On the Infinite Universe and Worlds


Graphic Rule

Graphic Rule


Philotheo. For as much as the Primal Origin is utterly simple, therefore if he were finite according to one attribute he would be finite according to all attributes. Or at least, if he were finite according to a certain intrinsic law of his nature and infinite according to another, we should inevitably regard him as composite. If then he is the active power of the universe, he certainly is infinite power, and produceth infinite effect; effect I say, inasmuch as all is dependent on him. Furthermore, as our imagination proceedeth easily to the infinite, and conceiveth dimensional size ever greater, and number beyond number according to a certain succession and "power" as it is called, so also we should understand that God actually conceiveth infinite dimension and infinite number; and from this conception there followeth the possibility and convenience and opportunity which we posit, namely that as [his] active power is infinite, so also as a necessary result, the subject thereof is infinite. For, as we have shewn on other occasions, [1] the power to create doth imply a power [that a subject] be created; that which may be measured implieth that which can be measured; the measurer implieth the measured. Moreover just as there do verily exist finite dimensional bodies, so also Prime Intellect conceiveth body and dimension; if he conceiveth this, he no less conceiveth it infinite; and if he conceiveth it infinite and conceiveth the body infinite, then such an infinite body must be intelligible, and being the product of the divine Intelligence it is most real; real indeed in such a sense that it hath a more necessary being than that which is actually sensible to our eyes. Whence it happeneth (if thou considerest well) that even as there is in truth one infinite and utterly simple individual entity, so also there is an immense dimensional infinite within that other, and within which is that other, in the same fashion as he is within all things and all things are within him. Moreover, if we perceive that a body hath corporeal quality whereby it hath power to increase itself to infinity, as may be seen in a fire which, as everyone will agree, would increase infinitely if sufficient consumable material came within reach; what argument will then maintain that the fire which can be infinite and can exist (and therefore can be created infinite) cannot actually exist infinite? Certainly I know not how we can feign that there is in matter somewhat of passive power that doth not exist in the Efficient Cause as active power, consequently also as action, the very same action. Certainly the statement that infinity existeth potentially [2] and in certain [conceivable] succession, but not in action, inevitably implieth that active power can posit the infinite in successive action but not in completed action, because the infinite can never be completed; whence it would follow that the Prime Cause hath not a single simple active and absolute power, but hath one active power to which correspondeth infinite successive potentiality, and another to which correspondeth potentiality indistinguishable from action. I do not here emphasize that if we regard the world as bounded and since it is impossible to imagine a corporeal object whose circumference is bounded by an incorporeal object, this world would have the quality and power of self-destruction and self-annihilation: for, so far as we understand, all bodies are dissoluble. I say that I will not remind you that no argument would then deny that the empty infinite (even though we cannot conceive it as endowed with active power) would on occasion absorb this world into non-existence. Nor will I point out that Position, Space and the Void, if not identical with matter, have a resemblance thereto, as it would seem is sometimes maintained perhaps not without reason, by Plato [3] and by all those who define position as a certain space. Now if matter hath an appetite which should not exist in vain, since such appetite is according to nature and proceedeth from the order of primal nature, it followeth that Position, Space and the Void have also such an appetite. I leave aside the fact indicated above that none of those who aver that the world is bounded can, having affirmed the boundary thereof, invent any way how this may be; and at the same time some of them while denying in their propositions and in words the void and empty, nevertheless as they proceed and in fact come inevitably to posit them. If there is an emptiness and a void, then it certainly hath containing power, and this can in no way be denied; since the same argument as maintaineth it to be impossible that in the space wherein is our world there is also at the same time contained another world, this same argument must maintain that in the space beyond our world or in that Nullity (for so Aristotle nameth that which he doth not wish to call the Void) [4] it is possible that such another world may be contained. The reason that he asserteth that two bodies cannot occupy the same space is the incompatibility of the dimensional volumes of the two bodies; [5] it followeth then, in so far as this argument doth require, that where the dimensional volume of the one is not, there the dimensional volume of the other can be. If there existeth this possibility, then space is in a certain sense matter; if it is matter it hath quality, if it hath quality, by what argument can we deny it action?

Elpino. Very good. But prithee proceed further. Make clear to me wherein you distinguish between the world [6] and universe.

Philotheo. The difference is well known except to the Peripatetic School. The Stoics distinguish between world and universe in that the world is all that which is filled and doth constitute a solid body; the universe is not merely the world but also the void, the empty space beyond the world; and therefore they call the world finite but the universe infinite. Epicurus similarly nameth the whole and the universe a mixture of bodies and of the void; and in this universe and in the capacity thereof to contain the void and the empty, and furthermore in the multitude of the bodies contained therein he maintaineth that the nature of the world, [7] which is infinite, doth exist. [8] We do not call aught Void as being mere nullity, but rather accept the view whereby that which is not corporeal nor doth offer sensible resistance is wont, if it hath dimension, [9] to be named Void, since we do not usually understand as corporeal that which hath not the property of offering resistance; whence they say that just as that is not flesh which is not vulnerable, so that which doth not offer resistance is not corporeal. In the same way we name infinite that which is an immense ethereal region in which are innumerable and infinite [numbers of] bodies such as the earth, the moon, and the sun, and these are called by us worlds, composed of Plenum and of Void: for this spirit, this air, this ether not only surroundeth these bodies but also penetrateth within them and becometh inherent in everything. Furthermore we speak of the Void according to the view with which we replied to his enquiry, where is the infinite ether and its worlds? [10] We replied, it is in an infinite space, a bosom in which the whole hath his being and is harmoniously conceived. Nor is it possible that the whole should exist or be conceived in any other space soever. Now Aristotle here confusedly giveth these two meanings to the Void, and a third one too he doth feign, which he himself is unable either to name or to define, while he seeketh in debate to deny the Void, and thinketh with this same line of argument to defeat completely all opinions concerning the Void, which, however, he no more doth than as if, having banished the name of a thing, anyone were to imagine the thing itself banished; for he destroyeth the Void if at all by destroying that argument which perhaps no one hath supported, since the ancients like ourselves regarded the Void as that in which a body may have its being, that which hath containing power and doth contain atoms and bodies. Aristotle is alone in defining the Void as that which is nullity, within which is nullity and which can be naught save nullity. Giving to the Void a name and meaning accepted by none else, he raiseth castles in the air, and destroyeth his own Void, but not the Void discussed by all others who have used the term.

