Aristotle · a new plain-English translation from the original language
1| With a view to the science we are seeking, we must first go over the questions that need to be worked through first. These are all the points on which some thinkers have held differing views, together with anything besides these that happens to have been overlooked. For those who wish to find a good way through, it is useful first to work well through the difficulties; for the later resourcefulness is a resolution of the difficulties raised earlier, and one cannot loosen a knot without knowing it. Rather, the perplexity of our thinking about a subject reveals this very knot; for so far as it is perplexed, thought is in a condition like that of people who are bound, since in both cases it is impossible to go forward. Hence one must have surveyed all the difficulties beforehand, both for these reasons and because those who inquire without first working through the difficulties are like people who do not know where they need to walk, and who moreover cannot even tell, if they should ever find what they are seeking, whether they have found it or not; [995b] for the goal is not clear to such a person, while it is clear to one who has already worked through the difficulties beforehand. Further, one who has heard all the arguments, as if listening to opposing litigants and disputants, is necessarily in a better position to judge. Now the first difficulty concerns the matters we raised in our introductory remarks: whether it belongs to one science or to many to study the causes; and whether it is the task of this science to look only at the primary principles of substance, or also at the principles from which everyone demonstrates things — for example, whether it is possible to affirm and deny the same single thing at the same time, or not, and concerning other such matters.
2| And if it does concern substance, whether there is one science over all substances or several; and if several, whether they are all akin to one another, or whether some of them should be called wisdom and the others something else. And this itself is among the things one must necessarily investigate: whether we should say that only perceptible substances exist, or that there are others besides these as well, and whether there is only one kind of substance or several kinds, as is held by those who posit the forms and also the objects of mathematics as intermediate between these and perceptible things. About these matters, then, as we say, one must inquire, and also whether the inquiry concerns substances alone or also the attributes that belong to substances in their own right; and besides these, concerning sameness and difference, likeness and unlikeness, and contrariety, and concerning prior and posterior and all the other such things about which the dialecticians try to inquire, making their examination out of reputable opinions alone — whose business it is to study all of these. Further, one must consider whatever belongs to these very things in their own right, and not only what each of them is, but also whether one thing is contrary to just one thing; and whether the principles and elements are the genera, or the constituents into which each thing is divided.
3| And if they are the genera, whether they are the ones predicated last of the individuals, or the first ones — for example, whether animal or man is more of a principle, and exists to a greater degree apart from the particular. But above all one must inquire into and work through whether there is, apart from matter, some cause in its own right or not, and whether this is separable or not, and whether it is one in number or more than one, and whether there is something apart from the composite (by "composite" I mean whenever something is predicated of the matter) or nothing at all, or this holds for some things and not for others, and which sorts of beings are of this kind.
4| [996a] Further, whether the principles are determinate in number or in kind — both those in our definitions and those in the underlying subject; and whether the principles of perishable and imperishable things are the same or different, and whether all of them are imperishable, or those of perishable things are themselves perishable. Further, the hardest question of all, and the one containing the greatest difficulty: whether the one and being are not something else but are the substance of the things that are, as the Pythagoreans and Plato said; or whether this is not so, and the underlying subject is something else, as Empedocles says it is Love, another says it is fire, and another water or air. And whether the principles are universal, or particular like the individual things themselves, and whether they exist potentially or actually; further, whether they are principles in some other way, or in respect of motion; for these questions too would furnish much difficulty. Besides these, whether numbers and lengths and figures and points are substances of some sort or not, and if they are substances, whether they are separate from perceptible things or exist within them. For concerning all these matters, it is difficult not only to arrive successfully at the truth, but even to work through the difficulties well in argument is not easy. First, then, concerning the matter we mentioned first: whether it belongs to one science or to several to study all the kinds of causes.
