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.
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_.
Italics are represented thus _italic_.
* * * * *
THE
RAY SOCIETY.
INSTITUTED MDCCCXLIV.
[Illustration: Portrait of a man, signed W Bagg]
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.
[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.
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.
[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.
PAGE
Conception of the Science 1
Division of the Science. Truth.
PART I. MATHESIS 5
Nothing, § 31. Something, § 50.
A. _PNEUMATOGENY_ 13
Primary Act, § 55. Primary Consciousness, § 59. God, § 61.
a. Primary Rest, § 71. b. Time, § 72. Polarity, § 76. Motion,
§ 80. Man, § 93. c. Space, § 108. Point, Line, Surface,
Globe, Rotation.
B. _HYLOGENY_ 35
a. Gravity, § 148. Matter, Æther, Heavenly Bodies. b. Light,
§ 182. c. Heat, § 198. Fire.
PART II. ONTOLOGY 49
A. _COSMOGENY_ ib.
a. Rest, Centre, § 209. Motion, Line, Planets, § 215. c. Form,
§ 231. Planetary System, Comets.
B. _STÖCHIOGENY_ 59
Condensation, § 253. Simple matters, Elements. a. Air § 282.
b. Water, § 294. c. Earth, § 303.
C. _STÖCHIOLOGY_ 68
Functions of the Elements. 1. Functions of the Æther, § 317.
a. Gravity, § 320. b. Light, § 321. Inflexion, Refraction, Reflexion,
Colours, § 354. Colours and Planets, § 379. c. Heat,
§ 385. 2. Function of the Air, § 410. Electrism. 3. Function of
the Water, § 432. Solution. 4. Function of Earth, § 438.
Crystallization.
D. _KINGDOMS OF NATURE_ 95
Individuals, § 463.
FIRST KINGDOM--MINERALS 96
I. _MINERALOGY_, § 474. Division, § 490.
a. Chemical Division 103
b. Genetic Division. Classes 106
Class I. Earth-Earths Earths.
II. Water-Earths Salts.
III. Air-Earths Inflammables.
IV. Fire-Earths Ores.
Table A to face page 120
II. _GEOLOGY_ 121
_I._ Form of the Planet, § 546. Primary Valleys. _II._
Organs of the Planet, § 570.
A. _Earths_ 127
a. Earth Formation--Primary Rocks, § 573. Granite, Gneiss,
Mica-schist, Lamination, Primary Limestone. b. Water-formation,
§ 622. Transition-rocks, Sedimentary or Stratified Rocks,
Stratified Limestone, Petrifactions or Fossil Remains.
c. Air-formation--Trap-rocks, § 681. d. Fire-formation--Volcanic
Rocks, § 690.
B. _Metallic Ores_ 148
a. Metallic Veins, § 693. b. Production of Ore, § 698. c. Poison,
§ 755. d. Magnetism, § 760. e. Earth-magnetism, § 771.
C. _Inflammables_ 166
a. Sulphur, § 801. b. Coal, § 819.
D. _Salts_ 170
a. Salt-periods, § 827. b. Chemism, § 847.
PART III. BIOLOGY 178
A. _ORGANOSOPHY_ ib.
I. _Organogeny._ Galvanism, § 867. Primary Organism, § 882.
Creation of the Organic 184
a. Elementary Body--Protoplasma or Primary Mucus, § 898.
Change. b. Form--Globe, § 926. Primary Vesicle, § 933. Infusoria,
§ 935. Theory of Generation, § 943. c. Processes of the
Organic. 1. Earth-process--Nutrition, § 964.
2. Water-process--Digestion, § 971. 3. Air-process--Respiration,
§ 977. 4. Motion, § 984.
II. _Organognosy_ 197
Division of the Organism, § 933, into Planetary and Cosmic Organism.
Processes of the Cosmic Organism, § 1014. 1. Process of Gravity,
§ 1021. 2. Process of Heat, § 1024. 3. Process of Light, § 1027.
SECOND KINGDOM--VEGETABLE KINGDOM 204
I. _PHYTOGENY_, § 1038.
A. _Planetary Organs_--Vegetable Trunk 206
I. _Tissues_, § 1055. 1. Water-organ--Cellular Tissue, § 1056.
2. Earth-organ--Vascular Tissue, § 1062. 3. Air-organ--Tracheal
Tissue, § 1065.
