The undivided does not differ, therefore, from the divided, nor does the
absolutely
simple differ from the infinite, nor does the centre differ from the circumference.
Bruno-Cause-Principle-and-Unity
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without resorting to the fantastical ideas of Plato, since you are so hostile to them, you will be forced and obliged to say, either that the permanent actuality is found in the efficient cause - but this you can- not do, since you say that this efficient cause is what draws out and extracts the forms from the potency of matter - or that their permanent actuality is found in the bosom of matter.
And, in fact, that is what you will be forced to say, because all the forms which appear as it were on the surface of mat- ter - those that were as much as those that are or will be - and which you call individual forms in act, are not themselves the principle, but are principled things.
(I think, in fact, that the particular form is found on the surface of matter, in the same way as the accident is at the surface of the composite substance.
Whence it follows that the actuality of the expressed form must be recognized as inferior to that of matter, just as the actuality of the accidental form is recognized as inferior to that of the composite.
)
? ? ? ? ? ? ? . Indeed, Aristotle concludes lamely by declaring, in con- cert with all the ancient philosophers, that principles must always be
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Fourth dialogue
? permanent; later on, if we seek further in his doctrine for the place where the perpetual seat of natural form which floats on the back of matter might be, we will not find it either in the fixed stars - since the particular forms which we see do not descend from on high - nor in the ideal signs, sepa- rate from matter - for if these are not monsters, they are assuredly worse than monsters, being chimeras and pointless fantasies. What then? Forms are in the bosom of matter. And what then? Matter is the source of actual- ity. Do you want me to carry on and make you see all the absurdities into which Aristotle gets himself ? He says that matter exists in potency, but ask him: When will it be in act? Together with a great crowd he will respond: When it possesses form. But insist and ask: When that occurs, what com- mences to exist? They will answer, despite themselves: The composite, not matter, since the latter is always identical to itself, never renews itself, never changes. The same goes for artificial things: when one makes a statue of wood, we do not say that the wood begins to exist, for it is no more nor less wood than before. In fact, that which receives being and actuality is the new product, the composite, I mean the statue. How can you grant potency, then, to something that will never be in act nor possess act? For it follows from this that matter is not that which is in potency of being or that can be, for it is always identical and immutable, and is that upon which and in which change takes place, rather than that which changes. What is altered, augmented, diminished, moved in location, corrupted, is always (as you Peripatetics, yourselves, say) the composite, never matter. Then, why do you say that matter is now in potency, now in act? No one surely could doubt that matter, whether it receives forms or sends them forth from itself, does not receive a greater or lesser actuality in terms of its essence or its substance; so that there is no reason to say that it exists in potency. For potency concerns what is in continual movement in relation to matter, and not matter itself, which is not only eternally at rest, but the very cause of that state of eternal rest. For if form, in keeping with its fundamental, specific being possesses, not only logically - in the concept and in reason - but also physically in nature, a simple, invariable essence, then form must exist in the perpetual potency of matter, which is a potency not distinct from act, as I have several times explained in my various discussions concerning potency.
? ? ? ? ? ? ? ? ? . Queso[Ibegyou],spareawordfortheappetiteofmatter, so that Gervasio and I can resolve a little dispute between us.
? ? ? ? ? ? ? ? . Yes, please, Teofilo, for this person has given me a pain in ? ?
Cause, principle and unity
? the head with his comparison between matter and woman. He says that women are no more content with males than matter is with forms, and so forth.
? ? ? ? ? ? ? . Seeingthatmatterdoesnotreceiveanythingfromform,why do you think it desires it? If (as we have said) it brings forms out of its bosom and so possesses them in itself, how can you claim that it desires them? It does not desire those forms which daily change on its back, for every ordered thing desires that from which it receives perfection. And what can a corruptible thing bring to an eternal one? What can an imper- fect thing, as is the form of sensible things, which is always in movement, give to another so perfect that, if well pondered, is understood to be a divine being in things, as perhaps David of Dinant meant, who was so poorly understood by those who reported his opinion? 20 Matter does not desire form in order to be preserved by it, because a corruptible thing does not preserve an eternal one. Moreover, since matter clearly preserves form, form must desire matter in order to perpetuate itself, and not the other way around. For when form is separated from matter it ceases to exist, as is not the case with matter, which has all it had before the coming of form and which can have other forms as well. Not to mention that when we speak of the cause of corruption, we do not say that the form flees from matter or that it leaves matter, but that matter throws off one form to assume another. There is as little reason to say that matter desires form as that it hates it (I mean those forms that are generated and corrupted, because it cannot desire the source of forms, which it has within itself, because nothing desires what it possesses). By the same line of reasoning, according to which it is said to desire what it sometimes receives or produces, it can also be said to abhor whatever it throws off or rejects. In fact, it detests more fervidly than it desires, for it eternally throws off that individual form after retaining it a very short while. If you will remember this, that matter rejects as many forms as it assumes, you must agree with me when I say that it loathes form, just as I can allow your statements concerning desire.
? ? ? ? ? ? ? ? . Herelie,then,inruinsnotonlyPoliinnio'scastles,butalso others'.
? ? ? ? ? ? ? ? ? . Parciusistaviris[Donotboasttoomuch]. ? ? ? ? ? ? ? . Wehavelearnedenoughfortoday. Untiltomorrow.
? 20 David of Dinant, author of De tomis idest de divisionibus. 'Thou who reported his opinion' probably refers to Aquinas, Summa contra Gentiles (? , ? ? ? ? ), where David of Dinant is said to have identified God with matter.
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Fifth dialogue
? ? ? ? ? ? ? ? . Then,goodbye.
End of the fourth dialogue
Fifth Dialogue
? ? ? ? ? ? ? . Theuniverseis,therefore,one,infiniteandimmobile. Isaythat the absolute possibility is one, that the act is one; the form, or soul, is one, the matter, or body, is one, the thing is one, being is one. The maximum, and the optimum, is one: it cannot be comprehended and is therefore inde- terminable and not limitable, and hence infinite and limitless, and conse- quently immobile. It has no local movement since there is nothing outside of it to which it can be moved, given that it is the whole. It does not engen- der itself because there is no other being that it could anticipate or desire, since it possesses all being. It is not corrupted because there is no other thing into which it could change itself, given that it is everything. It cannot diminish or grow because it is an infinity to or from which nothing can be added or subtracted, since the infinite has no measurable parts. It is not alterable in terms of disposition, since it possesses no outside to which it might be subject and by which it might be affected. Moreover, since it com- prehends all contraries in its being in unity and harmony, and since it can have no propensity for another and new being, or even for one manner of being and then for another, it cannot be subject to change according to any quality whatsoever, nor can it admit any contrary or different thing that can alter it, because in it everything is concordant. It is not matter, because it is not configured or configurable, nor it is limited or limitable. It is not form, because it neither informs nor figures anything else, given that it is all, that it is maximum, that it is one, that it is universal. It is neither measurable nor a measure. It does not contain itself, since it is not greater than itself. It is not contained, since it is not less than itself. It is not equal to itself, because it is not one thing and another, but one and the same thing. Being one and the same, it does not have distinct beings; because it does not have distinct beings, it has no distinct parts; because it has no distinct parts, it is not composite. It is limit such that it is not limit, form such that it is not form, matter such that it is not matter, soul such that it is not soul: for it is all indifferently, and hence is one; the universe is one.