5| For how could it belong to a single science to know the principles, given that they are not contraries? Further, not all of the principles belong to many of the things that are; for in what way is it possible for unmoved things to have a principle of motion, or to have the nature of the good, if indeed everything that is good in its own right and by its own nature is an end, and is in this way a cause because it is for its sake that the other things both come to be and exist — and the end, and that for the sake of which, is the end of some action, and all actions involve motion? So among unmoved things this principle could not exist, nor could there be any good-in-itself. That is why nothing in mathematics is demonstrated by way of this cause, and there is no demonstration there on the grounds that something is better or worse; indeed no one ever makes any mention whatsoever of anything of this sort. That is why, for these reasons, some of the sophists, such as Aristippus, used to disparage the mathematical sciences; for in the other crafts, even the menial ones, such as carpentry and shoemaking, everything is said on the grounds of better or worse, whereas the mathematical sciences take no account at all of goods and evils.
6| [996b] —But then, if there are several sciences of causes, and a different science for a different principle, which of them must we say is the one being sought, or which of those who have them has knowledge in the highest degree of the object sought? For it is possible for all the modes of causes to belong to the same thing — for example, in the case of a house, the source of motion is the craft and the builder, that for the sake of which is the work, the matter is earth and stones, and the form is the account. Now from what has long been determined, it makes sense, on various grounds, to call each of the sciences wisdom: on the one hand, the science which is most sovereign and most authoritative — the one which the other sciences, like slaves, have no right even to contradict — is the science of the end and the good, of this kind (for it is for the sake of this that the other things exist); on the other hand, the science which was determined to be the science of the first causes and of what is most knowable would be the science of substance, of this kind. For since the same thing is known in many ways, we say a person knows more who knows what a thing is by its being than one who knows it by its not being, and among these knowers themselves one more than another — and most of all the one who knows what it is, not the one who knows its quantity or quality or what it is naturally suited to do or undergo. Further, even in the other cases, we think we possess knowledge of each thing, including the things of which there are demonstrations, when we know what it is (for example, what squaring is, namely the finding of a mean proportional;
7| and likewise in the other cases as well), whereas concerning comings-to-be and actions and every kind of change, we think we possess knowledge when we know the principle of the motion; and this is different from and opposed to the end. So it would seem to belong to a different science to study each of these causes. But further, concerning the demonstrative principles too — whether they belong to one science or to several — this is disputable (I call demonstrative principles the common opinions from which everyone demonstrates), for example that everything must either be affirmed or denied, and that it is impossible for the same thing to be and not be at the same time, and all the other premises of this kind: is there one science of these and of substance, or a different one — and if not one, which of the two must we call the science now being sought? Well, it is not reasonable for there to be one science of them: for what makes grasping these any more proper to geometry than to any other science whatever? If then it belongs equally to any science whatever, but cannot belong to all of them,
8| [997a] then just as it is not proper to any of the other sciences, so too it is not proper to the science that knows substances to know about them. And at the same time, in what way will there be a science of them at all? For what each of these happens to be, we know even now (indeed, other crafts too make use of them as things known); but if there is demonstration concerning them, there will have to be some underlying genus, with some of them as affections and others as axioms of it (for it is impossible for there to be demonstration about everything whatever — demonstration must necessarily proceed from certain things, be about some subject, and be of certain things), so that it follows that there is a single genus for all the things that get demonstrated, since every demonstrative science makes use of the axioms. But then, if the science of substance and the science concerning these axioms are different, which of the two is by nature more authoritative and prior? For the axioms are the most universal things of all and the principles of everything; and if this does not belong to the philosopher, to whom else will it belong to study the true and the false about them? And in general, is there one science of substances, or are there several? If there is not one, then to what kind of substance must we assign this science? But it is not reasonable for there to be one science of all of them: for then there would be a single demonstrative science of all accidental attributes, given that every demonstrative science studies, concerning some one underlying subject, the attributes that belong to it in its own right, on the basis of the common opinions.
