CHAPTER IV

NATURE AND THE LIVING WORLDS

We have found that, according to Bruno, the universe is infinite in extent, and that there are innumerable worlds within it: it remains to know what are the materials that constitute the universe, and the moving principles that govern its changes and direct the worlds in their courses.

[Sidenote: Uniformity of Nature.]

Nature, he said, is the same in kind, in its substance, and in its elements, throughout its whole extent--a daring conception for a time when the empyrean and all space beyond it were still regarded as the special abode of divinity. He reminded his opponents of his own childish experiences:--when from Cicala he looked towards Mount Vesuvius, he thought it dark, gloomy, bare of trees and flowers; but when he approached it, he found it fairer than Cicala itself, while now the latter looked bare and dark.[339] The Aristotelians were committing a similar error in judging the distant stars and the firmament to be in reality as they appeared to our eyes, and in denying the existence of that which was not visible to us. "As the philosopher must not believe what cannot be demonstrated by evidence, so neither must he foolishly despise or find fault with what cannot be disproved by reason."[340] Had men, instead of bending so long over the books of Aristotle and his commentators, the _nebulosa volumina_, but turned their eyes to the book and light of nature, they would have formed a far different conception of the constitution of the heavens than that of the eight, nine, ten, or more spheres and innumerable epicycles of the Ptolemaic system. Bruno showed how as we rise from the surface of the earth our horizon becomes wider, while in detail less vivid, and he supposed himself to continue the ascension upwards to the surface of the moon.[341] A few miles away tree and mountain would not be distinguishable from the rest of the earth, but we should perceive only a wide circle of light with dark spots, the appearance of sea and of land respectively. As the distance increased the form of the earth would become more visible while it lost all appearance of opacity, and the whole would seem continuous light. As we neared the moon, the earth would come to appear exactly as the moon does to us from the earth. The moon also revolves round its own axis, and from it, as with us, the universe will appear to revolve round it as centre. It had been said that the appearance of the heavenly bodies had always been and continued to be the same, but Bruno points to the fact that although a mountain, when seen from at hand, changes its face from day to day, and from season to season, yet from a distance it seems always the same.[342] It is owing to the distance that the face of the moon appears to us never to change, although it is certainly subject to as many alterations as the earth itself; and to the dwellers on the moon the earth will appear equally changeless. The light and shadow seen on the surface of the moon are due to the variety of sea and land in it, the one reflecting light, the other absorbing. On the moon, as on the earth, Nature is in continuous change: for example, the relative positions of sea and land are ever altering; but the magnitude of the distance renders these invisible, and more especially the minuteness and gradual nature of the changes themselves. The lunar spectator will be presented with eclipses of the earth, and, according to the position of sea and land, _i.e._ of light and shadow, with phases of the earth.[343] In the same way Bruno applied his principle of similarity to show that from distant stars the earth would appear of uniform magnitude and unvarying position, while in the neighbourhood of other suns it and all the other planets would disappear. As matter is the same in kind throughout the universe, so it is subject everywhere to the same law of unceasing change:--"The sun in its rising never seeks twice the same point, all things by stress of the continuous flux are renewed, nor ever seek again the haunts they have left, nor is there any part of the earth which does not pass through every region, and a like force now carries each part in one direction or another, now drives it away; and if by chance any one revisit the centre, it is no longer in the same form, nor in the same connection (_ordine_)."[344] Not even the whole can ever be twice the same, since the order and arrangement of its parts are continuously changing. Even in things that seem ever to present the same face there is a latent alteration which time will bring to light. There would otherwise be nothing to prevent the whole of Nature being fixed, petrified, as it were, to all eternity. Yet the substance of things--the atom--is unchanging.[345] "All things are in flow; the parts of the earth, seas, and rivers vary their positions, by a certain ebbing and flowing order of Nature. As matter wanders, flowing in and out, now here, now there, so the forms travel through matter. For there is not any form which, once occupying a portion of matter, retains it always, nor any matter which, once obtaining a certain form, maintains it for ever. Hence it is that, matter always taking up one form or another, and having equal capacity for all, consequently by virtue of its eternity it must sometimes fall in with that which is able to bind it to itself for ever; if this were to happen, all things would be so constituted that there would be no alteration or difference in them."[346]

[Sidenote: The Ether.]

The universe to Bruno is transfused with spirit, soul or life, "the soul of the universe," which animates its every part. "The seat or place of God is the universe, everywhere the whole immeasurable heaven, empty space, of which He is the fulness." The material aspect, or, as Bruno sometimes seems to say, the _body_ of this spirit is the ether, a subtle fluid distinguished from the air we breathe by the absence of moisture. The ether is a purely passive, non-resisting medium, permeating the universe, without quality, and unimpressionable by force or action; thus it is penetrated by the heat of any radiating body without diminishing its force. It took the place, for Bruno, of the mythical Fifth Essence, which had so long fed the dreams of philosophers--"Divine yet corporeal, material yet without matter, a form without privation, conjoining act with potency, neither heavy nor light, suffering neither generation, nor corruption, nor alteration, neither increase nor decrease; beyond which no sensible existence is, first-born and creatrix of Nature, simplest of beings, all-containing, most powerful, most active, most living, most perfect of existences, endowed with life and intelligence, of its own nature moving circularly, etc., etc.--all this is at length proved to have been a most portentous shadow without body."[347] Heaven is either empty space, or it is an ethereal substance, "a very subtle kind of air, which is the first and most universal occupant of space."[348] Again, the ether is described as a vapour or smoke, a nebulous matter, penetrating throughout the depths of the void, interpenetrating all things and embracing all; as not entering into movement of its own accord, for it is but an exhalation of the wind--a kind of continuous vapour such as is contained in the bowels of the earth: in it is neither heat nor cold nor any similar effect (_passio_), but it is the medium through which these are borne. All these require moisture: moisture alone can "fix" light or darkness or combine atoms into a concrete body and prevent their random flight through the air.[349] It has been claimed that in this and other passages Bruno anticipated the modern theory of the ether; it must be noted, however, that he expressly denies to its parts any kind of motion--it is only the composite body which moves--and that he speaks of this heaven or ether as the soul which is at once immanent in and comprehends the stars, _i.e._ as the soul of the universe.

[Sidenote: Moisture.]

[Sidenote: Earth: Fire.]

