Transcriber's Notes

Obvious typographical errors have been silently corrected.

Variations in hyphenation have been standardised, but other variations in spelling, accents and punctuation are as in the original.

There are several very wide tables in the book (e.g. Table A is 16 columns/380 characters wide). These have been divided into blocks of 3 or 4 columns. The row alignment has been preserved and, where appropriate. the 1st column repeated for each block.

Where the use of ditto (") has been intermittent in tables, it is been replaced by the word represented.

The Errata and Corrigenda have been implemented, except for the final item:

For the words evolution and evolved, read passim in the Botanical and Zoological parts, perfection and perfected, as the text may require.

THE

RAY SOCIETY.

INSTITUTED MDCCCXLIV.

LONDON.

MDCCCXLVII.

ELEMENTS
OF
PHYSIOPHILOSOPHY.

BY

LORENZ OKEN, M.D.

PROFESSOR OF NATURAL HISTORY AT THE UNIVERSITY OF ZÜRICH; &c. &c.

FROM THE GERMAN

BY

ALFRED TULK,

MEMBER OF THE ROYAL COLLEGE OF SURGEONS OF ENGLAND.

LONDON:
PRINTED FOR THE RAY SOCIETY.
MDCCCXLVII.

C. AND J. ADLARD, PRINTERS,
BARTHOLOMEW CLOSE.

"Of all truths relating to phenomena, the most valuable to us are those which relate to the order of their succession. On a knowledge of these is founded every reasonable anticipation of future facts, and whatever power we possess of influencing those facts to our advantage. Even the laws of geometry are chiefly of practical importance to us as being a portion of the premises from which the order of the succession of phenomena may be inferred."

John Stuart Mill.

Begun in the autumn of the year 1845, without the cognizance, or at the suggestion of a single human being, the present Translation is due to the fact of its original having encountered a somewhat kindred spirit, and aroused therein the desire to render others participant, if possible, in the large amount of instruction it is so well calculated to afford. And now that the work is done, what remains for the labourer at second-hand to say by way of preamble to his newly-dressed wares? Had the book been printed within the pale of a philosophical or physico-theological sect, the Translator's final duty would have been clearly enough prescribed. Already bound to the profession of "particular tenets," his main object would be to indulge in a laudatory but servile abstract of his author's doctrines, or, if having set out with the expressed intention of illustrating their bearings upon the state of science past, present, and to come, he would become so drunk beforehand with the large and unbridled potation of his creed, as to surprise the casual reader by informing him that such an intention is useless, for the two stand in direct antithesis to each other. Examples of this mode of procedure are not wanting at the present day, whether at home or abroad. They are the produce of that spirit, which, rife enough in the Middle Ages, has been so graphically described by Professor Whewell under the title of the "Commentatorial," and "whose professed object is to explain, to enforce, to illustrate doctrines assumed to be true, but not to obtain additional truths or new generalizations." While from dealings of this character, as being utterly opposed to the sacred cause of Truth, I turn away with feelings of repugnance, to which the lessons of some personal experience have lent their aid, it is not my business, upon the other hand, to enter the lists of controversy against those who, having neither the capacity, nor the desire of its cultivation, for the higher walks of science, delight to dismiss a work of the present kind with some idle anathema of mysticism or evasive outcry for more facts.

I refrain from essaying to give any condensed formula or outline[A] of Professor Oken's Physio-philosophy: first, because its leading points have been already noted in his own prefaces to the German work and its translation; secondly, because the book will, I trust, best speak for itself to those who shall come with minds unprejudiced and duly prepared, each one in his particular department, to its study; and, lastly, because any such attempt would necessarily involve an amount of historical and critical details, which must be here superficially treated and so misplaced. Suffice it to observe, that the present work stands alone in Germany, as being the most practical application upon a systematic scale of the principles advanced by Schelling, more especially in the Mathesis and Ontology; for the concluding part or Biology stands almost "per se." As such it will form, apart from other and higher considerations, a readily available introduction to the writings upon similar subjects of Carus, Steffens, Hegel and others, and may induce further attempts to render, by translation or history, the English student familiar with much of what at present is known only by scattered fragments in journals, or through the medium of reviews. From what has been said, the reader will be at no loss to discern in what light the Translator humbly desires to be viewed in reference to the present work. He rests content with the confident hope that its pages will be, at least, found eminently suggestive, that new thoughts will be awakened by facts and their relations being here cast in a fresh mould, that shall stimulate others in the field of inquiry, and open paths hitherto untrod. In this he is but expressing the sentiments of the author himself, and acknowledging what the present time with its accumulating mass of knowledge presses upon us more and more—the necessity of work, wherein abstract science and experience, theory and facts shall advance together, the Ideal in part receiving and reflecting back with increased lustre the light which it has derived from the Real or outward semblance of things.

Meanwhile, it is with no small amount of diffidence and hesitation that the present Translation will quit my hands. Hemmed in by a rigid dialectic terminology upon all sides, I have had difficulties of no ordinary kind to contend with in adapting a language, composed of such varied elements as our own, to meet the requisites of general clearness and conciseness that form so prominent a feature of the German work. If errors and obscurities exist, the blame, it will be observed, attaches to myself, not to the distinguished author. Ill-health has conflicted much with the calmness and repose of mind so indispensable to an undertaking, at once novel in kind and character to the English reader; or otherwise, these (my last labours unto any extent as a Translator) might have been rendered more worthy of the Ray Society and the objects it has in view.

To those who have kindly afforded me assistance in the progress of the work, and to the latter body for undertaking it, I here return many grateful thanks. The Author himself in a letter to the Translator, dated Jan. 12, 1847, acknowledges the acceptance of his work by the Society in the following words:—"The intelligence of my Physio-philosophy having been deemed worthy of translation by so goodly and enlightened a Society, cannot be otherwise unto me than a source of delight."[B]

ALFRED TULK.

[A] For this the reader may be referred to the 3d vol. of Prof. Blainville's Hist. des Sciences de l'Organisation; Par. 1845; or better still, to the sketch (preceded by a view of Schelling's philosophy), which is given by M. Saint-Agy in the Tome Complémentaire of Cuvier's Hist. des Sciences Naturelles, 1845. He there rightly observes of Oken's work, that "pendant les quarante dernières années il n'a presque paru en Allemagne d'ouvrages d'anatomie, de physiologie, de physique et de chimie auxquelles elle n'ait servi de base." For what a master-mind like Oken's is capable of creating, I would especially refer to his theory of the Cranial Homologies, which has been in our own country so beautifully carried out, modified, and proved by the extensive researches of Professor Owen.

[B] "Die Nachricht dass meine Naturphilosophie von einer sociferigen und erleuchteten Gesellschaft der Uebersetzung für würdig erachtet worden ist, konnte nicht anders als mir Freude gewähren."

[AUTHOR'S PREFACE TO THE TRANSLATION.]

It is with no readiness or pleasure that I write introductions of any kind, and usually abstain from doing so, partly because they appear to me like a kind of apology or makeshift for the author, and partly because the contents of the book itself should indicate his status or position. With regard, however, to the history of the work, some few words are certainly requisite for its Translation.

I wrote the first Edition of 1810 in a kind of inspiration, and on that account it was not so well arranged as a systematic work ought to be. Now, although this may appear to have been amended in the second and third edition, yet still it was not possible for me to completely attain the object held in view. The book has therefore remained essentially the same as regards its fundamental principles, such as those concerning the formation of matter, the protoplasmic substance (Schleim-Substanz) and vesicular form of the organic mass, the signification and function of the organs, as also the principles of classification in Minerals, Plants and Animals, so that all this is consequently as old as the first edition. It is only the empirical arrangement into series of plants and animals, that has been modified from time to time in accordance with the scientific elevation of their several departments, or just as discoveries and anatomical investigations have increased and rendered some other position of the objects a matter of necessity. This susceptibility to change will of course be persistent in the future, although the principles themselves should continue wholly unchanged; ay, the very stability of the latter will tend the more to invite the naturalist to the pursuit of empirical inquiries, by determining beforehand in what direction he is to extend his point of view, and thus spare himself the trouble of blindly and laboriously groping about in the dense labyrinth of facts. Such a work therefore as the present can only approximate completion through the progress made in science, and each new edition will supply some defect of its predecessor in the distribution or parcelling out of things.

In the first edition the principle was raised of individual bodies being alone the object of Natural History, and that in the next place they are to be arranged according to the combination of their organs or component parts, and by no means after the division or mere form of a single organ; that, for example, a special organ or anatomical system lies as the basis of each Vegetable and Animal class, and that there must be therefore as many classes, and no more, as there are cardinal organs present upon which to found them. On that account it was absolutely necessary first of all to find out these cardinal organs, and determine their rank; and, in so doing, it was shown that organs and classes are at bottom of one kind, and that the development by stages or degrees of the embryo is the antetype of that of the classes; furthermore, that each class takes its starting-point from below, and consequently that the classes do not stand simply one above the other, but fall into a series of mutually parallel ranks. Now it is this which, along with the doctrine of the infusorio-vesicular form of the organic mass, and that touching the signification of parts, as to how e. g. the blossom is the repetition of the vegetable axis or trunk, the cephalic bones that of the vertebræ, the feet of the branchiæ, and the maxillæ in turn of the feet, appears to me the cardinal point attained in my Philosophy of Nature; more especially, because it was these very doctrines which were first of all, i. e. before all the others, comprehended and almost universally adopted. The inorganic matters and activities pass, however, parallel also to the anatomical formations and functions; and that this is the case too with the spiritual or psychical functions the philosophy of the future will probably be in the condition to point out.