9| So concerning the same genus, it belongs to one and the same science to study the attributes that belong to it in its own right, on the basis of the same opinions. For the subject about which a science speaks belongs to one science, and the things from which it demonstrates belong to one science too, whether it is the same science or a different one — so the accidental attributes belong to one science as well, whether the very sciences that study the subjects also study these attributes, or a single science does so on the basis of them. Further, is the study concerned only with substances, or also with the attributes that belong to them? I mean, for example: if the solid is a kind of substance, and so are lines and planes, is it the business of the same science to know these and the attributes concerning each genus that the mathematical sciences demonstrate, or of a different one? For if of the same science, then the science of substance too would be a demonstrative science, but it does not seem that there is demonstration of what a thing is; and if of a different science, what will the science be that studies the attributes concerning substance? For this is extremely hard to answer. Further, must we say that only the perceptible substances exist, or that there are others besides these, and whether the kinds of substances that there happen to be are only one, or several,
10| [997b] as for instance those who speak of both the forms and the intermediates, which they say the mathematical sciences are about? Now, the sense in which we speak of the forms as being both causes and substances in their own right has been stated in our first discussions about them; but since they present difficulty in many ways, one of the most absurd things is to say that there are certain natures besides those in the heavens, and yet to say these are the same as the perceptible things except that the former are eternal and the latter perishable. For they say there is a man-itself, a horse-itself, and a health-itself, and nothing else, doing something very like those who say the gods exist but are shaped like men: for the latter were doing nothing other than making eternal men, and the former are doing nothing other than making the forms eternal perceptible things. Further, if someone posits intermediates besides the forms and the perceptible things, he will face many difficulties: for it is clear that there will likewise be lines besides both the lines themselves and the perceptible lines, and so with each of the other genera. So that, since astronomy is one of these sciences, there will be some heaven besides the perceptible heaven, and a sun and a moon and the rest of the things in the heavens in the same way. And yet how are we to believe this?
11| For it is not reasonable for it to be unmoved either, and for it to be moving is altogether impossible. And the same holds for the things that optics deals with, and harmonics among the mathematical sciences: for these too, for the same reasons, cannot exist besides the perceptible things; for if there are intermediate perceptible things and perceptions, clearly there will also be animals intermediate between these and the perishable ones. One might also raise the difficulty of which class of existing things these sciences must be said to investigate. For if geometry differs from land-surveying only in this, that the one is concerned with things we perceive and the other with things not perceived, then clearly there will also be a science besides medicine, and besides each of the other sciences, intermediate between medicine itself and this particular medicine — and yet how is this possible? For then there would be certain healthy things besides the perceptible ones, and the healthy-itself as well. And at the same time it is not even true that land-surveying is concerned with perceptible and perishable magnitudes; for then it would perish as they perish. Nor, again, could astronomy be concerned with perceptible magnitudes, nor with this perceptible heaven.
12| [998a] For neither are the perceptible lines of the sort the geometer speaks of (for nothing among perceptible things is straight or round in that way — the circle touches the straightedge not at a point but as Protagoras used to say in refuting the geometers), nor are the motions and spirals of the heavens like those about which astronomy constructs its accounts, nor do the points have the same nature as the stars. But there are some who say that these so-called intermediates between the forms and the perceptible things do exist, though not separately from the perceptible things but in them; the impossible consequences of this view would take too long to go through in full, but it is enough to consider the following. It is not reasonable for the situation to hold only in this case; rather, it is clear that the forms too might just as well be in the perceptible things (for both claims rest on the same reasoning), and further it would be necessary for two solids to be in the same place, and for these to not be unmoved, given that they exist in things that are moving. And in general, for what purpose would one posit that these things exist, and exist in the perceptible things? For the same absurd consequences already mentioned will result: there will be some heaven besides the heaven, except not separate but in the same place —