II. _Anatomical Systems--Sheaths_, § 1075. 1. Tracheal
System--Wood, § 1077. Vascular System--Liber, § 1080. 3. Cellular
System--Bark, § 1084.
III. _Organs--Members_, § 1086. 1. Water-organ--Root, § 1090.
Earth-organ--Stalk, § 1096. 3. Air-organ--Leaves, § 1120.
B. _Æther-Organs_--Thyrsus or Flower 228
1. Floral Envelopes, § 1187. Involucrum, Calyx, Corolla--Numerical
Law, § 1209. Coloration, § 1241. Stamen-filaments, § 1252--Anthers.
2. Pistil, § 1276. Style. 3. Seed, § 1301. 4. Fruit,
§ 1335. Fruit of the Flowerless Plants, § 1346.
II. _PHYTO-PHYSIOLOGY_ 255
I. _Functions of the Trunk._ 1. Facts.
A. Constituent Parts. a. Inorganic Bodies--Elements, § 1364.
b. Organic Bodies, § 1368.
B. Preliminary Events 259
2. Processes 262
A. Cellular Processes, § 1385. Absorption, Evaporation, Digestion.
B. Vascular Processes, § 1399. Conveyance of Sap, Mixture of Sap,
Secretion.
C. Tracheal Processes, § 1411. Inspiration, Nutrition, Oxydation.
Galvanic Process--Sap-motion, § 1443.
II. _Functions of the Floral Organs_ 272
1. Function of the Corolla--Fecundation, § 1454. Irritability.
2. Function of the Ovarium, § 1473. 3. Function of the Seed.
Germination, § 1476. Growth, § 1481. Fall of the Leaf.
III. _PHYTOLOGY_ 279
_Vegetable System_, §§ 1508-1754.
Table B opposite to page 316
THIRD KINGDOM--ANIMAL KINGDOM 318
I. _ZOOGENY_ 318
Anatomy 326
I. _Tissues_ 327
1. Point-tissue--Nervous mass, § 1801. 2. Globe-tissue--Osseous
mass, § 1825. 3. Line-tissue--Muscular mass, § 1835. 4. Vesicular
tissue, § 1846. Integument.
II. _Anatomical Systems or Sheaths_ 338
A. _Vegetative_ 339
1. Intestinal System, § 1878. 2. Cutaneous System, § 1909.
Branchiæ, Tracheæ. 3. Vascular System, § 1926. 4. Sexual
System, § 1999.
B. _Animal Systems_ 356
1. Nervous System, § 2018. Brain, Senses. 2. Osseous System,
§ 2079. Vertebral Number, § 2109. 3. Muscular System, § 2118.
III. _Organs_ 378
A. _Vegetative_ 378
1. Intestinal Organs, § 2158. 2. Vascular Organs, § 2194.
Branchiæ, Lungs, Liver, Spleen, Kidneys. 3. Respiratory Organs,
§ 2246. Coverings, Hairs. 4. Sexual Organs, § 2285. Impregnation,
§ 2315. Urinary Organs, § 2337.
B. _Animal Organs_ 404
1. Osseous Organs--Limbs, § 2370. 2. Muscular Organs, § 2398.
3. Nervous Organs, § 2405--Senses. 1. Vascular Sense--Sense
of Feeling, § 2440. 2. Intestinal Sense--Taste, § 2454. 3. Pulmonic
Sense--Smell, § 2468. 4. Osseo-Muscular Sense--Hearing,
§ 2476. 5. Nervous Sense--Vision, § 2488.
II. _PHYSIOLOGY_ 423
A. _General Functions_ 423
B. _Special Functions_ 425
I. Functions of the Tissues, § 2539--Heat.
II. Functions of the Systems 429
A. Of the Vegetal Systems. 1. Digestion, § 2571. Poisoning.
2. Respiration, § 2639. 3. Circulation, § 2655.
B. Functions of the Animal Systems 442
1. Of the Osseous System, § 2672. 2. Of the Muscular System,
§ 2686. 3. Of the Nervous System, § 2700. Mesmerism, § 2721.