Nor doth this sophist act differently in discussing other propositions, such as those concerning motion, the infinite, matter, form, demonstration, being; for he buildeth always on the faith of his own definitions, and names used with a new meaning. Wherefore everyone not entirely bereft of judgment can easily convince himself how superficial is this man's consideration of the nature of things, how attached to his own suppositions which are neither accepted nor worthy of acceptance and are too vain in the domain of natural philosophy for them ever to succeed in feigning the realm of mathematics.

And you will see that Aristotle so gloried in his complacent vanity that even as regards the consideration of Nature, he aspired to be regarded as a ratiocinator or (as we may say) logician, and that by way of abuse he dubs as "natural philosophers" [11] those who have been most solicitous in the study of nature, reality and truth. Well, to pass to ourselves: since in his book on the Void [12] he sayeth naught which can justly militate either directly or indirectly against our belief, we will leave him where he is, returning to him perhaps on another more leisurely occasion. So, if it please thee, Elpino, do thou formulate and arrange those reasonings which persuade our adversaries against the infinite body; and after, bring forward the reasons which prevent their understanding that worlds are without number.

Elpino. I will do so. I will relate the opinions of Aristotle in order, and you will express such comments as occur to you. [13] We have to consider, saith Aristotle, whether there existeth an infinite body as some ancient philosophers have averred, or whether this be impossible; further we have to consider whether there be one world or more. Most important is the resolution of these questions, for the acceptance of either of the opposed solutions is of such consequence as to give rise to one of two entirely opposed and contrary philosophies. Thus for example, we see that those who have posited discontinuous parts have by this fundamental error so barred their own progress that they have gone astray in a great part of mathematics. [14] We are therefore unravelling a subject most important for [the avoidance of] past, present and future difficulties, since, however small an error may be in origin, it becometh by ten thousand repetitions ever greater, just as the smallest error of direction in the beginning of a path, becometh greater and greater the further the distance we traverse, so that finally an exactly opposite goal is reached to that which was proposed. The reason is that beginnings are small in size though very great in influence. That is the reasoning for the solution of this doubt.

Philotheo. All that he saith is most necessary and should be proclaimed no less by others. For even as he believeth that from a wrong understanding of this original point his adversaries have been led to great errors, so we on the contrary believe and see clearly that by the opposite opinion concerning this prime matter, he hath perverted all natural reason.

Elpino. He goeth on: We must then enquire whether there can be a simple body of infinite size. [15] And firstly this must be shewn to be impossible in that prime body whose motion is circular. Afterwards the same must be shewn of other bodies; for every body being either simple or compound, this which is compound will follow the disposition of that which is simple. If then simple bodies are not infinite either in number or size, then it followeth necessarily that neither can a composite body have these properties.

Philotheo. His argument promiseth well, for if he can prove that the body called the containing and prime body is indeed the containing first body and is finite, it becometh superfluous and vain to prove it afterwards of the contained bodies.

Elpino. Now he proveth that a round body is not infinite. [16] For if a round body be infinite, the radii from the centre thereof will be infinite, and the distance will be infinite between one radius and another -- the further they extend from the centre the greater will be the distance between them. For by the lengthening of the lines there necessarily resulteth a greater distance [between them], wherefore if the lines are infinite in length the distance between them will also be infinite. Now it is impossible that a body in motion can [completely] traverse infinite distance; and in circular motion one radius of the moving body must come in turn to occupy the position previously held by every other radius. [17]

Philotheo. This reasoning is good but it answereth not his adversaries. For never hath one been found so barbarous and so ignorant [18] as to have posited the infinite world, infinite in size, and to have attributed motion to it. And he sheweth himself forgetful of that which he relateth in his Physica; [19] that those who postulated a single being, one infinite origin, have similarly regarded it as immobile. Neither he nor any other person among his supporters can name a single philosopher or indeed any simple man who hath attributed motion to infinite size.

But like a sophist he taketh one part of his argument from the conclusion of his adversary; positing his own principle that the universe is mobile, also that it moveth and that it is of spherical form. Now observe whether, among the reasonings adduced by this beggar there is even one that doth militate against the belief of those who proclaim an infinite, motionless and formless immense universe, containing innumerable moving bodies which are the worlds, by some called stars, by others spheres, Just note in this and in other reasonings whether the premises that Aristotle adduced have been accepted by anyone.

Elpino. Certainly, all the six arguments are based on that presupposition, namely that his adversary asserteth the universe to be infinite and that he himself attributeth motion to this infinite body. Certainly this is foolish and absurd, even if we did not desire to accept the identification of motion and infinite stillness, which thou didst prove to me yesterday of individual worlds.

Philotheo. I do not assert this of the universe, to which by no reasoning should motion be attributed, for this is impossible; nor can, nor should motion appertain or be attributed to the infinite. Nor, as I have said before, hath anyone ever imagined such a thing. But this philosopher, as one who lacketh soil, raiseth his castles in the air.