13| which is more impossible. So there is much puzzlement both about these matters — how one must proceed if one is to arrive at the truth — and about the principles: whether we should suppose the genera to be elements and principles, or rather suppose as principles those primary constituents present within each thing out of which it is composed. For example, the elements and principles of an utterance seem to be the primary things out of which utterances are put together, not the universal "utterance" itself; and in the case of geometrical diagrams we call elements those propositions whose demonstrations are contained within the demonstrations of the others, either of all of them or of most; and further, in the case of bodies too, both those who say the elements are several and those who say there is one call principles the things out of which a body is composed and constituted — for example Empedocles says that fire and water and what goes with them are elements, as present constituents out of which the things that are, are made, but he does not speak of these as the genera of the things that are. Besides this, if one wishes to examine the nature of anything else as well —
14| [998b] a bed, say — one must ask out of what parts it is constituted and how they are put together, and then one knows its nature. From these arguments, then, the genera would not be the principles of the things that are; but if we know each thing through its definitions, and the genera are the principles of the definitions, then the genera must also be the principles of the things defined. And if to grasp knowledge of the things that are is to grasp the species according to which the things that are, are spoken of, then at any rate the genera are the principles of the species. And it appears that some of those who say that the one, or being, or the great-and-small are the elements of things use them as genera. But surely it is not possible to speak of the principles in both ways at once. For the account of the substance is one; but the definition given through the genera will be different from the one that states the constituents present out of which the thing is composed. Besides this, even granting fully that the genera are principles, must we hold that the first of the genera are the principles, or the last, those predicated of the individuals? For this too admits of dispute. If the more universal is always more a principle, clearly it is the highest of the genera that are the principles;
15| for these are predicated of everything. So there will be as many principles of the things that are as there are primary genera, so that being and the one will be principles and substances; for these are predicated of all the things that are more than anything else is. But it is not possible for either the one or being to be a single genus of the things that are; for it is necessary both that the differentiae of each genus exist and that each be one, but it is impossible either for the species of the genus to be predicated of its own differentiae, or for the genus to be predicated apart from its own species — so that if the one or being is a genus, no differentia will be either a being or a one. But then, if they are not genera, they will not be principles either, since the genera are the principles. Further, the intermediate terms, taken together with the differentiae, will be genera all the way down to the individuals (though at present some seem to be so and some do not); and besides this, the differentiae are even more principles than the genera are. And if these too are principles, the principles become, so to speak, infinite in number — especially if one also posits the first genus as a principle.
16| [999a] But then again, if the one is more of the nature of a principle, and the one is the indivisible, and everything indivisible is so either in quantity or in form, and the indivisible in form is prior, while the genera are divisible into species, then it would rather be the last thing predicated that is one; for man is not a genus of particular men. Further, in cases where there is a prior and a posterior, it is not possible for there to be something over and above these terms applying to them (for example, if the dyad is first among numbers, there will be no number over and above the species of numbers; likewise no figure over and above the species of figures; and if not of these, then hardly will there be genera over and above the species of other things either, since it is of these — numbers and figures — that genera seem most of all to exist); but among individuals there is no prior and posterior. Further, where one thing is better and another worse, the better is always prior, so that of these too there could be no genus. From these considerations, then, it appears rather that what is predicated of individuals is more the principles than the genera are. But again, it is not easy to say how, in turn, we should suppose these to be principles. For the principle and the cause must be over and above the things of which it is the principle, and must be capable of existing separated from them;
17| but why would one suppose that anything of this sort exists over and above the particular, except because it is predicated universally and of all its instances? But then, if that is the reason, the more universal things must be posited as more the principles, so that the first genera would be the principles. There is a puzzle connected with these, and it is the hardest of all and the most necessary to examine — the one our discussion now stands upon. For if there is nothing over and above particulars, and particulars are infinite in number, how can one possibly grasp knowledge of infinite things? For it is insofar as something is one and the same, and insofar as something universal belongs to things, that we know all things. But then, if this is necessary, and there must be something over and above particulars, it would be necessary for the genera to exist over and above particulars, either the last of them or the first; but we have just worked through the puzzle showing that this is impossible. Further, granting fully that there is something over and above the compound whenever something is predicated of the matter, must there — if there is — be something over and above everything, or over and above some things but not others, or over and above nothing at all?