Of the strictly material elements of the universe, the most important is _moisture_ or _water_. It is moisture which gives concreteness and therefore weight to things. Nothing has weight which has not been formed into one by the union of innumerable parts under the action of water.[350] Consistently with this, Bruno believed the heaviest bodies, as the metals, to be the most solid and concrete, and therefore to contain most moisture. It is moisture also which, penetrating through the arteries, veins, and bones of the earth, gives to it both variety of aspect and the power of life. The visible moisture on the earth's surface, the seas and lakes, is a mere nothing as compared to that which is diffused through its interior--is but the sweat, as it were, of the earth's body.[351] Bruno's passion for homogeneity led him to understand that in its surface the land under the sea is similar to that above it, with which the former is continually changing place, and it is divided up into plains, mountains, valleys, the islands and rocks of the sea being the tops of the mountains:--a remarkable intuition of the truth, however arrived at. As to the familiar elements, _earth_ and _fire_, Bruno could neither allow a special place or sphere nor a special direction of movement to either, as in the Aristotelian cosmology. The earth was not the centre of the universe, and there were earths or similar planets everywhere. To the several arguments of the Peripatetics[352] for the centrality of the earth,--from the heaviness, the darkness, solidity, composite character of the earth's matter, and the movements of its parts, from the idea that contraries shun one another so that the coldest element, for example, should be in the centre, the hottest at the extreme,--Bruno opposed the common-sense answers that his own theory suggested to him. His appeal was always from "fictitious order" to the evidence of "sense and reason." The argument has no longer any interest in itself, and to pursue it into detail would hardly be edifying; but so full is it, so weighty and so vigorous, that one wonders how even the "Peripatetics" failed to be convinced by it. Bruno's very errors are interesting. Fire for example, far from being the outermost, lightest, subtlest element, was regarded by him as a body of which the substance, (light and heat being _accidents_) was water mixed with earth;[353] and in general, he maintained, no element was ever found in isolation. As to the supposed coldness of the central element,--the earth,--he believed, again anticipating future discoveries, that the centre of the earth was not cold, but hot, the source of terrestrial warmth; but the theory loses something of its value, scientifically, from the imagined _vitality_ of the planet, by which it is supported.[354] It was natural that the _coincidence of contraries_ should be brought to do duty against the maxim on which the Aristotelian view was really based--namely, that contraries tend to rest at the greatest possible distance from one another, against which Bruno marshalled a whole army of facts. Away from the shadow of the earth there was perhaps no light but that of the sun, too strong for our eyes, for the daylight arose from a mixture of the light of the sun and the darkness of the earth; we could see other colours by it, for the reason that they were similarly composed--mixtures of light and darkness. The heat of the sun also was only bearable when tempered by the coolness of the earth or other planets. The body of the earth, great as it is, can bear this heat only through its swift revolution. As to the objection that if the earth moved we should feel its motion, Bruno remarked that when we are carried in a smoothly and continuously moving vehicle, not striking against any object, we do not perceive that we are moving, except by comparison with some object known to us to be fixed. Thus sense furnishes its own correction.[355] The differences in the distances of the planets from the sun, as seen from the earth, are explained much more readily by the assumption that they and the earth itself are moving about the sun, than by that of the centrality of the earth, which compelled astronomers to the complicated device of the epicycles.[356] The fact that the moon always turns the same face towards the earth disproved the Ptolemaic theory: were it on an epicycle, as was supposed, this would be impossible. According to the old doctrine, the earth was fixed immovably in the centre of the universe, while about it circled the spheres of sun, planets, and fixed stars. With Bruno, on the other hand, the centre of the universe is everywhere, or nowhere,--in other words it is relative to the body on which the spectator is supposed to stand.

The principle of continuous change was employed to explain, among other matters, the variation of the equinoxes, which was already known to occur; but the continuous change was itself accounted for on teleological grounds.--"The motion which causes the poles to tremble, and the equinoctial and solstitial points to vary irregularly, is on account of the variations which are always taking place in parts of the earth; for the frigid zones may not always be frigid, nor the torrid, torrid; all parts must rest and have holiday from each kind of 'affect,' and consequently take up every kind of disposition successively." ... "The centre of the earth, therefore, and its position relatively to the poles, will vary."[357] No star ever repeats one day the revolution of the previous, or any one year that of another. Mathematical exactness, as we have seen, is never found in the material world: the earth may not always present the same face to the sun, so that one pole must at length pass into the place of the other--a change which must occur sensibly and continuously, and irregularly, as natural bodies and elements of bodies are naturally in continuous alteration and movement. "The same composite body is never in exactly the same state at any two moments, nor consists of quite the same parts, for from all sides and everywhere there is, necessarily, an unceasing influx and efflux of elementary bodies."[358] The stars and planets are compared to a flock of birds, which float hither and thither in the clear ether, guided only by their desires.[359] Never does the flock present precisely the same appearance twice. In nature the law is vicissitude and succession, so that each thing may in actual fact come to be all things.[360]

[Sidenote: Earths and Suns.]

[Sidenote: Comets.]

All the stars consist of the same elements, since water cannot subsist without earth, nor fire without water; but in some stars the aqueous element predominates (planets), in others the igneous (suns). From sameness of appearance and of effects (_accidents_) we may infer sameness of substance. It is clear therefore to Bruno that moon, planets, stars, are all of precisely the same substance as the earth. It is unnecessary to point out by how long a period this brilliant philosophical faith preceded the slower if surer march of science. The great worlds of the universe are of two kinds--the suns, in which fire is the predominating element, and from which light is diffused; and the earths or planets, in which water predominates and which reflects light. To the first class belong the so-called fixed stars, from which our sun would appear no larger and no brighter than they appear to us; to the second belong the moon, Mercury, and other planets, all in one and the same ethereal space, suspended in free air and balanced by their own weight as is our earth. In all are seas and woods, rivers, men, cattle, reptiles, birds, fishes, as on the earth, and in all the same continuous changes occur.[361] No one is in the centre of the universe rather than another, for about all equally extends immeasurable space with its innumerable stars. Of these "first bodies" one kind could not exist without the other, for it is by the concourse of contraries and opposites that nature provides for movement, life, and growth in things. About each of the scintillating stars, or suns, which we see, there must circle planets which are for the most part invisible to us, but which _may_ become visible.[362] In the same way, both on account of the smallness of their bodies, and especially on that of the less intensity of reflected light in comparison with light of original force, the planets which are about our fixed star, the sun, would not be seen from any of the others. The discovery in the last half-century of what is almost certainly a satellite of Sirius confirms in this also Bruno's "anticipation of nature." Another of these was his theory of comets,[363] which he held to be of the same nature as planets, and to move in similar orbits. He believed also that there were other solar planets which never appeared to us because their position in the heavens precluded their reflecting any of the sun's rays to us:--a belief to which the reported eclipses of the sun by occult bodies has given some support. The shape of the comet, with its appendages, was only apparent, Bruno said, and was due to the angle made by the light reflected from its surface. In another reference, however, he compares it with the oblique reflection of light from a mirror, or from the surface of water; it is the watery matter, the vapours which are drawn out by the warmth of the sun, that give the unusual reflection.[364] This shows how nearly he approached the modern theory. In the true spirit of the Renaissance, however, he appealed to the authority of the ancients, of Aeschylus and Hipparchus of Chios, who, according to Aristotle, regarded the comets as planets.[365] The comets of the sixteenth century,[366] so far as observed, went wholly against the received view that their orbits must lie within the sphere of the moon, and proved that the substance of bodies beyond that sphere was the same as the elementary substance of the earth, as well as that there was penetrable space beyond. Both of these to Bruno were important consequences. Still greater, however, was their importance for humanity, in removing the grounds of the terror which comets and other heavenly wonders had hitherto inspired. "There are some," said Bruno, "who rest their faith in a virtue above and beyond nature, saying that God, who is above nature, creates these appearances in the heavens in order to signify something to us: as if those were not better, nay the very best, signs of divinity which arise in the ordinary course of nature; among which are those of which we speak, for they also are not apart from this order, although their order is hidden from us."

To account for the many appearances which seemed to conflict with his new view of the universe, Bruno had recourse to several slight experiments and analogies of daily observation such as a schoolmaster might employ at the present day before his class,[367] but by which even a man of Kepler's intelligence refused then to be convinced; at least he would not openly profess his conviction. Among other fruitful suggestions which Bruno makes is that the sun may perhaps turn on its own axis, and again that it may contain vapour and earth.[368] He had a curious theory that the heat of the sun is only directed outward _from the surface_, not inwards; that this is the general course of radiation; and that it leaves an inner surface of the sun cold, on which solar animals live; finally that meteors are "animals" expelled from the sun! So always the fruitful idea is accompanied by the absurd.

