non-sensible heaven can have no motion. It is the same with the objects of optics and the mathematical theory of harmony; these too, for the same reasons, cannot exist apart from sensible objects. Because if there are intermediate objects of sense and sensations, clearly there will also be animals intermediate between the Ideal animals and the perishable animals. If there are "intermediate," i.e. non-sensible, sights and sounds, there must be "intermediate" faculties of sight and hearing, and "intermediate" animals to exercise these faculties; which is absurd. One might also raise the question with respect to what kind of objects we are to look for these sciences. For if we are to take it that the only difference between mensuration and geometry is that the one is concerned with things which we can perceive and the other with things which we cannot, clearly there will be a science parallel to medicine (and to each of the other sciences), intermediate between Ideal medicine and the medicine which we know. Yet how is this possible? for then there would be a class of healthy things apart from those which are sensible and from the Ideally healthy. Nor, at the same time, is it true that mensuration is concerned with sensible and perishable magnitudes; for then it would perish as they do. Nor, again, can astronomy be concerned with sensible magnitudes or with this heaven of ours; for as sensible lines are not like those of which the geometrician speaks (since there is nothing sensible which is straight or curved in that sense; the circle i.e., the visible circle which we draw. Like the ruler, it is geometrically imperfect; thus they touch at more than one point.
touches the ruler not at a point, but <along a line> as Protagoras used to say in refuting the geometricians), so the paths and orbits of our heaven are not like those which astronomy discusses, nor have the symbols of the astronomer the same nature as the stars. Some, however, say that these so-called Intermediates between Forms and sensibles do exist: not indeed separately from the sensibles, but in them. It would take too long to consider in detail all the impossible consequences of this theory, but it will be sufficient to observe the following. On this view it is not logical that only this should be so; in clearly it would be possible for the Forms also to be in sensible things; for the same argument applies to both.
Further, it follows necessarily that two solids must occupy the same space; and that the Forms cannot be immovable, being present in sensible things, which move. And in general, what is the object of assuming that Intermediates exist, but only in sensible things? The same absurdities as before will result: there will be a heaven besides the sensible one, only not apart from it, but in the same place; which is still more impossible. The problem is dealt with partly in Aristot.
Met. 12.6-10, where Aristotle describes the eternal moving principles, and partly in Books 13 and 14, where he argues against the Platonic non-sensible substances. Thus it is very difficult to say, not only what view we should adopt in the foregoing questions in order to arrive at the truth, but also in the case of the first principles (vi.) whether we should assume that the genera, or the simplest constituents of each particular thing, are more truly the elements and first principles of existing things. E.g., it is generally agreed that the elements and first principles of speech are those things of which, in their simplest form, all speech is composed; and not the common term "speech"; and in the case of geometrical propositions we call those the "elements" Cf. Aristot. Met.
5.3.3. whose proofs are embodied in the proofs of all or most of the rest. Again, in the case of bodies, both those who hold that there are several elements and those who hold that there is one call the things of which bodies are composed and constituted first principles. E.g., Empedocles states that fire and water and the other things associated with them are the elements which are present in things and of which things are composed; he does not speak of them as genera of things. Moreover in the case of other things too, if a man wishes to examine their nature he observes, e.g., of what parts a bed consists and how they are put together; and then he comprehends its nature. Thus to judge from these arguments the first principles will not be the genera of things. But from the point of view that it is through definitions that we get to know each particular thing, and that the genera are the first principles of definitions, the genera must also be the first principles of the things defined. And if to gain scientific knowledge of things is to gain it of the species after which things are named, the genera are first principles of the species. And apparently some even of those The Pythagoreans and Plato. who call Unity or Being or the Great and Small elements of things treat them as genera. Nor again is it possible to speak of the first principles in both senses. The formula of substance is one; but the definition by genera will be different from that which tells us of what parts a thing is composed. Moreover, assuming that the genera are first principles in the truest sense, are we to consider the primary genera to be first principles, or the final terms predicated of individuals? This question too involves some dispute. For if universals are always more truly first principles, clearly the answer will be "the highest genera," since these are predicated of everything. Then there will be as many first principles of things as there are primary genera, and so both Unity and Being will be first principles and substances, since they are in the highest degree predicated of all things. But it is impossible for either Unity or Being to be one genus of existing things. For there must be differentiae of each genus, and each differentia must be one i.e., each differentia must have Being and Unity predicated of it.; but it is impossible either for the species of the genus to be predicated of the specific differentiae, or for the genus to be predicated without its species. The reasons are given in Aristot. Topica, 144a 36-b11. Hence if Unity or Being is a genus, there will be no differentia Being or Unity. But if they are not genera, neither will they be first principles, assuming that it is the genera that are first principles. And further, the intermediate terms, taken together with the differentiae, will be genera, down to the individuals; but in point of fact, although some are thought to be such, others are not. Moreover the differentiae are more truly principles than are the genera; and if they also are principles, we get an almost infinite number of principles, especially if one makes the ultimate genus a principle. Moreover, if Unity is really more of the nature of a principle, and the indivisible is a unity, and every thing indivisible is such either in quantity or in kind, and the indivisible in kind is prior to the divisible, and the genera are divisible into species, then it is rather the lowest predicate that will be a unity (for "man" is not the genus sc.