Sleep, § 2736. Periodicity, § 2761.
III. _Functions of the Organs_ 455
1. _Functions of the Encephalic or Brain-Animal_ 456
A. Organs of Motion.
B. Organs of Sensation 458
1. Sense of Feeling, § 2786. Sense of Taste, § 2821. Sense of
Smell, § 2835. Auditory Sense, § 2849. Speech. Sense of
Sight, § 2902.
2. _Functions of the Sexual Animal_ 477
A. Vegetal Sexual Organs--Formation of Urine, § 2934
B. Animal Sexual Organs 480
1. Male Organs, § 2946. 2. Female Parts, § 2952. Mammæ.
Development of the Fruit or Foetus, § 2981. Parallelism of the
Foetus with the Animal Classes, § 3034. Periods of Life, § 3502.
III. _ZOOLOGY_ 494
A. Division into Provinces 501
B. Division into Circles 502
C. Division into Classes 511
First Province, Somatozoa (Rumpfthiere) Splanchnozoa; 511
including the three Circles of Intestinal, Vascular, and
Respiratory Animals, or Protozoa, Conchozoa, and Ancyliozoa;
with their contained Classes up to 568
Metamorphosis of Insects, § 3291. Parallelism, § 3299.
Relationships, § 3301.
Second Province, Cephalozoa, (Kopfthiere); 544
including the two circles of Sarcose and Sense-Animals;
with their contained Classes up to 568
D. Division into Orders and Families 569
Of those included within the Classes of the First Province or
Splanchnozoa;
with their Tabular Co-arrangement up to 614
Of those comprised by the Classes of the Second Province or
Sarcozoa; with their Tabular Co-arrangement up to 653
IV. _PSYCHOLOGY_ 654
A. _Spiritual Functions of the Somato- or Dermatozoa_ 654
B. _Spiritual Functions of the Cephalozoa_ 658
ERRATA AND CORRIGENDA.
Page 4, § 30, _read_ upon the primary proposition of mathematics
or the axiom.
5, § 35, _for_ magnitudes _read_ quantities.
8, § 39, _for_ Manifold _read_ Different.
11, § 49, _l._ 10, _for_ elevating themselves in power,
_read_ becoming suppressed.
§ 50, _l._ 4, dele the second --.
12, _l._ 1, _for_ magnitudes _read_ quantities;
_l._ 5, _for_ -- _read_ 0.
§ 52, _for_ emerged _read_ been evolved out of
nothing, or been produced from it by addition; but it is, &c.
§ 54, _for_ removing _read_ suppressing.
14, § 59, _l._ 8, _for_ posits itself _read_ itself
posits.
16, _for_ presentation _read passim_, representation.
32, § 134, _for_ Disintegrated _read_ Dissevered.
32, § 137, _for_ never _read_ nowhere.
37, § 161, _l._ 7, _for_ it _read_ there.
38, § 164, _for_ inventive _read passim throughout
Part I._ postulate.
39, _l._ 1, _for_ and the axiom is _read_
the axiom being.
44, § 195, _l._ 15, _for_ that it may shine _read_
upon which it shines.
50, § 214, last line, _for_ darker _read_ dark.
59, § 253, _read_ heavy and material.
61, § 269, 1 and 2, _for_ caloric _read_ hydrogen,
_and for_ hydrogen _read_ carbon.
80, § 388, _for_ nitrogen _read_ hydrogen.
112, _l._ 6, _for_ Terpentin _read_ Serpentin;
_l._ 7 from bottom, _for_ Calces _read_
Calcareous earths.
124, § 562, _for_ the recent _read_ new.
139, § 633-4, _for_ disintegrations _read_ dispersions.
159, § 761, _for_ metallic read _magnetic_.
186, § 914, _for_ heat of blood _read_ blood-heat.
209, § 1060, _read_ constantly circulate therein.
213, § 1077, _l._ 6, _for_ but before _read_ and
whereas; _l._ 7, _for_ have _read_ previously,
_and dele_ it has then, _and read_ the appearance is now.
228, § 1161, _read_ has been reproduced _after_ trunk,
_and dele_ being.
