Front matter
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Preface
It is not our object, in the present work, to offer the facts of philosophy in a form more acceptable to ourselves than the elaborate works now current ; much less do we expect to add, at any point, to the fulness of these presentations. Our aim is simply to make, in as brief a compass as possible, a contribution to a clearer understanding of the facts of philosophy in their dependence on each other, and in the conclusions to which they naturally lead. In accomplishing this purpose, we shall have occasion only for a brief statement of the primary features in the different phases that philosophy has assumed, and shall take for granted considerable familiarity with the topics under discussion. If we render any aid, it will be aid in comprehending the facts rather than in securing a more complete knowledge of them.
We shall be more interested in the distinctive and extreme positions which writers and schools of philosophy have taken, the peculiar impulses they have felt and imparted, than in the limitations, qualifications, and partial retractions by which they have striven later to restore the balance of thought and to defend themselves against attack. The points emphasized will be those which define the directions of philosophical inquiry, and which best serve to mark the dependence of its successive positions in its descent to our time. Our work should be judged wholly by this its explanatory purpose.
VI PREFACE.
There are two sorts of superficiality — the possession of numerous facts that are not well understood, the possession of theories that are not well sustained by the facts. It is against the first of these that our contention chiefly lies in this interpretation of philosophy. The very multiplicity of phenomena may hide from us their significancy, and leave us content with the simple knowledge of acquisition. Our present effort is to penetrate the meaning of phenomena, not to multiply them. We shall be satisfied, on the side of instruction, if we do not misrepresent or pervert them ; we shall be wholly satisfied, on the side of exposition, if we assist the reader in pursuing the paths of philosophy with increased insight and pleasure. All these ingenious and obscure ramifications of thought have grown out of each other, have served partial and temporary purposes of explanation, and, in spite of appearances, have led us somewhat nearer the goal of truth. Their extreme statements have been compensatory movements which have helped to restore the equilibrium of the mind. This supreme fact in philosophy of coherency, we shall endeavor to bring more distinctly into the light. Metaphysics are often derided and avoided as worthless, sporadic products of speculation, because this their inevitableness, both in the efforts after growth and in the errors of growth, is not sufficiently felt. The most comprehensive outlook we can possibly take of the products of the human min'd is one in survey of those manifold phases of philosophy by which it has sought to explain the world to itself.
The dates given are, for the most part, those of Ueberweg.
Introduction
PAGE
§ I. An Interpretation of Philosophy implies what, . . . . i
§ 2. Philosophy and knowledge, ....... 2
PRELIMINARY CHAPTER.
DIVISIONS OF PHILOSOPHY.
§ I. European philosophy, . . . . . . . .8
§ 2. Ancient philosophy, 10
Part I. Ancient Philosophy
CHAPTER L
THE FIRST PERIOD IN GREEK PHILOSOPHY.
§ I. Speculative inquiry in Greece, ....... 12
§ 2. The beginning of philosophy, ....... 12
§ 3. Pythagoras and Doric philosophy, . . . . . .15
§ 4. Parmenides and the Eleatic School, ...... 17
i^ 5. Heraclitus and the Ionic School, ...... 20
§ 6. Democritus and the Atomists, ....... 23
§ 7. Empedocles and the later Ionic School, . . . . .24
Chapter II. Second Period In Greek Philosophy
§ 2. Protagoras — Gorgias, ......... 32
Vlll
CONTENTS.
^ 3. Socrates, .
§ 4. Disciples of Socrates,
§ 6. Ethics of Plato,
§ 7. Aristotle, .
§ 8. Ethics of Aristotle, .
§ 9. Socrates, Plato, and Aristotle,
§ 10. Two Schools in Ethics — Epicurus,
§11. Zeno and Stoicism, . . ,
§12. Scepticism, ....
§ 13. Eclecticism, ....
Chapter III. The Third Period In Greek Philosophy
§ I. Theosophy — three forms — Hellenistic form,
§ 2. Neo-Pythagoreans — Neo-Platonists, .
§ 3. Results — Exaltation of God,
§ 5. The material world and God,
PAGE
33 34 36
51 55 57 61
67 69
77 80
83 84
Part II. Medieval Philosophy
§ I. The transition, .... § 2. Character of mediaeval philosophy.
Chapter I. The Patristic Period
§ I. Judaism and Christianity, .......