but the species. of individual men). Further, in the case of things which admit of priority and posteriority, that which is predicated of the things cannot exist apart from them. E.g., if 2 is the first number, there will be no Number apart from the species of number; and similarly there will be no Figure apart from the species of figures.
But if the genera do not exist apart from the species in these cases, they will scarcely do so in others; because it is assumed that genera are most likely to exist in these cases. In individuals, however, there is no priority and posteriority. Further, where there is a question of better or worse, the better is always prior; so there will be no genus in these cases either. From these considerations it seems that it is the terms predicated of individuals, rather than the genera, that are the first principles. But again on the other hand it is not easy to say in what sense we are to understand these to be principles; for the first principle and cause must be apart from the things of which it is a principle, and must be able to exist when separated from them. But why should we assume that such a thing exists alongside of the individual, except in that it is predicated universally and of all the terms? And indeed if this is a sufficient reason, it is the more universal concepts that should rather be considered to be principles; and so the primary genera will be the principles. For partial solutions to the problem see Aristot.
Met. 7.10, 12-13. In this connection there is a difficulty which is the hardest and yet the most necessary of all to investigate, and with which our inquiry is now concerned. (7.) If nothing exists apart from individual things, and these are infinite in number, how is it possible to obtain knowledge of the numerically infinite? For we acquire our knowledge of all things only in so far as they contain something universal, some one and identical characteristic. But if this is essential, and there must be something apart from individual things, it must be the genera; either the lowest or the highest; but we have just concluded that this is impossible. In Aristot. Met.
3.3. Further, assuming that when something is predicated of matter there is in the fullest sense something apart from the concrete whole, if there is something, must it exist apart from all concrete wholes, or apart from some but not others, or apart from none? If nothing exists apart from individual things, nothing will be intelligible; everything will be sensible, and there will be no knowledge of anything—unless it be maintained that sense-perception is knowledge. Nor again will anything be eternal or immovable, since sensible things are all perishable and in motion. Again, if nothing is eternal, even generation is impossible; for there must be something which becomes something, i.e. out of which something is generated, and of this series the ultimate term must be ungenerated; that is if there is any end to the series and generation cannot take place out of nothing. Further, if there is generation and motion, there must be limit too.
For (a) no motion is infinite, but every one has an end; (b) that which cannot be completely generated cannot begin to be generated, and that which has been generated must be as soon as it has been generated. Further, if matter exists apart in virtue of being ungenerated, it is still more probable that the substance, i.e. that which the matter is at any given time becoming, should exist. And if neither one nor the other exists, nothing will exist at all. But if this is impossible, there must be something, the shape or form, apart from the concrete whole. But again, if we assume this, there is a difficulty: in what cases shall we, and in what shall we not, assume it? Clearly it cannot be done in all cases; for we should not assume that a particular house exists apart from particular houses. Moreover, are we to regard the essence of all things, e.g. of men, as one? This is absurd; for all things whose essence is one are one. Then is it many and diverse? This too is illogical. And besides, how does the matter become each individual one of these things, and how is the concrete whole both matter and form? For answers to these questions see Aristot. Met. 7.8, 13-14; Aristot. Met. 12.6-10; Aristot. Met.
the following difficulty might be raised about the first principles.