The reader will not expect to find that the serial arrangement of Plants and Animals, with their parallelism, has been in every instance thoroughly attained. The present is but a sample of how we are to proceed in our desire of obtaining a Natural system. With such an attempt one has something to change every year, and I have in the present translation made some alterations in respect to the Mollusca and Fishes. In this sense then it is my wish that the book may be regarded, and accordingly received with its due amount of indulgence.

LORENZ OKEN.

PREFACE.

The first principles of the present work I laid down in my small pamphlet entitled Grundriss der Naturphilosophie, der Theorie der Sinne und der darauf gegrundeten Classification der Thiere; Frankfurt bey Eichenberg, 1802, 8vo (out of print). I still abide by the position there taken, namely, that the Animal Classes are virtually nothing else than a representation of the sense-organs, and that they must be arranged in accordance with them. Thus, strictly speaking, there are only 5 Animal Classes: Dermatozoa, or the Invertebrata; Glossozoa, or the Fishes, as being those animals in whom a true tongue makes for the first time its appearance; Rhinozoa, or the Reptiles, wherein the nose opens for the first time into the mouth and inhales air; Otozoa, or the Birds, in which the ear for the first time opens externally; Ophthalmozoa, or the Thricozoa, in whom all the organs of sense are present and complete, the eyes being moveable and covered with two palpebræ or lids. But since all vegetative systems are subordinated to the tegument or general sense of feeling, the Dermatozoa divide into just as many or corresponding divisions, which, on account of the quantity of their contents, may be for the sake of convenience also termed classes. Thereby 9 classes of the inferior animals originate, but which, when taken together, have only the worth or value of a single class. So much by way of explaining the apparent want of uniformity in the system.

I first advanced the doctrine, that all organic beings originate from and consist of vesicles or cells, in my book upon Generation. (Die Zeugung. Frankfurt bey Wesche, 1805, 8vo.) These vesicles, when singly detached and regarded in their original process of production, are the infusorial mass, or the protoplasma (Ur-Schleim) from whence all larger organisms fashion themselves or are evolved. Their production is therefore nothing else than a regular agglomeration of Infusoria; not of course of species already elaborated or perfect, but of mucous vesicles or points in general, which first form themselves by their union or combination into particular species. This doctrine concerning the primo-constituent parts of the organic mass is now generally admitted or recognised, and I need not, therefore, add anything by way of apology for it or defence.

In mine and Kieser's Beyträgen zur vergleichenden Zoologie, Anatomie und Physiologie; Frankfurt bey Wesche, 1806, 4to, I have shown that the intestines originate from the umbilical vesicle, and that this corresponds to the vitellus. It is true Friedrich Wolf had already discovered it in the chick, but his was only a single instance, and completely forgotten. I have also discovered it and without knowing anything about my being anticipated, since it was nowhere taught. But I have elevated this structure to the light of a general law, and it is that unto which I may fairly lay claim. In the same essay I have introduced into the Physiology the Corpora Wolfiana, or Primordial Kidneys, but, having failed to recognise their signification, any one who pleases may filch away the credit of their bare detection.

In my Essay: Ueber die Bedeutung der Schädelknochen, (Ein Programm beym Antritt der Professur an der Gesammt-Universität zu Jena; Jena gedruckt bey Göpfert, 1807, verlegt zu Frankfurt bey Wesche, 4to,) I have shown that the head is none other than a vertebral column, and that it consists of four vertebræ, which I have respectively named Auditory, Maxillary or Lingual, Ocular and Nasal vertebra; I have also pointed out that the maxillæ are nothing else but repetitions of arms and feet, the teeth being their nails; all this is carried out more circumstantially and in detail in the Isis, 1817, S. 1204; 1818, S. 510., 1823. litt. Anzeigen S. 353 und 441. This doctrine was at first scoffed at and repulsed; finally, when it began to force its way, several barefaced persons came forward, who would have made out if they could, that the discovery was achieved long ago. The reader will not omit to notice that the above essay appeared as my Antritts-Programm, or Inaugural discourse, upon being appointed Professor at Jena.

In my Essay entitled Ueber das Universum als Fortsetzung des Sinnensystems; Jena bey Frommann, 1808, 4to, I showed that the Organism is none other than a combination of all the Universe's activities within a single individual body. This doctrine has led me to the conviction that World and Organism are one in kind, and do not stand merely in harmony with each other. From hence was developed my Mineral, Vegetable and Animal system, as also my philosophical Anatomy and Physiology.

In my Essay entitled Erste Ideen zur Theorie des Lichts, der Finsterniss, der Farben und der Wärme; Jena bey Frommann, 1808, 4to, I pointed out, that the Light could be nothing but a polar tension of the æther, evoked by a central body in antagonism with the planets; and that the Heat were none other than the motion of this æther. This doctrine appears to be still in a state of fermentation.

In my Essay entitled Grundzeichnung des natürlichen Systems der Erze; Jena bey Frommann, 1809, 4to, I arranged the Ores for the first time, not according to the Metals, but agreeably to their combinations with Oxygen, Acids, and Sulphur, and thus into Oxyden, Halden, Glanzen, and Gediegenen. This has imparted to the recent science of Mineralogy its present aspect or form.

In the first edition of my Lehrbuch der Naturphilosophie, 1810 and 1811, I sought to bring these different doctrines into mutual connexion, and to show, forsooth, that the Mineral, Vegetable, and Animal classes are not to be arbitrarily arranged in accordance with single or isolated characters, but to be based upon the cardinal organs or anatomical systems, from which a firmly established number of classes must of necessity result; moreover, that each of these classes commences or takes its starting-point from below, and consequently that all of them pass parallel to each other. This parallelism is now pretty generally adopted, at least in England and France, though with sundry modifications, which, from the principles being overlooked or neglected, are based at random, and are not therefore to be approved of. As in chemistry, where the combinations follow a definite numerical law, so also in Anatomy the organs, in Physiology the functions, and in Natural History the classes, families and even genera of Minerals, Plants and Animals, present a similar arithmetical ratio. The genera are indeed, on account of their great number and arbitrary erection to the rank whose title they bear, not to be circumscribed or limited in every case with due propriety, nor brought into their true scientific place in the system; it is nevertheless possible to render their parallelism with each other clear, and to prove that they by no means form a single ascending series. If once the genera of Minerals, Plants and Animals come to stand correctly opposite each other, a great advantage will accrue therefrom to the science of Materia Medica; for corresponding genera will act specifically upon each other.

These principles, which I have now carried out into detail, were retained in the second, and have been also in the third or present edition of the Physio-philosophy, the arrangement and serial disposition of the natural objects having, with my increase of knowledge and concomitant views of things, been amended, enlarged or diminished, as the case might require, especially in the Mineral, Vegetable and Animal systems. I am very well aware that there is many an object which does not stand in its right place; but where again is there a single system in which this is not still more strikingly the case? We have here dealt only with the restoration of the edifice, wherein, after years of long and oft-repeated attempts, the furniture may for the first time be properly distributed, without detriment to its general bearings or ground plan.

In my Lehrbuch der Naturgeschichte, the Mineralogical and Zoological portions of which are out of print, but the Botanical still to be had (Weimar, Industrie-Comptoir, 1826), I have arranged for the first time the genera and species in accordance with the above principles, and stated everything of vital importance respecting these matters. This was the first attempt to frame a scientific Natural History, and one unto which I have remained true in my last work, the Allgemeine Naturgeschichte, the principles whereof I have sought to develop more distinctly and in detail in the work now before the reader.

Thus then have I prosecuted throughout a long series of years one kind of principle, and worked hard to perfectionate it upon all sides. Yet, notwithstanding my endeavour to amass the manifold stores of knowledge so requisite to an undertaking like this, I could not acquire within the vast circuit that appertains thereunto, many things which might be necessary unto a system extending into all matters of detail. This it is to be hoped the reader will acknowledge, and have forbearance for the errors, against which every one will stumble who has busied himself throughout life with a single branch of the natural sciences. Natural History is not a closed department of human knowledge, but presupposes numerous other sciences, such as Anatomy, Physiology, Chemistry and Physics, with even Medicine, Geography and History; so that one must be content with knowing only the main facts of the same, and relinquishing the Singular to its special science. The gaps and errors in Natural History can therefore be filled up or removed only by numerous writers and in the lapse of time.

CONTENTS.

PHYSIO-PHILOSOPHY.

[INTRODUCTION.]

CONCEPTION OF THE SCIENCE.

1. Philosophy, as the science which embraces the principles of the universe or world, is only a logical, which may perhaps conduct us to the real, conception.

2. The universe or world is the reality of mathematical ideas, or, in simpler language, of mathematics.

3. Philosophy is the recognition of mathematical ideas as constituting the world, or the repetition of the origin of the world in consciousness.

4, 5. Spirit is the motion of mathematical ideas. Nature, their manifestation.

6. The philosophy of Spirit is the representation of the movements of ideas in consciousness.

7. The philosophy of Nature that of the phenomena or manifestations of ideas in consciousness.

8. The world consists of two parts: of one apparent, real, or material; and one non-apparent, ideal, spiritual, in which the material is not present, or which is naught in relation to the material.