Elpino. Certainly I should desire a reason which would impugn what you say, for five other reasons adduced by this philosopher all take the same road and march in step. It therefore seemeth to me superfluous to repeat them. After he hath produced these which concern a circular motion of the world, he propoundeth reasons based on motion in a straight line; and he declareth it to be equally impossible that anything can be endowed with infinite motion toward the centre [of the world] or downward, and also upward from the centre; and his demonstration concerneth firstly the proper motion of such bodies, as well of those in an outer as of those in an intermediate position. Motion upward, he saith, and motion downward, are opposed; and the site of the one motion is opposed to that of the other. [20] Of these contraries, again, if one is determined, so must the other be, and the intermediate, which participateth in the properties of both determinates, must even be as they. For that which should pass beyond the centre must start not from anywhere you please but from a certain position, for the limits of the centre must be within two boundaries, a beginning and an end. [21] Since then the centre is determined, the extremes thereof must needs also be determined; and if the extremes are determined, so must be also the centre; and if these positions in space are determined, so must be the bodies that occupy them, for otherwise motion would be infinite.

And as for weight and lightness, the body which travelleth upward can reach the body which is situate there, for no natural motion is in vain. Now since in an infinite world (mondo) there is no space, neither is there within it position, nor an infinite body. Again, as regards weight: there is no infinite weight or lightness, therefore there is no infinite body. For if a heavy body be infinite, then the weight thereof would of necessity be infinite, and from this reasoning there is no escape. For if thou wouldst say that an infinite body hath infinite weight, three awkward consequences would ensue. First, the weight or lightness of a finite body would be identical respectively with the weight or lightness of an infinite body. For I shall add to or subtract from a finite heavy body as much as the difference of the weight thereof from that of the infinite body until the finite body hath attained the same quantity of weight or of lightness as the infinite body.

Secondly, the weight of a body of finite size might be greater than that of infinity. [22] For the same reasoning whereby the finite body may be equal in weight to the infinite sheweth also that the weight of the finite body may exceed that of the infinite by the addition to the finite body of as much as you please of weighty body; or [the proportion may be changed by] subtracting part from it, or if you please, by adding to it a piece of lighter body.

Thirdly, the weight of a body of finite size and that of a body of infinite size would be identical [as shewn above]. And [furthermore] because the proportion of weight to weight is identical with the proportion of speed to speed, therefore it would follow similarly that speed or slowness of a finite body could be identical with speed or slowness respectively of an infinite body.

Fourthly, the speed of a finite body could be greater than that of the infinite.

Fifthly, the respective speeds could be equal. Or, indeed, even as weight may exceed weight, so speed would exceed speed: if the body have infinite weight, it will need to move through a certain space in less time than finite weight would take, or else it will move not at all, since speed and slowness depend on the size of the body. Wherefore, there being no proportion between finite and infinite, it will ultimately ensue that infinite weight will be immobile. For if it hath motion, it moveth not with a speed so great as to exceed that of any conceivable finite weight [23] traversing the same space.

Philotheo. It would be impossible to find another person who in the name of philosophy could invent vainer suppositions and fabricate such foolish and contrary reasons to accommodate such levity as is discernible in his arguments. As for what he saith concerning the spaces occupied by bodies, and of the determinate upper, lower, and intermediate, I would like to know against what opinion he is arguing. For all who posit a body of infinite size, ascribe to it neither centre nor boundary. For he who speaketh of emptiness, the void, or the infinite ether, ascribeth to it neither weight nor lightness, nor motion, nor upper, nor lower, nor intermediate regions; assuming moreover that there are in this space those countless bodies such as our earth and other earths, our sun and other suns, which all revolve within this infinite space, through finite and determined spaces or around their own centres. Thus we on earth say that the earth is in the centre; and all philosophers ancient and modern of whatever sect will proclaim without prejudice to their own principles that here is indeed the centre; just as we say that we are as it were at the centre of that [universally] equidistant circle which is the great horizon and the limit of our own encircling ethereal region, so without doubt those who inhabit the moon believe themselves to be at the centre [of a great horizon] that encircleth this earth, the sun and the other stars, and that is the boundary of the radii of their own horizon. [24] Thus the earth no more than any other world is at the centre; and no points constitute definite determined poles of space for our earth, just as she herself is not a definite and determined pole to any other point of the ether, or of the world space; and the same is true of all other bodies. From various points of view these may all be regarded either as centres, or as points on the circumference, as poles, or zeniths and so forth. Thus the earth is not in the centre of the universe; it is central only to our own surrounding space.

This disputant then hath proceeded by petition principii, first accepting that which he would prove. He beginneth, I say, by assuming the contrary of his opponent's views, assuming indeed a centre and a limit against those who, declaring the world (mondo) to be infinite, thereby necessarily deny limit and centre, and consequently deny motion either upward to the highest point or downward to the lowest depth.

The ancients indeed observed as we too observe that some things come to our earth, and some appear to depart from this earth or indeed from any place where we are; wherefore if we should wish to say that the motion of such things is upward or downward, it must be understood as applying only to a certain region from a certain viewpoint, so that if something receding from us proceedeth toward the moon, when we should say that it goeth upward, then the inhabitants of the moon, our own anticephali, would say that it is in descent. Motions then have no distinction of upward or downward, hither or thither in respect of the infinite universe; but only in respect of finite worlds which are within that universe, or according to the respective horizons of innumerable worlds, or to the number of innumerable stars. Hence it ensueth that the same thing, with the same motion, may be said to move upward and downward with respect to diverse bodies. Determinate bodies are therefore not endowed with infinite motion, but with motion finite and determined within their own limits. But the undetermined and infinite hath neither finite nor infinite motion, and knoweth no distinction of place or of time. Furthermore, as regards Aristotle's reasoning concerning heaviness and lightness, we will say [only] that this is one of the finest fruits produced by the tree of stolid ignorance. For weight, as we shall demonstrate in the appropriate place, is not situate throughout any whole body, or naturally disposed and concentrated therein; and therefore there is no distinction between the nature of one or other position in space nor of one or other species of motion. Furthermore we shall shew that heavy and light may be called the same thing directed by the same force and motion but in respect of diverse centres, just as in respect of diverse centres the same thing may be named high or low, in upward or in downward motion. And I say this in regard to individual bodies and individual worlds of which none is heavy or light; whose parts receding from them and dispersions are called light in weight, but returning to them are called heavy; just as particles of our earth and of terrestrial objects if directed toward the circumference of our ether are said to ascend and if toward the earth are said to descend.