From the principle of the identity of nature it follows that bodies which are remote from us are the same in kind with those that are with us and near us; nothing may be denied of the former which is affirmed of the latter, and _vice versa_. There can be no doubt, therefore, of their similar composition and similar parts. Thus if here on the earth we nowhere see fire subsisting without earth, nowhere earth without water or fire, while their composites are both contained in and penetrated by air and void, then the same is necessarily the case in the upper world also; neither sense nor reason compels us to assert or suspect otherwise.[369] Bruno has grasped, however confusedly, the idea that each individual, each being in the universe, is as it were an epitome of the universe itself; that each therefore stands in a peculiar relation to it, differing from it only in the "proportion" in which the elements are composed into unity. It is impossible not to see in this idea the germ of the most important development of Leibniz' philosophy, whatever the source may have been through which it came to the latter. It is true that here, at least, Bruno's conception appears much less spiritual than that of his successor, inasmuch as he is thinking rather of the actual physical elements which go to make up a body (and in which all bodies are similar to one another). On the other hand, the formation of the body is, in his view, the work of the soul, and it is in the last resort the identity of the universal soul of nature in all its members that brings each of these into correspondence with all others. It is true, also, that Bruno has no definite explanation of what constitutes an individual, and his readers are exposed to the dilemma either of regarding the physical atoms as themselves "_beseelt_,"--a view which Bruno nowhere sanctions,--or, on the other hand, of accepting a dualism of spirit (the soul of the universe or God) and matter (the material atoms, moisture, fire, and ether). Yet the tenour of Bruno's philosophy is wholly opposed to such a dualism. As a corollary of this theory, Bruno suggested an explanation of what has been called "spontaneous generation," supported, however, by tales of the credulous rather than by actual observation. "Dust that has been heated by the sun, as soon as moisture falls upon it, becomes a frog, the whole substance of dung goes into worms or flies, the body of a horse will turn into wasps, the provident bee rises from the body of an ox!"[370] As each thing is in its inner nature identical with every other, so it _may_, and in the natural course _does, become_ every other, as we have learned from the Italian works. Nevertheless, the outward appearances of things do not cease to be different from one another. "That is more latent in one subject which is more unfolded in the remainder." "The subject of all is one (_monas_), and all things are in truth one, although in individuals they seem to be many."

[Sidenote: Movements of bodies; their soul-principle.]

The movements of the earth and of other free-moving bodies are always attributed by Bruno to an "internal principle or _soul_." Movement from without could only take place through direct contact, and the liquid air or ether is too light to move these heavy bodies.[371] "It is taking things by the wrong end to say that the loadstone attracts the iron, the amber the straw, the sun the sunflower. In the iron there is a kind of sense, awakened by a spiritual (_i.e._ a subtly material) virtue diffused from the loadstone, ... and generally everything that desires and has intelligence moves towards the thing desired, converts itself into it as far as possible, beginning with the wish to be in the same place." By the same principle are explained the phenomena of _gravity_, which is defined as impulse towards the place of preservation, such as the earth is to the stone that has formed part of it; its opposite, "_levity_," is impulse away from the contrary or the injurious. "_Gravity_ and _levity_ are nothing but the impulse of parts to their place, where they may either move or be at rest, or to a place through which it is necessary for them to go (in the circular movement of all material things)." Thus the motions of the heavy and the light are merely relative movements; the same kind of motion does not belong always to the same kind of substance or element.[372]

The movement of the stars is determined not by considerations of place only, but also by the necessity that bodies of one kind are under of deriving sustenance from those of another,--the suns from the earths and the earths from the suns. It is through the soul that their needs are felt, and the soul directs their movements as does the human soul those of the human body. There are, however, no fixed limits to their movements: they are governed only by the convenience of life, as perceived by the sense and mind, which are inborn in each. By this fantastic principle Bruno explained what he thought to be the fact, that all heavenly bodies whatsoever are in movement; or perhaps we should say he inferred the fact from the principle:--which was first in the order of his thought it would be impossible to know. Like most of his contemporaries he looked upon the conception of a soul in all things with peculiar reverence--

_Porgimus haec paucis, vulgus procul esto prophanum, Ne liceat laico sacrum conscendere montem._

The method by which Bruno sought to know the nature of the souls of the worlds is one which the course of modern philosophy has rendered familiar to us in other connections. It rests upon the argument from the part to the whole. "Whatever we find in a part of the world belongs, in a higher sense (_sublimius_), to the whole, and must be attributed to it. All the capacities of each part are attributed to the whole--that is, their perfections and activities, not the qualities they possess as parts, and as less than the whole in any respect." Thus the hindrances to which lesser individuals are exposed, the necessity of taking in and giving out matter as their forms change, exist in the greater individual in a minimal degree. But in all parts of the earth Bruno found signs of life, sensation, and even intelligence. Stones of different kinds were universally believed to have a kind of sensibility and instinct: to move of their own accord, attract other bodies to themselves, act upon our human spirits and senses. The phenomena of animal instinct were a constant object of interest to Bruno, who saw in them the expression of a deeper intelligence than the merely human. It is true the observations on which he built may not always have been exact; but that does not detract from the value of his principle. Thus the porcupine (_istrix_) moved his admiration because of its careful storing up of a stock of darts in its back, with which to protect its life; it could, with unerring aim, cast one at its enemy, hearing, it is said, with its skin; and its precision far surpassed all that the cunning of man, with his many instruments, could do. With perfect skill it threw its darts, yet sparingly, so that no part of its body was ever defenceless, the spirit directing all its actions from one centre, to which, from every part of the body, report was made! "With how much higher reason will the _star_ be endowed, of the body of which animals are made, by whose spirit they flourish? So the earth from one centre directs all its actions and those of its parts; it never errs, neither it nor any of the worlds which dwell in the immeasurable ether."[373]

Bruno rejected[374] the popular notion that the behaviour of ants, spiders, and other animals does not spring from their proper foresight and artifice, but from divine, unerring intelligence acting upon them from without, giving them those "_thrusts_" (_spinte_) which are called "natural instincts"--a term which he regarded as meaningless. "Is this 'natural instinct' sense or intellect? If the former, is it internal or external? Clearly it is not external; but if internal, where is the internal sense from which they could have their foresight, their arts and artifices, their precautions, expeditions, to meet various conditions, both present and future? There must be some proximate principle, _i.e._ a form of _intelligence_ peculiar to each animal, which determines its actions. The divine and universal intelligence is merely the principle that _gives_ it intelligence, through which it understands."[375] The action of animals of a given kind were supposed to be after one perfect model, and to be undeliberate. Bruno therefore placed their intelligence higher than that of man, nearer the level of that of the world-souls. "The swallow makes its nest, the ants their cave, the spiders their web or nets, in one way only, than which they could not make them more admirably or suitably.... Who knows whether the spirit of man is rising upwards, that of others moving downwards? At least it is to be referred to a defect of light and divine force that men hesitate and deliberate in all that belongs to the means of life, the modes of worship and defence, for if all knew perfectly, all would be governed in the best, and consequently in one way only." It is, then, on the analogy of these supposed higher, unerring faculties of animals that Bruno considers the souls of the worlds to think and act. They have perfect freedom, since their life and soul are their own, not borrowed, as ours. "Thus as we breathe, see, sleep, without labour or anxiety, and while our soul performs the function of life, the vital humours and spirits continually circulate, so these, the chief members of the world, divine animals, have no need to undergo any anxious toil, for all things with them are done for the best." Their fixed aim of life defines for them certain determinate orbits, "in which they move freely by the force of that soul which is much more certainly present in these high, perfect, divine bodies than in us, of more ignoble condition, who draw from them spirit and body, come forth living out of their bosom, are nourished by them, and at length are dissolved and received back into them."[376]

It is to the internal spirit also that the spherical form of the worlds is due. The so-called mountains of the earth do not in the least detract from its spherical form. Bruno anticipated modern science in his discovery or intuition that the real mountains are not those we are accustomed to call such, but immense tracts of country,--the whole of France, for example. "I find the whole country of France to be one mountain, which rises gradually from the North Sea to Auvergne, where is its summit, marked on the west by the Pyrenees, where the Garonne flows, on the east by the Rhone, on the south by the Mediterranean Sea."[377] The whole earth is, however, as smooth in reality as is to us the pumice stone, which to the ant seems furrowed with mountains and valleys. It is on teleological grounds that Bruno accounts for this sphericity. Composite things are preserved through the harmony and union of their parts, while decay arises from dissolution. But such harmony and union are best secured by the spherical form: towards this form, then, every soul aspires in the moulding of its body. The most perfect animals, the stars, having fewer limitations, have the greater advantages; being almost independent, free, self-sufficient, they are most closely united in themselves, _i.e._ tend most nearly to the purely spherical form.[378]

However perfect they are, the stars are yet of mortal stuff. "You may say if you will that the worlds change and decay in old age, or that the earth seems to grow grey with years, and that all the great animals of the universe perish like the small, for they change, decay, dissolve. Matter, weary of old forms, eagerly snatches after new, for it desires to become all things, and to resemble, as far as may be, all being." The efflux and influx of atomic matter into the great bodies is continuous, and this is the only kind of motion which is unceasing.[379] "As the conflux of native matter is greater, so the bodies grow more and more, and increase up to a certain limit, on touching which they grow weary and become subject to a contrary order; as about the seed atoms are gathered and added continuously until the body and its limbs reach their maturity, when the same parts are cast out from the centre, and the breaking up of the composite is presented to our eyes." Hence there are atoms innumerable roaming through the void, while infinite changes succeed one another in bodies. Those in one region receive the atoms repulsed from another: there is no danger of their straying infinitely without reaching a goal, for everywhere are great bodies to receive what is expelled from other stars.