9. There are, accordingly, two parts or divisions of Philosophy, viz. Pneumato-and Physio-philosophy.

10. Physio-philosophy has to show how, and in accordance indeed with what laws, the Material took its origin; and, therefore, how something derived its existence from nothing. It has to portray the first periods of the world's development from nothing; how the elements and heavenly bodies originated; in what method by self-evolution into higher and manifold forms, they separated into minerals, became finally organic, and in Man attained self-consciousness.

11. Physio-philosophy is, therefore, the generative history of the world, or, in general terms, the History of Creation, a name under which it was taught by the most ancient philosophers, viz. as Cosmogony. From its embracing the universe, it is plainly the Genesis of Moses.

12. Man is the summit, the crown of nature's development, and must comprehend everything that has preceded him, even as the fruit includes within itself all the earlier developed parts of the plant. In a word, Man must represent the whole world in miniature.

13. Now since in Man are manifested self-consciousness or spirit, Physio-philosophy has to show that the laws of spirit are not different from the laws of nature; but that both are transcripts or likenesses of each other.

14. Physio-and Pneumato-philosophy range, therefore, parallel to each other.

15. Physio-philosophy, however, holds the first rank, Pneumato-philosophy the second: the former, therefore, is the ground and foundation of the latter, for nature is antecedent to the human spirit.

16. Without Physio-philosophy, therefore, there is no Pneumato-philosophy, any more than a flower is present without a stem, or an edifice without foundation.

17. The whole of philosophy depends, consequently, upon the demonstration of the parallelism that exists between the activities of Nature and of Spirit.

DIVISION OF THE SCIENCE.

18. It will be shown in the sequel that the Spiritual is antecedent to nature. Physio-philosophy must, therefore, commence from the spirit.

19. It will also be shown in the sequel that the whole Animal Kingdom, e. g. is, none other than the representation of the several activities or organs of Man; naught else than Man disintegrated. In like manner nature is none other than the representation of the individual activities of the spirit. As, therefore, Zoology can be termed the Science of the Conversion of Man into the Animal Kingdom, so may Physio-philosophy be called the Science of the Conversion of Spirit into Nature.

20. Physio-philosophy is divisible, therefore, into three parts. The first of these treats of spirit and its activities; the second, of the individual phenomena, or things of the world; the third, of the continuous operation of spirit in the individual things.

The first division is the doctrine of the Whole (de Toto)—Mathesis.

The second, that of Singulars (de Entibus)—Ontology.

The third, that of the Whole in the Singulars (de Toto in Entibus)—Biology.

21. The Science of the Whole must divide into two doctrines; into that of immaterial totalities—Pneumatogeny; and into that of material totalities—Hylogeny.

Ontology teaches us the phenomenon of matter. The first phenomenon of this are the heavenly bodies comprehended by Cosmogony; these develop themselves further, and divide into the elements—Stochiogeny.

From these elements the Earth element develops itself still further, and divides into minerals—Mineralogy; these minerals unite into one collective body, and this is Geogeny.

The Whole in Singulars is the living or Organic, which again divides into plants and animals.

Biology, therefore, divides into Organogeny, Phytosophy and Zoosophy.

After this division of the subject the question first of all arises, what is science, provided there is one.

TRUTH.

22. Science is a series of necessarily inter-dependent and consecutive propositions, which rest upon a certain fundamental proposition.

23. Now, if anything be certain it can only be one in number. If, then, there be only one certainty, there can also be only one science, from which all the rest must be derived.

24. The Mathematical is certain, and, by virtue of this character, it stands also alone. Mathematics is the only true science, and thus the primary science, the Mathesis, or Knowledge simply, as it was called by the ancients. The fundamental propositions of mathematics must, therefore, be fundamental propositions for all other sciences also.

25. Physio-philosophy is only a science when it is reducible to, i. e. can be placed upon an equal footing with, mathematics. Mathematics is the universal science; so also is Physio-philosophy, although it is only a part, or rather but a condition of the universe; both are one, or mutually congruent.

26. Mathematics is, however, a science of mere forms without substance. Physio-philosophy is, therefore, Mathematics endowed with substance.

27. The substance of Physio-philosophy must be of one kind with the form of Mathematics.

28. The certainty of mathematical propositions depends upon no proposition being essentially different from another. Though there may be much that is diversified or heterogeneous, there is nothing new in Mathematics.

For to prove a mathematical proposition is to show (or demonstrate) that it is equivalent, i. e. of the same kind with another proposition. All mathematical propositions must, consequently, resemble a first proposition.

29. Physio-philosophy must also show that all its propositions, or that all things, resemble each other, and, finally, some first proposition or thing.

30. These natural propositions or natural things must, however, resemble also mathematical propositions, and depend, after all, upon the primary proposition of mathematics or the axiom.

Now then comes the question, what is the first principle of Mathematics?

[PART I.]
MATHESIS—OF THE WHOLE.

NOTHING.

31. The highest mathematical idea, or the fundamental principle of all mathematics is the zero = 0.

The whole science of mathematics depends upon zero. Zero alone determines the value in mathematics.

32. Zero is in itself nothing. Mathematics is based upon nothing, and, consequently, arises out of nothing.

33. Out of nothing, therefore, it is possible for something to arise, for mathematics, consisting of propositions, is a something in relation to 0. Mathematics itself were nothing if it had none other than its highest principle zero. In order, therefore, that mathematics may become a real science, it must, in addition to its highest principle, subdivide into a number of details, namely, first of all into numbers, and, finally, into propositions. What is tenable in regard to mathematics must be equally so of all the sciences; they must all resemble mathematics.

34. The first act towards realization or the becoming something, is an origination of Many. All reality can, accordingly, manifest itself only in multiplicity.

That which belongs to the Many is a Definite; this again is a Limited; the Limited is a Finite. The Finite only is real.

The question now arises, how it happens that mathematics becomes a multiplicity, or, what is the same thing, a reality, a something.

35. The reality of mathematics consists in the universality of its quantities; viz. numbers or figures. Every number, and every thing which belongs to mathematics, can be derived from no other source than zero.

Mathematical multiplicity, or its reality, must have proceeded, therefore, out of zero.

36. Zero, however, contains no number and no figure really in itself; it contains, forsooth, neither 1 nor 2, neither a point nor a line within itself. The Singulars or details cannot, therefore, reside in a real, but only an ideal manner in zero; or, in other words, not actually, but only potentially. The conditions here are the same as with all mathematical ideas. We may conceive, e. g., an idea or definition of a triangle in so general a sense that it shall comprehend all triangles, without, however, a definite triangle being actually intended, or without even a triangle actually existing. In order that the idea of the triangle be realized, it must become a definite, in other words, an obtuse or an acute triangle. In short, the idea of the triangle must multiply itself, be self-evolved, or else it is as naught in reference to mathematics, or only a geometrical zero.

The individual objects or figures of mathematics thus attain existence, so far only as the idea comprising them emerges out of itself and assumes an individual character.

It is clear that all individual triangles taken together closely resemble the ideal triangle, or, to express the same in more general terms, that the Real is equivalent to the Ideal, that the former is but the latter which has become dissevered and finite, and that the aggregate of every Finite is equivalent to the Ideal. This will probably be rendered still more distinct by the example of ice and water. The crystals of ice are nothing else than water bounded by definite lines. So, also, are the Real and Ideal no more different from each other than ice and water; both of these, as is well known, are essentially one and the same, and yet are different, the diversity consisting only in the form. It will be shown in the sequel that everything which appears to be essentially different from another, is so only in the form.

The Real and Ideal are one and the same, only under two kinds of form. The latter is the same under an indefinite, eternal, single form; but the Real is also the same, yet under the form of quantity, and, as will be shown, of multiplicity. An infinity resides in both; in the Real an endlessness of individual forms; in the Ideal but one endless form; in the latter case an eternity, in the former an infinity. The quantity and multiplicity of the whole of mathematics is contained in the same manner in the 0, that the quantity and multiplicity of the triangles are in the ideal or primary triangle. Mathematics is a system of nullities or nothings, and this admits of being easily proved.

37. Zero is indeed the universality of mathematics, this, however, is not real, but only ideal. Every number issues out of zero, like the multiplicity of the real triangles out of the primary triangle. This progression of numbers out of zero takes place through a process of becoming determinate and limited; just as the real triangles are only definitions of the absolute triangle. The process of becoming determined is identical with becoming a Finite; becoming real is called becoming finite. Mathematical singulars or numbers can, therefore, be nothing else than zero disintegrated, or rendered real by determination.

What zero is in infinite intensity, that are numbers in endless extensity. Zero is of two forms: under the ideal it is mere intensity; under the real mere extensity, or a series of numbers. The latter is only expanded intensity; the former, extensity concentrated on the point; both are, consequently, one and the same in toto. Numbers are identical with zero; they are zero in a state of extension, while zero is equivalent to numbers in a state of intensity. The sense in which numbers are said to come out of zero is, therefore, very clear; they have not issued forth from zero as if they had previously resided individually therein, but the zero has emerged out of itself, has itself become apparent, and then was it a finite zero, a number. So, also, does the idea of a circle become a real circle, not from the latter emerging from the former, but from this itself becoming manifest. The individual circle is a manifestation or phenomena of the spiritual circle.

38. All realization, therefore, is not the origin of a something that has not previously been; it is only a manifestation, a process of extension taking place in the idea.

Thus the Real does not arise out of the Ideal, but is the Ideal itself in a condition of definition and limitation, as are, e. g. the actual triangle or the actual circle. If, then, the Ideal and Real be one, everything is necessarily identical, and this identity dominates not merely between the Ideal and Real in a general sense, but between all individual members of the Real.