18| [999b] Now if there is nothing over and above particulars, nothing would be an object of intellect, but everything would be an object of perception, and there would be knowledge of nothing, unless someone says that perception is knowledge. Further, nothing would be eternal or unmoved either, for all perceptible things perish and are in motion; but then, if nothing at all is eternal, coming-to-be cannot exist either. For there must be something that comes to be, and something out of which it comes to be, and the last of these must be ungenerated, if indeed the series comes to a stop and it is impossible for something to come to be out of what is not. Further, given that coming-to-be and motion exist, there must also be a limit (for no motion is infinite, but every motion has an end, and it is not possible for what cannot come to be to come to be; and what has come to be must exist as soon as it has come to be). Further, if matter exists because it is ungenerated, it is far more reasonable still that the substance should exist — that which the matter at some point becomes; for if neither this nor that will exist, nothing at all will exist, and if that is impossible, then there must necessarily be something over and above the compound — the shape and the form. But if, in turn, one posits this, there is a puzzle as to in which cases one will posit it and in which not.
19| That it is not possible in every case is clear; for we would not posit some house existing over and above particular houses. Besides this, will the substance of all of them be one, for example of all men? But that is absurd, for all things whose substance is one are one. But will their substances be many and different? This too is unreasonable. At the same time, how does the matter become each of these, and how is the compound both of these together? Further, concerning the principles one might also raise this puzzle. If they are one in form, nothing will be one in number, not even the one itself and being; and how will there be knowledge, if there is not some one thing holding over all instances? But then, if each of the principles is one in number, and not — as with perceptible things — different for different instances (for example, this syllable, being the same in form, has principles that are also the same in form, for even these exist as numerically different in different instances), but if it is not so, and instead the principles of things are one in number, then there will be nothing else over and above the elements; for to say "one in number" and to say "the particular" makes no difference at all, for this is how we speak of the particular — the numerically one — while the universal is what holds over these.
20| [1000a] Just as, if the elements of sound were determinate in number, it would be necessary that all the letters be as many as the elements, provided there are not two identical elements, or more. But no puzzle has been left less important, by either the moderns or their predecessors, than this one: whether the principles of perishable and imperishable things are the same, or different. For if they are the same, how is it that some things are perishable and others imperishable, and for what cause? Now Hesiod's circle, and all who as theologians attended only to what was persuasive to themselves, and had no regard for us — for by making the principles gods, and born of gods, they say that whatever did not taste of nectar and ambrosia became mortal, clearly using these names as familiar to themselves; and yet about the actual application of these causes they have spoken beyond our understanding: for if the gods touch nectar and ambrosia for the sake of pleasure, then nectar and ambrosia are in no way causes of their being; but if for the sake of being, how could they be everlasting when they need food? — but as for those who play the wise man mythically, it is not worth examining them seriously; from those, however, who speak by way of demonstration, one must inquire, pressing the question closely, why on earth, being from the same things, some beings are everlasting in nature while others perish.
21| Since they state neither a cause nor anything to make this reasonable, it is clear that the same principles, nor the same causes, could belong to both. For even the one whom someone might think speaks most consistently with himself, Empedocles, has suffered this very same thing: he posits a certain principle as cause of destruction, strife, but this would seem no less to generate the other things too, apart from the one; for everything else comes from this except god. At any rate he says: from which are all things that were, that are, and that will be hereafter — trees sprang up, and men and women, beasts and birds and water-nourished fish, and even the long-lived gods. (Empedocles, fr. 21.9-12) And apart from this it is clear:
22| [1000b] for if strife were not present in things, all would be one, as he says: but when they had come together, then last of all strife took its stand. (Empedocles, fr. 36.7) Hence it follows for him that the happiest god is less intelligent than the others; for he does not know everything, since he does not have strife in him, and knowledge is of like by like. For by earth, he says, we see earth, by water water, by aither the divine aither, but by fire consuming fire, by love love, and by baneful strife, baneful strife. (Empedocles, fr. 109) But — to return to the point from which this argument started — this much at least is clear: it follows for him that strife is no more a cause of destruction than of being, and likewise love is not a cause of being either, since by drawing things together into the one it destroys the rest. And at the same time he states no cause of the change itself except that this is simply its nature: but when great strife had been nourished within the limbs, it sprang up to its honors as the time was being fulfilled, which is fixed for them in turn by a broad oath. (Empedocles, fr. 30) — as though the change were necessary, yet he shows no cause of the necessity. But still, this much at least he alone states consistently: he does not make some beings perishable and others imperishable, but makes all things perishable except the elements.