Composite as the worlds are,--capable, therefore, of dissolution and destruction,--yet, as Timaeus had suggested, the power and providence of the divine purpose may maintain them eternally as they are.

CHAPTER V[380]

THE LAST AND THE LEAST THINGS: ATOMS AND SOUL-MONADS

The reaction against Aristotelianism had, as one of its results, a renascence of the atomic theory of Democritus and Lucretius; and one of the earliest adherents of the renovated doctrine was Bruno. Although a complete presentation of the theory was not given until his later works, the _De Minimo_ and the _Articuli adv. Mathematicos_, appeared, yet already in the Italian dialogues there were frequent references to it. In the _Cena_,[381] for example, it is said that in the physical division of a finite body infinite progress is impossible, and, as we shall afterwards find, in Bruno there is no distinction between physical and mathematical division. Again, in the _Cena_ an animistic atomism is suggested, which presents a curious anticipation of some of Leibniz' characteristic views. "It is more than probable, as all things partake of life, that many or innumerable individuals live not only in us, but in all composite things; when anything "dies," as is said, we must believe it to be not death, but change only; the accidental composition or concord ceases, the things that enter into it remaining always immortal; and this is truer of those things we call spiritual than of those we call corporeal or material."[382] Thus every body or organism, for all bodies are organisms to Bruno, is itself constituted by other living beings, the atoms--living atoms--being alike the origin and the end of all. So Leibniz wrote:--"Every living body has a presiding entelechy, which is the soul in the animal; but the members of this living body are full of other living beings--plants, animals,--each of which, again, has its entelechy or presiding soul."[383] In the _Infinito_ Bruno refers to the continuous changes of all composite bodies as arising from the ceaseless flux of atoms out of and into each body, even the greater "animals," the stars and planets, sending out particles, which wander through the universe from one to another.[384] Again, when discussing the four elements, he ascribes to water the power of holding together the atoms of earth, or "the dry." "If from the earth all water were to be removed, so that there remained purely dry matter, this remainder would necessarily be an incoherent, rare, loose substance, easy to be dispersed through the air, in the form of innumerable discontinuous bodies; for while the air or ether makes a continuum, that which makes a _coherent_ continuum is water or moisture."[385] These indivisible "prime bodies," of which the worlds are originally composed, are spoken of as flying throughout space from world to world, in infinite movement, entering now into this, now into that "composition."[386] Finally, in the _Spaccio_, we are reminded that "every trifle, however worthless, is of value in the order of the whole, the universe, for great things are composed of little, little things of the least, and these of the individuals (or indivisibles) or minima."[387] In its main outlines, accordingly, Bruno's atomic theory was already formed in his mind when he wrote his earlier philosophical works, and even some of his peculiar applications of it had already suggested themselves. It is hardly possible, therefore, to find any very marked development in this regard between the London and the Frankfort periods. There is elaboration and completion rather than development in any definite direction;[388] and, as we have seen, the writing of the larger works, containing the developed system, was projected in London, and even carried out to a certain extent before Bruno left England.[389] In the _Acrotismus_, which occupies a middle place between the two periods, the doctrine is equally in evidence, in reference both to the atoms and to the continuous ether in which they move. "There is a limit to the division of nature--an indivisible something; the division of nature arrives at ultimate minimal parts, unapproachable by human instruments. Of these minimal bodies every sensible body is composed, and such a body, resolved into its minima, can retain no semblance of complexity; for these are the first bodies out of which all others are made, and which are, in the truest sense, the matter of all things that have corporeal existence. Resolved into these parts, stone has no look of stone, flesh of flesh, bone of bone; in their elements, bone, stone, and flesh do not differ, but only when formed out of these, compounded, compacted, and arranged in diverse manners, do flesh, stone, and bone and other things become different one from another."[390] And Bruno describes how, between the heavenly bodies, there is a substance, "ingenerable and incorruptible, the immeasurable air, a kind of spiritual body"--the ether.[391]

[Sidenote: Object of _De Minimo_.]

[Sidenote: Atomism a metaphysical doctrine.]

Its full extension, however, the theory receives in the _De Minimo_, where the atom, or corporeal unity, is not the sole minimum discussed. The full title of the work is:--"On the threefold minimum, and measure, being the principles of the three speculative sciences and of many practical arts." We find nowhere any distinct statement as to what Bruno meant by the "threefold minimum," and the three speculative sciences to which its several members refer. It was supposed that the minima were (1) the monad or unity which is the unit of number, (2) the point, which is the unit of the line, and (3) the atom, which is the unit of body. But arithmetic and geometry can hardly be called speculative sciences, and Tocco has shown that Bruno had in view the triad of _God_, the _soul_ and the _atom_--the three kinds of simple substance, each immortal and indestructible:--_God_ as the supreme and most simple unity, Monad of Monads; _soul_ as that which lives in each composite being and holds in unity the atoms which from time to time enter into its composition; and the _atom_, the most simple of material substances, in the sum of which, with their containing ether, the material universe consists. Had Bruno carried out his subdivision of the speculative sciences, he would probably have referred God, as the substance of all reality, to a speculative theology, of Neoplatonist type; soul as the simple substance of animate beings to metaphysics proper; and the atoms, the substance of body, to a speculative physics, dealing with the metaphysical presuppositions of the general theory of nature, which was set forth in the _De Immenso_. The scheme, however, was never fully carried out,[392] the times being not yet ripe for the complete separation of the speculative and the experimental or observational sciences. In referring the atomic theory to metaphysics, Bruno showed a true instinct, for while in one sense atomism is a scientific hypothesis capable of furnishing laws which explain the interaction of bodies,--the corpuscular theory,--and as such has proved its value by the brilliant developments of recent years, on the other hand, it is also a presupposition of knowledge, a ground of the possibility of our knowledge of body, and therefore has its place in speculative theory, or metaphysics, in the widest sense. Both points of view are presented in Bruno's doctrine, but that from which he starts is the epistemological, following in this the guidance of Nicholas of Cusa.

[Sidenote: Knowledge implies the atom.]

[Sidenote: Relativity of minimum.]