Indeed, in this one, the height is no greater than the length or depth, so that it is called a sphere by analogy, although it is not a sphere. Length,
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? breadth and depth in the sphere are identical, because they have the same limit, but in the universe, length, breadth and depth are identical because they are all equally without limit and infinite. If they have no half, quarter or other fraction, if there are no fractions at all, then there is no measurable part, nor, strictly, any part that differs from the whole. For, if you wish to speak of part of the infinite, you are obliged to call that infinite as well; if it is infinite, it coincides in one and the same being with the whole: therefore, the universe is one, infinite, indivisible. And if in the infinite you cannot find any difference as of part from whole, nor any difference as of one part from another, the infinite is undoubtedly one. There is no smaller part and greater part within the infinite's comprehension, for any part, however large, comes no nearer the proportion of the infinite than does any other, however small. In infinite duration, an hour is no different from a day, a day from a year, a year from a century, a century from an instant, because nei- ther moments nor hours exist any more than do centuries, and because none is more commensurable with eternity than another. Similarly, in the immensity, the palm is not different from the stadium1 , nor the stadium from the parasang2 , because the parasang is no nearer the immensity's pro- portions than is the stadium. Hence, there are no more infinite hours than there are infinite centuries, nor infinite palms in greater number than infinite parasangs. You come no nearer to commensurability, likeness, union and identity with the infinite by being a man than by being an ant, or by being a star than by being a man, for you get no nearer to that infinite being by being the sun or the moon than by being a man, or an ant. This is because, in the infinite, there is no difference between those things - and what I say of them applies just as well to all other existent particular things.
Now, if, in the infinite, all these particular things are not differentiated, are not divided into species, it necessarily follows that they have no num- ber: the universe, therefore, is one and immobile. Because it comprises everything, does not take on one being after another, and suffers no change neither by nor in itself, it is, consequently, all that it can be, and in it (as I said the other day), act does not differ from potency. If potency does not differ from act, it is necessary that, in the infinite, the point, the line, the surface and the body do not differ. For there, the line is surface because, by moving, it may become surface, and there the surface moves and becomes body, insofar as it may move and become, by its flow, a body. In the infinite, therefore, the point necessarily does not differ from the body, for, from its
1 Seenote? onp. ? ? above. 2 Seenote? onp. ? ? above. ? ?
? Fifth dialogue
? status as point, it becomes a line; from its status as line, it becomes a sur- face; from its status as surface, it becomes a body. So the point, because it possesses the potency to become a body, does not differ from the status of a body, where the potency and the act are one and the same thing.
The undivided does not differ, therefore, from the divided, nor does the absolutely simple differ from the infinite, nor does the centre differ from the circumference. Since the infinite is all that it can be, it is immobile; since in it everything is indifferent, it is one; and since it possesses all the greatness and perfection that can possibly be possessed, beyond all limit, it is the maximum and supreme immensity. If the point does not differ from the body, nor the centre from the circumference, nor the finite from the infinite, nor the maximum from the minimum, we may certainly affirm that the universe is entirely centre, or that the centre of the universe is every- where, and the circumference nowhere insofar as it is different from the centre; or else that the circumference is everywhere, but the centre is nowhere insofar as it differs from the circumference. Here, then, is how it is not impossible, but rather necessary, that the optimum, the maximum, the incomprehensible is everything, is everywhere, is in everything, for, being simple and indivisible, it can be everything, be everywhere and be in everything. Thus, not for nothing is it said that Jove fills all things, inhabits all parts of the universe, is the centre of everything which has being: one in all, and that through which all is one, and is that which, being all things and comprehending all being in itself, causes everything to be in everything.
But you will say to me, 'Then why do things change? Why does partic- ular matter turn itself into other forms? ' My answer is that mutation is not striving for another being, but for another mode of being. And this is the difference between the universe and the things of the universe: for the universe contains all being and all modes of being, while each thing of the universe possesses all being but not all modes of being. Each thing cannot possess, in act, all particularities and accidents, because many forms are incompatible within the same subject, either because they are contrary or because they belong to different species - for example, there cannot be the same individual substance under the accidents of a horse and a human being, or under the dimensions of a plant or an animal. What is more, the universe comprehends all being totally, for nothing can exist outside of or beyond infinite being, because there is no outside or beyond infinity. By contrast, each of the things of the universe comprehends all being, but not
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Cause, principle and unity
? totally, because outside each one of them there exists an infinity of other things. You must conceive, therefore, that everything is in everything, but not totally or under all modes in each thing. Understand, therefore, that each single thing is one, but not in the same way.
We are, therefore, correct in affirming that being - the substance, the essence - is one, and since that one is infinite and limitless, both with respect to duration and substance, as it is in terms of greatness and vigour, it does not have the nature of either a principle or of what is principled;3 for each thing, coinciding in unity and identity (that is to say, in the same being), comes to have an absolute value and not a relative one. In the infi- nite and immobile one, which is substance and being, if there is multiplic- ity, the number which is a mode and multiformity of being by which it comes to denominate things as things, does not, thereby, cause being to be more than one, but to be multi-modal, multiform and multi-figured. So, following closely the reasoning of natural philosophers and leaving the logicians to their fantasies, we discover that everything that causes difference and number is pure accident, pure figure, pure complexion. Every production, of whatever kind, is an alteration, while the substance always remains the same, since there is only one substance, as there is but one divine, immortal being. Pythagoras, who did not fear death but saw it as a transformation, reached this conclusion. Those philosophers who commonly go by the name of physical philosophers4 also were able to understand this. They said that nothing, in terms of substance, is begotten or is corrupted - unless we understand by this the process of change. Solomon inferred this as well, saying, 'there is nothing new under the sun, but what is, has already been'. 5 You see, then, how the universe is in all things and all things are in the universe, we in it and it in us: thus, every- thing coincides in perfect unity. See, then, how our spirit should not be afflicted, how there is nothing that should frighten us: for that unity is sta- ble in its oneness and so remains forever. It is eternal, while every aspect, every face, every other thing is vanity and nothingness - indeed, outside this one there is nothing. Those philosophers who have discovered this unity have found their beloved Wisdom. For wisdom, truth and unity are indeed the same thing, though not everyone has understood this, since some have adopted the manner of speaking, but not the manner of under- standing of the truly wise. Aristotle, among others, did not discover the
? 3 I. e. there is no distinction between an active and passive component within infinite substance. 4 Ionic philosophers. 5 Ecclesiastes, ? , ? ? .
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Fifth dialogue
? one, nor being, nor the true, because he did not recognize being as one. Although he could have adopted the meaning of being which is common to substance and accident, and further, distinguished his categories accord- ing to as many genera and species as there are specific differences, nonethe- less he perceived truth badly, not going deeply enough into the knowledge of this unity and of this indistinction of the eternal nature and eternal being. With his harmful explanations and his irresponsible arguments, this arid sophist perverted the sense of the ancients and hampered the truth, less, perhaps, out of intellectual weakness, than out of jealousy and ambition.