If they are one in kind, none of them will be one in number, not even the Idea of Unity or of Being. And how can there be knowledge unless there is some universal term? If the principles are one in kind only, particular things cannot be referred to the same principle but only to like principles; i.e., there will be no universal terms, without which there can be no knowledge. On the other hand if they are numerically one, and each of the principles is one, and not, as in the case of sensible things, different in different instances (e.g. since a given syllable is always the same in kind, its first principles are always the same in kind, but only in kind, since they are essentially different in number)—if the first principles are one, not in this sense, but numerically, there will be nothing else apart from the elements; for "numerically one" and "individual" are identical in meaning. This is what we mean by "individual": the numerically one; but by "universal" we mean what is predicable of individuals. Hence just as, if the elements of language Or "letters of the alphabet." Cf. Aristot. Met. 1.9.36n. were limited in number, the whole of literature would be no more than those elements—that is, if there were not two nor more than two of the same <so it would be in the case of existing things and their principles>. For the answer to the problem see Aristot. Met.
12.4-5, Aristot.
Met. 13.10. (ix.) There is a difficulty, as serious as any, which has been left out of account both by present thinkers and by their predecessors: whether the first 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? The school of Hesiod, and all the cosmologists, considered only what was convincing to themselves, and gave no consideration to us. For they make the first principles Gods or generated from Gods, and say that whatever did not taste of the nectar and ambrosia became mortal—clearly using these terms in a sense significant to themselves; but as regards the actual applications of these causes their statements are beyond our comprehension. For if it is for pleasure that the Gods partake of them, the nectar and ambrosia are in no sense causes of their existence; but if it is to support life, how can Gods who require nourishment be eternal? However, it is not worth while to consider seriously the subtleties of mythologists; we must ascertain by cross-examining those who offer demonstration of their statements why exactly things which are derived from the same principles are some of an eternal nature and some perishable. And since these thinkers state no reason for this view, and it is unreasonable that things should be so, obviously the causes and principles of things cannot be the same. Even the thinker who might be supposed to speak most consistently, Empedocles, is in the same case; for he posits Strife as a kind of principle which is the cause of destruction, but none the less Strife would seem to produce everything except the One; for everything except God The expressions "the One" and "God" refer to Empedocles' Sphere: the universe as ordered and united by Love.
Cf. Empedocles, Fr. 26-29 (Diels). proceeds from it. At any rate he says From which grew all that was and is and shall be In time to come: the trees, and men and women, The beasts and birds and water-nurtured fish, And the long-living Gods. Empedocles, Fr. 21.
9-12. And it is obvious even apart from this; for if there had not been Strife in things, all things would have been one, he says; for when they came together "then Strife came to stand outermost." Empedocles, Fr. 36.
7. Hence it follows on his theory that God, the most blessed being, is less wise than the others, since He does not know all the elements; for He has no Strife in Him, and knowledge is of like by like: By earth (he says) we earth perceive, by water water, By air bright air, by fire consuming fire, Love too by love, and strife by grievous strife. Empedocles, Fr.
109. But—and this is the point from which we started—thus much is clear: that it follows on his theory that Strife is no more the cause of destruction than it is of Being.
Nor, similarly, is Love the cause of Being; for in combining things into one it destroys everything else. Cf. Aristot. Met.
1.4.6. Moreover, of the actual process of change he gives no explanation, except that it is so by nature: But when Strife waxing great among the members i.e., of the Sphere. Sprang up to honor as the time came round Appointed them in turn by a mighty oath, Empedocles, Fr.
30. as though change were a necessity; but he exhibits no cause for the necessity. However, thus much of his theory is consistent: he does not represent some things to be perishable and others imperishable, but makes everything perishable except the elements. But the difficulty now being stated is why some things are perishable and others not, assuming that they are derived from the same principles. The foregoing remarks may suffice to show that the principles cannot be the same. If however they are different, one difficulty is whether they too are to be regarded as imperishable or as perishable. For if they are perishable, it is clearly necessary that they too must be derived from something else, since everything passes upon dissolution into that from which it is derived. Hence it follows that there are other principles prior to the first principles; but this is impossible, whether the series stops or proceeds to infinity.