Knowledge is measurement, and all measure implies a minimum in each kind of being. Were it possible to subdivide anything _ad infinitum_, the half would be potentially equal to the whole, and measurement frustrated. There must be a limit to division, an ultimate part, which itself has no parts, and which is the _substance_ of the composition into which it enters, the composition on the other hand being an "_accident_" of this minimum. As it is primarily a condition of measurement, the minimum differs in the different spheres of measure or knowledge to which the category of quantity applies. In magnitudes of one or two dimensions it is the point, in bodies the atom, in numbers the monad or unity. Thus number is accident of the monad, monad is the essence of number, as composition is accident of the atom, atom is essence of the composite. Again, the "sensible minimum" must be far greater than the natural or real minimum, for in so far as minimum is qualified by sensible, it is implied that the minimum is not absolutely such, but is a composite. The minimum of taste, touch, etc., must possess certain qualities, by which it has relation to sense, and these can derive only from some form of composition. In their primary form the minima of nature must be without difference; therefore that some are sensible, others not, must be due to some addition in the former.[393]

Thus each species of existence, as light, moisture, vital force,[394] has its own minimum, and the minimum is relative in this sense also, that there are different kinds of existence not resolvable one into another: the absolute minimum would be God, who is also the absolute maximum. The relative minimum, accordingly, is determined either by the thought and design of the observer, or by the species of existence to which the subject belongs; nature has set limits, both lower and upper, within which the individual of any species must stay, or cease to belong to that species. Accordingly, what _one_ regards as great and composite, _another_ may take as first and minimum: the unit of one science may be analysed in another into further elements. "Pythagoras in his philosophy started with the monad and numbers; Plato with atoms, lines and surfaces; Empedocles with the four elements; the physicians with the four humours, and so on; but the Pythagorean monad is prior to the placed monad (the atom), Plato's matter of bodies to the qualified bodies of Empedocles, the four simple bodies of Empedocles to the four first combinations of these, the four humours. So to the universe the whole solar system, the sun and all its planets, may be a simple unit."[395]

Here Bruno suggests two principles for the classification and systematising of the sciences, to which it would have been well had he himself and his successors faithfully adhered. The one is, that the modes of measurement, _i.e._ the methods and laws of the sciences, must differ for the different kinds of existence studied: that a biological law, for example, cannot be adopted as an explanation of mental phenomena, nor the atomic theory account for the phenomena of life. On the other hand there are _orders_ of existence, according to the complexity of the subjects involved. If we regard the science which deals with the more concrete subject as "higher," then each higher science (_e.g._ psychology) must take for granted the principles and results of each lower science (biology, physics, mathematics),--each must adopt and retain a unit for itself, which it has not further to analyse.

[Sidenote: The "minima" in the classification of sciences.]

In the same way the minima offer a ground for the distinction of the more abstract sciences one from another. The term "individual nature" (_atoma natura_) may, according to Bruno, have one of several uses. It may be applied either "negatively or privatively, and if negatively, then either accidentally or substantially." His instance of the _accidental_ use is a voice or sound, which expands spherically, is wholly wherever it is, _i.e._ the full content of the sound is heard, wherever its influence extends, not a part here, a part there, although the intensity may vary in degree. Of the _substantial_ use examples are the spirit, which is wholly in the whole body of man, or that spirit which is in the whole extent of the life of the earth, by whose life we live and in which we have our being, or, above this substantial nature or individual soul, that of the universe, and supreme above all, the mind of minds, God, one spirit completely filling all things.[396] The atom-nature is _privatively_ so-called, when it is the element and substance of a magnitude which is the same in kind with it, and may be reduced to it, and it is distinguished from the atom _negatively_ so-called, because it is not divisible, either in genus or in species, either _per se_ or _per accidens_. Examples are, (1) in discrete quantities:--unity to the mathematician, the universal proposition to the logician, the syllable to the grammarian; and (2) in continuous quantities, varying with the species of continuum:--the minimal pain, sweetness, colour, light, triangle, circle, straight line, curve; in duration, the instant; in place, the minimal space; in length and breadth, the point; in body, the least and first body.

[Sidenote: Minimum as substance.]

In the second place, the atom or minimum is also a metaphysical [Greek: pou stô]; not only is it the last result of analysis, but it is also the permanent substance of being, and again it contains all being in itself--it is essence of being. Thus such an individual nature "never comes into existence by way of generation, nor passes out of it by way of corruption or dissolution; only _per accidens_ may we say that it now is, now is not."[397] Certain of them, however, the souls, deities, God, are in their intrinsic nature eternal, immortal, indissoluble. Of these it was Bruno's intention to treat at large in a _Metaphysics_ and a _De Anima_ which he purposed to write "if God granted him time."[398] Unfortunately, it was willed otherwise.

Nothing that becomes, changes, decays, is real (_ens_). It is by meditating on this perpetual unity of nature, by conforming ourselves, and preserving ourselves in likeness to it, that we come to partake in the life of the gods, and to deserve the name of substance. That which time, movement, fate bring to us is nought; for while they are, they are not. "Let us then," cries Bruno, "supply the mind with material, in the contemplation of the _minimum_, through which it may exalt itself to the _maximum_."[399] Since the real minimum, whether atom or soul, is immortal and indestructible, we know, as Pythagoras saw, that there is no death, but only transition; death is a dissolution which can occur only to the composite, for the composite is never _substance_, but is always _adventitious_. Otherwise we should be changing our substance every moment with the continuous influx of atoms into our bodies. Only by the individual substance of the soul are we that which we are; about it as a centre, which is everywhere in its whole being (_ubique totum_), the disgregation and aggregation of atoms takes place. According to a law of the soul-world, all bodies and forces tend to the spherical form; God, as monad of monads, is the perfect or infinite sphere, of which the centre is at once nowhere and everywhere; and in Him (as in all minima, simple substances, monads) all opposites coincide, the many and the few, finite and infinite; therefore that which is _minimum_ is also _maximum_, or anything between these, each is all things, the greatest and the whole.[400] Therefore, if contemplation is to follow in the footsteps of nature, it must begin, continue, and end with the _minimum_.[401] In other words, the minimum in each sphere of being contains implicitly in itself the whole reality of that sphere. The minimum is its substance, not merely the ultimate of analysis, but the actual source, the dynamic origin of reality, as God is implicitly the whole universe and also the source of the universe as it actually exists. It is because the minimum is all reality, is the _maximum_, that the knowledge of it gives us that of the whole.

[Sidenote: Uniqueness of all things.]

[Sidenote: Sense and knowledge.]

[Sidenote: Relativity.]

[Sidenote: Judgment based upon sensation.]

In the third place the atomic theory offers an explanation of the uniqueness of each natural existence, which Bruno's philosophical theory already assumed. The ever moving atoms present a mechanism by which the infinite diversity and infinite succession of change in things may be brought about. The _appearance_ of similarity, exactness, etc., is, as we have found, an illusion. Mathematically exact figures or bodies--a true circle, for example--are unattainable by sense, even if they exist in nature; but they do not exist in nature. Sense is the primary faculty, through which the material of all others must pass, so that what has not entered through that window of the soul cannot be known at all. But a single point out of place on the circumference of a circle makes it cease to be a true circle, and our sense-apprehension is necessarily so confused and indistinct that we cannot distinguish between the true and the false, where truth depends upon so inappreciable a difference. Moreover sense-knowledge is relative to the knowing subject, or to the subject's position with regard to the object. What to the eye of one is too large is to another too small; a sound which is pleasant to one ear is not so to another; the food which to the hungry man tastes sweet, to the full man is nauseous; the ape to the ape is beautiful, but to the man is of laughter-inspiring ugliness. Hence the circumspect will not say "this has a good odour, taste, sound, this has a beautiful appearance," but will add "to me," "now," "sometimes." Nothing is good or evil, pleasant or painful, beautiful or ugly, _simply_ and _absolutely_; but the same objects in relation to individual subjects receive from the senses contrary denominations, as they in fact produce contrary effects. In deciding what is to be called good or bad, honourable or base, nature and custom have been the chief agents, and alterations have issued from the slow rise and victory of different opinions. Among the Druids and Magi certain things were performed publicly at sacrifices which now, even when committed in privacy, are regarded as execrable, and are so by way of law, and in the present condition of affairs. Philosophy, as it teaches to abstract from particulars, to bring the nature and condition of things as far as possible under an absolute judgment, must define differently the useful and good in an _absolute_ sense, from the useful and good as _contracted_ to the human species. Objectively there is no definitely good or definitely evil, definitely true or definitely false, so that from one point of view we may say that all things are good; from another that all things are evil; from a third that nothing is good or evil, as neither of the contraries is true; from a fourth that all things are both good and evil, as each of the contraries is true. No sense deceives or is deceived: each judges of its proper object according to its own measure. There is no higher tribunal to which to refer its object, nor can reason judge of colour any more than can the ear; sensible truth does not follow any general or universal rule, but one which is particular, mutable, and variable. In the working of an external sense there may be different degrees of perfection or defect, but not of truth or falsity, which consist in the reference of the subject and predicate to one another. The faculty by which we judge this or that to be _true_ colour or light, and distinguish from apparent colour or light, is not in the eye. To affirm that man is an animal, we must know both man and animal, know that animal nature is in man, and other things which, as means or circumstances, concur directly or indirectly in this knowledge. External sense can apprehend only one species or image of the object; from the colour and figure to pass to its name, its truth, its difference from other objects, belongs to a more inward faculty. Yet the latter is always based upon sense;--a deaf man can neither imagine nor dream of sounds which he has never heard, nor a blind man of colours and figures which he has never seen.[402] This digression on the relativity of knowledge, and on the different functions of sense and reason, in which Bruno follows partly the teaching of Lucretius, partly the Peripatetic doctrine of knowledge, shows that even if a true or perfectly exact geometrical figure existed in nature, none of the faculties with which we are endowed could apprehend it, since it is not given by external sense.[403]