But as for the universe and infinite body, who hath ever called it heavy or light? Or, indeed, who ever posited such premises or so raved that it was possible to infer from his statement that the infinite be heavy or light, could rise, ascend or soar? We shall demonstrate that no infinite body is either heavy or light. For these qualities belong to parts in so far as these tend toward their own whole, the place wherein they may best survive. Such qualities appertain not to the universe, but to the actual worlds wherein are contained the particles. Thus on our earth the particles of Fire seeking to escape and mount toward the sun, carry ever with them some particles both of Earth and of Water with which they are conjoined; and these becoming increased, do thus by their own natural impulse return to their own place. So it is the more certain that great bodies can by no possibility be heavy or light, the universe being infinite, nor can they have an affinity to be either distant from or close to either the circumference or the centre of the infinite universe. Wherefore the earth in her own space is no heavier than the sun in his space or than Saturn or the North Star in their own. We can, indeed, say that just as particles of the earth return to earth by the force of their weight (since we thus choose to describe the impulse of the parts toward the whole, of the wanderer toward his own place), such also is the action of the parts of other bodies; for there may be an infinite number of other earths or similar bodies, an infinite number of other suns or fires or similar bodies; and the parts of these all move from outer positions toward the bodies which contain them as toward a centre.

It would follow that there must be an infinite number of heavy bodies; nevertheless weight will not be infinite intensively in a single subject; but rather extensively in innumerable subjects. And this may be deduced from the sayings of all the ancients and ourselves; nor can our disputant produce any contrary argument. That which he asserteth of the impossibility of infinite weight, is so true and so patent that I am ashamed to mention it; and it contributeth no whit either to destroy his opponent's philosophy or to support his own. For all these arguments and words are thrown to the wind.

Elpino. The vanity of the fellow's arguments is here more than obvious, so that not the whole art of persuasion would suffice to excuse it. Listen now to these arguments that he addeth to prove generally that there existeth no infinite body. "Now," saith Aristotle, [25] "it being clear to those who study individual cases that there is no infinite body, it remaineth to investigate whether such be a general possibility. For someone might aver that just as the world is disposed around us, so it were not impossible that there might be yet more heavens." But before we reach this problem, let us reason of the infinite universally.

Now every body must either be infinite [or finite] and if infinite it must be composed either of similar or dissimilar parts, which in turn must be either of finite or of infinite species. It is not possible that it be of infinite species if we accept our presuppositions aforesaid of other worlds similar to our own, since even as our world is disposed around us [i.e., around the Earth] so also it is disposed around other bodies; moreover there are other heavens. For if the primary motions around the centre are determined, then so also must be the secondary motions. And since we distinguish already five sorts of bodies, of which two are simply heavy or light, two moderately heavy or light, and one neither heavy nor light but active around the centre, so must there be also in the other worlds. Wherefore it is not possible that they be of infinite species. Nor yet can they comprise finite species. At the outset he proveth by Four arguments that they do not consist of Dissimilar Finite Species. Firstly, each of these infinite parts must be Water or Fire, and must therefore be heavy or light, which hath been shewn to be impossible since heaviness or lightness cannot be infinite.

Theophilo. To this we have already replied adequately.

Elpino. I know it: and he addeth the Second argument, saying that each of these species must be infinite, and must therefore occupy infinite space; it followeth that each must be endowed with infinite motion, which is impossible, for a descending body cannot fall infinitely low, as is manifest from what happeneth in all motion and transmutations. Similarly generation cannot seek to produce that which cannot be produced, nor doth local motion seek a position which can never be attained. That which cannot exist in Egypt cannot move toward Egypt, since Nature permiteth no vain process. It is therefore impossible that a body should move toward a goal that it cannot reach.