§ 2. The Greek Church and the Latin Church, . . . ,
Chapter II. Themes Of Discussion In Medieval Philosophy
§ I. Nature and government of God, . . . . . § 2. Nature of general terms,
96 99
102 104
CONTENTS.
IX
PAGE
§3. Results, 113
§4. Three forms of general terms, 121
Chapter III. Persons In Medieval Philosophy
§ I. Johannes Scotus Erigena, 127
§ 2. Roscellinus — Anselm — Abelard, ....... 129
i^ 3. Averroes — Alexander of Hales — Albertus, 133
§ 5. Johannes Duns Scotus, ........ 145
§ 6. William of Occam, 148
§ 7. Results, 149
Chapter I. Causes Of The New Era
§ I. Decay of scholasticism,
§ 2. Development of science,
§3. Unbelief, .
^ 4. Reformation,
155 158 159 159
Chapter II. Transitional Persons
§ I. Sir Francis Bacon,
§ 2. Rene Descartes, .
^5,3. Monism vs. dualism, .
§4. Baruch de Spinoza,
§ 5. Gottfried Wilhelm Leibnitz
164 167 181 186 193
CHAPTER HI.
ENGLISH PHILOSOPHY.
§ I. The new era,
^ 2. National life and philosophy,
203 204
X CONTENTS.
Part I. The Early Empirical Movement In English Philosophy
PAGE
§5. David Hartley, 218
§ 6. Joseph Priestley — Erasmus Darwin, ...... 220
PART II.s
THE LATER EMPIRICAL MOVEMENT IN ENGLISH PHILOSOPHY.
§ II. Herbert Spencer, ......... 244
§ 12. "William B. Carpenter, 255
§ 13. George John Romanes, ........ 257
§ 14. Evolution and empiricism, ....... 259
Chapter V. __ Philosophy In America
§ I. Jonathan Edwards, 310
§2. James McCosh, 315
§3. Mark Hopkins, . . 318
§ 5. Empirical philosophy, 321
§ 6. Idealistic philosophy, 322
CPIAPTER VI.
PHILOSOPHY IN FRANCE.
§ I. National character, . 325
Part I. French Materialism
§ 2. Julien Offroy de la Mettrie,
§ 3. Etienne Bonnet de Condillac,
§4. Baron d'Holbach,
§ 5. H. A, Taine,
§ 6. Auguste Comte, .
§ 7. Positivism and Sociology, .
327 330 331 332 335 346
Part II. Intuitional Philosophy In France
§ 8. Nature of intuitionalism, . . . . . . . . 355
§ II. Reaction against empiricism, ....... 366 xu
CONTENTS.
Chapter VII. Philosophy In Italy
§ I. Position held by Italy,
§ 2. Giovachino Ventura and others,
§ 3. Antonio Rosmini and others.
PAGE
368 369
Chapter VIII. The Philosophy Of Germany
I. Methods in philosophy, . . . . .
PART I.
§ 2. Immanuel Kant,
§ 3. "Critique of the Pure Reason,"
§ 4. Illusions of Kant's philosophy, ,
§ 5. The nature of things-in-themselves,
§ 6. Powers of mind,
§ 7. Antinomies of Kant,
§ 8. The being of God,
§ 9. Form-elements,
§ 10. Categories of Kant, .
§ II. " Critique of the Practical Reason,"
§ 12. ** Critique of the Faculty of Judgment,"
PART II.
IDEALISM IN GERiMANY.
§15. Immanuel Hermann Fichte,
§16. " "
§ 17. Friedrich Wilhelm Schelling,
§ 18. Georg Wilhelm Friedrich Hegel,
§ 19. The movement by triplets,
§ 20. Idealism — Monism, .
382 386 389 395 397 404
405 410 416
423 426
436 438 442 445 447
CONTENTS. xiii
Chapter IX. The Conclusion
§ I. German philosophy, ......... 498
§ 3. The growth of philosophy and constructive realism, . . . 504
AN
HISTORICAL INTERPRETATION OF PHILOSOPHY.
INTRODUCTION.
