But if the science of substance and the science which deals with the axioms are different, which of them is by nature more authoritative and prior? The axioms are most universal and are principles of all things. And if it is not the business of the philosopher, to whom else will it belong to inquire what is true and what is untrue about them?24
(3) In general, do all substances fall under one science or under more than one? If the latter, (15) to what sort of substance is the present science to be assigned?—On the other hand, it is not reasonable that one science should deal with all. For then there would be one demonstrative science dealing with all attributes. For every demonstrative science investigates with regard to some subject its essential attributes, (20) starting from the common beliefs.25 Therefore to investigate the essential attributes of one class of things, starting from one set of beliefs, is the business of one science. For the subject belongs to one science, and the premisses belong to one, whether to the same or to another; so that the attributes do so too, whether they are investigated by these sciences or by one compounded out of them.26
(4)27 Further, (25) does our investigation deal with substances alone or also with their attributes? I mean for instance, if the solid is a substance and so are lines and planes, is it the business of the same science to know these and to know the attributes of each of these classes (the attributes about which the mathematical sciences offer proofs), (30) or of a different science? If of the same, the science of substance also must be a demonstrative science; but it is thought that there is no demonstration of the essence of things. And if of another, what will be the science that investigates the attributes of substance? This is a very difficult question.28
(5) Further, must we say that sensible substances alone exist, (35) or that there are others besides these? And are substances of one kind or are there in fact several kinds of substances, as those say who assert the existence both of the Forms and of the intermediates, with which they say the mathematical sciences deal?—The sense in which we say the Forms are both causes and self-dependent substances has been explained in our first remarks about them;29 while the theory presents difficulties in many ways, (5) the most paradoxical thing of all is the statement that there are certain things besides those in the material universe, and that these are the same as sensible things except that they are eternal while the latter are perishable. [997b] For they say there is a man-himself and a horse-itself and health-itself, with no further qualification—a procedure like that of the people who said there are gods, (10) but in human form. For they were positing nothing but eternal men, nor are the Platonists making the Forms anything other than eternal sensible things.
Further, if we are to posit besides the Forms and the sensibles the intermediates between them, we shall have many difficulties. For clearly on the same principle there will be lines besides the lines-themselves and the sensible lines, and so with each of the other classes of things; so that since astronomy is one of these mathematical sciences there will also be a heaven besides the sensible heaven, (15) and a sun and a moon (and so with the other heavenly bodies) besides the sensible. Yet how are we to believe in these things? It is not reasonable even to suppose such a body immovable, but to suppose it moving is quite impossible.—And similarly with the things of which optics and mathematical harmonics treat; for these also cannot exist apart from the sensible things, (20) for the same reasons. For if there are sensible things and sensations intermediate between Form and individual, evidently there will also be animals intermediate between animals-themselves and the perishable animals.—We might also raise the question, (25) with reference to which kind of existing things we must look for these sciences of intermediates. If geometry is to differ from mensuration only in this, that the latter deals with things that we perceive, and the former with things that are not perceptible, evidently there will also be a science other than medicine, intermediate between medical-science-itself and this individual medical science, and so with each of the other sciences. Yet how is this possible? There would have to be also healthy things besides the perceptible healthy things and the healthy-itself. (30)—And at the same time not even this is true, that mensuration deals with perceptible and perishable magnitudes; for then it would have perished when they perished.
But on the other hand astronomy cannot be dealing with perceptible magnitudes nor with this heaven above us. (35) For neither are perceptible lines such lines as the geometer speaks of (for no perceptible thing is straight or round in the way in which he defines ‘straight’ and ‘round’; for a hoop touches a straight edge not at a point, but as Protagoras used to say it did, in his refutation of the geometers), nor are the movements and spiral orbits in the heavens like those of which astronomy treats, (5) nor have geometrical points the same nature as the actual stars. [998a]—Now there are some who say that these so-called intermediates between the Forms and the perceptible things exist, not apart from the perceptible things, however, but in these; the impossible results of this view would take too long to enumerate, (10) but it is enough to consider even such points as the following:—It is not reasonable that this should be so only in the case of these intermediates, but clearly the Forms also might be in the perceptible things; for both statements are parts of the same theory. Further, it follows from this theory that there are two solids in the same place, and that the intermediates are not immovable, since they are in the moving perceptible things. And in general to what purpose would one suppose them to exist indeed, (15) but to exist in perceptible things? For the same paradoxical results will follow which we have already mentioned; there will be a heaven besides the heaven, only it will be not apart but in the same place; which is still more impossible.30
3 (6) Apart from the great difficulty of stating the case truly with regard to these matters, (20) it is very hard to say, with regard to the first principles, whether it is the genera that should be taken as elements and principles, or rather the primary constituents of a thing; e. g. it is the primary parts of which articulate sounds consist that are thought to be elements and principles of articulate sound, (25) not the common genus—articulate sound; and we give the name of ‘elements’ to those geometrical propositions, the proofs of which are implied in the proofs of the others, either of all or of most. Further, both those who say there are several elements of corporeal things and those who say there is one, (30) say the parts of which bodies are compounded and consist are principles; e. g. Empedocles says fire and water and the rest are the constituent elements of things, but does not describe these as genera of existing things. [998b] Besides this, if we want to examine the nature of anything else, we examine the parts of which, e. g., a bed consists and how they are put together, and then we know its nature.