Theophilo. To this argument we have amply replied, and we declare that there are an infinity of earths, an infinity of suns, and an infinite ether -- or, as Democritus and Epicurus have it, an infinite Plenum and an infinite Vacuum, the one placed within the other. [26] There are, moreover, diverse finite species, one within another, and one related to another; and these diverse species concur as it were to form a single infinite universe. And again, they are as infinite parts of the infinite, inasmuch as from an infinity of earths similar to our own, there ariseth in fact one infinite earth, not as a single continuum but as a composite whole composed of their innumerable multitude. So also must it be understood of other species of bodies, whether four or two or three or what number you will, which I do not at present determine; since they are, in such fashion as we may use the phrase, parts of the infinite, therefore they must be infinite according to the dimension which resulteth from such multitude. Nor doth this require that the heavy body proceedeth infinitely downward. For as this heavy body seeketh the nearest or natural neighbour, so also doth that to the next, and it to the next again. This earth hath her parts which belong to her, another earth hath her own parts which belong to herself; so also the sun compriseth those parts which disperse away from him and then seek to return to him; and other bodies similarly reassemble naturally their own parts. Wherefore just as limits and distances from individual body to body are finite, so also are motions finite. And as no one setteth forth from Greece to journey to the infinite, but journeyeth rather to Italy or Egypt, so also when parts of this earth or of the sun are in motion, their goal is not infinity but is finite and determined. Nevertheless, the universe being infinite, and the bodies thereof transmutable, all are therefore constantly dispersed and constantly reassembled; they send forth their substance, and receive within themselves wandering substance. Nor doth it appear to me absurd or inconvenient, but on the contrary most fitting and natural that finite transmutations may occur to a subject; wherefore particles of [elemental] earth may wander through the ethereal region and may traverse vast space now to this body, now to that, just as we see the same particles change their position, their disposition and their form, even when they are yet close to us. Whence we deduce that if this earth be eternal, it is not so by virtue of the stability of any one part or individual, but through the vicissitudes of many parts, some being expelled therefrom, and their place taken by others. Thus soul and intelligence persist while the body is ever changing and renewed part by part. [27] This may be observed also in animals which survive only by absorption of nutriment and by evacuation of excrement. Whoever considereth well, will recognize that we have not in youth the same flesh as in childhood, nor in old age the same as in youth; for we suffer perpetual transmutation, whereby we receive a perpetual flow of fresh atoms, and those that we have received previously are ever leaving us. As atom joineth atom around the sperm by virtue of general intellect and soul (by means of the structure to which, as matter, they contribute), so the body attaineth form and growth when the influx of atoms exceedeth the efflux. Moreover this same body is of a certain consistency when the efflux equals the influx, and finally declineth when the efflux exceedeth the influx; but I do not speak of absolute efflux and influx, rather the efflux of what is convenient and native and the influx of what is foreign and inconvenient. This latter cannot be overcome by the original source which is weakened owing to the continuous efflux of vital as well as non-vital matter. Coming then to my point, I declare that on account of such vicissitudes, it is not inconvenient but on the contrary most reasonable to state that the parts and the atoms have an infinite course and infinite motion, owing to the infinite vicissitudes and transmutations both of form and of position. It would, indeed, be inconvenient if an object were found which tended to infinity as to a close prescribed limit of local motion or of change. This is impossible since a body is no sooner moved from one position than it findeth itself in another; no sooner is it deprived of one disposition than it hath acquired another, and no sooner hath it shed his being than it hath adopted another. This followeth necessarily from the change which is itself necessarily consequent upon local motion. So that a proximate and shaped subject cannot move except in a finite sense, for it easily changeth form if it changeth position. But the primal subject capable of form moveth infinitely through space and through an infinity of forms while the parts of the [composing] matter enter and go forth again, ever changing their position, their own parts and their containing whole. I understand perfectly.

Elpino. He addeth for his Third argument, [28] that if the infinite were regarded as discrete and discontinuous, so that there were an infinity of separate fire particles, each of them finite, yet the fire which resulteth from all these individual particles would be infinite.

Theophilo. I have already admitted this and because it was known, he ought not to have opposed that which leadeth to no inconvenient conclusion. For if the body become separated and divided into distinctly located parts, of which one weigheth a hundred units, another a thousand, another ten, it will follow that the whole will weigh one thousand, one hundred and ten units. But this will be in virtue of several discrete weights and not in virtue of one continuous weight.

Now neither we nor the ancients have considered it an inconvenient hypothesis that discrete parts should meet in an infinite weight. For from these parts there resulteth logically, arithmetically or geometrically, a weight; but in truth and in nature they do not form a single infinite weight, even as they do not form a single infinite mass. But they form innumerable finite masses and finite weights. That this is stated, imagined and is the case is by no means the same as in the former hypothesis, but far different, for from this hypothesis there followeth not one infinite body of one species, but one species comprising an infinity of finite bodies. Nor, indeed, is one infinite weight made up of an infinity of finite weights, since this infinity [of finite weights] is not continuous, but is composed of discrete parts, which are in an infinite continuum which is the space, position and measurable form capable of containing the whole infinity of parts. Therefore it is by no means inconvenient that there should be this infinite number of discrete weights which do not constitute a single weight. Similarly an infinite number of drops of water do not form an infinite stretch of water, nor do an infinity of earth particles form an infinite earth, for there are bodies which, though infinite in number, yet do not physically form a single body of infinite size, and herein is the great difference; as may be seen in the same way in the hauling of a ship, which is achieved by [the co-operation of] ten persons united; nor will the ship ever be hauled even by a myriad of men not pulling together, or by each of them separately.

Elpino. By this and other reasoning you have a thousand times resolved the problem posed in Aristotle's Fourth argument, wherein is set forth that, if [the definition of] an infinite body is understood, it must necessarily be understood as infinite in every dimension, since on no side can there be aught beyond it. Wherefore it is impossible that within an infinite body there may be various dissimilar bodies, each infinite. [29]

Theophilo. All this is true and in no way contradicteth that which we have so many times stated, namely that there are many dissimilar finite bodies within a single infinity, and we have considered how this may be. Perhaps it may be expressed proportionately, as if one were to assert that many continuous parts form a unity, as for example in the case of a liquid mud, where throughout and in every part, water is continuous with water, earthy matter with earthy matter; wherefore, since the concourse of the atoms of earth, and the atoms of water, is beyond our sensible apprehension, these minima are called neither discrete nor continuous, but form a single continuum which is neither water nor earth, but is mud, while another person may as well please to state that water atom is not actually continuous with water atom, nor earth with earth, but that the water is continuous with the earth and so is the earth with the water; still a third may deny both these statements and may aver that mud only is continuous with mud. And according to these reasonings the infinite universe may be regarded as a single continuum in which discreteness is no more introduced by the interpolation of ether between the large celestial bodies than it can be within the mud by the interposition of air among the dry and the liquid particles, the difference being solely in the fineness and subtlety of the parts of the mud exceeding our sensible apprehension, as against the greatness, larger size and sensible qualities of the parts of the universe. And thus contrary and diverse mobile parts converge to constitute a single continuous motionless body, wherein contraries converge to the constitution of a single whole, and pertain to a single order and finally form a single whole. It would certainly be both inconvenient and impossible to posit two infinites distinct from one another, since it would be impossible to conceive the dividing line between them, where the one infinity would end and the other begin; [30] wherefore each of the two would terminate within the other. Moreover it is most difficult to imagine [31] two bodies, each finite in one and infinite in the other boundary.