23| The puzzle now being stated is this: why are some things perishable and others not, if they come from the same things? That the principles could not be the same, then, let this much suffice to say. But if the principles are different, one puzzle is whether these too will be imperishable or perishable. For if perishable, clearly these too must come from certain things — for everything perishes into the things from which it is — so that it follows that there are other, prior principles of the principles, and this is impossible, whether the series comes to a stop or goes on to infinity. Further, how will perishable things exist at all, if the principles are to be destroyed? But if imperishable, why is it that perishable things come from these imperishable ones, while imperishable things come from the others? For this is not reasonable, but is either impossible or requires a great deal of argument. Further, no one has even attempted different principles, but they all speak of the same principles for everything.
24| [1001a] But they nibble away at the first puzzle raised, as though this were some small matter to grant. Of all questions, the hardest to investigate, and the most necessary for knowing the truth, is whether being and the one are the substances of the things that are — each of them not being something else besides, one being simply the one and the other simply being — or whether one must instead inquire what being and the one are, on the supposition that some other nature underlies them. For some think the nature is the one way, others the other way. Plato and the Pythagoreans think that being and the one are not something else, but that this is their very nature, since their substance is precisely being one and being. But those who study nature — Empedocles, for instance — speak as though reducing it to something more familiar when he says what the one is; for he would seem to be saying that this is love (at any rate this is the cause of being one for all things); others say it is fire, and others say it is air, that is this one and this being, out of which the things that are, both are and have come to be. And likewise, too, with those who posit several elements: for these too must say that the one and being are as many as the number of principles they say there are.
25| It follows that if someone does not posit that the one and being are some substance, then none of the other universals will be substances either — for these are the most universal of all things — and if there is no one itself and no being itself, then scarcely could any of the other things exist apart from the things called particulars. And further, if the one is not a substance, clearly number could not exist either, as a nature separated from the things that are — for number is units, and a unit is precisely a kind of one. But if there is some one itself and being itself, it is necessary that being and the one be their substance; for it is not something else universal that is predicated of them, but these very things. But then, if there is to be some being itself and some one itself, there is great difficulty in how there could be anything else besides these — I mean, how the things that are could be more than one. For what is other than being, is not; so that it necessarily follows, by Parmenides' argument, that all the things that are, are one, and this is being.
26| [1001b] Either way it is difficult. For whether the one is not a substance, or whether it is one and the same one, it is impossible for number to be a substance. If it is not, it has already been said why; but if it is, the same puzzle arises about being as well. For out of what, besides the one, will there be another one itself? For it must not be one; but all the things that are, are either one, or many things of which each is one. Further, if the one itself is indivisible, then by Zeno's axiom it would be nothing at all — for whatever, by being added or by being taken away, makes a thing neither greater nor smaller, he says is not among the things that are, on the assumption, clearly, that what is, is a magnitude; and if a magnitude, then bodily, since that is what is in every respect; while other things, when added, will in some way make a thing greater, in some way not — a plane and a line, for example, but a point and a unit not at all. But since Zeno examines the matter crudely, and it is possible for there to be something indivisible in another sense, so that in this way too there would be some defense against him — for such a thing, when added, will not make a thing greater, but will make it more numerous — the question still stands: how will there be magnitude out of one such thing, or out of several such things? For that is like saying that a line too is made of points.