? ? ? ? ? ? ? . So that this world, this being, this truth, this universe, this infinity, this immensity is found entire in each of its parts: it is the ubique [everywhere] itself. Thus, everything in the universe, in relation to the uni- verse, exists everywhere according to its capacity, whatever its relation might be with other particular bodies; for it is above, below, right, left and so on, in keeping with all local differences, since, in the totality of the infi- nite, there are all these differences and none of them. Whatever thing we take in the universe, it has in itself that which is entire everywhere, and hence comprehends, in its own way, the entire world soul (although, as we have said, it does not comprehend it totally), and that world soul is entire in every part of the universe. This is why, even if the act is one and consti- tutes a single being, wherever it may be found, we must not think that there is, in the world, a plurality of substance and of that which is truly being.
Following on this, I know that you take as manifest that each of these innumerable worlds, which we see in the universe, is not found there so much as if in a containing site, nor as in an interval or a space, but is found there as in a place that comprehends it, a conserver, mover and efficient, which itself is comprised in its entirety in each of these worlds, as the soul is found in its entirety in each of the parts of that world. For that reason, although a particular world moves towards or around another, as the earth moves to and around the sun, nonetheless, with respect to the universe, nothing moves to or around it, but only within it.
You, further, hold that, just as the soul (to take up the common way of speaking once more) pervades that great mass to which it gives being, remaining altogether indivisible, so that it is altogether present in the whole and any of its parts, so the essence of the universe is one both in the infinite and in anything taken as a member of the universe; so that, substantially, the whole and each of its parts are but one. In your opinion, Parmenides was, therefore, right to say that the universe is one, infinite and immobile
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Cause, principle and unity
? (although it is not entirely clear what he intended, his words having been reported by a commentator who is not particularly reliable). 6
You say that all the differences seen in bodies, from the point of view of formation, constitution, figures, colours and other individual or common characteristics, are nothing but the diverse aspects of the same substance: fleeting, mobile and corruptible aspects of an immobile, persistent and eternal being in which all forms, figures and members exist, though indis- tinctly and (so to speak) conglomerated - exactly as in the seed, where the arm is not distinct from the hand, nor the bust from the head, or the nerve from the bone, and where differentiation and separation do not produce another or a new substance, but bring into act and accomplish certain qual- ities, differences, accidents and dispositions related to that substance. And what is said of the relation between the seed and the members of animals may also be said of food in relation to chyle, to blood, to phlegm, to flesh and seed. This goes for any other thing which precedes the alimentary state, or other state. It also goes for all things, from the lowest level of nature to the highest, climbing from the physical totality philosophers know to the archetype in which theologians believe, if you like, until we reach a single original and universal substance, the same for all, which we call being, the basis of all species and all different forms. Similarly in the art of carpentry there is a single substance of wood which is subject to all dimensions and shapes, which are not themselves wood but are of wood, in the wood or involving the wood. That is why everything that makes for the diversity of genera, species, differences, properties, all that which consists in genera- tion, corruption, alteration and change, is not being, is not essence, but condition and circumstance of being or essence, which is one, infinite, substratum, matter, life, soul, truth and goodness.
You say, then, that, since being is indivisible and absolutely simple, because it is infinite, and is act in its fullness in the whole and in every part of it (in the same way we speak of parts in the infinite, but not of parts of the infinite), we cannot think in any way that the earth is a part of being, nor that the sun is part of substance, since the latter is indivisible. But it is quite reasonable to speak of the substance of the part, or better still, of the substance in the part; just as it is not reasonable to say that a part of the soul is found in the arm or another part in the head, but it is legitimate to say that the soul is in the part that is the head, and that the substance is sub- stance of the part - or in the part - that is the arm. For to be portion, part, 6 Aristotle. See the end of the third dialogue, where Aristotle's opinion of Parmenides is mentioned.
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Fifth dialogue
? member, the whole, equal to, larger or smaller, like this or like that, relative to this or to that, identical to or different from, etc. , respond to other con- cepts which do not express an absolute, and hence cannot designate the substance, the one or being, but, in terms of modes, determinations and forms, exist through the substance, in the one, and relative to being. Thus, just as it is commonly said that quantity, quality, relation, action, passion and other kinds of accidents are relative to one and the same substance, in the same way one could say that the one and supreme being, in which act does not differ from potency, can be all absolutely and is everything that it can be. It is in a complicative manner one, immense, infinite and compre- hensive of all being, and in an explicative manner, it is present in sensible bodies and in the potency and the act that we see distinguished in them. That is why you hold that what is generated and generates (be it a question of an equivocal agent or of a univocal agent, as is commonly said in phil- osophy), as well as that of which the generation is made, are always of the same substance. Your ears will, therefore, not be jarred by the thesis of Heraclitus, which declares all things to be but one - the one which, thanks to its mutability, contains all things in itself. And since all forms are in it, it follows that all definitions accord with it, so that all contrary propositions are true. And what creates multiplicity in things is not being, is not the thing, but what appears, what is offered to the senses and lies on the sur- face of things.
? ? ? ? ? ? ? . Exactly. But I would like you to read further in this most important science and of this solid foundation of the truths and the secrets of nature. First, therefore, I would like you to note that nature descends to the production of things, and intellect ascends to the knowledge of them, by one and the same ladder. Both ways proceed from unity to unity, pass- ing through a multitude of middle terms. Not to mention that the philo- sophical method of the Peripatetics and of many Platonists is to have the multitude of things as middle term, preceded by the pure act, at one extremity, and the pure potency, at the other; similar to other philosophers who affirm metaphorically that the darkness and the light come together in the constitution of innumerable degrees of forms, images, figures and colours. But beside all these philosophers, who take into consideration two principles and two princes, others rise up who, impatient with and hos- tile towards polyarchy, make the two principles coincide into one, which is at the same time abyss and darkness, clarity and light, profound and impenetrable obscurity, and supernal and inaccessible light.
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Cause, principle and unity
? Secondly, consider that the intellect, wishing to liberate and detach itself from the images to which it is bound, not only resorts to mathematical and symbolic figures or analogies drawn from them in order to comprehend the being and the substance of things, but also ascribes the multiplicity and diversity of species to one and the same root. Thus, Pythagoras, who posited numbers as the exclusive principles of things, understood unity to be the basis and substance of all of them. Thus, Plato and other philoso- phers who made species to consist of figures conceived of the point as sub- stance and universal genus, inasmuch as it is the common stock and root of all figures. And perhaps surfaces and figures are what Plato meant ulti- mately by his 'great', and the point and the atom are what he meant by his 'small', two principles of specification of things which refer, then, to one, as everything that is divided refers to the undivided. Therefore, those who say that the one is the substantial principle mean that substances are like numbers, and others who think of the substantial principle as a point mean that the substances of things are like figures, but all agree in positing an indivisible principle. However, Pythagoras' method is better and purer than Plato's, because unity is the cause and the reason for individuality and the point, and it is a principle which is more absolute and appropriate to universal being.
? ? ? ? ? ? ? ? . Why has Plato, who came after him, not done as well or better than Pythagoras?