[Sidenote: No exactness or similarity in composites.]

But in the second place[404] reason tells us that no true circle, or other figure, is possible in nature: for there is in nature no similarity except in the atoms; a true circle would imply the equality of all lines from the centre, but no two lines in nature are entirely and in all respects equal to one another. The circle or part of a circle which appears most perfect to us--the rainbow--is an illusion of the senses, due to the reflection of the light of the sun from the clouds; so the circles made by a stone falling into water cannot be perfect, for this would mean that the stone itself is perfectly spherical, that the water is everywhere of the same density, that no wind is playing upon its surface. Sound is not equally diffused owing to differences in the density and rarity of the air, nor is the horizon ever a perfect circle, owing to differences of clearness in different directions. Object and faculty alike are in continuous change; all natural things are continually altering their form or changing their position; therefore although they seem to sense to remain fixed for a time, we know that this is impossible, from the nature of things.[405] Whatsoever falls in the scope of sense-perception, even the distant sphere and stars, we judge to consist of the same elements, therefore to be subject equally to perpetual variability and vicissitude. Thus--the atoms alone being simple, and remaining ever the same--no composite thing can be the same for one moment even, as each is being altered continually in all parts and on all sides by the efflux and influx of innumerable atoms.[406] "Hence nothing is perfectly straight, nothing perfectly circular among composites, nothing absolutely solid but the atoms, nothing absolutely void but the spaces between them." The facet of a diamond appears to be a perfect plane, perfectly compact, yet in reality it is rough and porous.[407] In matter no two lines or figures are entirely equal, nor can the same figure be repeated twice.[408] No man is twice of the same weight, the very instruments by which we measure and weigh things are themselves in constant change, and the flux of atoms is never equal, but now denser, now rarer. In general no two things are of the same weight, length, sound, or number, nor are two motions or parts of motion ever the same. To say that ten trees are equal to ten others is to speak merely from a _logical_ point of view, for in fact each is _one_ in a peculiar and special sense.[409] "Equality is only in those things which are permanent and the same; changing bodies are unequal to themselves at any two instants."[410] "Nothing variable or composite consists at two moments of time wholly of the same parts and the same order of parts, since the efflux and influx of atoms is continuous, and therefore not even from the primary integrating parts will you be able to name a thing as the same twice."[411]

Number itself is not an absolute, but a relative determination: it does not touch the nature of the thing itself. Nature has no difference of number, as we have, of odd and even, tens and hundreds; nor do the gods, spirits, or other rational beings define the numbers and measures of objects by the same series of terms. Both numbers and the methods of numbering are as diverse as are the fingers, heads, and mental equipment of the numberers. That which fits in with the numbers of nature will therefore never fit in with our numbers. Thus ten horses and ten men, although determined arithmetically by one and the same number, are in nature, or physically, wholly unequal to one another.[412]

[Sidenote: The atoms.]

[Sidenote: Time and space.]

In order that men's minds may be better disposed for the reception of truth, it is necessary first to demolish the foundations of error;[413] Bruno accordingly sets himself to disprove the infinite divisibility of the continuum.[414] It was the common belief that there were no limits set to the dividing power of either nature or art, so that, however small a part might be arrived at, it was possible to divide it into yet smaller parts, on the analogy of the division of a fraction into tens of thousands of parts. Bruno denied this analogy to be justifiable, as in the latter case we are concerned not with division but with multiplication or addition, not with a continuum, but with discrete quantities, and it was part of his general theory that the addition of discretes might be carried on _ad infinitum_; the inverse process he denied. He thus held opinions directly contrary to those of Aristotle, with whom the mass of the universe was finite, limited by its enclosing sphere, the parts of the universe unlimited. Aristotle had an upper but not a lower limit; Bruno a lower but not an upper. So time and space, which Aristotle had treated as _finite_ in duration or extent, but as _infinitely divisible_, like the universe itself, are regarded by Bruno as unlimited in their dimensions, but as consisting of discrete minimal parts. "In every point of duration is beginning without end, and end without beginning"; it is the centre of two infinities. Therefore the whole of duration is one infinite instant, both beginning and end, as immeasurable space is an infinite _minimum_ or centre. "The beginning and source of all errors, both in physics and in mathematics, is the resolution of the continuous _in infinitum_. To us it is clear that the resolution both of nature and of true art, which does not advance beyond nature, descends from a finite magnitude and number to the atom, but that there is no limit to the extension of things either in nature or in thought, except in regard to the form of particular species. Everywhere and always we find the _minimum_, the _maximum_ nowhere and never. The _maximum_ and _minimum_, however, may in one sense coincide, so that we know the maximum to be everywhere, since from what has been said it is evident that the maximum consists in the minimum and the minimum in the maximum, as in the many is the one, in the one the many. Yet reason and nature may more readily separate the minimum from the maximum than the maximum from the minimum. Therefore the immeasurable universe is nothing but centre everywhere; eternity nothing but a moment always; immeasurable body an atom; immeasurable plane a point; immeasurable space the receptacle of a point or atom."[415]

The chief source of error on the part of the Peripatetics was their failure to distinguish between the minimum as a part, and the minimum a _terminus_ or limit. Hence their idea that no combination of physical minima would give a magnitude, since two or more would touch one another with their whole surface, _i.e._ would coincide:--otherwise the minimum would have parts, a part of each touching the other, and a part not touching. On their theory it would follow that magnitudes do not consist of parts, or at least not of elementary parts. This is inconsistent with nature, for existing magnitudes must have been built up out of nature's elements, and with art, for art can measure only on the assumption of first parts. It is true that what is posited as first part in one operation may be the last result in another, for the _minimum_, as we have seen, is a relative conception, but _some_ first part is always assumed in any operation. And as the operation of art is not infinite, so neither is there infinite subordination of parts.[416] When two minima touch one another, they do not do so with their whole body, _or any part of it_, but one with its terminus or limit may touch several others; no body touches another with the whole of itself or a part, but with either the whole or the part of its _limiting_ surface. The _terminus_ of a thing is therefore no part of it, and by implication not a minimal part. Hence there are two kinds of _minima_ concerned--that of the touching body, or part, and the minimum of that by which the contact is effected, the _terminus_.[417] The atom, which is the minimal sphere, touches in the absolutely minimal point, the smallest _terminus_. Other spheres do not touch in a point simply, but in more than one, or in a plane circle.[418] By adding limit to limit we never obtain a magnitude; the _terminus_ is no part, and therefore if in contact it would touch with its whole self, so that magnitude is not made up of _termini_, whether points, atoms, lines, or surfaces which are termini; and this was the false ground on which the Aristotelians denied the possibility of the atom. It remained to ask if the _termini_ were infinite, since the atoms were not; but it was clear that their number was determined by that of the atoms. For two limits do not touch one another:--"They do not cohere or make a _quantum_, but through them others in contact with one another make a _contiguum_ or _continuum_."[419] It may be added that if the parts of a divisible body were infinite in number, the parts of the whole would be equalled by the parts of the half, for in the infinite there can be no greater and less. In the infinite, as we have seen above, there is no difference between palms, digits, miles, between units and thousands, nor in the infinite time that has elapsed are there more months than years, more years than centuries. If any one set of these were less than the others it would be finite, and if one finite number may be applied to the whole, then the whole is finite.[420] The force of the Achilles dilemma was derived from the false idea that the _minimum_ of one kind had some relation to that of another kind, _e.g._ that of time to that of motion, that of impulsive force to that of the motion produced. A thing of one kind does not define or measure a thing of another, and the duration of one does not compare in the same sense with the duration of another. Parts of different things are only equivocally called parts, and _minima_ are _minima_ only according to their proper (and diverse) definitions; therefore one is not measured by another, except in a rough way, for practical purposes.[421]

[Sidenote: The vacuum. Atoms spherical.]