And further, how can perishable things exist if their principles are abolished? On the other hand if the principles are imperishable, why should some imperishable principles produce perishable things, and others imperishable things? This is not reasonable; either it is impossible or it requires much explanation. Further, no one has so much as attempted to maintain different principles; they maintain the same principles for everything. But they swallow down the difficulty which we raised first i.e., whether all things have the same principles. as though they took it to be trifling. For Aristotle's views about the principles of perishable and imperishable things see Aristot. Met. 7.7-10, Aristot. Met. 12.1-7. But the hardest question of all to investigate and also the most important with a view to the discovery of the truth, is whether after all Being and Unity are substances of existing things, and each of them is nothing else than Being and Unity respectively, or whether we should inquire what exactly Being and Unity are, there being some other nature underlying them. Some take the former, others the latter view of the nature of Being and Unity. Plato and the Pythagoreans hold that neither Being nor Unity is anything else than itself, and that this is their nature, their essence being simply Being and Unity. But the physicists, e.g.
Empedocles, explain what Unity is by reducing it to something, as it were, more intelligible—or it would seem that by Love Empedocles means Unity; at any rate Love is the cause of Unity in all things. Others identify fire and others air with this Unity and Being of which things consist and from which they have been generated. Those who posit more numerous elements also hold the same view; for they too must identify Unity and Being with all the principles which they recognize. And it follows that unless one assumes Unity and Being to be substance in some sense, no other universal term can be substance; for Unity and Being are the most universal of all terms, and if there is no absolute Unity or absolute Being, no other concept can well exist apart from the so-called particulars. Further, if Unity is not substance, clearly number cannot be a separate characteristic of things; for number is units, and the unit is simply a particular kind of one. On the other hand, if there is absolute Unity and Being, their substance must be Unity and Being; for no other term is predicated universally of Unity and Being, but only these terms themselves. Again, if there is to be absolute Being and absolute Unity, it is very hard to see how there can be anything else besides these; I mean, how things can be more than one. For that which is other than what is, is not; and so by Parmenides' argument By to\ o)/n Parmenides meant "what is," i.e. the real universe, which he proved to be one thing because anything else must be "what is not," or non-existent. The Platonists meant by it "being" in the abstract. Aristotle ignores this distinction. it must follow that all things are one, i.e.
Being. In either case there is a difficulty; for whether Unity is not a substance or whether there is absolute Unity, number cannot be a substance. It has already been stated why this is so if Unity is not a substance; and if it is, there is the same difficulty as about Being. For whence, if not from the absolute One or Unity, can there be another one? It must be not-one; but all things are either one, or many of which each is one. Further, if absolute Unity is indivisible, by Zeno's axiom it will be nothing. For that which neither when added makes a thing greater nor when subtracted makes it smaller is not an existent thing, he says Cf. Zeno, Fr. 2, and see Burnet, E.G.P. sects. 157 ff.; clearly assuming that what exists is spatial magnitude. And if it is a spatial magnitude it is corporeal, since the corporeal exists in all dimensions, whereas the other magnitudes, the plane or line, when added to a thing in one way will increase it, but when added in another will not; and the point or unit will not increase a thing in any way whatever. But since Zeno's view is unsound, and it is possible for a thing to be indivisible in such a way that it can be defended even against his argument (for such a thing e.g., a point is indivisible and has no magnitude, yet added to other points it increases their number. when added will increase a thing in number though not in size)—still how can a magnitude be composed of one or more such indivisible things? It is like saying that the line is composed of points. Moreover, even if one supposes the case to be such that number is generated, as some say, from the One itself and from something else which is not one, we must none the less inquire why and how it is that the thing generated will be at one time number and at another magnitude, if the not-one was inequality and the same principle in both cases. The reference is to the Platonists. Cf. Aristot. Met. 14.1.5, 6; Aristot. Met. 14.2.13, 14. For it is not clear how magnitude can be generated either from One and this principle, or from a number and this principle. For the answer to this problem see Aristot. Met. 7.16.3, 4; Aristot. Met. 10.2; and cf.
Aristot. Met.