? ? ? ? ? ? ? . Becausehepreferredtospeaklesswell,inamannerlessade- quate and less appropriate, and to be acclaimed as a master, than to say something better, in a better manner and be reputed a disciple. I mean that the goal of his philosophy was more his personal glory than the truth; see- ing that, as I cannot doubt, he knew very well that his manner was more appropriatetocorporealthingsorthingsconsideredcorporeally,whilethat of Pythagoras was no less suitable and adequate for corporeal things than it was for those things which reason, imagination, intellect, and both intelli- gible and sensible nature can forge. As everyone will acknowledge, Plato was not ignorant of the fact that unity and numbers are essential in order to justify and explain points and figures, but that these latter are not essen- tial for justifying and examining unity and numbers, as dimensional and corporeal substance depends on the incorporeal and the indivisible. Furthermore, he knew that unity and number are independent from points and figures, because numbers may be explained without reference to measure, but measure is not independent from numbers, because the understanding
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Fifth dialogue
? of measure cannot be found without an understanding of numbers. That is why arithmetical analogy and proportion are better suited than geometry to guide us, by means of multiplicity, in the contemplation and appre- hension of that indivisible principle which, because it is the unique and radical substance of all things, cannot possess a distinct and limited name, or any term that has a positive rather than privative meaning. Therefore, it has been called by some 'point', by others 'unity', and by still others 'infinity', and so on, with various like terms.
Add to what has been said, that when the intellect wishes to grasp the essence of something, it proceeds by simplifying as much as possible: I mean that it shuns composition and multiplicity, rejecting accidents, which are corruptible, as well as dimensions, signs and figures, and turns to what lies beneath these things. Just as a lengthy, long-winded oration cannot be understood but by reducing it to a simple conceit. By so doing, the intel- lect clearly demonstrates how the substance of things consists of unity, which it looks for either in reality, or by analogy. The man who could reduce to a single proposition all the propositions disseminated in Euclid's principles would be the most consummate and perfect geometrician; like- wise, the most perfect logician would be he who reduced all propositions in logic to one. Herein lies the level of intelligence, because inferior intel- lects cannot understand multiplicity except through many species, analo- gies and forms, superior intellects do better with less, and the very best do perfectly with very little. The premier intelligence embraces everything in a single, absolutely perfect idea, and the divine mind and the absolute unity, with no species, is that which understands and that which is under- stood simultaneously. So that, to ascend to perfect knowledge, we proceed by grouping and restricting the many, just as unity, descending to the pro- duction of things, proceeds by unfolding into many. The descent moves from a single being to an infinity of individuals and innumerable species; the ascent moves from the latter to the former.
Therefore, to conclude this second consideration, I say that when we aspire and strive towards the principle and substance of things, we progress towards indivisibility, and that we must never believe we have arrived at the first being and the universal substance until we have come to this indivisi- ble one in which all is comprised. Meanwhile, let us not be led into believ- ing we can understand of the substance and essence more than what we can understand concerning indivisibility. Peripatetics and Platonists gather the infinity of individuals into a simple concept, which is their species; they
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Cause, principle and unity
? gather countless species under determined genera, which Archytas first declared to be ten in number; they gather the determined genera into one being, a single thing: but this thing, this being, is understood by them as a name, a term, as a logical concept, and finally a vain thing. For then, when they treat of the physical, they no longer recognize a single principle of reality and of being for all that is, as they have recognized a common con- cept and name for all that which is expressible and intelligible. All this is due to their intellectual weakness.
Thirdly, you must know that substance and being are distinct from and independent of quantity, so that number and measure are not substance, but relative to substance; not being, but relative to being. We must define substance, therefore, as essentially without number and without measure and, consequently, as one and undivided in all particular things - which, themselves, owe their particularity to number, that is, to things relative to substance. Thus, whoever apprehends Poliinnio as Poliinnio does not apprehend a particular substance, but apprehends substance in the partic- ular and in the differences which characterize it and which, by these differences, comes to place this man under a species in number and multi- plicity. 7 And here, just as certain accidents of man cause the multiplication of what we call human individuals, so certain accidents of animals multiply the species of animality. Similarly, certain accidents of what is vital cause the multiplication of what is animated and alive. It is no different for certain corporeal accidents which cause the multiplication of corporeality, in the same way certain accidents of the substantial multiply the substance. And finally, in the same way, certain accidents of being cause the multi- plication of entity, truth, unity, being, the true, the one.
Fourthly, if you consider the signs and the proofs thanks to which we wish to demonstrate the coincidence of contraries, it will not be difficult to infer that all things are one in the end. All number, be it odd or even, finite or infinite, is reduced to a unity which, repeated in a finite series, posits number, and by an infinite repetition, negates number. You will adopt signs from mathematics and proofs from other moral and specula- tive sciences. Let us look at signs first: tell me what is more unlike a straight line than the circle? Is there anything more opposite to a straight line than a curve? And yet, they coincide in the principle and the minimum, since
? 7 The one substance of Bruno's world is manifest in Poliinnio, and since he belongs to a number of different species, such as man, philosopher, tall, etc. , the number and multiplicity which are associ- ated with Poliinnio result from his belonging to various species rather than from the unity of sub- stance which is manifested in him.
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Fifth dialogue
? (as the Cusan8, the inventor of geometry's most beautiful secrets, divinely pointed out) what difference could you find between the minimum arc and the minimum chord? Furthermore, in the maximum, what difference could you find between the infinite circle and the straight line? Do you not see that the larger the circle, the more its arc approximates straightness? Who is so blind that he cannot see (fig. 1) how the arc BB, by being larger than the arc AA, and the arc CC, by being larger than the arc BB, and the arc DD, by being larger than the other three, tend to be parts of ever-larger circles, and, therefore, approach ever more closely the straightness of the infinite line of the infinite circle, indicated by IK? We must, therefore, say and believe with absolute certainty that, as that line which is longer is also, because of its greater length, more straight, the longest of all must superlatively be the straightest. The infinite straight line thus finally becomes the infinite circle. Here, then, is how not only the maximum and the minimum converge into one being, as we have already shown elsewhere, but also how, in the maxi- mum and the minimum, contraries come to be but one, and to be indistinct.
fig. ? .
Moreover, compare, if you will, the finite species to a triangle, since all finite things are seen to participate, by a certain analogy, in the finitude and the limitation of the first finite and first limited thing (just as in all genera, the analogous predicates draw their degree and order from the first and loftiest of the genus), so that the triangle is the first shape which cannot be resolved into another species of simpler shape (while the quadrangle, for instance, can be resolved into triangles), making the triangle the primary foundation of every limited and configurated thing. You will find that the
8 Nicolas of Cusa, in his De mathematica perfectione and De berillo. ? ?
? ? Cause, principle and unity
? triangle, as it cannot be resolved into another figure, likewise cannot be composed into triangles whose three angles are greater or smaller, even if the triangles are diverse and varied, of diverse and varied types in terms of greater or lesser size, minimal or maximal. Therefore, if you posit an infi- nite triangle (I do not mean really and absolutely, since the infinite has no figure; I mean infinite hypothetically, insofar as its angle is useful for our demonstration), it will not have an angle greater than that of the smallest finite triangle, and likewise for that of any intermediate triangle and of another, maximum triangle.
But leaving off the comparison between one shape and another, I mean between triangles, and considering angles, we see that they are all equal, whatever their size, as in this square (fig. 2). This square is divided diago- nally into several triangles, and we see that not only are the angles of the
fig. ? .
three squares A, B and C equal, but also that all the acute angles resulting from the division made by the said diagonal, which doubles the series of triangles, are all equal. From this we can very clearly see, by a very marked analogy, how the one infinite substance can be whole in all things, although in some in a finite manner and in others in an infinite manner, in some in lesser measure and in others in greater measure.