249, § 1314, _for_ umbilicus _read_ hilum, _and for_
cause _read_ basis.
307, § 1679, _instead of_ stipaceous _read_ hypogynous.
308, § 1687, _l._ 2, _read_ Stielblumen or Hypogynes.
320, § 1763, _after_ light-æther _read_ from the dead mass, &c.
327, § 1800, _for_ substance, &c., _read_ contents become, &c.
328-9, _for_ Myxozoa _read_ Protozoa, _and for_ Medusæ
_read_ Acalephæ _here and passim_.
330, _l._ 2, _after the word_ radiating _read_ æther.
332, § 1824, _for_ substance _read_ contents, _and_
§ 1827, _for_ substance _read_ mass.
334, § 1837, _read_ upon the middle rate of oxydation.
327, _l._ 5, _transpose the words_ matter _and_ spirit.
345, § 1928, _read_ elemental matter.
346, § 1931, _read_ at certain points, _after_ each other.
354, § 1992, _read_ through the medium of the gills, the water
through that of the intestine, &c.
355, § 2006, _for_ along with _read_ which belong to the
category of.
361, § 2039, _read_ plexus-forming ramules; § 2046, _for_
is imparted _read_ furnishes us, _and for_ by
_read_ with.
362, § 2050, _for_ oesophageal _read_ pharyngeal,
_passim_, _as also_, pharynx _for_ oesophagus.
372, § 2114, _for_ enter into the composition of _read_
appertain to; _and for_ Mammalia _read_ Thricozoa.
376, § 2141, _read_ the bone, the fluid which has been
secreted from it and rigidified.
381, § 2176, _for the last word_ cyst _read_ cyst,
_hic et passim_.
386, § 2211, _read_ bivalve Mollusca, _passim throughout
Zoogeny_.
393, _l._ 1, _read_ exsecernent.
398, § 2313, _read_ Snail-type of organization.
405, § 2371, _read_, or the integument _after_ respiratory
organ.
408, § 2387, _for_ carnivorous _read_ false molars;
_for_ incisor _read_ laniary molar; _for_
premolar _read_ second, _and for_ tuberculous
_read_ third true molar.
493, § 3054, _for_ testaceous Mollusca _read_ Conchozoa
or Shell-animals.
515, § 3170, _for_ stock _read_ trunk.
544, § 3301, _after_ analogy _read_ which at best is but
a word of random definition.
532, § 3256, _read_ pharyngeal or pneumogastric nerves, _to
end of paragraph_. _For the words_ evolution _and_
evolved, _read passim in the Botanical and Zoological parts_,
perfection _and_ perfected, _as the text may require_.
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.
ÆTHER.
169. The matter, which is the direct position of God, which fills the
whole universe, which is the time in a state of tension and motion, the
formed space, the heavy primary essence, I call the _Primary matter_,
the matter of the world, cosmic matter, _Æther_. The æther is the
first realization of God, the eternal position of the same. It is the
first matter of creation. Everything has consequently originated out
of it. It is the highest, divine element, the divine body, the primary
substance = 0 +-.
170. The æther fills out the whole universe, and is, consequently, a
sphere, yea, the world's sphere itself; the world is a rotating globe
of æther.
171. The sphere of æther, not as yet individualized, I call _chaos_.
From the beginning was chaos, and this was æther, and unto the end
will chaos become æther. The æther is the apparent nothing, and thus
it is the chaos. This was not the latter and not the former, but an
existing nothing.
172. The æther is the imponderable matter, because it is gravity and
totality itself, because it is the infinite matter.
173. The æther has no life; it is the only mortuum, because it is the
heavy 0. In æther, however, reside all the principles of life, all
numbers; it is the substratum, the essence of life. There is only one
universal substratum in nature.
HEAVENLY BODY, POINT, CENTRE, GRAVITY.
174. Everything which emerges out of æther and is posited as a finite
matter, can be nought else than a repetition of the sphere.
175. The æther subdivides into an endless number of subordinate
rotating spheres, and so it must, because the world is not a whole
devoid of parts, but only a whole in the parts, only a repetition of
_positions_. The chaotic sphere of æther consists essentially at one
and the same time of an infinity of spheres.
