Giordano Bruno

LEAST THINGS: ATO

g 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

ce, 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 car

inimum.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

ich 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

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

re, 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

g. 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,

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

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

ous 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 line

r 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

totle, 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. Time and space.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, whic

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.

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]

eteen. 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 di

mplification 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 mos

n 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 whi

l 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

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

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 s

e. 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

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 o