Add to this (to see further that, in this one, in this infinity, contraries coincide) that the acute and the obtuse angles are two contraries. But do you not see (fig. 3) that they are formed from a unique, undivided, identi- cal principle, that is, from the inclination made by the line M, which joins perpendicularly the horizontal line BD at point C? Pivoting on point C, and by a simple inclination towards point D, that perpendicular line, that produces, first, two identical right angles and highlights, then, the difference between the acute and the obtuse angle as it approaches point D.
? ? ? ? ? ? ? . Indeed, Aristotle concludes lamely by declaring, in con- cert with all the ancient philosophers, that principles must always be
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Fourth dialogue
? permanent; later on, if we seek further in his doctrine for the place where the perpetual seat of natural form which floats on the back of matter might be, we will not find it either in the fixed stars - since the particular forms which we see do not descend from on high - nor in the ideal signs, sepa- rate from matter - for if these are not monsters, they are assuredly worse than monsters, being chimeras and pointless fantasies. What then? Forms are in the bosom of matter. And what then? Matter is the source of actual- ity. Do you want me to carry on and make you see all the absurdities into which Aristotle gets himself ? He says that matter exists in potency, but ask him: When will it be in act? Together with a great crowd he will respond: When it possesses form. But insist and ask: When that occurs, what com- mences to exist? They will answer, despite themselves: The composite, not matter, since the latter is always identical to itself, never renews itself, never changes. The same goes for artificial things: when one makes a statue of wood, we do not say that the wood begins to exist, for it is no more nor less wood than before. In fact, that which receives being and actuality is the new product, the composite, I mean the statue. How can you grant potency, then, to something that will never be in act nor possess act? For it follows from this that matter is not that which is in potency of being or that can be, for it is always identical and immutable, and is that upon which and in which change takes place, rather than that which changes. What is altered, augmented, diminished, moved in location, corrupted, is always (as you Peripatetics, yourselves, say) the composite, never matter. Then, why do you say that matter is now in potency, now in act? No one surely could doubt that matter, whether it receives forms or sends them forth from itself, does not receive a greater or lesser actuality in terms of its essence or its substance; so that there is no reason to say that it exists in potency. For potency concerns what is in continual movement in relation to matter, and not matter itself, which is not only eternally at rest, but the very cause of that state of eternal rest. For if form, in keeping with its fundamental, specific being possesses, not only logically - in the concept and in reason - but also physically in nature, a simple, invariable essence, then form must exist in the perpetual potency of matter, which is a potency not distinct from act, as I have several times explained in my various discussions concerning potency.
? ? ? ? ? ? ? ? ? . Queso[Ibegyou],spareawordfortheappetiteofmatter, so that Gervasio and I can resolve a little dispute between us.
? ? ? ? ? ? ? ? . Yes, please, Teofilo, for this person has given me a pain in ? ?
Cause, principle and unity
? the head with his comparison between matter and woman. He says that women are no more content with males than matter is with forms, and so forth.
? ? ? ? ? ? ? . Seeingthatmatterdoesnotreceiveanythingfromform,why do you think it desires it? If (as we have said) it brings forms out of its bosom and so possesses them in itself, how can you claim that it desires them? It does not desire those forms which daily change on its back, for every ordered thing desires that from which it receives perfection. And what can a corruptible thing bring to an eternal one? What can an imper- fect thing, as is the form of sensible things, which is always in movement, give to another so perfect that, if well pondered, is understood to be a divine being in things, as perhaps David of Dinant meant, who was so poorly understood by those who reported his opinion? 20 Matter does not desire form in order to be preserved by it, because a corruptible thing does not preserve an eternal one. Moreover, since matter clearly preserves form, form must desire matter in order to perpetuate itself, and not the other way around. For when form is separated from matter it ceases to exist, as is not the case with matter, which has all it had before the coming of form and which can have other forms as well. Not to mention that when we speak of the cause of corruption, we do not say that the form flees from matter or that it leaves matter, but that matter throws off one form to assume another. There is as little reason to say that matter desires form as that it hates it (I mean those forms that are generated and corrupted, because it cannot desire the source of forms, which it has within itself, because nothing desires what it possesses). By the same line of reasoning, according to which it is said to desire what it sometimes receives or produces, it can also be said to abhor whatever it throws off or rejects. In fact, it detests more fervidly than it desires, for it eternally throws off that individual form after retaining it a very short while. If you will remember this, that matter rejects as many forms as it assumes, you must agree with me when I say that it loathes form, just as I can allow your statements concerning desire.
? ? ? ? ? ? ? ? . Herelie,then,inruinsnotonlyPoliinnio'scastles,butalso others'.
? ? ? ? ? ? ? ? ? . Parciusistaviris[Donotboasttoomuch]. ? ? ? ? ? ? ? . Wehavelearnedenoughfortoday. Untiltomorrow.
? 20 David of Dinant, author of De tomis idest de divisionibus. 'Thou who reported his opinion' probably refers to Aquinas, Summa contra Gentiles (? , ? ? ? ? ), where David of Dinant is said to have identified God with matter.
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Fifth dialogue
? ? ? ? ? ? ? ? . Then,goodbye.
End of the fourth dialogue
Fifth Dialogue
? ? ? ? ? ? ? . Theuniverseis,therefore,one,infiniteandimmobile. Isaythat the absolute possibility is one, that the act is one; the form, or soul, is one, the matter, or body, is one, the thing is one, being is one. The maximum, and the optimum, is one: it cannot be comprehended and is therefore inde- terminable and not limitable, and hence infinite and limitless, and conse- quently immobile. It has no local movement since there is nothing outside of it to which it can be moved, given that it is the whole. It does not engen- der itself because there is no other being that it could anticipate or desire, since it possesses all being. It is not corrupted because there is no other thing into which it could change itself, given that it is everything. It cannot diminish or grow because it is an infinity to or from which nothing can be added or subtracted, since the infinite has no measurable parts. It is not alterable in terms of disposition, since it possesses no outside to which it might be subject and by which it might be affected. Moreover, since it com- prehends all contraries in its being in unity and harmony, and since it can have no propensity for another and new being, or even for one manner of being and then for another, it cannot be subject to change according to any quality whatsoever, nor can it admit any contrary or different thing that can alter it, because in it everything is concordant. It is not matter, because it is not configured or configurable, nor it is limited or limitable. It is not form, because it neither informs nor figures anything else, given that it is all, that it is maximum, that it is one, that it is universal. It is neither measurable nor a measure. It does not contain itself, since it is not greater than itself. It is not contained, since it is not less than itself. It is not equal to itself, because it is not one thing and another, but one and the same thing. Being one and the same, it does not have distinct beings; because it does not have distinct beings, it has no distinct parts; because it has no distinct parts, it is not composite. It is limit such that it is not limit, form such that it is not form, matter such that it is not matter, soul such that it is not soul: for it is all indifferently, and hence is one; the universe is one.