13.8. (13.) Out of this arises the question whether numbers, bodies, planes and points are substances or not. If not, the question of what Being is, what the substances of things are, baffles us; for modifications and motions and relations and dispositions and ratios do not seem to indicate the substance of anything; they are all predicated of a substrate, and none of them is a definite thing. As for those things which might be especially supposed to indicate substance—water, earth, fire and air, of which composite bodies are composed— their heat and cold and the like are modifications, not substances; and it is only the body which undergoes these modifications that persists as something real and a kind of substance. Again, the body is less truly substance than the plane, and the plane than the line, and the line than the unit or point; for it is by these that the body is defined, and it seems that they are possible without the body, but that the body cannot exist without them. This is why the vulgar and the earlier thinkers supposed that substance and Being are Body, and everything else the modifications of Body; and hence also that the first principles of bodies are the first principles of existing things; whereas later thinkers with a greater reputation for wisdom supposed that substance and Being are numbers. As we have said, then, if these things are not substance, there is no substance or Being at all; for the attributes of these things surely have no right to be called existent things. On the other hand, if it be agreed that lines and points are more truly substance than bodies are, yet unless we can see to what kind of bodies they belong (for they cannot be in sensible bodies) there will still be no substance. Further, it is apparent that all these lines are divisions of Body, either in breadth or in depth or in length. Moreover every kind of shape is equally present in a solid, so that if "Hermes is not in the stone," Apparently a proverbial expression.
neither is the half-cube in the cube as a determinate shape. Hence neither is the plane; for if any kind of plane were in it, so would that plane be which defines the half-cube. The same argument applies to the line and to the point or unit. Hence however true it may be that body is substance, if planes, lines and points are more truly substance than Body is, and these are not substance in any sense, the question of what Being is and what is the substance of things baffles us. Because, in addition to the above arguments, absurd results follow from a consideration of generation and destruction; for it seems that if substance, not having existed before, now exists, or having existed before, subsequently does not exist it suffers these changes in the process of generation and destruction. But points, lines and planes, although they exist at one time and at another do not, cannot be in process of being either generated or destroyed; for whenever bodies are joined or divided, at one time, when they are joined one surface is instantaneously produced, and at another, when they are divided, two. Thus when the bodies are combined the surface does not exist but has perished; and when they are divided, surfaces exist which did not exist before. (The indivisible point is of course never divided into two.) And if they are generated and destroyed, from what are they generated? It is very much the same with "the present moment" in time. This too cannot be generated and destroyed; but nevertheless it seems always to be different, not being a substance. And obviously it is the same with points, lines and planes, for the argument is the same; they are all similarly either limits or divisions. For arguments against the substantiality of numbers and mathematical objects see Aristot. Met.
6. In general one might wonder why we should seek for other entities apart from sensible things and the Intermediates: Cf. Aristot. Met. 3.2.20ff.. e.g., for the Forms which we Platonists assume. If it is for the reason that the objects of mathematics, while differing from the things in our world in another respect, resemble them in being a plurality of objects similar in form, so that their principles cannot be numerically determined (just as the principles of all language in this world of ours are determinate not in number but in kind—unless one takes such and such a particular syllable or sound, for the principles of these are determinate in number too— and similarly with the Intermediates, for in their case too there is an infinity of objects similar in form), then if there is not another set of objects apart from sensible and mathematical objects, such as the Forms are said to be, there will be no substance which is one both in kind and in number, nor will the principles of things be determinate in number, but in kind only. Thus if this is necessarily so, it is necessary for this reason to posit the Forms also. For even if their exponents do not articulate their theory properly, still this is what they are trying to express, and it must be that they maintain the Forms on the ground that each of them is a substance, and none of them exists by accident. On the other hand, if we are to assume that the Forms exist, and that the first principles are one in number but not in kind, we have already stated Aristot. Met. 3.4.9, 10. the impossible consequences which must follow. This problem is not stated in ch. 1., but is akin to problems 5. and 8., which see. (12.) Closely connected with these questions is the problem whether the elements exist potentially or in some other sense. If in some other sense, there will be something else prior to the first principles. For the potentiality is prior to the actual cause, and the potential need not necessarily always become actual. On the other hand, if the elements exist potentially, it is possible for nothing to exist; for even that which does not yet exist is capable of existing. That which does not exist may come to be, but nothing which cannot exist comes to be. For the relation of potentiality to actuality see Aristot. Met.
9.1-9. The second point raised in this connection in ch.