39. The identity of every Different, or of all things among themselves and with the highest unity, is the essence of things. The limitation or definition of the Ideal is their form. Limitation is the Impartient of form.

40. Limitation is originally only a quantitative relation, e. g. the size of the angle in a triangle; later on it becomes also a relation of direction or of position.

In both cases the limitation is only an ideal relation. Realization also takes place, therefore, only in an ideal manner; and the Real is therefore ideal, not simply as it regards its form, but also its essence. Every Plural resembles itself and the highest principle in essence; or, in other words, all Singulars are united through essence with the highest One. All diversity of the Plural resides merely in the form, limitation or manifestation. The one unchanging essence possesses one ideal form, which is that of pure unity, and the same essence has a limitation, a real form, which is that of subdivision. There is only one essence in all things, the 0, the highest identity; but there are infinitely numerous forms.

Numbers are naught else than different forms of the one unchangeable essence, namely, the 0.

If, then, all numbers are only zero in a state of extension, and are consequently identical with it, the question arises, what are the first finitings of zero, or as what does it appear when it is no longer merely ideal or indefinite; in short, what is the first form of the real zero, or of the essence in general?

ESSENCE OF NOTHING.

41. The ideal zero is absolute unity, or monas; it is not a singularity, such as one individual thing, or as the number 1; but an indivisibility, a numberlessness, in which neither 1 nor 2, neither a line nor a circle can be found; in short, an unity without distinction, an homogeneity, brightness, or translucency, a pure identity.

42. The mathematical monas is eternal. It succumbs to no definitions of time and space, is neither finite nor infinite, neither great nor small, neither quiescent nor moved; but it is and it is not all this. That is the conception of eternity.

Mathematics is thus in possession of an eternal principle.

43. Since all the sciences are equivalent to mathematics, nature must also possess an eternal principle.

The principle of nature, or of the universe, must be of one and the same kind with the principle of mathematics. For there cannot be two kinds of monades, nor of eternities, nor of certainties. The highest unity of the universe is thus the Eternal. The Eternal is one and the same with the zero of mathematics. The Eternal and zero are only denominations differing in accordance with their respective sciences, but which are essentially one.

44. The Eternal is the nothing of Nature.

As the whole of mathematics emerges out of zero, so must everything which is a Singular have emerged from the Eternal or nothing of Nature.

The origin of the Singular is nothing else than a manifestation of the Eternal. Thereby unity, brightness, homogeneity are lost, and converted into multiplicity, obscurity, diversity.

Unity posited manifoldly is an expansion without termination, but one that always remains the same.

Realization or manifestation is an expansion of the Eternal.

FORMS OF NOTHING.

45. The first form of the expansion or manifestation of the mathematical monas, or of 0 is + -. The + - is nothing else than the definition of 0. 0 is the reduction of the positive and negative series of numbers, upon which the whole of arithmetic depends. A series of numbers is, however, nothing else than a repetition of a + 1 or a-1; consequently, the whole of arithmetic reduces itself to + 1-1.

What, however, is a + 1, or-1? Obviously nothing else than a single + or-. The figure is quite superfluous, and only indicates how often + or-has been assumed; instead, therefore, of + 1 we can posit +; instead of-1 simply-. The series + 1 + 1 + 1 is synonymous with + + +; or instead of 3 we may posit + + +, and so on for every figure ad libitum. The figures are nothing more than shorter signs for the two highest mathematical forms or ideas of numbers. Numbers are nothing different from the ideas of numbers; they are the latter themselves, only several times posited. Essentially numbers do not exist, but only their two ideas. These ideas, however, exist an infinite number of times.

Multiplicity or real infinity is, accordingly, nothing special or particular, but only an arbitrary repetition of the Ideal, an incessant positing of the idea. The idea posited is reality, non-posited it is = 0.

46. The first multiplicity is duality, + -. This duality alters nothing in the essence of the monas, for + - is = 0. It is the monas itself only under another form. In multiplication it is thus the form alone that changes.

There are many forms, but not many essences.

47. The first or primary duality is not, however, a double unity, both members of which are of equal rank, but an antagonism, disunion, or diversity. Many diversities are multiplicity. The Many is thus complex. The first form is not therefore a simple division of zero or the primary unity, but an antagonistic positing of itself, a becoming manifold.

48. Every Finite is in the same manner only the self-definition of the Eternal. The Eternal becomes, accordingly, real, by binary self-division. When the Eternal is manifested, it is either a positive or negative. The whole of arithmetic is nothing else than a ceaseless act of positing and negating, of affirming and denying.

All realization is nothing else than the act of positing and negating. The act of positing and negating of the Eternal is called realization.

49. Positing and negating is, however, an act or function. Arithmetic is, therefore, a ceaseless process of acting or performing. Numbers are acts of the primary idea, or, properly speaking, stationary points of its function, and hence proceeds a division into the two ideas + and -. If these remain always alone nothing is added to them. They alone produce the whole science of arithmetic, and simply because they are never exhausted by the act of positing themselves repeatedly, but capable after this of again becoming suppressed. Since + is in essence nothing else than a simple positing, a mere affirmation, and-a mere suppression of this affirmation, a negation; so is the positive unity = 1 nothing but an affirmation once declared, and the whole series of numbers is a reiterated affirmation. The act of affirmation alone gives the number, and the latter is thus the definite quantity devoid of intrinsic value. Bare affirmation alone without reference to any substance is unity, duality, &c.

SOMETHING.

50. Still, however, there must be something, which is posited and negatived. The form must have a substance.

This something is the primary idea, or the very Eternal of mathematics, the zero; for + - is = 0. The + is naught else than zero affirmed; the-naught else than this + 0 negatived = - 0. Now since an affirmation once declared is = 1, so are unity and zero identical. Zero differs only from finite unity in that it is not affirmed.

51. The - is not simply the want of affirmation, but its explicit abstraction. The + presupposes the 0; the - the + and 0; the 0, however, presupposes neither + nor -. Purely negative quantities are, as is known, a nonentity, because they can only bear reference to positive quantities. The - is, indeed, the retroversion of + into 0; yet alone, therefore, it is not perfectly equal to 0. It is a retrovertent, and consequently the second act, which presupposes the positive. By the - we know what is not; the 0 is, however, a nothing in every respect. The-is the copula between 0 and +.

52. If the + is the 0 posited, so is it a nothing posited or determined. This position is, however, a number, and therefore a mathematical something. The nothing thus becomes a something, a Finite, a Real, through the simple positing of itself, and the something becomes a nothing by the removal of this self-position. The nothing itself is, however, the mere neglect of its self-position. The something, the + -, has consequently not arisen or been evolved out of nothing, or been produced from it by addition; but it is nothing itself; the whole undivided nothing has become unity. The nothing once posited as nothing is = 1. We cannot speak of production or evolution in this case; but of the complete identity and uniformity of the nothing with the something; it is a virgin product or birth.

53. Zero must be endlessly positing itself, for in every respect it is indefinite or unlimited, eternal. The number of finite singularities must, therefore, pass into the Infinite.

54. The whole of Arithmetic is nothing but the endless repetition of nothing, an endless positing and suppressing of nothing.

We can become acquainted with nothing but the nothing, for the Original of our knowledge is the 0.

There is no other science than that which treats of nothing.

Every Real, if it were such in itself, could not be known, because the possibilities of its properties would pass into the Infinite. The nothing alone is cognizable, because it has only a single property, namely, that of having none; concerning which knowledge no doubt can be entertained.

A.—PNEUMATOGENY.

PRIMARY ACT.

55. The + - or, in other words, numbers are acts or functions. Zero is, consequently, the primary act. Zero is, therefore, no absolute nothing, but an act without substratum. Generally speaking there is, therefore, no nothing; the mathematical nothing is itself an act, consequently a something. The nothing is only postulate.

56. An act devoid of substratum is a spiritual act. Numbers are, accordingly, not positions and negations of an absolute nothing, but of a spiritual act.

57. The zero is an eternal act; numbers are repetitions of this eternal act, or its halting points, like the steps in progression. With zero the Eternal therefore originates directly, or both are only different expressions for one and the same act, according with the difference of the science wherein they are employed. Mathematics designates its primary act by the name of zero; Philosophy by that of Eternal. It is an error to believe that numbers were absolute nothings; they are acts and consequently realities. While numbers in a mathematical sense are positions and negations of Nothing, in the philosophical they are positions and negations of the Eternal. Everything which is real, posited, finite, has become this out of numbers; or, more strictly speaking, every Real is absolutely nothing else than a number. This must be the sense entertained of numbers in the Pythagorean doctrine, namely, that everything or the whole universe had arisen from numbers. This is not to be taken in merely a quantitative sense, as it has hitherto been erroneously, but in an intrinsic sense, as implying that all things are numbers themselves, or the acts of the Eternal. The essence in numbers is naught else than the Eternal. The Eternal only is or exists, and nothing else is when a number exists. There is, therefore, nothing real but the Eternal itself; for every Real, or everything that is, is only a number and only exists by virtue of a number. Every Singular is nothing for itself, but the Eternal is in it, or rather it is itself only the Eternal, though not the Eternal in itself, but affirmed or negatived. The existence of the Singular is not its own existence, but only that of the Eternal subjected to an arbitrary repetition; for the act of being and affirming are of one kind.

58. The continuance of Being is a continuous positing of the Eternal, or of nothing, a ceaseless process of becoming real in that which is not. There exists nothing but nothing, nothing but the Eternal, and all individual existence is only a fallacious existence. All individual things are monades, nothings, which have, however, become determined.