Indeed, in this one, the height is no greater than the length or depth, so that it is called a sphere by analogy, although it is not a sphere. Length,
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Cause, principle and unity
? breadth and depth in the sphere are identical, because they have the same limit, but in the universe, length, breadth and depth are identical because they are all equally without limit and infinite. If they have no half, quarter or other fraction, if there are no fractions at all, then there is no measurable part, nor, strictly, any part that differs from the whole. For, if you wish to speak of part of the infinite, you are obliged to call that infinite as well; if it is infinite, it coincides in one and the same being with the whole: therefore, the universe is one, infinite, indivisible. And if in the infinite you cannot find any difference as of part from whole, nor any difference as of one part from another, the infinite is undoubtedly one. There is no smaller part and greater part within the infinite's comprehension, for any part, however large, comes no nearer the proportion of the infinite than does any other, however small. In infinite duration, an hour is no different from a day, a day from a year, a year from a century, a century from an instant, because nei- ther moments nor hours exist any more than do centuries, and because none is more commensurable with eternity than another. Similarly, in the immensity, the palm is not different from the stadium1 , nor the stadium from the parasang2 , because the parasang is no nearer the immensity's pro- portions than is the stadium. Hence, there are no more infinite hours than there are infinite centuries, nor infinite palms in greater number than infinite parasangs. You come no nearer to commensurability, likeness, union and identity with the infinite by being a man than by being an ant, or by being a star than by being a man, for you get no nearer to that infinite being by being the sun or the moon than by being a man, or an ant. This is because, in the infinite, there is no difference between those things - and what I say of them applies just as well to all other existent particular things.
Now, if, in the infinite, all these particular things are not differentiated, are not divided into species, it necessarily follows that they have no num- ber: the universe, therefore, is one and immobile. Because it comprises everything, does not take on one being after another, and suffers no change neither by nor in itself, it is, consequently, all that it can be, and in it (as I said the other day), act does not differ from potency. If potency does not differ from act, it is necessary that, in the infinite, the point, the line, the surface and the body do not differ. For there, the line is surface because, by moving, it may become surface, and there the surface moves and becomes body, insofar as it may move and become, by its flow, a body. In the infinite, therefore, the point necessarily does not differ from the body, for, from its
1 Seenote? onp. ? ? above. 2 Seenote? onp. ? ? above. ? ?
? Fifth dialogue
? status as point, it becomes a line; from its status as line, it becomes a sur- face; from its status as surface, it becomes a body. So the point, because it possesses the potency to become a body, does not differ from the status of a body, where the potency and the act are one and the same thing.
The undivided does not differ, therefore, from the divided, nor does the absolutely simple differ from the infinite, nor does the centre differ from the circumference. Since the infinite is all that it can be, it is immobile; since in it everything is indifferent, it is one; and since it possesses all the greatness and perfection that can possibly be possessed, beyond all limit, it is the maximum and supreme immensity. If the point does not differ from the body, nor the centre from the circumference, nor the finite from the infinite, nor the maximum from the minimum, we may certainly affirm that the universe is entirely centre, or that the centre of the universe is every- where, and the circumference nowhere insofar as it is different from the centre; or else that the circumference is everywhere, but the centre is nowhere insofar as it differs from the circumference. Here, then, is how it is not impossible, but rather necessary, that the optimum, the maximum, the incomprehensible is everything, is everywhere, is in everything, for, being simple and indivisible, it can be everything, be everywhere and be in everything. Thus, not for nothing is it said that Jove fills all things, inhabits all parts of the universe, is the centre of everything which has being: one in all, and that through which all is one, and is that which, being all things and comprehending all being in itself, causes everything to be in everything.
But you will say to me, 'Then why do things change? Why does partic- ular matter turn itself into other forms? ' My answer is that mutation is not striving for another being, but for another mode of being. And this is the difference between the universe and the things of the universe: for the universe contains all being and all modes of being, while each thing of the universe possesses all being but not all modes of being. Each thing cannot possess, in act, all particularities and accidents, because many forms are incompatible within the same subject, either because they are contrary or because they belong to different species - for example, there cannot be the same individual substance under the accidents of a horse and a human being, or under the dimensions of a plant or an animal. What is more, the universe comprehends all being totally, for nothing can exist outside of or beyond infinite being, because there is no outside or beyond infinity. By contrast, each of the things of the universe comprehends all being, but not
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Cause, principle and unity
? totally, because outside each one of them there exists an infinity of other things. You must conceive, therefore, that everything is in everything, but not totally or under all modes in each thing. Understand, therefore, that each single thing is one, but not in the same way.
We are, therefore, correct in affirming that being - the substance, the essence - is one, and since that one is infinite and limitless, both with respect to duration and substance, as it is in terms of greatness and vigour, it does not have the nature of either a principle or of what is principled;3 for each thing, coinciding in unity and identity (that is to say, in the same being), comes to have an absolute value and not a relative one. In the infi- nite and immobile one, which is substance and being, if there is multiplic- ity, the number which is a mode and multiformity of being by which it comes to denominate things as things, does not, thereby, cause being to be more than one, but to be multi-modal, multiform and multi-figured. So, following closely the reasoning of natural philosophers and leaving the logicians to their fantasies, we discover that everything that causes difference and number is pure accident, pure figure, pure complexion. Every production, of whatever kind, is an alteration, while the substance always remains the same, since there is only one substance, as there is but one divine, immortal being. Pythagoras, who did not fear death but saw it as a transformation, reached this conclusion. Those philosophers who commonly go by the name of physical philosophers4 also were able to understand this. They said that nothing, in terms of substance, is begotten or is corrupted - unless we understand by this the process of change. Solomon inferred this as well, saying, 'there is nothing new under the sun, but what is, has already been'. 5 You see, then, how the universe is in all things and all things are in the universe, we in it and it in us: thus, every- thing coincides in perfect unity. See, then, how our spirit should not be afflicted, how there is nothing that should frighten us: for that unity is sta- ble in its oneness and so remains forever. It is eternal, while every aspect, every face, every other thing is vanity and nothingness - indeed, outside this one there is nothing. Those philosophers who have discovered this unity have found their beloved Wisdom. For wisdom, truth and unity are indeed the same thing, though not everyone has understood this, since some have adopted the manner of speaking, but not the manner of under- standing of the truly wise. Aristotle, among others, did not discover the
? 3 I. e. there is no distinction between an active and passive component within infinite substance. 4 Ionic philosophers. 5 Ecclesiastes, ? , ? ? .
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Fifth dialogue
? one, nor being, nor the true, because he did not recognize being as one. Although he could have adopted the meaning of being which is common to substance and accident, and further, distinguished his categories accord- ing to as many genera and species as there are specific differences, nonethe- less he perceived truth badly, not going deeply enough into the knowledge of this unity and of this indistinction of the eternal nature and eternal being. With his harmful explanations and his irresponsible arguments, this arid sophist perverted the sense of the ancients and hampered the truth, less, perhaps, out of intellectual weakness, than out of jealousy and ambition.
? ? ? ? ? ? ? . So that this world, this being, this truth, this universe, this infinity, this immensity is found entire in each of its parts: it is the ubique [everywhere] itself. Thus, everything in the universe, in relation to the uni- verse, exists everywhere according to its capacity, whatever its relation might be with other particular bodies; for it is above, below, right, left and so on, in keeping with all local differences, since, in the totality of the infi- nite, there are all these differences and none of them. Whatever thing we take in the universe, it has in itself that which is entire everywhere, and hence comprehends, in its own way, the entire world soul (although, as we have said, it does not comprehend it totally), and that world soul is entire in every part of the universe. This is why, even if the act is one and consti- tutes a single being, wherever it may be found, we must not think that there is, in the world, a plurality of substance and of that which is truly being.