176. A chaos has never existed. The General never exists, but only the
Particular. Chaos was from eternity a multiplicity of ætherial globes.
Chaos is only postulate.
177. Every sphere of æther is complete in itself and closed, and
therefore rotating around its axis and around the universal axis of the
æther.
178. The new rotation in the heavenly bodies condensed in the periphery
of the æther, follows as a necessary result, on account of the unequal
velocity of its outwardly and inwardly lying points.
179. Every individual sphere has _two_ motions in itself; the one
depends upon the representation of the primary act in itself by the
_special_ rotation; the other re-attempts to regain the primary centre,
through the _general_ rotation around the universal axis.
180. Such a sphere rotating for itself is called _a Heavenly body_. A
heavenly body again is the image or metatype of the Eternal; it is a
whole, it is alive; everything, even the highest, can originate out of
it; everything develop itself out of the coagulated, individualized
æther. The heavenly body has a double life, an individual and an
universal, since it is for itself and at the same time in the general
centre. Every _Individual_ must have a double life.
181. The heavenly bodies are as old as the æther, consequently they
are from the beginning, and endure also without end. As they are only
coagulated æther, so are they susceptible of being resolved into the
same, such as are probably the comets.
b. LIGHT, LINE. (_Second form of the World. Motion._)
182. The æther is from eternity, not merely monas, but also dyas;
from eternity it stands in a state of tension with itself, when, as
the image of the existing primary act, it has emerged out of itself
into two poles. This self-egression or self-manifestation of æther,
or of substance simply, is the self-egression of the point into the
periphery. As dyas, æther exists under the form of polarity, of
central and peripheric effort; the æther in a state of tension is a
centroperipheric antagonism.
183. The æther is separated from eternity into a central and peripheric
substance, and that indeed through its simple position as a globe. The
universe is a duplicity in the form of æther; it is both indifferent
and different æther, both central and peripheric. The central mass
of æther may be called sun, the peripheric planet. Only one sun can
originate in a globe of æther, but many planets.
184. Between the central and peripheral mass of the æther, between the
sun and planets, there is tension. Through this solar-planetary tension
the æther fluctuating between the two becomes polarized.
185. The tension of the æther proceeds from the centre and thus from
the sun. Were the sun to be removed, the polarity of the æther would be
annulled; it would be again the indifferent chaotic æther, the null and
void matter. For the absolute substance to exist it needed not simply
itself, but an identical centre and a dissevered periphery. Is there
no peripheric mass, no planet, so also is the tension annulled; centre
cannot be without periphery, sun not without planet, nor vice versâ.
The tension of æther is thus excited by the sun and conditioned by the
planet. The planet is not the principle, but the Redintegrant of the
tension of æther by the opposition.
186. At that part of the universe where no periphery stands opposed to
centre, no planet to the sun, the æther is not tense, but indifferent,
annulled. There can thus only be columns of æther, which are rendered
tense, namely, those _columns_ of æther which are found between the
sun and the planets. Near to the planets the æther is void of action,
indifferent, non-apparent. There are consequently as many apparent
æther-columns, as there are heavenly bodies, that stand in the process
of polarity opposed to each other. These columns move with the
planets around the suns. The indifferent æther of the world-space is,
therefore, successively rendered tense, as the planets move around
suns, and becomes again indifferent behind the planets.
187. But besides this, that columns of tension only exist, and
therefore that the æther is nowhere active as a sphere, there is still
no spot in the world-space where there would be only indifferent æther,
nothing; for the æther consists of many globes of æther. There is thus
nowhere an indifferent æther, consequently nowhere an empty space. The
idea of the repletion of space is not that of the sphere, but of the
columns of tension, which by their crossing in every direction form a
sphere only externally.
188. That which is thought of as originally filling space is not the
quiescent but only the moved, tensed æther. The former is the void
space, the nothing.
189. The tension of æther is an action, which operates according to the
line. This linear activity, which makes its exit from the central mass
and is excited hence to the peripheral mass, is _Light_, or in short,
light is tension of æther.