The Eternal must posit without cessation, for otherwise it would be an actual nothing, while in fact it is an act; but it must incessantly suppress also this position, else it would be only a finite act, or an act which had only one kind of direction, that of affirmation + + + +, and so on, which represents only the half of arithmetic. The totality of the Finite is, therefore, of eternal duration also: the Singular, however, issues forth and disappears like the numbers in arithmetic. The eternal duration of the Finite consists, however, only in ceaseless repetition. Such an Eternal is to be distinguished therefore from the Primary eternal, and is called the Infinite. The totality of finite things is not therefore eternal, but only infinite.

PRIMARY CONSCIOUSNESS.

59. Two tendencies are present in the primary act, both of which being inseparable are one in kind. It has the tendency to posit, and also to suppress, itself. The unity strives unto binary division or to antagonism, even as the 0 strives to produce + or -. While the primary act itself posits, it does this indeed out of its own strength, and that which it posits is also none other than itself; it itself posits i. e. actively; and is itself posited i. e. passively; it itself posits itself, is the self-position of itself; for + is nothing else than 0 self-posited. The positing and posited act are of one kind; the latter, however, is the Real, the Finite; the former the Ideal, the Eternal. Both are distinguished from each other through this only, that the Real is the posited, numbered, and consequently determined act; the ideal, however, the positing, consequently numbering and thus undetermined act. While, however, the + is nothing else than 0, it must necessarily bear a relation to it, and thus retrograde into the 0. This retrogression is an act in the reverse direction, or what is indicated in mathematics by negation. The - has been therefore necessarily granted with the +, else the + would not be represented as = to 0. The act of positing is therefore at the same time also an act of negation. So soon as the 0 is or exists, it is = + -. The realization of the Eternal is accordingly a complete antagonism of itself. For 0 is equal to + -, not simply = + or = to-.

60. The being of the Eternal is therefore a self-manifestation. Every Singular is nothing but a self-manifestation; since all numbers are only positions of zero or of +, which can never be without-. In every essence there are two, but the two are the one essence itself, which posits itself by division. The Positing of the Eternal in the sense in which it has been hitherto adopted, namely, as a realization of the same, is not merely an act of positing, not an indeterminate Positing, but an antagonism of itself. The zero is simply the indeterminate Positing, or the negative Positing; but the number, or the real is the antagonism of zero, the + -, or the self-manifestation. The 0 cannot be thought of for itself alone without the +; the latter, however, not without 0, as well as the-also not without 0; for it is the suppression of the posited 0, namely, the +. Every act of self-manifestation is therefore twofold, a manifestation (= +), but a manifestation of itself, consequently a retrogression into 0 (= -). Through negation the Finite becomes united with the Eternal. Every disappearance of the Finite is a retrogression into the Eternal; for it must return to whence it came. It has arisen out of nothing, is itself the existing nothing; it must therefore retrograde again into the nothing.

GOD.

61. The self-manifestation of the primary act is self-consciousness. The eternal self-consciousness is God.

62. The continued act of self-consciousness, or becoming self-conscious repeated, is called representation. God is therefore comprehended in ceaseless representation. Representations are single acts of self-consciousness. Single acts, however, are real things. All real things, however, are the world. The world therefore originates with the representations of the Eternal.

63. The representations are, however, manifested or attain only reality through expression. The world is therefore the language of God; the creation of the world the speaking of God. "God spake, and it was." It is not merely said, God thought and it was. Thought belongs merely to spirit; in so far, however, as it becomes apparent, it is a word, and the sum of all apparent thoughts is speech. This is the created, realized system of thought. The thought is only the idea of the world, but speech is the idea actualized.

64. As thought differs from speaking, so does God from the world. Our world consists in our apparent thoughts, namely, the words. The universe is the language of God. So far as the thoughts lie at the foundation of the words, it can be said, that our world were the play of our thoughts, and the actual world that of God's. The word has become world. Worldly things have no more reality for God, than our words or our language for us. We carry a world within us while we think; we posit or create a world without us while we speak. Thus God carries the world within himself while he thinks; he posits the same without himself or creates it, while he speaks. In so far as thought necessarily precedes speech, it may be said, that there would have been no world, if God had not thought. In the same sense it may be also said, that all things are nothing but representations, thoughts, ideas of God. So soon as God thinks and speaks is there a real thing. To speak and to create are one. All, that we perceive, are words, thoughts of God; we are ourselves nothing else than such words or thoughts of God, consequently his metatypes or images, in as far as we unite in ourselves the whole system of speech. There is therefore no being without self-consciousness. That only which thinks is (for itself); that which does not think is not for itself, but only for some other consciousness. The world differs from God as doth our speech from us. The self-consciousness of God is independent of the world, even as our self-consciousness is independent of our speech.

65. The divine laws are also the laws of the world; this has therefore been created and governed in accordance with eternal and immutable laws.

66. Physio-philosophy is the history of creation; the creation, however, is the language of God. The system of thought, however, lies necessarily at the foundation of the system of speech. Now the science of the laws of thought is called logic; physio-philosophy is therefore a divine doctrine of speech or a divine logic. The laws of speech instruct us in the genesis of language. Physio-philosophy is, therefore, the science of the genesis of the world, or Cosmogony.

FORM OF GOD—TRIUNITY.

67. As the complete principle of mathematics consists of three ideas, so also does the primary principle of nature, or the Eternal. The primary principle of mathematics is 0; so soon, however, as it is actual, is it + and-; or the primary idea resolves itself in being at once into two ideas, each of which resembles the other in essence, but differs from it in form. Thus it is here one and the same essence under three forms, or three are one. Now that which holds good of mathematical principles, must hold good also of the principles of nature. The primary act is manifested, or operates under three forms, which correspond to the 0, + and-.

These three ideas of the Eternal are all equivalent to each other, are the same primary act, each of them being whole and undivided, but each otherwise posited. The positing primary act is the whole Eternal; the posited is likewise the whole Eternal, and that which is subtractive, retrogressive, combining the two first, is also the whole Eternal. Although all three ideas are equivalent to each other, still the positing idea ranks first, the posited second, and the combining third; not as if they had first arisen successively (this is impossible, for they are coexistent, namely, before all time), nor as if they occupied different positions (for they are everywhere); but only according to their order and value. How one may be three and three one, is thus rendered comprehensible only by mathematics.

68. The first idea is the original, that therefore which is thoroughly independent, which having arisen from and being based upon itself, has consequently emerged from nothing else; in short, it is the eternal idea, like the mathematical 0 = Monas aoristos. Everything is possible with it; it can propose and solve all problems, knows therefore everything and creates everything. It is the generative, creative and paternal idea.

69. The two other ideas have emerged out of the first, although apparently equivalent to it; yea, they have themselves issued out of themselves. The second idea is, therefore, Dyas aoristos, and corresponds to the mathematical +; the third idea is the Trias aoristos, and corresponds to the mathematical-, so that by the three the primary trinity 0 + - is completed. The first idea labours or, what is more, rejoices from all eternity to convert itself into the two others. The action or the life of God consists in eternally manifesting itself, eternally contemplating itself in unity and duality, eternally dividing itself and still remaining one. The second idea has issued next from the first, and is therefore related to it as Son is to Father, when the ideas are viewed as personified. The third idea has emerged conjointly from the second and first, and forms therefore the spiritual union, the mutual love between both. It may be therefore simply called Ghost or Spirit, if it is thought of as personified.

70. Since every Singular, having been produced through the primary trinity, is only the expressed word of the primary trinity, so also must their qualities be recognizable in the same. The Singular is not simply therefore a position of one idea, but of all three. All things have issued out of the trinity. The essence of the universe consists in the trinity which is unity, and in the unity which is trinity; for it is a likeness of the primary trinity. Being, generally, is an act, and that, indeed, of a threefold nature. Apart from act or function there is no being. That, which is called nothing, is in itself an act, and there is, therefore, no absolute nothing. The nothing is only something relative to a particular being. Even the mathematical zero is not nothing, but an act. It is nothing only in reference to particular numbers. Numbering is a repetition of one and the same act. The forms or conditions of the primary act are Rest, Motion, and Extension or expansion.

a. PRIMARY REST. (First form of the Primary Act.)

71. The primary idea is the position simply without any relation, or any antagonism; it is the oscillating resting point in the universe, around which everything collects itself, and from which everything emerges; the Centrum ubique, circumferentia nusquam. The primary idea is the substratum of everything, which will come before us in the sequel of this work. Everything depends upon this primary essence; all action, motion, and form issues forth from it; or rather, in all phenomena naught else appears than the primary essence in different stages of position, just as in all numbers naught else appears but the zero. The primary idea is the absolute beginning. This primary idea is the non-representable, the never apparent and yet omnipresent, idea; but which is always withdrawing itself from our view when we imagine or believe that we gaze upon it; in short, the Spiritual, which declares itself in everything and yet always remains the same. The origin of all action may be termed the primary force.

b. MOTION, TIME. (Second form of the Primary Act.)

72. The primary idea operates only, while it posits; through positing, however, arises a succession of positing, or numbers; positing and successive positing are one. The function of the primary idea consists in an eternal repetition of the essence; the primary act is a continuous self-repeating act. Repetition of the primary act devoid of another substratum is Time. Time is none other than the eternal repetition of the positing of the Eternal, corresponding to the series of numbers + 1 + 1 + 1 + n. Time has not been created, but has emerged directly out of the primary act and its position; it is the function of God himself. Something has thus already originated, which appears to conduct us into the universe. Time is the first portal through which the operation of God passes over into the world. Time is the infinite succession of numbers or the mathematical nothings. The mathematising, numbering act is Time. Numbers, however, are Singulars or finitudes, which constitute the world.