Following on this, I know that you take as manifest that each of these innumerable worlds, which we see in the universe, is not found there so much as if in a containing site, nor as in an interval or a space, but is found there as in a place that comprehends it, a conserver, mover and efficient, which itself is comprised in its entirety in each of these worlds, as the soul is found in its entirety in each of the parts of that world. For that reason, although a particular world moves towards or around another, as the earth moves to and around the sun, nonetheless, with respect to the universe, nothing moves to or around it, but only within it.
You, further, hold that, just as the soul (to take up the common way of speaking once more) pervades that great mass to which it gives being, remaining altogether indivisible, so that it is altogether present in the whole and any of its parts, so the essence of the universe is one both in the infinite and in anything taken as a member of the universe; so that, substantially, the whole and each of its parts are but one. In your opinion, Parmenides was, therefore, right to say that the universe is one, infinite and immobile
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Cause, principle and unity
? (although it is not entirely clear what he intended, his words having been reported by a commentator who is not particularly reliable). 6
You say that all the differences seen in bodies, from the point of view of formation, constitution, figures, colours and other individual or common characteristics, are nothing but the diverse aspects of the same substance: fleeting, mobile and corruptible aspects of an immobile, persistent and eternal being in which all forms, figures and members exist, though indis- tinctly and (so to speak) conglomerated - exactly as in the seed, where the arm is not distinct from the hand, nor the bust from the head, or the nerve from the bone, and where differentiation and separation do not produce another or a new substance, but bring into act and accomplish certain qual- ities, differences, accidents and dispositions related to that substance. And what is said of the relation between the seed and the members of animals may also be said of food in relation to chyle, to blood, to phlegm, to flesh and seed. This goes for any other thing which precedes the alimentary state, or other state. It also goes for all things, from the lowest level of nature to the highest, climbing from the physical totality philosophers know to the archetype in which theologians believe, if you like, until we reach a single original and universal substance, the same for all, which we call being, the basis of all species and all different forms. Similarly in the art of carpentry there is a single substance of wood which is subject to all dimensions and shapes, which are not themselves wood but are of wood, in the wood or involving the wood. That is why everything that makes for the diversity of genera, species, differences, properties, all that which consists in genera- tion, corruption, alteration and change, is not being, is not essence, but condition and circumstance of being or essence, which is one, infinite, substratum, matter, life, soul, truth and goodness.
You say, then, that, since being is indivisible and absolutely simple, because it is infinite, and is act in its fullness in the whole and in every part of it (in the same way we speak of parts in the infinite, but not of parts of the infinite), we cannot think in any way that the earth is a part of being, nor that the sun is part of substance, since the latter is indivisible. But it is quite reasonable to speak of the substance of the part, or better still, of the substance in the part; just as it is not reasonable to say that a part of the soul is found in the arm or another part in the head, but it is legitimate to say that the soul is in the part that is the head, and that the substance is sub- stance of the part - or in the part - that is the arm. For to be portion, part, 6 Aristotle. See the end of the third dialogue, where Aristotle's opinion of Parmenides is mentioned.
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Fifth dialogue
? member, the whole, equal to, larger or smaller, like this or like that, relative to this or to that, identical to or different from, etc. , respond to other con- cepts which do not express an absolute, and hence cannot designate the substance, the one or being, but, in terms of modes, determinations and forms, exist through the substance, in the one, and relative to being. Thus, just as it is commonly said that quantity, quality, relation, action, passion and other kinds of accidents are relative to one and the same substance, in the same way one could say that the one and supreme being, in which act does not differ from potency, can be all absolutely and is everything that it can be. It is in a complicative manner one, immense, infinite and compre- hensive of all being, and in an explicative manner, it is present in sensible bodies and in the potency and the act that we see distinguished in them. That is why you hold that what is generated and generates (be it a question of an equivocal agent or of a univocal agent, as is commonly said in phil- osophy), as well as that of which the generation is made, are always of the same substance. Your ears will, therefore, not be jarred by the thesis of Heraclitus, which declares all things to be but one - the one which, thanks to its mutability, contains all things in itself. And since all forms are in it, it follows that all definitions accord with it, so that all contrary propositions are true. And what creates multiplicity in things is not being, is not the thing, but what appears, what is offered to the senses and lies on the sur- face of things.
? ? ? ? ? ? ? . Exactly. But I would like you to read further in this most important science and of this solid foundation of the truths and the secrets of nature. First, therefore, I would like you to note that nature descends to the production of things, and intellect ascends to the knowledge of them, by one and the same ladder. Both ways proceed from unity to unity, pass- ing through a multitude of middle terms. Not to mention that the philo- sophical method of the Peripatetics and of many Platonists is to have the multitude of things as middle term, preceded by the pure act, at one extremity, and the pure potency, at the other; similar to other philosophers who affirm metaphorically that the darkness and the light come together in the constitution of innumerable degrees of forms, images, figures and colours. But beside all these philosophers, who take into consideration two principles and two princes, others rise up who, impatient with and hos- tile towards polyarchy, make the two principles coincide into one, which is at the same time abyss and darkness, clarity and light, profound and impenetrable obscurity, and supernal and inaccessible light.
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Cause, principle and unity
? Secondly, consider that the intellect, wishing to liberate and detach itself from the images to which it is bound, not only resorts to mathematical and symbolic figures or analogies drawn from them in order to comprehend the being and the substance of things, but also ascribes the multiplicity and diversity of species to one and the same root. Thus, Pythagoras, who posited numbers as the exclusive principles of things, understood unity to be the basis and substance of all of them. Thus, Plato and other philoso- phers who made species to consist of figures conceived of the point as sub- stance and universal genus, inasmuch as it is the common stock and root of all figures. And perhaps surfaces and figures are what Plato meant ulti- mately by his 'great', and the point and the atom are what he meant by his 'small', two principles of specification of things which refer, then, to one, as everything that is divided refers to the undivided. Therefore, those who say that the one is the substantial principle mean that substances are like numbers, and others who think of the substantial principle as a point mean that the substances of things are like figures, but all agree in positing an indivisible principle. However, Pythagoras' method is better and purer than Plato's, because unity is the cause and the reason for individuality and the point, and it is a principle which is more absolute and appropriate to universal being.
? ? ? ? ? ? ? ? . Why has Plato, who came after him, not done as well or better than Pythagoras?
? ? ? ? ? ? ? . Becausehepreferredtospeaklesswell,inamannerlessade- quate and less appropriate, and to be acclaimed as a master, than to say something better, in a better manner and be reputed a disciple. I mean that the goal of his philosophy was more his personal glory than the truth; see- ing that, as I cannot doubt, he knew very well that his manner was more appropriatetocorporealthingsorthingsconsideredcorporeally,whilethat of Pythagoras was no less suitable and adequate for corporeal things than it was for those things which reason, imagination, intellect, and both intelli- gible and sensible nature can forge. As everyone will acknowledge, Plato was not ignorant of the fact that unity and numbers are essential in order to justify and explain points and figures, but that these latter are not essen- tial for justifying and examining unity and numbers, as dimensional and corporeal substance depends on the incorporeal and the indivisible. Furthermore, he knew that unity and number are independent from points and figures, because numbers may be explained without reference to measure, but measure is not independent from numbers, because the understanding
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Fifth dialogue
? of measure cannot be found without an understanding of numbers. That is why arithmetical analogy and proportion are better suited than geometry to guide us, by means of multiplicity, in the contemplation and appre- hension of that indivisible principle which, because it is the unique and radical substance of all things, cannot possess a distinct and limited name, or any term that has a positive rather than privative meaning. Therefore, it has been called by some 'point', by others 'unity', and by still others 'infinity', and so on, with various like terms.