Elpino. Aristotle giveth Two Further reasons against an infinite body composed of similar parts. The First [32] reason is that to such a body there must appertain one of these species of local motion; therefore it must either be of infinite weight or infinite lightness, or it must have an infinite circular movement; and the impossibility of all these we have already demonstrated.

Theophilo. And we have also made clear how vain are these discourses and arguments; and that the infinite whole moveth not, and that neither it nor, indeed, any other body occupying his own natural position is either heavy or light in itself, nor have the separate parts thereof these qualities when they have travelled a certain distance from their own regions. An infinite body then is according to our view neither potentially nor actually mobile; nor is it potentially or actually either heavy or light; so far is it from possessing infinite lightness or infinite weight in our view and in the view of others against whom the Peripatetic buildeth such fine castles.

Elpino. The Second [33] argument is then equally vain, for from one who will never admit motion of the infinite, either potential or actual, it is vain to enquire whether the infinite moveth of its own innate nature or by impressed force.

He next proveth [34] that there is no infinite body, using arguments based on motion in general, after having reasoned from common motion. He declareth that an infinite body cannot act on a finite body, still less be patient of action by a finite body. And this he maintaineth with three arguments: First [35] that the infinite cannot be patient of the finite; for all motion and consequently all impressed motion is within Time. For if it be so [i.e., if there can be action between an infinite and a finite body], and since it may happen that a smaller body may suffer action in proportion to his size; therefore it will follow that the proportion between the finite patient and the finite agent will be like to that of the finite patient to the infinite agent. This will be seen if we take the infinite body A, the finite body B, and, since all motion is within time, we will have time G, within which A either moveth or is moved [by B, Diagram II]. We will then take the smaller body B [i.e., smaller than infinity]; and the line D shall act on another body H, so that the action is completed in the same time G. Thus it will be observed that the proportion between D, the smaller [finite] agent, and B, the larger, is equal to the proportion between the finite patient H, and [some] finite part of A, viz., AZ. [D:B::H:AZ; Diagram II]. Now when we change the proportion between the first term, agent D, and the third term, patient H, so that this proportion shall equal that between the second term, agent B, and the fourth term, patient AZ, that is to say, the proportion will be the same between D and H as between B and AZ [D:H::B:AZ] -- then B will in fact have taken the same time G to complete action on the finite and on the infinite, that is on AZ part of the infinite, and on A the infinite. This is Impossible. (See p. 290. [37])

Therefore an infinite body cannot be either agent [36] or patient. For two equal patients will receive equal impress in the same time from the same agent; a lesser patient will receive equal impress from the same agent in less time, and a greater patient in a longer time. Moreover, when there are different agents during the same time, and their action is completed, the proportion between agent and agent will be like to the proportion between patient and patient. Further, every agent acteth on the patient in finite Time (I speak of every agent which completeth action, not of the agent with continuous motion; and only the motion of translation can be completed); for finite action cannot take place in infinite time. Here then is the primary manifestation that the finite cannot achieve complete action on the infinite:

[Diagram II]

Secondly, [38] it is shewn in the same way that the infinite cannot act on the finite. For let there be an infinite agent A and a finite patient B and let A act on B, in finite time G; and let the finite body D act on BZ part of B, in the same time G. [And let H be a finite agent larger than D such that] the proportion between the patient BZ and the whole [finite] patient B is like to the proportion between the [finite] agent D and the other finite agent H [BZ:B::D:H; Diagram III]; and if the proportion between the agent D and the patient BZ be changed to correspond to the proportion between the agent H and the whole patient B [D:BZ::H:B], then B will be moved by H in the same time during which BZ hath been moved by D, that is in time G, within which time, however, B hath been moved by the infinite agent A. And this is Impossible. [39] This impossibility followeth from that which we have said -- that if an infinite object act in finite time, the action cannot be in time, because there is no proportional relationship between finite and infinite. If then we take two diverse [finite] agents, which exert the same force on the same patient, the action of these two will necessarily occupy two different periods of time; and there will be between the times a relationship proportionate to that between the agents. But if we posit that two agents, one infinite and one finite, have the same action on the same patient, then it must necessarily follow either that the action of the infinite taketh place in a [finite] instant, or that the action of the finite agent taketh place in infinite time. Either alternative is Impossible.

[Diagram III]

Thirdly, [40] it is clear that an infinite body cannot act on another infinite body. [41] For, as is related in the Physicae auditus, [42] it is not possible that action or passion be endless; when, therefore, we have shewn that action of the infinite on the infinite can never be complete, it will have been proved that there can be no action between them. Let us then take two infinities, one B, patient of the other A in finite time G; for finite action is necessarily in finite time. We will, then, posit that part BD of the patient [B] suffereth the action of A; it will certainly be clear that the sufferance of the part BD will take place in a time Z shorter than G. The proportion then between time Z and time G will be like to that between BD part of the infinite patient [B], and BDH [some] greater part of the infinite patient B [Z:G::BD:BDH]; and BDH will be patient of A in [finite] [43] time G. But the whole infinite B hath already suffered the action of A in the same time G. And this is false, for it is impossible that two patients [B and BDH], the one infinite, the other finite, should suffer the same action from the same agent, in the same time, whether the efficient cause be finite or, as we have posited, infinite. [44]

[Diagram IV]

Philotheo. All that is said by Aristotle I would deem well said if well applied, and when it concludeth cogently. But as we have already said, the method of no other philosopher who hath discoursed concerning the infinite can lead to such inconveniences as doth that of Aristotle. Nevertheless, not by way of reply, for [here] he differeth not from us, but solely to consider the importance of his opinions, let us examine his manner of reasoning.