190. Light is a traction of lines or radial action; consequently an
antetype of magnetism. A ray of light is a radius. The ray of light
has two extremities different from each other; that turned towards the
sun is 0, that which comes in contact with the planets is ±. Light is,
therefore, a splitting, rending action.
191. Light is the life of the æther. Hitherto the æther was an inactive
nothing, mere substratum for a future. This nothing, when it becomes
centroperipheric, seeks to tear the mathematical point into radii and
circumferences, _appears_; and this centroperipheric manifestation we
call light.
192. The untensed, indifferent æther is, therefore, _darkness_, and
this is the essence, the rest of æther. Chaos was thus darkness; the
world arose out of darkness when light became. Light has originated out
of darkness when the chaos was moved. Were it possible therefore for
all light to vanish, the world would again return into its old nothing;
for darkness and nothing are one. God has separated the light from the
darkness.
193. If light be only a column of æther in a state of tension, light
is or exists only between the planet and the sun; near to the planet
and behind it is darkness. The primary sphere is a dark sphere,
transpierced only by single rays of light. Each star, however, stands
in a state of tension with another; thus many thousand rays of light
stream forth from each, and fill out the world-space in all directions.
There is therefore no absolute darkness, because there are infinitely
numerous rays of light. In the night also there is always as much
light present as is necessary to maintain the heavenly bodies in their
action. For the world there is no night, but only for the planets.
It will be shown that the air maintains its existence simply through
the operation of light; were it therefore always dark, were night
to endure for ever, the air must soon assume another composition or
mixture, and everything that lives in it must fall to ruin. This is
shown also by the diseases and crises of the same.
194. Light is from eternity, for the tense æther was from eternity.
The dark chaos exists only as postulate. Light is time that has become
real, the first manifestation of God; is God himself positing, is
the dyadic God. The dyas is not merely radiality but light; or both
are one, time and light are one, motion and light are one. When God
numbers, when he draws lines, he thus creates light. God becoming
self-conscious is light. Light is God illuminating. Darkness has
accordingly never existed, although the light is derived from the
darkness, like numbers and figures are out of nothing.
195. Light is no matter. There is no substance called light, but the
æther is illuminant through its binary division. The sun does not,
therefore, stream forth when it illumines the planets, and loses
nothing of its magnitude; it is not to be feared that we shall ever
lose it. That the sun is an undulating sea of flame, that it is
throughout a volcano, that combustions or electrical processes of
light, appearing to us as light, occur in its atmosphere; that the
velocity of rotation hurls about the light-particles, and that these
particles scattered in the world-space are, by an unknown route, or by
means of comets, again brought back to the sun, are opinions unworthy
the inquirer into nature. The sun gives out nothing but the impulse,
not, however, the mechanical, which makes the space of heaven tremble
upon which it shines; but the purely spiritual, as the nerves rule the
muscle. The sun can never be extinguished, never become dark; for it
gives out light, not as a fire, but simply by reason of its standing
in the midst; its simple position, its enchainment to the planets is
light. A fire upon the sun would not be perceived by us; it would
not lighten nor warm us, because of its having no relation to us.
The central relation of the sun toward us cannot, however, remain
unobserved, and this observation is even that of light.
196. Matter has become by means of light, is a child of light, is but
illuminating æther. Every binary division of matter manifests itself as
light.
197. The whole universe is transparent, because everything has issued
out of the tension of æther. Everything which is matter is light, and
without light there is nothing. Without light the universe is not
only dark but it is even not. Light is the universe, and every Finite
is only a different position of light. The world is a thoroughly
illuminating globe, a rotating globe of light. The solar system must
have been created according to the laws of light. The phenomena
of the world are only representations of optics, consequently of
living geometry. What we see is nothing but optical construction or
figuration. (Vid. Oken's 'Essay über das Licht;' Jena. Fromann. 1808.)
c. HEAT, DENSITY. (_Third form of the World. Shape._)
198. Light is not simply a motion in itself, a mere continuous
excitation of polarity in the æther, but it is also the æther itself
_set in motion_ thereby. All polar actions resolve themselves finally
into motion of the polarized masses. The end of electricity, galvanism,
magnetism, is motion. It will be, however, shown that all these polar
functions are only repetitions of the primary polarity; this must
therefore produce what the former did, namely, ætherial motion.