73. Time is infinite, for it is the totality of positing; it is only the points or numbers in it that are the Finite.

74. All things are created in time; for time is the totality of Singulars. Time is no stationary quantity, which is always changing itself into something new during its progressive flux. It is not a continuous stream, but a repetition of one and the same act, namely, the primary act, like as it were to a rolling ball, which constantly returns upon itself. There is no endless, still less an eternal thing; for things are only positions of time. Time itself is, however, only repetition, and thus also a suppression of these positions. The vicissitude of things is in fact time; if there be no change, there is also no time. Time is an universal property of things. Exemption from time is only in the Eternal.

75. Time, not being itself the Finite, but creating it, is not itself a Real, but still an Ideal, a form only of the primary act, an idea, with which finite things have been directly posited. Time is the act of numbering; numbering is thinking; thinking is time. Our thinking is our time. In sleep there is no time for us. God's thought is God's time; God's time, however, is all time, consequently time of the world. Time is not of earthly but heavenly descent or origin. In so far a divine quality belongs to all finite things. They are divine, in so far as they are time; terrestrial, in so far as they are evanescent moments of time.

POLARITY.

76. Time is an action of the primary power; and all things are active only in so far as they are filled or inspired with the idea of time. The whole activity of things, all their forces arise out of the primary act or primary power, are only moments of the same. There are, however, no positive without negative numbers, consequently also no moments of time without suppression of the same. There is, therefore, no single force, but each is the position of + and-. A force consisting of two principles is called Polarity. Time is, therefore, the primary polarity, and polarity is manifested at the very instant in which the creation of the world is stirring.

77. Polarity is the first force which appears in the world. If time is eternal, polarity must also be eternal. There is no world, and in general nothing at all without polar force.

78. Every single thing is a duplicity.

79. The law of causality is a law of polarity. Causality is valid only in time, is only a series of numbers. Time itself has no causality. Causality is an act of generation. The sex is rooted in the first movement of the world.

MOTION.

80. Polarity may be viewed as a single positing of + -; if, however, this positing repeats itself, Motion originates, viz. when many + - + - are consecutively posited, and thus the principal poles separate from each other, as in an iron bar when magnetizing. Time is a polar positing of the primary act, and an endless repetition of this positing; through this originate individual things, whose succession is motion.

81. Primary motion is the result of primary polarity. All motion has originated from duplicity; consequently from the idea in a dynamic not a mechanical manner. A mechanical motion, which might be produced ad infinitum by mechanical impulses, is an absurdity. There is nowhere a purely mechanical motion; nothing, as it is at present in the word, has become so by impulse; an internal act, a polar tension lies at the bottom of all motion.

82. Motion itself, however, is not twofold in character; it is unity, but the result of duality. In time we have to distinguish the polar act of position, and the act of repeating this position, which is motion. Motion is the simple repetition of the polar, twofold act, or the ceaseless separation of poles; but, as in every polar line the two poles are in all cases together, so even is this mutual separation of poles only a repetition of polarity.

83. Motion also is not created, but has emerged directly from the Eternal, is the primary function itself repeated. Motion is the ever self-manifesting, consequently progressive God.

84. Motion is thought, which is manifested as speech. Thought polarizes the fingers. If the thought be powerful it moves them, and through them other bodies. Speech is only a thought that has passed over into motion. The world is the thought of God that has been translated into motion, the moved thought of God—thought spoken. It is here evident that the world is not simply the thought but the language of God; for there is no action without motion; consequently no thought without speech, and vice versâ.

85. There is no thing which were without motion, just as there is none without time. A Finite without everlasting motion is a contradiction. All rest in the world is only relative, is but a combined motion. There is only rest in the Eternal, in the nothing of nature.

86. The primary motion is only possible in a circle, because it fills every thing.

87. The motion of finite things by polarity may, in a wider sense, be called life; for life is motion in the circle. Polarity, however, is a constant retrogression into itself. Without life there is no being. Nothing is, simply by virtue of being, e. g. by its mere presence; but everything of which a being can be declared, is only, or manifests itself, by its polar motion or by life. Being and life are inseparable ideas. While God acts, he creates life.

88. Life is nothing new, that came first into the world, after it was created, but an Original, an idea, a moved thought of God, the primary act itself with all its consequences.

89. There is in the universe no vital force of its own; the individual things lie not there some time and await the polarizing breath, but they first become through the breath of God. The Causa existentiæ is life.

90. There is nothing properly dead in the world; that only is dead which is not, only the nothing. Something can only cease to live, when its motion ceases; this, however, ceases only when deprived of its polarity; the polarity dissolved, however, is zero. Thus individual things retreat into the Absolute, if they cease to live. Everything in the world is endowed with life; the world itself is alive, and continues only, maintains itself, by virtue of its life; just as an organic body maintains itself, only while it is constantly being generated anew by the vital process.

91. Every living thing is twofold in character. It is one persistent in itself, and one immersed in the universe. In everything, therefore, are two processes, one individualizing, vitalizing, and one universalizing, destructive. By the process of destruction, the finite thing seeks to become the universe itself; by the vitalizing process, however, the variety of the universe, and yet with that to remain a Singular. That only is truly living which represents the Eternal, and the whole multiplicity of the universe in the Singular.

92. The whole in the singular is called Individual. The individual is an example of computation, which admits only of being developed, from its comprehending the whole of arithmetic in itself. Nothing individual can persist eternally; it must eternally move itself, consequently fill up everything, displace everything, must become itself the universe.

MAN.

93. Time consists of single acts; i. e. the life or the absolute act does not work with one stroke, but an infinite number of times. All acts, therefore, taken together, all finite things in time, are equal to the primary act or the Eternal.

94. There are two totalities, a primary totality 0 + -, and a secondary, or the summing up of all numbers 0 + n-n; the former the eternal, the latter the finite totality, or the one the eternity, the other the infinity.

95. The more a thing has adopted into itself of the Manifold of the universe, by so much the more is it animated, by so much the more does it resemble the Eternal. It is conceivable, for a finite or living essence to unite all numbers or acts in itself, without, however, its being the very Eternal. It would, however, be obviously the most perfect finite essence, and, as a secondary totality, be the likeness of the primitive; the former the compound universality, the latter the identical.

96. Such an essence would be necessarily the highest and last, whereunto creation could attain; for more than the universe cannot be represented in one thing. With such an essence creation would be closed or would terminate.

97. Since the realization of the Eternal is a becoming self-conscious, so is the highest creature also a Self-conscious, but a Singular. Such a creature is the finite God, or God become corporeal. God is Monas indeterminata, the highest creature is Monas determinata, Totum determinatum. A finite self-conscious being we call Man. Man is an idea of God, but that in which God wholly, and in every single act becomes an object unto himself. Man is God represented by God in the infinity of time. God is a Man representing God in one act of self-consciousness, without time.

98. Man is God wholly manifested. God has become Man, zero has become + -. Man is the whole of arithmetic, compacted, however, out of all numbers; he can therefore produce numbers out of himself. Man is a complex of all that surrounds him, namely, of element, mineral, plant and animal.

99. The other things below man are also ideas of God, but none of these ideas is the whole representation of arithmetic. They are only parts of the divine conscience posited in time; but man is God, planted or posited uninjured in time. Man is the object in the self-consciousness of God; the creatures below man are, however, the objects only of the consciousness of God. Thus, if God places before and from himself only single qualities, there are worldly things; if, however, God in this crowd of representations attains to his own entire representation, then arises Man. God is = + 0-, Man = + [oo] 0-[oo], the animal is = + n 0-n. The animals are only represented in part. The subject of self-consciousness is = + 0-; the objects, however, are the numbers which are equivalent to this, being = [oo] + 3 + 2 + 1 + 0-1-2-3-[oo]. Thus if all numbers, all world-elements, together with their perfections, occur in consciousness = + 0-, there is a Man; if only single, and perhaps but few things, such as food, stones, &c. (with the entire exception of the celestial bodies), enter consciousness, there is an animal. They are represented only partly or in a portion of the universe, but man is represented wholly or in all its parts. Animals are fragments of man.

100. No creatures below Man can possess self-consciousness. They have, indeed, consciousness of their several acts and of their sensations, and possess memory; but as these several acts are only parts of the world, or of the great consciousness, and are not the Whole, they can never become objective unto themselves, never imagine. Animals are men, who never imagine. They are imaginative, but never of themselves wholly; they are therefore beings who never attain to consciousness concerning themselves. They are single accounts; Man is the whole of mathematics.

FREEDOM.

101. An action, which is not determined by some other action, is free. God is free, because apart from him there is none other action.

102. Man, as being an image of God, is likewise free; as being an image of the world he is devoid of freedom. Man is, therefore, in his primary commencement or principle free, but not in his end or object to be attained. In the resolution Man is free, in the execution he is not free. The mathematician can select at pleasure any proposition; but having selected it, must solve it in accordance with necessary laws and with definite numbers and figures. Man is a twofold being, compounded of freedom and necessity.

RETROSPECT.

103. Hitherto we have considered simply the arithmetical relations of the primary act and of the universe. We have shown, to wit, that all ideas fluctuate simply under the forms of numbers; that everything was comprised in the 0 + -. Time was only the active series of numbers; motion was the actual arithmetical calculation, namely, the process of reducing numbers to absolute identity, to zero.