1 is not discussed here; for actuality and motion see Aristot. Met. 12.6, 7. (xi.) Besides the foregoing problems about the first principles we must also raise the question whether they are universal or such as we describe the particulars to be. For if they are universal, there will be no substances; for no common term denotes an individual thing, but a type; and substance is an individual thing. But if the common predicate be hypostatized as an individual thing, Socrates will be several beings: himself, and Man, and Animal—that is, if each predicate denotes one particular thing. These then are the consequences if the principles are universal. If on the other hand they are not universal but like particulars, they will not be knowable; for the knowledge of everything is universal. Hence there will have to be other universally predicated principles prior to the first principles, if there is to be any knowledge of them. For the answer to this problem see Aristot. Met. 7.13-15, Aristot. Met. 13.10.
There is a science which studies Being qua Being, and the properties inherent in it in virtue of its own nature. This science is not the same as any of the so-called particular sciences, for none of the others contemplates Being generally qua Being; they divide off some portion of it and study the attribute of this portion, as do for example the mathematical sciences. But since it is for the first principles and the most ultimate causes that we are searching, clearly they must belong to something in virtue of its own nature. Hence if these principles were investigated by those also who investigated the elements of existing things, the elements must be elements of Being not incidentally, but qua Being. Therefore it is of Being qua Being that we too must grasp the first causes. The term "being" is used in various senses, but with reference to one central idea and one definite characteristic, and not as merely a common epithet. Thus as the term "healthy" always relates to health (either as preserving it or as producing it or as indicating it or as receptive of it), and as "medical" relates to the art of medicine (either as possessing it or as naturally adapted for it or as being a function of medicine)—and we shall find other terms used similarly to these— so "being " is used in various senses, but always with reference to one principle. For some things are said to "be" because they are substances; others because they are modifications of substance; others because they are a process towards substance, or destructions or privations or qualities of substance, or productive or generative of substance or of terms relating to substance, or negations of certain of these terms or of substance. (Hence we even say that not-being is not-being.) And so, just as there is one science of all healthy things, so it is true of everything else. For it is not only in the case of terms which express one common notion that the investigation belongs to one science, but also in the case of terms which relate to one particular characteristic; for the latter too, in a sense, express one common notion. Clearly then the study of things which are, qua being, also belongs to one science. Now in every case knowledge is principally concerned with that which is primary, i.e. that upon which all other things depend, and from which they get their names. If, then, substance is this primary thing, it is of substances that the philosopher must grasp the first principles and causes. Now of every single class of things, as there is one perception, so there is one science: e.g., grammar, which is one science, studies all articulate sounds. Hence the study of all the species of Being qua Being belongs to a science which is generically one, and the study of the several species of Being belongs to the specific parts of that science. Now if Being and Unity are the same, i.e. a single nature, in the sense that they are associated as principle and cause are, and not as being denoted by the same definition (although it makes no difference but rather helps our argument if we understand them in the same sense), since "one man" and "man" and "existent man" and "man" are the same thing, i.e.
the duplication in the statement "he is a man and an existent man" gives no fresh meaning (clearly the concepts of humanity and existence are not dissociated in respect of either coming to be or ceasing to be), and similarly in the case of the term "one," so that obviously the additional term in these phrases has the same significance, and Unity is nothing distinct from Being; and further if the substance of each thing is one in no accidental sense, and similarly is of its very nature something which is—then there are just as many species of Being as of Unity. And to study the essence of these species (I mean, e.g., the study of Same and Other and all the other similar concepts— roughly speaking all the "contraries" are reducible to this first principle; but we may consider that they have been sufficiently studied in the "Selection of Contraries" It is uncertain to what treatise Aristotle refers; in any case it is not extant. ) is the province of a science which is generically one. And there are just as many divisions of philosophy as there are kinds of substance; so that there must be among them a First Philosophy and one which follows upon it. For Being and Unity at once entail genera, and so the sciences will correspond to these genera. The term "philosopher" is like the term "mathematician" in its uses; for mathematics too has divisions—there is a primary and a secondary science, and others successively, in the realm of mathematics. Now since it is the province of one science to study opposites, and the opposite of unity is plurality, and it is the province of one science to study the negation and privation of Unity, because in both cases we are studying Unity, to which the negation (or privation) refers, stated either in the simple form that Unity is not present, or in the form that it is not present in a particular class; in the latter case Unity is modified by the differentia, apart from the content of the negation (for the negation of Unity is its absence); but in privation there is a substrate of which the privation is predicated.— The opposite of Unity, then, is Plurality; and so the opposites of the above-mentioned concepts—Otherness, Dissimilarity, Inequality and everything else which is derived from these or from Plurality or Unity— fall