§ I. An historical interpretation of the progress of philosophy impHes a general knowledge of the development of truth in this direction ; the ability to indicate distinctly the position occupied by each person, each school, each era. In this progressive movement ; a recognition of their dependence In growth on each other, and so, as the allimportant result, the power to understand the contributions and confirmations which they bring to our present convictions. If we believe in the essential integrity of the human mind — and if we do not, it is hardly worth our while to waste our emotions on so earnest inquiry — we cannot doubt that our power to-day to lay down, with any certainty, the leading lines of truth, must turn very much on our apprehension of the results of thought in the years that are past. If knowledge, in each period, is partial and relative — as it assuredly Is — Its chief value is found in offering a safe, transitional term to that more perfect presentation which is to spring out of It. We need to distinguish terminal from lateral buds, and, by means
2 INTRODUCTION.
of the general symmetry of growth, separate those more sporadic systems which have simply filled in unoccupied spaces from those central ones which have advanced us along the axis of development. If there is a true growth in thought, it will show this pushing, centralizing tendency, compared with which all other movements are secondary and subordinate. We shall thus be able to confirm the truth we now hold by the support which it derives from the increasing insight of men hitherto, and by the open way it still offers to inquiry. Directions rather than positions, lines rather than points, are the true results of research in the higher fields of knowledge ; and these are laid down by the movements of mind, by its successive and successful efforts in the past. If we really know the ground over which we have travelled in philosophy, and where we now are, we are in the best possible condition for defining the right methods of development, and for discerning the issues to which all investigation is tending.
§2. Philosophy brings a clear, deep, light-bearing atmosphere to the knowledge of men. It spreads above the narrow bonds of association the living products of thought, the broad concave of truth, and brings lifegiving impulses from every quarter to minister to them. Knowledge is not defined by philosophy. It already exists in the experience of men, in hourly affirmations, confirmed by them in a thousand ways amid the manifold processes of life. The question for philosophy to answer is not whether this knowledge is correct or incorrect. Its correctness is already established in that general conviction, so broad in its premises, so irresistible in its authority, as compared Avith the speculations of any one man or set of men concerning it. Philosophy is not
NATURE OF PHILOSOPHY. 3
competent to question knowledge, but only to broaden and correct it ; to determine whether the mists that press in close upon this field of vision can be dispersed, and the depths which quietly infold it laid open. Philosophy is the astronomy of our intellectual system, and its office is to carry, in harmonious extension, the principles of knowledge we already hold in these centres of observation to the very verge of thought. What the mind longs for is that the little shall be enclosed in the large, the transient be included in the permanent, and one pure medium of light envelop us everywhere. We may know but a trifle of the vastness about us. We are content to abide under its infinity. What we do desire is that it shall be everywhere penetrable to inquiry, that it shall be the one indivisible, homogeneous, and eternal field of thought, our inheritance of truth.
Whatever conclusions philosophy may reach, they must be thoroughly consistent with knowledge. Knowledge must be transparent under this more comprehensive light, and be only the more luminous by means of it. Familiar truths must grow brilliant in it, like crystals, and offer, on all sides, facets of reflection. A philosophy that contradicts knowledge, or lies to one side of it, has arisen in forgetfulness of its own problem. That problem is the exposition of the wider relations of truth, the tracing outward of the indications of knowledge, that the mind may return inward again with an increased justification of knowledge to itself. It is impossible that philosophy, itself a later and more speculative product of mind, should contradict knowledge. Knowledge is the historic fruit of human thought, working in all persons, all places, and all periods. It is, by its own inertia, as immovable as the world itself. It is folly to confront universal conviction
4 INTRODUCTION.
by one man's thought. The philosophy that undertakes this task will be ground to dust as a small thing, a stone pressed and revolved by the undying strength of a glacier. That a single person, in remote, wayward speculation, should attempt to set aside, or even to interpret in some remote way, the accumulated experience of all time, growing into universal convictions under the double ministration of physical , tendencies and spiritual appetencies, is an absurdity. It is as if one should strive to alter the orbit of the earth by jumping on it. A theory of knowledge that contradicts knowledge is one that pushes aside the subject-matter with which it has to deal, and expounds the generic movement of the race by the erratic departure of individuals from it. There may come corrections of knowledge out of knowledge itself, corrections wholly in harmony with its fundamental methods, but there can be no criticism by mind that invalidates the processes of mind and the conclusions held under them. It is not the popular as opposed to the disciplined mind that is magnified by the assertion, but the normal as opposed to the exceptional activity of mind.