Add to what has been said, that when the intellect wishes to grasp the essence of something, it proceeds by simplifying as much as possible: I mean that it shuns composition and multiplicity, rejecting accidents, which are corruptible, as well as dimensions, signs and figures, and turns to what lies beneath these things. Just as a lengthy, long-winded oration cannot be understood but by reducing it to a simple conceit. By so doing, the intel- lect clearly demonstrates how the substance of things consists of unity, which it looks for either in reality, or by analogy. The man who could reduce to a single proposition all the propositions disseminated in Euclid's principles would be the most consummate and perfect geometrician; like- wise, the most perfect logician would be he who reduced all propositions in logic to one. Herein lies the level of intelligence, because inferior intel- lects cannot understand multiplicity except through many species, analo- gies and forms, superior intellects do better with less, and the very best do perfectly with very little. The premier intelligence embraces everything in a single, absolutely perfect idea, and the divine mind and the absolute unity, with no species, is that which understands and that which is under- stood simultaneously. So that, to ascend to perfect knowledge, we proceed by grouping and restricting the many, just as unity, descending to the pro- duction of things, proceeds by unfolding into many. The descent moves from a single being to an infinity of individuals and innumerable species; the ascent moves from the latter to the former.
Therefore, to conclude this second consideration, I say that when we aspire and strive towards the principle and substance of things, we progress towards indivisibility, and that we must never believe we have arrived at the first being and the universal substance until we have come to this indivisi- ble one in which all is comprised. Meanwhile, let us not be led into believ- ing we can understand of the substance and essence more than what we can understand concerning indivisibility. Peripatetics and Platonists gather the infinity of individuals into a simple concept, which is their species; they
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Cause, principle and unity
? gather countless species under determined genera, which Archytas first declared to be ten in number; they gather the determined genera into one being, a single thing: but this thing, this being, is understood by them as a name, a term, as a logical concept, and finally a vain thing. For then, when they treat of the physical, they no longer recognize a single principle of reality and of being for all that is, as they have recognized a common con- cept and name for all that which is expressible and intelligible. All this is due to their intellectual weakness.
Thirdly, you must know that substance and being are distinct from and independent of quantity, so that number and measure are not substance, but relative to substance; not being, but relative to being. We must define substance, therefore, as essentially without number and without measure and, consequently, as one and undivided in all particular things - which, themselves, owe their particularity to number, that is, to things relative to substance. Thus, whoever apprehends Poliinnio as Poliinnio does not apprehend a particular substance, but apprehends substance in the partic- ular and in the differences which characterize it and which, by these differences, comes to place this man under a species in number and multi- plicity. 7 And here, just as certain accidents of man cause the multiplication of what we call human individuals, so certain accidents of animals multiply the species of animality. Similarly, certain accidents of what is vital cause the multiplication of what is animated and alive. It is no different for certain corporeal accidents which cause the multiplication of corporeality, in the same way certain accidents of the substantial multiply the substance. And finally, in the same way, certain accidents of being cause the multi- plication of entity, truth, unity, being, the true, the one.
Fourthly, if you consider the signs and the proofs thanks to which we wish to demonstrate the coincidence of contraries, it will not be difficult to infer that all things are one in the end. All number, be it odd or even, finite or infinite, is reduced to a unity which, repeated in a finite series, posits number, and by an infinite repetition, negates number. You will adopt signs from mathematics and proofs from other moral and specula- tive sciences. Let us look at signs first: tell me what is more unlike a straight line than the circle? Is there anything more opposite to a straight line than a curve? And yet, they coincide in the principle and the minimum, since
? 7 The one substance of Bruno's world is manifest in Poliinnio, and since he belongs to a number of different species, such as man, philosopher, tall, etc. , the number and multiplicity which are associ- ated with Poliinnio result from his belonging to various species rather than from the unity of sub- stance which is manifested in him.
? ?
Fifth dialogue
? (as the Cusan8, the inventor of geometry's most beautiful secrets, divinely pointed out) what difference could you find between the minimum arc and the minimum chord? Furthermore, in the maximum, what difference could you find between the infinite circle and the straight line? Do you not see that the larger the circle, the more its arc approximates straightness? Who is so blind that he cannot see (fig. 1) how the arc BB, by being larger than the arc AA, and the arc CC, by being larger than the arc BB, and the arc DD, by being larger than the other three, tend to be parts of ever-larger circles, and, therefore, approach ever more closely the straightness of the infinite line of the infinite circle, indicated by IK? We must, therefore, say and believe with absolute certainty that, as that line which is longer is also, because of its greater length, more straight, the longest of all must superlatively be the straightest. The infinite straight line thus finally becomes the infinite circle. Here, then, is how not only the maximum and the minimum converge into one being, as we have already shown elsewhere, but also how, in the maxi- mum and the minimum, contraries come to be but one, and to be indistinct.
fig. ? .
Moreover, compare, if you will, the finite species to a triangle, since all finite things are seen to participate, by a certain analogy, in the finitude and the limitation of the first finite and first limited thing (just as in all genera, the analogous predicates draw their degree and order from the first and loftiest of the genus), so that the triangle is the first shape which cannot be resolved into another species of simpler shape (while the quadrangle, for instance, can be resolved into triangles), making the triangle the primary foundation of every limited and configurated thing. You will find that the
8 Nicolas of Cusa, in his De mathematica perfectione and De berillo. ? ?
? ? Cause, principle and unity
? triangle, as it cannot be resolved into another figure, likewise cannot be composed into triangles whose three angles are greater or smaller, even if the triangles are diverse and varied, of diverse and varied types in terms of greater or lesser size, minimal or maximal. Therefore, if you posit an infi- nite triangle (I do not mean really and absolutely, since the infinite has no figure; I mean infinite hypothetically, insofar as its angle is useful for our demonstration), it will not have an angle greater than that of the smallest finite triangle, and likewise for that of any intermediate triangle and of another, maximum triangle.
But leaving off the comparison between one shape and another, I mean between triangles, and considering angles, we see that they are all equal, whatever their size, as in this square (fig. 2). This square is divided diago- nally into several triangles, and we see that not only are the angles of the
fig. ? .
three squares A, B and C equal, but also that all the acute angles resulting from the division made by the said diagonal, which doubles the series of triangles, are all equal. From this we can very clearly see, by a very marked analogy, how the one infinite substance can be whole in all things, although in some in a finite manner and in others in an infinite manner, in some in lesser measure and in others in greater measure.
Add to this (to see further that, in this one, in this infinity, contraries coincide) that the acute and the obtuse angles are two contraries. But do you not see (fig. 3) that they are formed from a unique, undivided, identi- cal principle, that is, from the inclination made by the line M, which joins perpendicularly the horizontal line BD at point C? Pivoting on point C, and by a simple inclination towards point D, that perpendicular line, that produces, first, two identical right angles and highlights, then, the difference between the acute and the obtuse angle as it approaches point D.