104. Life is moreover only a mathematical problem, which, the higher it ascends, approaches so much the nearer to absolute zero in its attainment of the infinity of numbers, becomes so much the more endowed with life.

105. Arithmetic is the science of the second idea, or that of time and motion, or of life; it is, therefore, the first science; mathematics not only begins with it, but creation also, with the becoming of time and of life. Arithmetic is, accordingly, the truly absolute or divine science, and therefore everything in it is also directly certain, because everything in it resembles the Divine. Theology is arithmetic personified.

106. Hence it follows in the most perfect manner, that every science, if it would possess certainty, must resemble arithmetic. Now a science always implies a science treating of certain objects; all certain objects must, therefore, resemble the objects of arithmetic; or all objects, of whatever denomination, whether natural or spiritual, must correspond to arithmetical objects, consequently in idea be numbers, an actual arithmetical problem, as it were the numbers of motion, of life.

107. A natural thing is nothing but a self-moving number; an organic or living thing is a number moving itself out of itself, or spontaneously; an inorganic thing, however, is a number moved by another thing; now, as this other thing is also a real number, so then is every inorganic thing a number moved by another number, and thus ad infinitum. The movements in nature are only movements of numbers by numbers; even as arithmetical computation is none other than a movement of numbers by numbers, but with this difference, that in the latter this operates in an ideal manner, in the former after a real.

c. FORM, SPACE. (Third form, of the Primary Act.)

108. Viewed arithmetically every position is a number, geometrically, however, it is a point. What the 0 is in arithmetic, the point is in geometry; the one the arithmetical, the other the geometrical nothing. Both sciences commence with nothing and are only different views of nothing. The 0 is a temporal nothing (a number), the point a spatial nothing (a figure).

109. The first motion of numbers or of points is the motion of the primary number, the 0, or the primary act; and this motion depends upon the multiplicity of numbers or points, upon the disintegration of the identical primary number, upon the + -. The first motion of the primary act is an expansion of itself into multiplicity, whereby not merely sequence but an addition also is posited. The primary act is not simply positing, but also posited; as the former it is time, as the latter it is time posited universally. Time remaining stationary is Space. Space is not different in essence from time, but only according to position; it is only time resting, while this is moved, active space.

110. Space has first arisen out of time, as the third idea out of the second, but only ideally. It has arisen out of it, while, time being the act of positing, it is the posited; now as time posits from eternity, so is space also from eternity and in eternity. The eternity of space, however, depends not upon duration, but upon extension; it is unlimited.

111-112. Space is everywhere, as time is ever. Two spaces can no more exist than two times. There is only one Eternal. Time and space are, however, nothing special that has attained unto the Eternal, but the Eternal itself. They are also not two kinds of qualities subsisting near each other, but are one in kind. The series of numbers is infinite, thus universal; space is consequently universal.

113. Space is an idea like time, a form of God like time; it is the passive form, the extended 0 = + 0-.

114. All temporal things are also in space and limited. An unlimited thing extended through the whole of space is an absurdity. God's operation only is extended through the whole of space; it is space itself; when he willed to act, he became time; but when he was time, he became space.

115. Space has not been created, but has emerged out of the Eternal; it is nothing new in the universe, nothing next to God and present with him, but coexistent with God.

116. Single things must be both in space and in time; or a real thing first originates, where time and space cross each other at one point; they cross, however, everywhere, and therefore things are everywhere.

117. There is no void or empty space, no time and no place, were a Finite could not be; for time and space are virtually the manifesting primary act, the zero that has become thing.

POINT.

118. Time has begun with number, space with the point, with the spatial nothing, with the zero of space. This point necessarily posits itself "ad infinitum;" it extends itself also in all directions, and necessarily in equal distances. Such an extended point is the Sphere.

119. The sphere is nothing peculiar, nothing new in the thoughts of God, but only the point expanded, while this again is but a contracted sphere, just as the totality of numbers is an expanded 0, and this their contracted sphere.

120. Space is spherical, and, indeed, an infinite sphere. The sphere has been posited with space, and consequently from eternity; it is also an idea, and that, indeed, the total idea; for time and space have in it been posited together.

121. For God to become real, he must appear under the form of the sphere. There is no other form for God. God manifesting is an infinite sphere.

122. The sphere is, therefore, the most perfect form; for it is the primary, the divine form. Angular forms are imperfect. The more spherical a thing is in form, by so much the more perfect and divine is it. The Inorganic is angular, the Organic spherical.

123. The universe is a globe, and everything, which is a Total in the universe, is a globe.

LINE, LIGHT, MAGNETISM.

124. While the point expands, it is active; this active expansion is a simple repetition of the point, and this is a Line, which in the sphere, however, is a Radius. With time originates not merely a series of numbers, but together with it also the line. The line and time are of one kind, repeated positions of the nothing, of the point. It is consequently clear, how that time were a repeated positing of the Eternal itself: for the line is only a repeated self-positing of the point, of the nothing. God fluctuating in his eternity, and the point, are one in kind; but God acting is a line, being or existing a sphere, i. e. the point in the act of being.

125. The line is nothing new in creation, but time itself, when regarded more closely. God creates the line as little as he does time; but this originates unto him, while he moves, while he thinks. It is impossible to think without producing a line. The line is therefore from eternity, is a series of numbers.

126. The essence of the line does not consist in its two extremities being continued with equal significance into the Infinite; but in its radiality, i. e. that one extremity turned towards the centre has become central, converging, absolute; but the other turned towards the periphery has become divergent, finite, multiplicity. The primary line is a line produced with two antagonized characters. The central extremity is 0, the peripheral is the bisected zero = ±. This radial line gives us the antetype of a new polarity. The two extremities are not related as + and-towards each other, but as 0 and + -. At the instant, when a line originates in the universe, it is not a line merely, or an indefinite line that originates; but one that is definite at both extremities, polar, indeed, but after a determinate fashion. Nothing, not even a finite thing, exists in an indefinite manner.

127. There is no mathematically straight line in the world: all real lines are polar; they are all rooted in God by one extremity, by the other in finitude. The primary act becomes in its first operation not merely a posited nothing, a numerical series; not merely time, not merely an aoristic line, but a Linea determinata; in short, God can step forth into time only as radius. The Monas determinata is a Monas radialis, or a centroperipheric monas.

128. The essence of the primary antagonism is a centroperipheric antagonism. As centre is related to periphery, so is here one pole related to the other. Polar existence and central or peripheral existence are one. Primary polarity is centroperiphery. The primary line is constantly in a state of polar action, which is called tension; for it is always converging and diverging, at once central and peripheric. Every line originates, therefore, only by tension, and is only by it, yea, every line is nothing else than this tension.

129. A line, one extremity whereof strives towards the centre, the other to the periphery, the one to identity, the other to duality, will exhibit itself in the world as a line of Light, in the planet as a Magnetic line. Magnetism is centroperipheric antagonism, a radial line, 0—±, the action of the line being cleft at one extremity. Magnetism has its root in the beginning of creation. It is prophesied with time.

SURFACE, ELECTRICITY, OXYDATION.

130. The periphery is the boundary of the sphere, and is, consequently, a superficies or Surface. This, therefore, originates also directly with the positing of the Eternal.

131. As the primary line is not a purely polar, but a radial line, so is the primary surface not a level, but a curved or convex surface.

132. There is no level surface in the universe, no pure surfaces any more than pure lines. All surfaces are curved. For example, those of drops, of the heavenly bodies, of animals. The surface of a sphere is no Continuum; but consists properly of the divided peripheric and upright extremities of the radii; it is a ±.

133. The surface of a globe has no centre, no 0, like the radius; but is an absolute Dualized, a ± without 0.

134. This mode of operating of the primary act is manifested as electricity. Electricity is a merely peripheric antagonism, without centre, thus without union; an eternally Dissevered without rest. Electricity is thus also a special form, under which polarity makes its appearance, and is likewise rooted in the primary creation. There is, consequently, no thing which were not magnetic and electric.

135. The idea of a surface is constantly that of surrounding. It is not generated by a section of a globe, but by the completion, the circumferential limitation of the sphere. The essence of the sphere is boundary. Every surface is finite, is convex. In the divine position a surface never occurs, save on the boundary of the primary sphere.

136. As no thing can exist without a line, without a radius, so also none can be without surface, without circumscription. The single surface is identical with the Locus of the old philosophers. Every Finite is a closed whole, and that thing is of the most perfect kind which has the most perfect closure, surface, periphery (or skin).

137. The surface is also not different from the primary act, but a form of the primary act itself; or a boundary, which, however, nowhere remains stationary, but is always displaced by means of the eternal act. Therefore the world is at once unlimited and limited; the latter in reference to the closure of the surface, the former to the endless expansion of the same.

138. The periphery is the object in divine consciousness, the point which, posited without the centre, is thus one and the same, centre (subject) and periphery (object). It is everywhere the same point, the same 0, wherever it be posited. Hence the profound saying, "Mundus est Sphæra, cujus centrum ubique, circumferentia nusquam."

139. The surface stands in antagonism to the line, like periphery and centre; it stands perpendicular upon the radius, and can never pass parallel to linear action. Electricity ranks in eternal antagonism to magnetism.

SPHERE, HEAT, CHEMISTRY.