Science is homogeneous with knowledge. It does in minor directions precisely what philosophy should do in major ones. It makes our insight deeper and more con sistent. It accepts the habitual force of thought, and bears it forward in a full performance of its oflfice. It tests its own ad'ditions and corrections by their concurrence with knowledge, by their ability to carry familiar lines of light a little farther. Philosophy must start from the same centres of truth and return to them. All conclusions that lie beyond the primary convictions of men will b( aberrations, vagaries. An historic interpretation of phi losophy will enforce this fundamental fact, and show how meteoric, flickering, and ineffectual have been all theories of the physical and spiritual universe which have not planted themselves at once on the first terms of experience.
§ 3. Knowledge is made up of two portions, ultimate terms and the relations between these terms. These terms, as simple, are of necessity primary, and capable of no further establishment than that involved in a direct recognition of their being. First terms once accepted, the reflective powers find play in tracing their interactions ; and the great bulk of what we call knowledge is a knowing of the relations of things to each other. Philosophy is found, first, in correct analysis, reaching true ultimates and accepting them as such ; and, second, in a just estimate of the value of thought, and of its inherent limitations in tracing the dependencies of these primitive terms. The first is more preeminently the problem of philosophy ; though the proper extension and correct balance of our mental processes within themselves remain to be determined by philosophy in every possible bearing of them. The winning of true ultimates has been the most difificult and perplexing labor of mind. There has been a very general feeling that what is here termed an ultimate is a negation of philosophy ; a vexatious limit of thought which must itself be transcended. It is the work of philosophy not to carry comprehension beyond itself, but to inquire into its directions and conditions. Comprehension is not an unconditional act, but one thoroughly conditioned. The very desire to overleap the limits of knowledge arises from the absence of true philosophy ; from a vague, verbal tendency of thought, as if the unconditioned were the antecedent and source of the conditioned ; as if we had not reached the secrets of
6 INTRODUCTION.
knowledge till we had transcended knowledge, or found the ultimate till we had passed beyond all terms of experience. It is the office of philosophy to overcome this wayward proclivity ; to explore the eternal conditions of order; and to reject utterly the chaotic and formless as a productive region that encloses the definite creations of reason and contains their germs. We define philosophy as a discussion of the nature and limits of knowledge.
Analysis, a search after ultimates, is the first and everreturning labor of philosophy. These ultimates, whether they are elements in the physical world, sensations in the sensuous world, ideas in the intellectual world, are all to find their confirmation in experience. Being correctly taken, they yield at once the entire field of inductive and deductive reasoning by which we trace their connections with each other. Thus the physical world starts in phenomena, and the intellectual world in form elements, and these being conceded, we are prepared to follow out their constructive dependencies. The hope to evoke all things out of nothing, or — which is another phase of the same effort — all things out of one thing, is an illusion of thought which it is the instant duty of philosophy to dispel. It should be the ambition of philosophy not to overleap itself — a form of transcendent folly — but to define itself, remembering that definition and creation are always identical, equally in the first and in the latest act.
If this view is correct, knowledge lies, from the nature of the case — that is, by the insight of reason — between two distinct terms, including them both, data and the relation of data ; insights and expositions ; positions, as in geometry, and the bearings of positions on each other. The historic progress of philosophy will be primarily disclosed by its search after a more correct analysis, a more distinct cognition of ultimates, as indispensable and valid terms of truth ; and, afterward, by attaining more restrained and better harmonized processes of thought under them. Our philosophy will thus, in its most speculative action, grow up within our experience, and look to it momentarily for confirmation. The stakes will be driven and the cords drawn, not in a purely subjective region, much less in one merely objective, but in a field of facts constantly illuminated by a clear atmosphere of ideas that rounds over it like the vault of heaven. Philosophy has slowly pitched its tent between earth and sky, and it will be our pleasure to see how it has lifted and spread wide its canvas, and bound it fast under all the flaws of controversy.
PRELIMINARY CHAPTER.
DIVISIONS OF PHILOSOPHY.