First then, he proceedeth on unnatural foundations, wishing to take this or that part of the infinite, though the infinite cannot have parts; unless, indeed, we would name the part infinite; and this implieth the contradiction that there would be a greater part of the infinite and a lesser part, or a part which beareth a greater, and a part which beareth a lesser, proportion to the whole. But thou approachest no nearer to the infinite by hundreds than by threes, for infinite number compriseth infinite threes no less than infinite hundreds; infinite measure appertaineth to infinite feet no less than to infinite miles; therefore when we would speak of the parts of an infinity we do not say "a hundred miles," or "a thousand parasangs," for these terms can equally be used for parts of a finite whole. And they are in truth parts only of that finite whole, to which they bear a ratio; and they cannot and should not be regarded as parts of that to which they bear no ratio. Thus a thousand years are not parts of eternity, because they bear no ratio to the whole; but they are truly parts of some measure of time, as for example, of ten thousand years or of a hundred thousand centuries.

Elpino. Expound then to me. What would you say are the parts that make up infinite duration?

Philotheo. Parts of a time duration which bear a ratio to the duration and to time, but not to infinite duration or infinite time. For in infinite duration, the maximum time, that is, the greatest proportional part of a duration, becomes equivalent to the minimum, since infinite centuries have no greater duration than infinite hours. I say, indeed, that in infinite duration, which is eternity, there are not more hours than centuries. So that everything which can be described as a part of the infinite is in virtue thereof itself infinite, both in duration and in size. From this teaching, you may judge how careful is Aristotle in his hypotheses when he imagineth finite parts of the infinite; and you may estimate the force of the arguments of certain theologians who consider that the eternity of time involveth the inconvenience of as many infinites, one greater than another, as there are species of numbers. By my teaching I say you may escape from innumerable pitfalls. [45]

Elpino. Particularly from that which resulteth from our intent of infinite feet and infinite miles, from which they would make a lesser infinite and another greater infinite within the immensity of the universe.

Philotheo. Secondly, Aristotle doth not fortify his argument by demonstration. For since the universe is infinite and since there are in it an infinity of parts (I do not say they are parts thereof, [46] for it is different to speak of parts within and parts Of the infinite); and since all these parts experience both action and passion, and in consequence can be transmuted one into another; therefore Aristotle would infer either that the infinite doth experience action upon or passion from the finite, or that the infinite acteth upon the infinite and that this latter suffereth action and transformation from the former. We however maintain that this inference is not physically valid though logically it may be correct; since, however much, by computing with our intellect, we may discover infinite parts both active and passive; and these be regarded as contrary to those: yet, since the parts in nature are, as we see, not discrete or separate within distinct boundaries, they do not force or even incline us to say that the infinite is either agent or patient; but rather that within the infinite, innumerable finite parts exercise both action and passion. It may therefore be granted not that the infinite is mobile or alterable, but that there are therein innumerable mobile and alterable bodies; not that the finite suffereth action from the infinite, nor the infinite from the finite, nor the infinite from the infinite, in the natural and physical sense of infinity; but that just as from a logical and rational aggregation, within the infinite all weights are as one weight, though all weights do not make up one weight; so the infinite whole, resting ever immobile, unalterable, incorruptible, within it there can be and are motions and alterations, innumerable and infinite, perfect and complete. Moreover, add to what hath been said that, given two bodies which on the one hand are infinite and on the other hand are bounded each by the other, it doth not follow as Aristotle believed that the mutual action and passion would necessarily be infinite, for if one of the two bodies is acting on the other, the agent would not be exerting influence throughout his size and extent, since it is not throughout the whole of the latter or throughout all the parts thereof, neighbouring, near or joined and continuous with the other.

We therefore posit the case in which two infinite bodies A and B are continuous and joined to one another along the line or surface FG [Diagram V]. Certainly neither will come to act on the other with his whole force: because not all the parts of the one are in propinquity to parts of the other, since mutual continuity is possible only along finite boundaries. And I say furthermore that even if we suppose the surface or line [F G] to be infinite, it will not follow that the bodies which are coterminous therein exert infinite action and [receive] infinite passion, since they are not intentive but extended, [47] and the parts also are extended. Whence it happeneth that in no part doth infinity exert his total force; but only part by part, extensively, discretely and separately.

[Diagram V] [48]

Supposing, for example, that the parts of two opposed bodies capable of action one on another are in propinquity as A to 1, B to 2, C to 3, D to 4 [Diagram V], and so on to infinity, thou wilt never be able to trace [49] infinite intensive action between them, for the parts of these two bodies can act on one another only within a certain and determined distance; [50] wherefore M and 10, N and 20, O and 30, P and 40 have not aptitude to act one on the other. Behold then the proof that, given two infinite bodies, infinite action between them would not follow. I say yet further that however much it may be supposed and conceded that these two infinite bodies can act intensively one on another with their whole force, nevertheless this doth not imply any effect of action or of passion, for the one is no less potent to oppose and resist than is the other to attack and insist, wherefore no change would ensue. Behold then the proof that if two infinite contraries be opposed, either a finite change or none at all will come to pass.

Elpino. Then what will you say if we suppose one of the opposed bodies be finite and the other infinite? As, for example, if the earth were a cold body, and the heaven were fire and all the stars fires, supposing that the heaven were of infinite immensity and the stars innumerable? Do you consider that the result would be, as inferred by Aristotle, that the finite would be absorbed in the infinite?

Philotheo. Certainly not, as can be deduced from what we have said. For if corporeal power were diffused throughout an infinite body, it would not thereby act on the finite body with infinite vigour and power, but it would be effective only with such force as it could diffuse from those finite parts within a certain limited distance; since it would be impossible that it should operate with the force of all the parts, but possible only with those nearest. This may be seen in our demonstration above [Diagram V] where we suppose A and B two infinite bodies which are not able to transmute one another except by means of those parts which are at the distance between [the group] 10, 20, 30, and 40 [on the one hand] and [the group] M, N, O, and P [on the other]; and however far B may move and grow toward infinity, naught will avail that the action [of B on A] be increased or gain in vigour -- even though the body A remain finite. [51] Behold then the proof that when two contraries are opposed to one another, there ensueth always finite action and finite alteration; and this is no less true if we suppose that one of the two be infinite and the other finite than if we suppose both to be infinite.