To, judge from these arguments, then, the principles of things would not be the genera; but if we know each thing by its definition, (5) and the genera are the principles or starting-points of definitions, the genera must also be the principles of definable things. And if to get the knowledge of the species according to which things are named is to get the knowledge of things, the genera are at least starting-points of the species. And some also of those who say unity or being,31 or the great and the small,32 (10) are elements of things, seem to treat them as genera.
But, again, it is not possible to describe the principles in both ways. For the formula of the essence is one; but definition by genera will be different from that which states the constituent parts of a thing.33
(7) Besides this, even if the genera are in the highest degree principles, (15) should one regard the first of the genera as principles, or those which are predicated directly of the individuals? This also admits of dispute. For if the universals are always more of the nature of principles, evidently the uppermost of the genera are the principles; for these are predicated of all things. There will, then, be as many principles of things as there are primary genera, so that both being and unity will be principles and substances; for these are most of all predicated
of all existing things. (20) But it is not possible that either unity or being should be a single genus of things; for the differentiae of any genus must each of them both have being and be one, but it is not possible for the genus taken apart from its species (any more than for the species of the genus) to be predicated of its proper differentiae; so that if unity or being is a genus, (25) no differentia will either have being or be one. But if unity and being are not genera, neither will they be principles, if the genera are the principles.—Again, the intermediate kinds, in whose nature the differentiae are included, will on this theory be genera, down to the indivisible species; but as it is, some are thought to be genera and others are not thought to be so. Besides this, (30) the differentiae are principles even more than the genera; and if these also are principles, there comes to be practically an infinite number of principles, especially if we suppose the highest genus to be a principle.—But again, if unity is more of the nature of a principle, and the indivisible is one, and everything indivisible is so either in quantity or in species, and that which is so in species is the prior, and genera are divisible into species (for man is not the genus of individual men), that which is predicated directly of the individuals will have more unity. [999a] (5)—Further, in the case of things in which the distinction of prior and posterior is present, that which is predicable of these things cannot be something apart from them (e. g. if two is the first of numbers, there will not be a Number apart from the kinds of numbers; and similarly there will not be a Figure apart from the kinds of figures; and if the genera of these things do not exist apart from the species, (10) the genera of other things will scarcely do so; for genera of these things are thought to exist if any do). But among the individuals one is not prior and another posterior. Further, where one thing is better and another worse, the better is always prior; so that of these also no genus can exist.
From these considerations, then, the species predicated of individuals seem to be principles rather than the genera. (15) But again, it is not easy to say in what sense these are to be taken as principles. For the principle, and must be capable of existing in separation from the principle, and must be capable of existing in separation from them; but for what reason should we suppose any such thing to exist alongside of the individual, except that it is predicated universally and of all? But if this is the reason, (20) the things that are more universal must be supposed to be more of the nature of principles; so that the highest genera would be the principles.34
4 (8) There is a difficulty connected with these, (25) the hardest of all and the most necessary to examine, and of this the discussion now awaits us. If, on the one hand, there is nothing apart from individual things, and the individuals are infinite in number, how then is it possible to get knowledge of the infinite individuals? For all things that we come to know, we come to know in so far as they have some unity and identity, and in so far as some attribute belongs to them universally.