§ I. The one line of speculative thought whose fruits we are enjoying is that of European philosophy. We shall consider no other except in connection with it, and as modifying, in their formation, these theories of the universe. European philosophy readily falls into three periods, strongly separated from each other in their directions of inquiry and in the form of life which accompanied each phase of development. They are ancient, mediaeval, and modern philosophy. Ancient philosophy is that of Greece, and, chiefly by transfer, that of Rome ; mediaeval philosophy is primarily that of the Latin Church during its period of unity and power ; modern philosophy is that of the last three centuries, and has been associated with a marked diversity in religious beliefs and national life. While each succeeding period has felt strongly the influence of the preceding one, it has been separate from it and distinct in its own ruling tendency.
Ancient philosophy was primarily one of cosmology, medieval philosophy of theosophy, and modern philosophy of ontology. These are the three divisions of philosophy, and they naturally arise in the order of discussion here indicated. The attention of the mind is first directed to the construction and origin of the world about us as a complex fact. Out of this inquiry springs the question
DIVISIONS OF PHILOSOPHY. 9
of the existence of the Divine Being, of his nature, and of his creating and governing power. This discussion in turn leads to a more profound consideration of the relation of matter and of mind, and of their respective claims as primitive, independent forms of being. The earliest inquiry pushes toward this question and helps to raise it, but it is not till a later period that it becomes the absorbing point of exposition.
Leading features in cosmology, in the meantime, are settled by physical investigation ; while psychology, in its effort to grasp the true character of mental powers, becomes a field of vigorous strife. The ultimate terms of knowledge and forms of being accepted by us must turn on our estimate of the nature of mind. In ancient philosophy the separation between matter and mind was left relatively obscure ; the two were discussed together as parts of one problem — the origin of things. In mediaeval philosophy, the distinction, as a minor one, was overshadowed by the attributes of God. In modern philosophy, the two forms of being, physical and spiritual, have been under constant consideration as the key of all speculative thought. Cosmology and theosophy are both seen to be involved In their relation. This dependence once settled, other conclusions follow with ease and certainty.
Philosophy, a consideration of the nature and limits of knowledge, touches all modes of science and forms of faith. It is thus mingled with various inquiries. It is intimately associated with cosmology, theosophy, and psychology. Cosmology discusses the formation of the [world ; theosophy, the nature of God ; and psychology, the owers of the mind. Psychology is properly preliminary to any inquiry into the nature of knowledge ; ontology is of the substance of philosophy, as it investigates the ultilO PRELIMINARY CHAPTER.
mate forms of being. The logical form of inquiry would be psychology, ontology, cosmology, theosophy. Having defined the range of our own powers, we are ready to determine by means of them the ultimate terms of being, to trace these terms in the unfolding of events, and from these events to approach the problem of the Divine Presence.
The natural order is never the logical order. Complex phenomena first offer themselves to us. Only by many analyses and many references do we slowly approach ultimate truths. We explore the river of knowledge from the mouth upward. These various associated forms of inquiry combine and re-combine in very many ways in the slow, irregular progress of thought.
§ 2. Ancient philosophy falls into three periods. The first extends from the dawn of inquiry to the time of Socrates ; the second, from the time of Socrates to the Christian era ; the third, from the Christian era to the opening of mediaeval philosophy. The first period covers the gradual development of speculative thought in Greece ; the second, its stage of highest attainment ; and the third, its slow decline. The first era is more purely one of cosmology ; the second adds to this discussion that of anthropology ; and the third passes on to theosophy. The first and the second periods are definitely divisible from each other. Socrates was not only the earliest of the great men of the middle era ; he gave a decisively new and more intellectual direction to inquiry. The second and the third periods are indivisible, otherwise than arbitrarily, both in time and in theme. The transitions are slight and slow, arising with different degrees of distinctness in different places. There is also the same obscurity of dividing lines in the passage from ancient to mediaeval
DIVISIONS OF PHILOSOPHY. II
philosophy. The former "gradually decayed with the decay of Roman civilization, and the latter slowly grew with the growth of Latin Christianity. The two, therefore, lay in the soil together during the centuries of overthrow, the one as the dissolving life of the past, the other as the slowly informing life of the future ; the one as the mould of departing civilization, the other as the seeds of coming civilization. The movement which opened modern philosophy was well-defined and general. A new era, however, is never a question of quantities. That which remains of the old counts for little ; that which expresses fresh power counts for much.
