## §5. The Divisions of Philosophy

276. The question, however, is, What is the natural mode of measuring time? Has it absolute beginning and end, and does it reach or traverse infinity? Take time in the abstract and the question is merely mathematical. But we are considering a department of philosophy that wants to know how it is, not with pure mathematical time, but with the real time of history's evolution. This question concerns that evolution itself, not the abstract mathematical time. We observe the universe and discover some of its laws. Why, then, may we not discover the mode of its evolution? Is that mode of evolution, so far as we can discover, of such a nature that we must infer that it began and will end, whether this beginning and this end are distant from us by a finite number of days, hours, minutes, and seconds, or infinitely distant? In order to aid the reader in conceiving of a department of study which should make use of the discoveries of science to settle questions about the character of time as a whole, I have drawn three varieties of spirals.1) The first of these has the equation θ = (360•/Log 3)log((r-1 inch)/(3 inches-r)). Imagine each revolution round the centre of the pencil point tracing the spirals, to represent the lapse of a year or any other cycle of time; and let r, the radius vector, represent the measure of the degree of evolution of the universe — it is not necessary to attach any more definite idea to it. Then, if the universe obeys this law of evolution, it had an absolute beginning at a point of time in the past immeasurable in years. The degree of its stage of evolution was from the very first a positive quantity, 1; which constantly increases toward 3 which it will never surpass until its final destruction in the infinitely distant future. The second spiral is not strictly logarithmic. Its equation is θ = 360• tan ((90•r)/(1 inch)) Here again the universe is represented improving from a stage where r = 1 in the infinitely distant past to a stage where r = 3 in the infinitely distant future. But though this is infinitely distant when measured in years, evolution does not stop here, but continues uninterruptedly; and after another infinite series of years, r = 5; and so on endlessly. We must not allow ourselves to be drawn by the word »endless« into the fallacy of Achilles and the tortoise. Although, so long as r has not yet reached the value 3, another year will still leave it less than 3, yet if years do not constitute the flow of time, but only measure that flow, this in no wise prevents r from increasing in the flow of time beyond 3; so that it will be a question of fact whether or not, so far as we can make it out, the law of general evolution be such as to carry the universe beyond every fixed stage or not. It is very curious that in this case we can determine at exactly what season of the year in the infinitely distant future the value of r changes from being infinitesimally less to being infinitesimally more than 3. In the third spiral, of which the equation is 1/( r -1/2 inch) = 3 log (1 + anti-log (90•/(θ-90•)), the universe was created a finite number of years ago in a stage of evolution represented by r = 1/2, and will go on for an infinite series of years approximating indefinitely to a state where r = 2, after which it will begin to advance again, and will advance until after another infinite lapse of years it will then in a finite time reach the stage when r = 3 1/2, when it will be suddenly destroyed. This last spiral is much the most instructive of the three; but all are useful. The reader will do well to study them.

277. Whether it is possible to make any scientific study of such questions and of the corresponding questions concerning physical geometry is a problem into which careful inquiry will have to be made in a subsequent chapter.1) I must assume that my reader will desire to have this difficult problem cleared up; for if he is still in that stage of intellectual development in which he holds that he has already reached infallible conclusions on certain points, e.g., that twice two makes four, that it is bad manners to marry one's grandmother, that he exists, that yesterday the sun set in the west, etc., so that to hear them seriously doubted fills him with disgust and anger (a little merriment could, perhaps, hardly be suppressed, and would not imply absolute infallibility), he cannot yet gain much from the perusal of this book, and had better lay it aside. Meantime, while it is still doubtful whether or not any knowledge of this kind is attainable, in view of the extreme interest of the questions, and in view of the fact that men of no small intellectual rank are endeavoring to illuminate them, we should by all means leave, for the present, a lodging for this group of studies in our scheme of classification.

278. One might well ask, however, whether their proper place is in philosophy or not rather in idioscopy, since they rest in part upon special observation. Every department of idioscopy builds upon philosophy, as we have seen. How then are these studies not idioscopic? Or, if they are not that, why not treat them as the zoölogists treat the tunicates, which, being neither strictly vertebrates nor by any means worms, are held to constitute a separate branch of the animal kingdom? As to that, I confess I am a little sceptical as to the decision of the zoölogists. But keeping to our proper question, every department of idioscopy is based upon special observation, and only resorts to philosophy in order that certain obstacles to its pursuing its proper special observational inquiries may be cleared out of the way. The sciences which we are now considering, on the contrary, are based upon the same sort of general experience upon which philosophy builds; and they only resort to special observation to settle some minute details, concerning which the testimony of general experience is possibly insufficient. It is true that they are thus of a nature intermediate between coenoscopy and idioscopy; but in the main their character is philosophical. They form, therefore, a second subclass of philosophy, to which we may give the name of theôrics. As inquiry now stands, this subclass has but two divisions which can hardly rank as orders, but rather as families, chronotheory and topotheôry. This kind of study is in its first infancy. Few men so much as acknowledge that it is anything more than idle speculation. It may be that in the future the subclass will be filled up with

other orders.

279. The first subclass, that of necessary philosophy, might be called epistêmy, since this alone among the sciences realizes the Platonic and generally Hellenic conception of {epistémé}.P1) Under it, three orders stand out clearly.

280. The first of these is Phenomenology, or the Doctrine of Categories, whose business it is to unravel the tangled skein [of] all that in any sense appears and wind it into distinct forms; or in other words, to make the ultimate analysis of all experiences the first task to which philosophy has to apply itself. It is a most difficult, perhaps the most difficult, of its tasks, demanding very peculiar powers of thought, the ability to seize clouds, vast and intangible, to set them in orderly array, to put them through their exercises. The mere reading of this sort of philosophy, the mere understanding of it, is not easy. Anything like a just appreciation of it has not been performed by many of those who have written books. Original work in this department, if it is to be real and hitherto unformulated truth, is — not to speak of whether it is difficult or not — one of those functions of growth which every man, perhaps, in some fashion exercises once, some even twice, but which it would be next to a miracle to perform a third time.

281. Order II consists of the normative sciences. I wonder how many of those who make use of this term see any particular need of the word »normative.« A normative science is one which studies what ought to be. How then does it differ from engineering, medicine, or any other practical science? If, however, logic, ethics, and esthetics, which are the families of normative science, are simply the arts of reasoning, of the conduct of life, and of fine art, they do not belong in the branch of theoretic science which we are alone considering, at all. There is no doubt that they are closely related to three corresponding arts, or practical sciences. But that which renders the word normative needful (and not purely ornamental) is precisely the rather singular fact that, though these sciences do study what ought to be, i.e., ideals, they are the very most purely theoretical of purely theoretical sciences. What was it that Pascal 1) said? »La vraie morale se moque de la morale.« It is not worth while, in this corner of the book, to dwell upon so prominent a feature of our subject. The peculiar tinge of mind in these normative sciences has already been much insisted upon. It will come out in stronger and stronger colors as we go on.

282. Order III consists of metaphysics,2) whose attitude toward the universe is nearly that of the special sciences (anciently, physics was its designation), from which it is mainly distinguished, by its confining itself to such parts of physics and of psychics as can be established without special means of observation. But these are very peculiar parts, extremely unlike the rest.

 §4. The Divisions of Science - §6. The Divisions of Mathematics

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