27| But further, even if someone supposes, as some people say, that number comes to be out of the one itself and something else that is not-one, we must no less inquire why and how what comes to be will sometimes be number and sometimes magnitude, if the not-one was inequality and the same nature in both cases. For it is not clear how magnitudes could come to be either from the one and this not-one, or from some number and this not-one. Next to these is the puzzle whether numbers and bodies and planes and points are substances at all, or not. For if they are not, what being is, and what the substances of the things that are, escapes us. For affections and motions and relatives and dispositions and ratios do not seem to signify the substance of anything (for all of these are said of some underlying subject, and none of them is a this); but the things that would most seem to signify substance are water and earth and fire and air, out of which composite bodies are constituted,
28| [1002a] and of these, hot and cold and affections of that sort are not substances, but the body that has undergone them alone persists as something that is and as a kind of substance. Yet the body is less a substance than the surface, and the surface less than the line, and the line less than the unit and the point; for the body is bounded by these, and it seems possible for these to exist without body, but impossible for body to exist without them. This is why most people, and the earlier thinkers, supposed that substance and being were body, and that the other things were affections of it, so that the principles of bodies were also principles of the things that are; while later thinkers, who were held to be wiser than these, supposed them to be numbers. As we said, then, if these are not substance, there is no substance at all and nothing is being; for surely the accidents of these things are not worth calling beings. But if, on the other hand, this is granted — that lengths and points are more substance than bodies — and yet we do not see of what bodies these could be the lengths and points (for it is impossible for them to belong among perceptible things), then there would be no substance at all. Further, all of these evidently are divisions of body, one into breadth, one into depth, one into length.
29| Further, in the same way any shape whatever is present in a solid; so that if Hermes is not present in the stone, neither is the half of the cube present in the cube as something marked off. Then neither is a surface present in it either (for if any surface at all were present, this would be the one marking off the half); and the same argument applies to the line and the point and the unit. So if body is most of all substance, and these are more substance than it, and yet these are not substances at all, then what being is and what the substance of the things that are, escapes us. For besides what has been said, absurd consequences also follow about coming-to-be and passing-away. For it seems that substance, if it now is though it previously was not, or previously was though it later is not, undergoes this along with coming-to-be and passing-away; but points and lines and surfaces cannot either come to be or pass away, though at one time they are and at another they are not. For whenever bodies touch or are divided,
30| [1002b] at the same time one point comes to be when they touch, and two when they are divided; so that they do not exist while the bodies are joined together, but have perished, and when the bodies are divided, points exist that did not exist before (for surely the indivisible point was not divided into two); and if they come to be and pass away, out of what do they come to be? A similar situation holds also for the now in time: this too cannot come to be and pass away, yet it always seems to be something different, not being some one substance. It is clear that the same holds likewise for points and lines and planes, for the argument is the same, since all of these alike are either limits or divisions. In general one might also raise the puzzle why we need to look for anything else besides the perceptible things and the intermediates — I mean the things we posit as forms. For if it is because the objects of mathematics differ from the things here in some other respect, but do not differ in there being many of the same kind, so that their principles will not be determinate in number but only in form (just as the principles of the letters here are not determinate in number for all of them, but are determinate in kind — unless one takes the letters of this particular syllable or this particular sound,
31| in which case they will also be determinate in number for these) — and the same holds for the intermediates too, since there also the things of the same kind are unlimited in number — then, if there is nothing besides the perceptible things and the objects of mathematics other than the things some people call the forms, substance will not be one in number but one in form, and the principles of the things that are will not be a certain number of individuals but a certain form. If this is necessary, then it is necessary for this reason to posit the forms as well. For even if those who speak of them do not articulate it well, still this is what they mean, and they must be saying this: that each of the forms is a certain substance, and none of them exists accidentally. But if, on the other hand, we shall posit both that the forms exist and that the principles are one in number and not merely one in form, we have already stated the impossibilities that must follow. Close to these is the puzzle whether the elements exist potentially or in some other way. For if in some other way, something else will be prior to the principles (for
32| [1003a] the potentiality is prior to that cause, and what is possible need not always turn out that way); but if the elements exist potentially, it is possible for none of the things that are to exist. For what is not yet can also be possible to be; for what is not comes to be, but nothing that is incapable of being comes to be. These, then, are the puzzles that must be raised about the principles, and also whether they are universal or are as we say particulars are. For if they are universal, they will not be substances (for none of the common things signifies a this but rather a such, whereas substance is a this; and if what is predicated in common is to be posited as a this and one, Socrates will be many animals — himself, and man, and animal — if each of these signifies a this and a one). If, then, the principles are universal, these consequences follow; but if they are not universal but are as particulars are, they will not be objects of scientific knowledge (for knowledge of everything is universal), so that there will be other principles prior to the principles, namely the ones predicated universally, if indeed there is to be knowledge of the principles.