140. The line and surface are density, the representation of time and space; they have therefore like these originated out of nothing, namely, out of the point. The sphere is the expanded nothing. Nothing thus extended, or nothing posited, becomes a something, viz. line, surface, density, polarity. The line is a long nothing, the surface a hollow nothing, the sphere a dense nothing; in short, the something is a nothing which has received only predicates. All things are nothings with different forms. The point is = 0, the line = +, the surface = + -, the sphere = + 0-.

141. The internal motion of the globe, or the becoming of the globe, is manifested in the universe as Heat, in the planet as Chemistry.

ROTATION.

142. The primary sphere is rotating, for it has originated through motion; the motion of the sphere cannot, however, be progressive, for it fills everything. God is a rotating globe. The world is God rotating. All motion is circular, and there is everywhere no straight motion any more than there is a single line or straight surface. Everything is comprehended in ceaseless rotation. Without rotation there is no being and no life; for without it, there is no sphere, no space and no time.

143. The more perfectly circular the motion of a thing is, so much the more perfect is it. Straight motion is only the mechanical; such, however, exists not through itself. The more a body moves in a straight direction, the more mechanical and ignoble is it. Straight motion too yields only straight form.

GEOMETRY.

144. The sphere with its attributes is the totality of numbers, is thus a rotating number. The universe is the same. In arithmetic the quantity of divine positions is regarded; in the sphere, however, the direction of these positions, or of series of numbers.

145. The doctrine of the sphere is Geometry; for all forms are contained in the sphere. All geometrical proofs admit of being conducted through the sphere. Geometry has originated directly from arithmetic, or is arithmetic itself, with this difference, that the latter regards series of numbers as individualities, the former, however, as a whole. Arithmetic is a geometry seriebus discretis; geometry is an arithmetic seriebus continuis, a solidified arithmetic.

146. Geometry is a science of equal value with arithmetic; it is even as certain, because it has no other propositions; it is equally eternal, is the same realization of the primary act, the Deus geometrizans of the Pythagoreans. Everything to be certain must therefore resemble geometry, must be itself a position of geometry, only under other relations.

147. Geometry is more real, more finite, therefore also more apparent, and, as it were, more material than arithmetic. The ideas in it have become something determinate, have assumed form, while before they still fluctuated formless in arithmetic; here were they mere ghosts without veils, but in geometry they have received these veils. Time has received for its form, its body, the line; space, the surface; life, the globe, consequently the rotation for its form or body. It is to be here remarked, that ideas always become more real and more finite, always approximate nearer to actual manifestation, the lower they descend or the more they are considered individually. Geometry has not originated later than arithmetic, but is only a more individual view of ideas, arithmetic being more universal. Geometry is arithmetic with stationary numbers, = points. The Divine thus approximates to manifestation, to materiality, the more individual it becomes; and this is very natural, for it verily limits itself more and obtains always more predicates. The more a thing obtains predicates, by so much the more perfect is its finiteness. By geometry we are actually transferred into the universe, but only into the formal, in which it has, like a skeleton, been sketched for us solely upon a general plan; namely, as infinite extension, in which line and periphery, central and peripheric action, magnetism, electricity, and rotation, &c., have been prefigured.

B.—HYLOGENY.

a. GRAVITY. (First form of the World. Rest.)

148. In arithmetic the divine acts are only undetermined = numbers. In geometry the numbers obtain determinate or finite directions, become figures. All figures have, however, an especial direction to the centre. Figures are nought but centres manifoldly posited.

149. The direction to a centre is, however, an act, which never ceases to operate. The primary act strives therefore to posit ad infinitum nought else than a centre, i. e. points.

150. If there are points without the centre, it so happens only because the succeeding points have been displaced by the points that were first posited. The peripheric points are only with reluctance out of the centre. The globe only exists in an uneasy state, because it has no place in the centre.

151. Every finite thing strives towards the centre. The finite is only something, in so far as it is posited in the centre, and it maintains its value according to its distance from the centre. This exertion or endeavour, by virtue of which things would be in the centre, is Gravity.

152. What the retrogression of numbers into 0 is, that is the gravity in the sphere. The gravity is a geometrical reduction of position unto nothing. The sphere is only produced by action, and that indeed by the centroperipheric. This action must therefore manifest itself in two ways, as centrifugality and centripetality. The first is the dispersion of the primary act or of points, the second is the collection of the primary acts or points into the unity, and this is gravity. Centrifugality originates only in a constrained manner or with reluctance, for the primary act always seeks the centre, and only moves towards the periphery, because it has no longer any place there. If centripetality be regarded as a force, then is centrifugality no force, but only centripetality itself retreating from the centre; even as cold and darkness are probably no particular forces in themselves, but only weaker degrees of heat or light.

153. Gravity is not motion simply, but motion unto a centre, unto rest.

154. That which is itself in the very centre is therefore not heavy. The primary act is not heavy.

155. As all finite things are positions of the primary act in the sphere out of the centre, so are all of them heavy. Gravity is the force that strives unto the centre, and which is there impeded by other forces already present therein. A finite thing, that is not heavy, is a contradiction. The gravity of the single thing is weight. The world itself has no weight, or else it must be heavy in relation to something else without it. The ideas of gravity and weight, as we speak of them in reference to individual things, are not applicable to the world, still less to God.

156. Gravity is also nothing new in the world, but it is only the positing of the centre in space. As necessarily as the Eternal, when it manifests itself, must appear under a definite form, so also must it be necessary with the eternal effort, to return into itself or appear as gravity. Gravity is nothing different from the primary act, nothing specially created; but the spherical position of the same tending unto the centre.

157. Now, as the sphere has originated out of nothing, so also has gravity originated out of the same. The form is a formed nothing: the form is, however, no form without internal forming force, and to this gravity belongs. The being of form and the being of gravity are one. Gravity is a weighty nothing, a heavy essence, striving towards centre, a realization of the first divine idea. Gravity cannot, therefore, be perceived in the universe as a whole, but only in its parts.

158. If gravity is the primary act that has become real, so must everything originate out of gravity, or everything must acknowledge gravity to be the common mother of the finite. It is in all cases, or in every individual thing, only the gravity, the Ponderose, which exists, otherwise nothing exists; for verily nothing exists without the divine primary, which is incessantly a central, act.

MATTER.

159. Points, which strive towards the centre, are compressed, because they would all occupy one and the same spot. These points, however, are forces, which take up space and therefore exclude other points. A space that excludes another is Matter. Everything which has been said of gravity holds good in respect to matter; for matter is only another word for gravity. A heavy thing is a material thing.

160. To the totality of a thing belongs not merely its figure nor its tension or motion simply, but also its gravity. This is, however, a whole sphere. Matter is, consequently, a total position of the primary act, a trinity of ideas.

161. Matter has been imparted with space and time. All space is material; ay, matter is itself the space and the time, the form and the motion; for space is nothing special, but only extended or formed force. It is here also shown that the nothing does not exist. There is as little nothing in the universe as there is an 0 in mathematics. So soon as the nothing is, there is something. The whole universe is material, is nothing but matter; for there is the primary act eternally repeating itself in the centre. The universe is a rotating globe of matter.

162. But the universe is an acting gravity, a matter, in which the centroperipheric antagonism is active; it is therefore everywhere matter only, which acts. There is no activity without matter, but also no matter without activity, both being one; for gravity is itself the activity, and itself the matter. Matter is only limited activity. A matter which does not move is not; it can only subsist through continuous origination, through life. There is no dead matter; it is alive through its being, through the eternal that is in it. Matter has no existence in itself, but it is the Eternal only that exists in it. Everything is God, that is there, and without God there is absolutely nothing.

163. It is an illusion to believe that matter were an actual something subsisting in itself. It is even so with numbers, upon which a reality also is bestowed, when they are still demonstrable nothings. A number is nothing truly than an affirmation several times repeated, a reiterated deposition of what is nothing, what is no number. This deposition happens likewise in the universe, where it is the primary act, that is deposited. Where, however, this is, no other station can occur. This exclusive property is usually called the Impenetrable, the Material. It cannot be said in what spot matter arises, so secretly and suddenly does it start into existence. It is matter properly at the first manifestation of being, of time and of space; for at the same instant also the line, surface, density and gravity have been given. The line does not exist if it does not act; the sphere does not exist if it be not inert, i. e. if its forces do not strive towards the centre, and consequently to connexion. Nothing exists if it is not material. Matter is accordingly coexistent with the presence of God.

164. The Immaterial does not exist; for even the Material which is not, is the Immaterial. Everything that is, is material. Now, however, there is nothing that is not; consequently, there is everywhere nothing immaterial. Immateriality is only a postulate principle, by which to get at matter, like the 0 in mathematics, which is nothing in itself, does not even exist, but that still must be posited, in order that numbers may bear a reference to it.

165. God only is immaterial; he is the only permanent immaterial invention, and the axiom being the Formless, Polarless, Timeless. A spirit with form is a contradiction. But the matter also does not exist, because matter is nothing, because it is only a sphere of central actions, which is gravity.

166. The material universe is called nature. There can be only one nature, as well according to time as to space and to divine animation. There is only one God, whose operations expressed, or materially posited, are nature. Nature has originated out of nothing like time and space; or with these has nature also been. God has made heaven and earth out of nothing.

167. God has not found matter co-eternal with himself, and, like an architect, arranged this to his fancy; but he has, out of his own eternal omnipotence, by his will simply, evoked the world out of nothing unto existence. He has thought and spoken, and it was.

168. The doctrine of matter is the Philosophy of Nature. It is therefore the science also of all Singulars, like geometry and arithmetic; thus at bottom is only the third part of mathematics, and is even as certain and demonstrable as this.