As the atoms come into contact with one another, not in all points of their surface, but in a definite number, it follows that there is a space between them, in the interstices; it was this thought which led Democritus to posit a vacuum.[422] The figure of the corporeal minimum must be spherical, for any mass which has projections can always be thought of as smaller, when these projections have been removed; and nature itself suggests this, by the gradual rounding off of substances through time, and the apparent roundness and smoothness of rough and jagged bodies when the observer is at a distance.[423] Diversity of forms of composite bodies results easily from spherical atoms, through differences in situation and order, differing amounts of vacuum and solid; but a simple vacuum with solid bodies is not sufficient,--there must be a certain matter through which the latter cohere together.[424] Although all other determinations may be abstracted from, figure at least must be predicated of the atoms; quantity cannot be asserted of that which is thought to be unfigured. These determinations of the minimum, though not given to sense, may nevertheless be made object of thought, by analogy or inference from the combinations of sensible _minima_ in larger composites, the same forms of aggregation being repeated in the higher which occur in the lower forms.[425]

From the consideration of mathematical figures as consisting of _minima_, Bruno attempted both to remodel and to simplify the existing mathematical theory, and, unfortunately fell foul of the new analytical mathematics, the theory of rationals and of approximations, which at that time was receiving marked extensions, and which has since justified itself so completely by results. It is true he did not entirely reject it, but he regarded it as merely an artifice for rough practical measurements. The true measure is always the _minimum_, inferred by analogy from the combinations of greater parts, which are perceived by sense. Thus the minimal circle, after the atom itself, consists of seven minima, the minimal triangle of three, and the minimal square of four, and as each figure increases not by the addition of one atom merely, but by a number determined by the original number of atoms in the figure, it follows that no one figure is ever equal to another. Thus the second triangle is of six minima, the second square of nine, the second circle of nineteen. The "squaring of the circle" is therefore impossible,[426] although it may be approximately reached through the ultimate coincidence of arc and chord, by which the circle becomes equal to a polygon with an infinite number of sides.[427] This, however, is only an approximation of sense, which fails to observe the infinitesimal differences that are caused by the existence of a few atoms, more or less, in a figure. They are visible to the eye of reason, which comprehends that no two figures in nature are ever exactly equal. In exact geometry the number of one species of figure has nothing in common with that of another. It is clear, however, that even on his own ground Bruno was in error in this regard; for example, the seventh triangle and the fifth square are each composed of thirty-six minima.[428] But it is hardly necessary to take seriously his teaching in this respect. He was wholly governed by the belief in the infinite diversity of nature, and the absolute incommensurability of any member of one species of beings with one of a different species. "Since a definite minimum exists, it is not possible either in reality or in thought for a square to be equalled by a circle, nor even a square by a pentagon, a triangle by a square, nor in fine any species of figure by a figure of another species; for difference in the number of sides implies also difference in the order and number of parts. As figures in this respect are as numbers, and one species of number cannot be equalled by another either 'formally' or fundamentally (_i.e._ either in idea or in fact), we can never make an equilateral figure of any kind equal to one of another by first parts."[429] Where this transformation is apparently carried out, as where a cube of wax is moulded to another figure, the result is due to the varying degrees of density in the different parts of the material; no solid parts are added or subtracted, but the disposition and extent of the pores or vacua are altered. But no argument can be drawn from this rough method, for the principles of practice are different from those of science.[430]

The latter principles are then applied boldly to geometrical science: thus it is shown that an angle, although it may be multiplied indefinitely, can be divided only into two parts; all its lines, it is understood, consisting of _fila_ or rows of atoms;[431] that the circle has not an infinite number of radii, for from the circumference to the centre only six such lines can be drawn;[432] that not every line can be divided into two equal parts, for the physical line or _filum_ may, naturally, consist of an odd number of atoms;[433] in any case geometrical bisection can at best be a near approximation,--though the two halves be apparently equal, they may really differ by many atoms. On this basis, in the fourth and fifth books of the _De Minimo_, Bruno offers a simplification of the geometry of Euclid. As nature itself is the highest unification of the manifold, and the monad is the unity and essence of all number, so we are taught to pass "from the infinite forms and images of art to the definite forms of nature, which the mind in harmony with nature grasps in a few forms, while the _first mind_ has at once the potentiality and the reality of all particular things in the (simple) monad."[434] In accordance with the method of simplification suggested by this doctrine, Bruno sets himself to show that the greater part of Euclid may be intuitively presented in three complicated figures, named respectively the _Atrium Appollinis_, _Atrium Palladis_, and _Atrium Veneris_. He hoped that by this means, "if not always, for the most part at any rate, without further explanation, the demonstration and the very evidence of the thing might be presented to the senses of all, without numbers,--not after the partial method of others, who in considering a statue take now the foot, now the eyes, now the forehead, now other parts separately,--but explaining all in each and each in all."[435] It is no part of the purpose of this book to go at length into the mathematics of Bruno, which unfortunately have not yet met with a competent exposition. Apart from the difficulty of the matter itself, the poetical form and setting of his theorems is an additional stumbling-block in the way of understanding. Bruno was put to many shifts in order to give a poetical colouring to the most prosaic of subjects.

We have gone thus fully into the detail of Bruno's atomic theory, more so perhaps than its intrinsic value seems to demand, because this aspect of his doctrine is the most important philosophically, and has exercised the greatest influence upon the course of speculation. It also provides most clearly an exemplification of the return which was made, or thought to be made, by the Renaissance to the older pre-Aristotelian philosophy and science. The rejection by Aristotle and his scholastic followers of the atomic theory of Leucippus and Democritus had been based upon the identification of space and body. The possibility of a vacuum in the corporeal world was denied, on the ground that discreteness was inconsistent with the continuity which was felt to be a necessary condition of space. Accordingly, the reintroduction of the atom was possible only in one of two ways--either by the distinction between body and space, or by the application of the atomic constitution of body to space itself. The former and truer solution was not open to Bruno. His time was still too much under the domination of Peripatetic thought for him to be able to take the important step of critically separating these two notions. The latter way, therefore, was that which he followed. Hence the curious attempt to remodel mathematical theory on the basis of the atom, which we have described above, and the reduction of mathematical certainty to an illusion of sense. Figure is to be found only in the combinations of atoms; and owing to the spherical form of the atom, the infinite number of them existing in any body which is presented to sense, and the space which lies between their surfaces, mathematical equality and exactness are impossible. Neither straight line, therefore, nor perfect circle are to be found in reality. Mathematics, which should be based upon, or which presupposes, continuity, is confounded with physics, which presupposes the analysis of body into discrete, impenetrable atoms. Physical atomism finds its justification in the experienced fact of resistance, which is the primary quality of body as perceived by our senses. In mathematical space, on the other hand, we abstract from all qualities except that of dimension only. Resistance would be inexplicable were it possible to proceed _ad infinitum_ in dividing matter; it implies an ultimate irreducible and indestructible unit, whether we regard this unit as a centre of force or as an inert substance merely.