199. Every point of the æther becomes polar, every one attracts and
_repels_ the other; whereby motion arises in the innermost parts of
the æther itself. Not a portion of the æther is moved on, but motion
originates in the mass of æther itself. The æther-atoms quit each other.
200. The æther is, however, that which is filling space, is space
itself, the Expansissimum of the world, the Formless and therefore that
which adopts all forms. The formless æther, when it moves itself,
must be connected with a phenomenon, that depends upon its expansion
and identification, which is polarized by light. This action of the
æther does not therefore depend upon the tension of æther, not upon
production from differences in the same, but upon dissolution of the
tension, therefore upon extension, upon the indifferent representation
of space. This action, which is at the same time universal, can only be
heat. Moved æther is _Heat_.
201. Heat is the contest of the indifferent æther with light; light
alone produces heat. Without light the world were not only dark, but
also absolutely cold. Cold is untensed and quiescent æther, death,
nothing; dark and cold are one. Heat is therefore the result of light,
but equally eternal with it; it is space represented really, as that is
real time.
202. Heat is not moved indifferent ether, which is = nothing; but moved
and tensed or the _moved light_.
203. Heat penetrates into thickness as an extending function, but does
not oscillate between two poles like light. It is only the function
of density, and depends upon nothing else, not upon lines or mere
surfaces, but upon the living sphere.
204. Heat and light, although characters of _one_ substance, yet
stand in an antagonism like thickness and line, or as indifference
and difference. Heat is properly the first perfected position of the
primary act, while light is only the act of positing; the latter
therefore is +, the former-. Or also, gravity is the absolute position,
simply = 0; light is the commencing egression of this position out
of itself +-, heat the completion + 0-, and therefore the position
everywhere; it will everywhere deposit, therefore it is motion,
repletion of space, expansion. Light is gravity become real, or 0
become real; 0 however, rendered real, is +-. Heat is as-at the same
time +-and 0, or light and gravity, material light, light that is
filling. Both will also assert the antagonism of their genesis through
all forms of the world. The heat seeks to destroy the line, which the
light endeavours to establish; heat seeks to produce homogeneity in the
Dissimilar, light to effect the reverse. Heat is slow in its motion;
with it the mass of æther must continually move, or move whither it
will operate; light, however, acts spiritually and rapidly, without
motion of the mass, but only glides continually with the latter. Heat
is not created, it is no special matter different from æther. There is
no _body of heat_.
205. Heat is everywhere where the æther is, and must consequently be
regarded as a sphere. Heat is not present merely in the columns of
æther between the heavenly bodies, but everywhere. Therefore heat does
not move itself in the direction of the line, but it extends itself on
all sides, as real space.
FIRE.
206. Light and heat were the first phenomena of the world. Heat with
light, however, are _Fire_. Fire is the totality of æther, is God
manifested in his totality. God, previous to his determination to
create a world, was darkness; in the first act of creation, however, he
appeared as fire. There is no higher, more perfect symbol of divinity
than fire. God's whole consciousness, apart from individual thoughts,
is fire. The Holy Scriptures therefore usually admit of God appearing
under the form of a fire, as a fiery bush, a flame. The world is none
other than a rotating globe of fire.
207. Everything that is, has originated out of fire; everything is
only _cooled_, rigidified fire. As everything has become out of fire,
so must everything to be annihilated have recourse to fire. If finite
things be only fire singly posited, so must every change occurring in
the same be an igneous change. Nothing changes in the world but fire.
The essential change of things take place only by fire.
RETROSPECT.
208. The Triplicity of the primary act in the universe has now been
completely demonstrated. The first manifestation of God is monas; to
this corresponds _Gravity_, _Æther_, darkness, the cold of chaos. The
second manifestation of God is the dyas; to this corresponds the æther
in a state of tension, the _Light_. The third manifestation of God is
the trias; to this corresponds the want of form, _Heat_. _God being in
himself is Gravity_; _acting_, self-emergent, _Light_; _both together_,
or returning into himself, _Heat_. These are the _three Primals_ in the
world, and equal to the three which were prior to the world. They are
the manifested triunity = _Fire_.