Chapter I. The First Period In Greek Philosophy
§ I. The Greek was well fitted for speculative Inquiry, not only by original vivacity of mind, not only by many distinct centres of civic life, which both by their separation and by their union promoted the most lively individuality of thought, but also by the absence of any overbearing ecclesiasticism. The religious life of the Greek was not such as to intimidate the mind, to lay down for it any directions which it must pursue, or any limits within which it must confine itself. It has rarely happened in the world's history that any religious system has laid lighter intellectual restraints on its votaries. The gods of Olympus, themselves a higher kind of human beings, were so enclosed in nature as to give very few hints by which to settle its constructive problems. The myths of religion bore a poetic, free form, and did not, like those of oriental faith, involve a cosmogony, or burden the mind with the leading features of a speculative method. No dominant notion, like that of emanation, predetermined the direction of thought.
§ 2. Grecian philosophy made a definite beginning with
Thales (640) of Miletus. He gave rise to the Ionian school, whose early representatives were Anaximander (611) and Anaximenes, also of Miletus. Thales regarded water as the primitive element ; Anaximenes gave this position to air ; while Anaximander accepted, in place of specific substances, an indeterminate substance, infinite in quantity, from which the later varieties of matter were evolved. We thus have an early example of an obscure, general form accepted as the source of special forms ; of the definite referred to the indefinite. The world was regarded by this school as a living thing. As the soul of man, which is air, animates the body, so the atmosphere, which is vital and intelligent, gives animation to the world. Matter and life are inseparable. Life is the one arranging power.
These early speculations show how much easier it is to hit on right directions of thought than it is to walk with due restraint in them. The mind, in its satisfaction with what is explained, overlooks the many things which are not explained. It treats the problem before it in a very fragmentary way, and not as one whole. Struck with some slight resemblance, it turns it at once into a complete correspondence. Water and air are very diffusive, penetrative substances, and play an especially important part in living processes. They thus came to be regarded as constructive terms of primary importance. Yet many facts, close at hand and equally obvious with those which had drawn attention, were neglected in the assertion that either of them was the primitive element. A knowledge of the facts was not aided but obstructed by this assertion.
An indeterminate substance, the world-stuff of Anaximander, is a suggestion that opens a door to inquiry, but brings no explanation till the steps of separation and
PYTHAGORAS. 1 5
evolution by which it passes into specific things can at least be suggested. . The speculation is rather an instinctive response to the demand which our rational powers make upon us for causes, than an intelligible meeting of that demand. Air is closely associated with life, but the identification of the two is not only hasty, it is wholly obscure. It confounds thought, to begin with, though it gratifies it with some later explanations. Hylozoism, the reference of all construction to life, is an induction, but one so precipitate as to carry no light with it. There is a plastic power of arrangement in all living things which we term life. Comparing one living thing with another, in this particular, we reduce the mystery to its simplest terms by observing its uniformity throughout the organic world.
But if we carry life beyond this world of organisms, conditions become so diverse, so antagonistic even, that not a glimmer of additional insight is given by the extension. The affirmation is simply a blind impulse of reason, willing to satisfy itself with an inadequate statement rather than to be left without any explanation. The inevitableness, and yet the insufficiency, of this movement of thought indicate its instinctive, tentative character. We very slowly learn to give an ultimate fact, like life, its simplest expression, and then to carefully confine it, under experience, within its own range of operations.
§ 3. The philosophy which flourished among the Doric Greeks is primarily referable to Pythagoras (582), who removed from Samos to Crotona, Italy, and there established a secret fraternity. The method of thought represented by him may, with peculiar fitness, be called a school. It grew up among the disciples of Pythagoras, who were closely united to him as a master, none of them l6 THE FIRST PERIOD IN GREEK PHILOSOPHY.
attaining any marked preeminence. The doctrines ascribed to Pythagoras cannot be given an exact, personal reference with any certainty. They were the fruits of the fraternity, were associated with a rigid ethical temper, and with an unbounded reverence for the one dominant mind.
The ruling idea in this philosophy was that of number. Number, according to it, is the very substance of things. This conception was amplified into many fantastic explanations. One is reason, unchangeable. Two is opinion, divisible, feminine. Three is indivisible, masculine. Four is justice, divisible into equal parts. Five is marriage, the union of two and three.
Number enters especially into music, and music became a prominent term in the fanciful constructions of the Doric school. The soul of man, transiently united to the body, is a harmony. The earth and its counter-earth revolve around a central fire, and the motion of the spheres is musical, made so by the intervention of spaces which have the ratios of music.
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