The same influence of Aristotelian thought led Bruno to posit a subtle matter, the Ether, as filling up the interstices between the atoms. Space and body having been identified, it was seen that a vacuum was inconsistent with the nature of things. The Aristotelian _plenum_ was reintroduced in this form, that there might be some reality where the discrete atoms were not. The bolder step of asserting the fact, and indeed, the necessity of a vacuum as a presupposition of knowledge of the material world, was not taken until there appeared the work of Gassendi, by whom the final blow was given to the old conception of body and space, and through whom the critical separation of the one from the other was first rendered possible. It is curious that Bruno did not think of applying to the continuous ether any geometrical measure; had he done so, he would have understood the value of the new theory of infinitesimals and irrationals which he opposed so strongly. Again, had he carried out more fully the distinction which he draws between the atom and the _terminus_ or limit, the same result would have followed. Pure geometry is the geometry of the limit; for the limit is not only between atom and atom, or body and body, but also between atom and vacuum or ether. In this sense it is both continuous and figured, the compatibility of which qualities Bruno had denied; the continuous is measured, not by making it discrete, but by making the number, the measure, fluid or continuous.

[Sidenote: Metaphysical atomism.]

Lasswitz has shown that there are in Bruno's theory three distinct aspects, not, however, clearly separated one from another, of the atomic hypothesis: they may be named severally the metaphysical, the physical, and the critical aspects. From the metaphysical point of view the atom is the ultimately simple, indeterminate substance of things; its conception results from the effort to find the real substance which is outside of, and unaffected by, the change and decay apparent on the surface of things, but felt to be unreal. Simplicity, unity, substance, is that which is sought, an abiding somewhat underlying the flux of the universe, which is regarded as an illusory appearance to sense. From this aspect it is that the identity of _minimum_ and _maximum_, of the least with the greatest, is to be explained. Number, plurality, and diversity no longer apply to the absolutely simple: all are determinations of human and finite origin which are here no longer valid. In the simple all contraries coincide, for the very reason that it has no determinations in itself; even the highest qualities which men would attribute to God, for example,--justice and goodness,--are improperly predicated of him, for as in him the greatest and the least coincide, so do goodness and evil and all other contrary qualities. In this respect Bruno was following closely in the footsteps of Nicolaus of Cusa.

[Sidenote: Physical Atomism.]

[Sidenote: Critical Atomism.]

From the second point of view, that of _physical_ atomism, the atom is nothing more than a hypothesis to explain the constitution and qualities of nature as we experience it. We seek to account for the differences in material bodies and in their ways of acting upon one another by the interaction of ultimate elements of which the nature and laws may be variously interpreted. Of this point of view also there are traces in Bruno, although for it he had least regard. He does not attempt, for example, to apply the theory of the atoms to explain the four elements which had come down from Aristotle. He leaves them practically intact, and we have seen that they form a standing difficulty in the way of a consistent theory. The earth alone is atomic in its nature; water, air, and fire seem alike fluid and continuous in quality, but wherein their difference from one another consists he was unable, or did not care, to make clear. Perhaps, if we take his view at its best, we should say that all three represent strata, varying in density, of the one fluid and all-pervading ether. Had he worked out this conception, which was evidently present, on occasions, to his mind, he would have given an example of what is meant by physical atomism. But this was left for another century to fulfil. From the third or _critical_ point of view, which inquires into the presuppositions or the possibility of knowledge, Bruno may be regarded as being, to some extent, a forerunner of Kant, in the stress he lays upon the relation of the minimum to measure or knowledge, and in his doctrine of the relativity of the conception of the _minimum_. The minimum, instead of a last of division, becomes a first of composition--a ground which we must necessarily assume in order to account for the experienced fact of composition. To know a composite is to measure it, and measurement implies the _minimum_ or first part, without which quantity in any form cannot be explained. As the comparison of numbers with one another, their determination as greater or less, is only possible on the assumption of a unit, a common measure to which each may be referred, so the comparison of bodies with one another, as to quantity and quality alike, demands a corporeal minimum, to which their differences must be reduced. This relation to knowledge carries with it the relativity of the minimum according to the subject-matter with which the knower is for the time being concerned. If all knowledge is of the same type, then in each application of it--each subdivision of knowledge as a whole--there is presupposed the corresponding minimum. That which is least in one sphere may be greatest in another; that which is element of one science may be that which another seeks to analyse into lesser constituents. The celestial body, which is a highly complex combination of elements, may be the unit of astronomical science. The phrase, which is the unit of the rhetorician, is analysed by the logician and the grammarian into terms and words; these are analysed by another science into syllables and letters; these by the mathematician into lines and points. Thus every science has its own (relative) minimum. Only one _minimum_ is _absolutely_ so named,--God as the monad of monads. It is to be noted that the relativity of the monad is dependent upon the origin of its conception, in the conditions of knowledge; it is because quantity is universal that a minimum is necessary, and it is because quantity differs in kind, in each subject of knowledge,--because it is, in scholastic phrase, equivocally applied in the different cases,--that the minima differ from one another. The minimal number is no measure of the minimal body nor of the geometrical figure, and the numbers which are in use among men are not those which may be employed by other and higher rational beings. Thus, even number itself is a relative determination; ten horses, said Bruno, are not _really_ equal to ten men, but only _conventionally_.

The ancient atomism upon which Bruno founded his theory was, at any rate in its traditional rendering, frankly materialistic. It admitted nothing but atoms and the void, all things else being dependent upon the _composition_ of atoms, which itself, and all that results from it, is merely an appearance to sense, without corresponding reality in nature. All physical operations were explained by mechanical arrangement and movement of the atoms. The method which was pursued thus unscientifically, without consciousness of the extent of its validity, modern atomic theory has followed scientifically, with full comprehension of its bearings, and perhaps without due consideration of its limits. Bruno tells us that he had at one time been an adherent of Democritus' atomic theory, but on reflection had been unable to rest satisfied with his materialistic account of the nature of things. In this case also he showed himself unable to get rid of the ties which bound all the thought of his time--even that thought which most believed itself to be free.

Aristotle's distinction of form and matter in nature, of pure activity and pure passivity, had still sufficient influence to render even in Bruno's time a purely mechanical treatment of nature an impossibility. The opposing school, the Neo-Platonism which attracted so many minds of that period, because of its supposed inconsistency with Aristotle's system, was itself an offshoot, to some extent, of that system, and was still less scientific in its tendency. Mysticism, of which it was partly a cause and partly an effect, lent its weight also against any mechanical interpretation of nature. Thus even while apparently governed by scientific aspiration, Bruno gives a teleological scheme of the universe which renders any scientific explanation of it impossible. Not only, as we have seen, is the ether identified with the first substance, spirit, or soul of the universe, but also the greater and lesser organic bodies are governed each by its individual soul, which is somehow distinguished from the universal spirit, and within each of these is an infinite number of smaller living bodies. In other words, the atoms themselves are animated _virtually_, if not _actually_. This animistic interpretation is in direct conflict with the mechanical interpretation which science has followed, and which it must continue to follow if it is to produce any result. Thus, motion and the changes of composition that derive from motion are explained not by the mechanical impact of atoms and bodies upon one another, but by the action of the intrinsic soul in each being, which causes the motion of the body, in accordance with its need and desire of self-preservation. All motion, even the slightest, is thus explained by a final cause. In the whole universe also, the constantly occurring changes and transformations are due to a similar final cause--the need for each thing to become _explicitly_ that which it already is _implicitly_, _i.e._ the whole of reality. It required once more a critical separation of the spheres of validity of the respective conceptions of nature and spirit, such as Kant attempted, before full scope could be given to mechanical interpretation on the one side, and teleology restricted to the domain of spirit only on the other.