathematical principles in particular are not imposed on existence or on nature ab extra, but are found in and abstracted from the subject-matter and march of experience. To exist things have to wear some form, and the form they happen to wear is largely mathematical. This being the case, the mind in shaping its barbarous prosody somewhat more closely to the nature of things, learns to note and to abstract the form that so strikingly defines them. Once abstracted and focussed in the mind, these forms, like all forms, reveal their dialectic; but that things conform to that dialectic (when they do) is not wonderful, seeing that it is the obvious form of things that the mind has singled out, not without practical shrewdness, for more intensive study.
Forms are abstracted from existence by intent.
The difference between ideal and material knowledge does not lie in the ungenerated oracular character of one of them in opposition to the other; in both the data are inexplicable and irrational, and in both investigation is tentative, observant, and subject to control by the subject-matter. The difference lies, rather, in the direction of speculation. In physics, which is at bottom historical, we study what happens; we make inventories and records of events, of phenomena, of juxtapositions. In dialectic, which is wholly intensive, we study what is; we strive to clarify and develop the essence of what we find, bringing into focus the inner harmonies and implications of forms—forms which our attention or purpose has defined initially. The intuitions from which mathematical deduction starts are highly generic notions drawn from observation. The lines and angles of geometers are ideals, and their ideal context is entirely independent of what may be their context in the world; but they are found in the world, and their ideals are suggested by very common sensations. Had they been invented, by some inexplicable parthenogenesis in thought, it would indeed have been a marvel had they found application. Philosophy has enough notions of this inapplicable sort—usually, however, not very recondite in their origin—to show that dialectic, when it seems to control existence, must have taken more than one hint from the subject world, and that in the realm of logic, too, nothing submits to be governed without representation.