Elpino. You have entirely satisfied me, so that it appeareth to me superfluous to marshal those further wild arguments whereby Aristotle seeketh to prove that there is no infinite body beyond the heaven. Such is the argument that every body occupying a position is perceptible to our senses, but beyond the heaven no body is accessible to our senses; therefore there is no such region. [52] Or the following: "Every body perceptible to us occupieth a place, but there is no place beyond the heaven; therefore no body is there. Still less is aught beyond; [53] because the word beyond implieth a difference of place, namely, of perceptible place, and cannot therefore be applied to a spiritual and intelligible body: Or as one might put it, that which is perceptible to our senses is finite." [54]

Philotheo. I believe and understand that beyond this imagined edge of the heaven there is always a [further] ethereal region with worlds, stars, earths, suns, all perceptible one to another, that is each to those which are within or near; though owing to the extreme distance they are not perceptible to us. And in this matter, consider what foundation hath this man who maintaineth that because there are no bodies perceptible to us beyond our supposed circumference, therefore no such bodies exist. Wherefore he persuadeth himself that there is naught but the eighth sphere beyond which the astrologers of his time believed no heaven to exist. [55] And because they referred the apparent circular movement of the world around our earth always to one primum mobile, supreme above all others, therefore they established [a system with] such foundations that they continued even further, endlessly adding sphere to sphere, and they believed that some contained no stars, and therefore no perceptible bodies. Whilst the astrological suppositions and conceits have condemned this opinion, it is yet more completely condemned by those who understand better how the bodies said to belong to the eighth sphere nevertheless differ from one another by their greater or smaller distance from our earth's surface no less than do the bodies in the other seven spheres, for the argument concerning their equidistance resteth only on the utterly false assumption of the fixity of our earth, against which all nature crieth aloud, all judgement and all reasoned opinion and informed mind must ever protest. Yet be this as it may, it is asserted against all reason, that the universe must terminate exactly at the limit of our perceptive power, because perceptibility is the cause of our inferring the existence of bodies. But invisibility may be caused by defect of our perceptive power and not by absence of the perceptible object, and it warranteth not the slightest suspicion that the bodies do not exist. For indeed if truth depended on such perceptive power on our part, bodies which appear close to one another or adjoining would be so in very fact. But we judge that a certain star that appeareth small in the heaven, and is named of the fourth or fifth magnitude, may be much larger than one named of the second or the first magnitude, because our perception falleth into error, being unable to recognize the effect. [56] of the greater distance [of the apparently smaller star]. But, because we have recognized the motion of the earth, we know that those worlds are not equidistant from our own, and are not as it were in a deferen. [57]

Elpino. You would deny that they are as it were embedded in a single cupola, a ridiculous notion which children might conceive, imagining perhaps that if they were not attached to the celestial tribune and surface by a good glue, or nailed with stoutest nails, they would fall on us like hail from the air immediately above us. But you consider that those innumerable other earths and vast bodies hold their positions and their proper distances in ethereal space just as doth our earth, which by her own revolution giveth an impression that they are all chained together and are revolving around her. You would say that there is no need to posit a spiritual body beyond the eighth or ninth sphere; but that just as this same air surroundeth and containeth earth, moon and sun, so also it is extended infinitely to contain other infinitely numerous stars and great animals; and this air becometh thus the common and universal space, the infinitely spacious bosom which holdeth and embraceth the whole infinite universe, no less than that part which is perceptible to us owing to the innumerable lamps thereof. [58]

You would say that it is not this air, this enveloping body which moveth in a circle, sweeping [59] with itself the stars such as earth, moon and the others; but that these by their own impulse move within their own spaces, and have each their own motion, besides that mundane apparent motion which resulteth from the motion of our own earth, and besides the further movements which appear common to all stars, as though they were attached to a moving body, for they all have this appearance to us owing to the diverse motions of this star inhabited by ourselves, whose motion is quite imperceptible to us. You therefore would say that the air and the parts which inhabit the ethereal region have no motion save by way of restriction or amplification which must exist for the sake of the progress of these solid bodies through the ethereal region, while some circle around the others, and it is necessary that this spiritual body should fill the whole.

Philotheo. Truly. Moreover I say that this infinite immensity is an animal though it have no determined form nor perception of exterior things; for it is imbued with all soul and embraceth all life and it is the whole of life. Moreover I declare that no inconvenience ariseth from this conception as doth happen from that of two infinities, for the universe being an animate body, it hath within it infinite motive power and infinite capacity to receive motion -- in discrete manner as we have described. For the whole continuum is immobile both as regards spinning motion around his own centre and as regards motion in a straight line either toward or away from his own centre; for itself hath neither centre nor boundary. Moreover we say that it is not convenient to attribute the motions of heaviness and lightness either to an infinite body, or even to any complete and perfect body within the infinite or to any part of these bodies, for each part occupieth his natural position and rejoiceth in his natural disposition. Once more I repeat that nothing is heavy or light absolutely, but only relatively to the position toward which the diffused and separated parts thereof retreat and congregate.

And now we have to-day sufficiently considered the infinite extent of the universe. To-morrow I will await you since you wish to understand concerning the infinite number of worlds within this infinite universe.

Elpino. Though I believe that the teaching on the former matter hath enlightened me also concerning this further doctrine, nevertheless I will return in the hope of hearing further important details.

Fracastoro. And I shall come solely as audience.

Burchio. And I too, since as I find myself little by little and more and more beginning to understand you, so by degrees I attain to holding as most likely or perhaps even as truth that which you pronounce.

End of the Second Dialogue.

Graphic Rule

Graphic Rule