But if this is necessary, and there must be something apart from the individuals, (30) it will be necessary that the genera exist apart from the individuals—either the lowest or the highest genera; but we found by discussion just now that this is impossible.35
Further, if we admit in the fullest sense that something exists apart from the concrete thing, whenever something is predicated of the matter, must there, if there is something apart, be something apart from each set of individuals, or from some and not from others, or from none? (A) If there is nothing apart from individuals, there will be no object of thought, but all things will be objects of sense, and there will not be knowledge of anything, unless we say that sensation is knowledge.36 [999b] Further, nothing will be eternal or unmovable; for all perceptible things perish and are in movement. (5) But if there is nothing eternal, neither can there be a process of coming to be; for there must be something that comes to be, i. e. from which something comes to be, and the ultimate term in this series cannot have come to be, since the series has a limit and since nothing can come to be out of that which is not. Further, if generation and movement exist there must also be a limit; for no movement is infinite, (10) but every movement has an end, and that which is incapable of completing its coming to be cannot be in process of coming to be; and that which has completed its coming to be must be as soon as it has come to be.37 Further, since the matter exists, because it is ungenerated, it is a fortiori reasonable that the substance or essence, that which the matter is at any time coming to be, should exist; for if neither essence nor matter is to be, (15) nothing will be at all, and since this is impossible there must be something besides the concrete thing, viz. the shape or form.
But again (B) if we are to suppose this, it is hard to say in which cases we are to suppose it and in which not. For evidently it is not possible to suppose it in all cases; we could not suppose that there is a house besides the particular houses.—Besides this, (20) will the substance of all the individuals, e. g. of all men, be one? This is paradoxical, for all the things whose substance is one are one. But are the substances many and different? This also is unreasonable.—At the same time, how does the matter become each of the individuals, and how is the concrete thing these two elements?38
(9) Again, one might ask the following question also about the first principles. If they are one in kind only, nothing will be numerically one, (25) not even unity-itself and being-itself; and how will knowing exist, if there is not to be something common to a whole set of individuals?
But if there is a common element which is numerically one, and each of the principles is one, and the principles are not as in the case of perceptible things different for different things (e. g. since this particular syllable is the same in kind whenever it occurs, the elements of it are also the same in kind; only in kind, for these also, (30) like the syllable, are numerically different in different contexts),—if it is not like this but the principles of things are numerically one, there will be nothing else besides the elements (for there is no difference of meaning between ‘numerically one’ and ‘individual’; for this is just what we mean by the individual—the numerically one, and by the universal we mean that which is predicable of the individuals). [1000a] Therefore it will be just as if the elements of articulate sound were limited in number; all the language in the world would be confined to the ABC, since there could not be two or more letters of the same kind.39
(10) One difficulty which is as great as any has been neglected both by modern philosophers and by their predecessors—whether the principles of perishable and those of imperishable things are the same or different. (5) If they are the same, how are some things perishable and others imperishable, and for what reason? The school of Hesiod and all the theologians thought only of what was plausible to themselves, and had no regard to us. For, asserting the first principles to be gods and born of gods, (10) they say that the beings which did not taste of nectar and ambrosia became mortal; and clearly they are using words which are familiar to themselves, yet what they have said about the very application of these causes is above our comprehension. For if the gods taste of nectar and ambrosia for their pleasure, (15) these are in no wise the causes of their existence; and if they taste them to maintain their existence, how can gods who need food be eternal?—But into the subtleties of the mythologists it is not worth our while to inquire seriously; those, however, who use the language of proof we must cross-examine and ask why, (20) after all, things which consist of the same elements are, some of them, eternal in nature, while others perish. Since these philosophers mention no cause, and it is unreasonable that things should be as they say, evidently the principles or causes of things cannot be the same. Even the man whom one might suppose to speak most consistently—Empedocles—even he has made the same mistake; for he maintains that strife is a principle that causes destruction, (25) but even strife would seem no less to produce everything, except the One; for all things excepting God proceed from strife. At least he says:—
From which all that was and is and will be here
after—
Trees, (30) and men and women, took their growth,
And beasts and birds and water-nourished fish,
And long-aged gods.
The implication is evident even apart from these words; for if strife had not been present in things, all things would have been one, according to him; for when they have come together, ‘then strife stood outermost.’ [1000b] Hence it also follows on his theory that God most blessed is less wise than all others; for he does not know all the elements; for he has in him no strife, (5) and knowledge is of the like by the like. ‘For by earth,’ he says,
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