3. Resumes the discussion of this inquiry.

But if, doubtless, this is acknowledged, that dimensions and points are substance, rather than bodies themselves, yet we do not perceive to what sort of bodies these would belong (for that they be inherent in things that fall under cognisance of the senses, this is impossible); in this case, then, there would not be any substance in existence. Further, however, it appears that all these entities are divisions of body, one indeed, into breadth, and another into depth, and a third into length. But, in addition to these things, in like manner, there is in the solid every kind of figure whatsoever; so that, if neither mercury is in the stone, nor the half of a cube in the cube, in such a way as has been defined neither, in this case, would one surface exist in body: for if this would be the case with anything whatsoever, it would be with that which would separate the half. Now, there is the same mode of reasoning in the case of a line, and a point, and a monad; wherefore, if body especially be substance, and if these are substance rather than this, and these have no existence, nor do certain substances exist, there eludes our comprehension what entity is, and what is the substance of entities. For, in addition to the statements that have been made, those irrational consequences relating to generation and corruption, also, take place. For, indeed, substance-when not previously existing it comes into existence now, or when it which formerly had an existence afterwards ceases to exist-the substance, I say, appears to undergo these affections, namely, production and corruption; but points, and lines, and surfaces, cannot possibly arise or be destroyed, though sometimes these have a subsistence, and sometimes they have not. For when bodies mutually touch or intersect each other, at the same time that they touch they become one, and at the same time that they intersect they become two. So that points, lines, and surfaces, when bodies are compounded together, have no subsistence, but then have been reduced to corruption: but when bodies are divided, these rise into existence, though previously they had no existence. For a point, truly, that is indivisible is not capable of being divided into two; and, if

1

The student would do well to consult Mosheim's Dissertation on "A Creation out of Nothing;" to be found amongst his commentaries en Cudworth.

they are produced and destroyed, they are produced from something. But, in a similar way, is it the case respecting the present time, which is contained in duration; for neither does this admit of being generated and destroyed, but, nevertheless, invariably seems to be a thing that is different, not that it is, however, any particular substance. In like manner, also, it is evident that it is the case both respecting points, and lines, and surfaces, for the reasoning is the same; for all these, in like manner, are either bounds or divisions.

CHAPTER VI.1

1. Are there any

other principles over and above entities and

mathematical

sensibles?

BUT, upon the whole, would one feel perplexity why also it is necessary to investigate into certain other entities besides sensibles and media, for example, such as we posite as forms? For if it is on this account, because mathematical entities, indeed, differ from those that are here in a certain other respect, yet, in regard of there being many of them of the same species, there is no difference in this. Wherefore, the first principles of these will not be limited in number, as neither of all the lines which are here are the first principles limited in number, but in species, unless one takes the principle of this particular syllable, or of this particular voice, and the first principles of these will be limited in number. In like manner, also, is it the case with things that are intermediate; for there, likewise, things of the same species are infinite. Wherefore, unless, in addition to sensibles and mathematical entitities, there are certain others, such as some call the forms, there will not be a substance onė in number and species; nor will there be certain first principles of entities so many in number, but in species. If, then, this is necessary, the subsistence of forms, on this account, is necessary also. For even although they who make such assertions do not propound their theories with distinctness,

1 This brings us to the close of the examination of the doubts that had been started in the commencement of this book. Some of them are discussed with almost studied obscurity. They, however, strongly illustrate the state of ontological science in Aristotle's time, who may be called its progenitor.

. The mode of

yet it is this which they aim at; and they must needs affirm this, that each of the forms is a certain substance, and that not one of them subsists according to accident. But, doubtless, if we posite the existence of the forms and of the first principles as one in number, but not in species, we have declared the impossibilities which must need come to pass. Contiguous, also, to this inquiry is the question the subsistence whether elements subsist in potentiality,1 or in of principles. some other manner? For if, indeed, in some other manner, there will be something else that is prior to first principles; for potentiality is prior to that cause: but it is not necessary that everything that is potential should be disposed in that way. But if elements are existent in potentiality, it is admissible that none of the entities should have a subsistence; for it is possible for that to exist which not as yet has any existence: for, indeed, that which has no existence is being produced, but nothing of things that are impotential is produced.

3. Shall we pre

of universals or

And these doubts, then, is it necessary to dicate reality moot respecting first principles; and there reof singulars? mains, also, the inquiry whether universals exist, or, as we say, singulars? For if, indeed, universals exist, they will not be substances; for nought of those things that are general signify this particular thing, but a thing of such a sort; but the substance is this particular thing. But if it will be possible to exhibit this particular thing, and that which thereof may in common be predicated, in such a case many animals will Socrates himself be, and man and animal if each signify this certain particular thing, and that which is one. If, indeed, therefore, first principles are universal, these consequences take place; but if they are not universal, but are as singulars, they will not be objects of scientific knowledge; for the sciences are conversant about all things that are universal. Wherefore, will there be different first principles prior to principles, namely, those that are predicated universally, in case there is likely to be a science

of them.

1 The subject of potentiality, or capacity in general, is examined into more at large by Aristotle in book VIII.

BOOK III.'

CHAPTER I.

Ontology an

universal science of entity

and not a parti cular science

of it.

THERE is a certain science which makes, as the object of its speculation, entity, as far forth as it is entity, and the things which are essentially inherent in this. But this is the same with none of those which are called particular sciences; for none of the rest of the sciences examines universally concerning entity so far forth as it is entity: but, cutting away a certain portion of it, they investigate what is accidental in regard of this; as, for example, the mathematical sciences. But, whereas we are in search of first principles and the topmost causes, it is evident that they must needs be absolutely of a certain nature. If, therefore, they, also, who investigate the elements of entities were accustomed to investigate these first principles, it is necessary, likewise, that the elements of entity should not have a subsistence according to accident, but so far forth as they are entities. Wherefore, also, must we ascertain the first causes of entity, so far as it is entity.

CHAPTER II.

Now, entity is spoken of in various senses, 1.Significations indeed, but in reference to one,2 and to one of entity or the certain nature, and not equivocally; but, in like manner, also, as everything conducive to health is termed

τὸ ὄνο

1 Some make this book to be book IV., instead of book III. Aristotle now proceeds to lay before his readers what is to form the subjectmatter of his treatise on Metaphysics, namely, entity, as such, or unity, with the ontologist an interchangeable term. The foregoing book was disputative, whereas this is explanatory. In the one he merely starts difficulties, whereas in the other he does not enumerate the doubt without deciding it one way or the other.

2 The aim of Aristotle seems to be to show that the unity of metaphysical science is not destroyed by the multiplicity of subjects which fall under its province.

so in reference t, health, partly, indeed, in its preserving that state, and partly in giving rise to it, and partly in being an indication of health, and partly in being receptive of it; and, in like manner, as the medicinal is styled so ir reference to the art of medicine; for, indeed, a thing is called medicinal partly in reference to its possessing the medicinal power, partly in its being by nature adapted for the possession of such, and partly in its being the work of the medicinal art: and we shall receive the predication of other things in a similar manner with these. Thus, however, is entity,1 also, spoken of in various ways indeed; but every entity in reference to one first cause: for some things, because they are substances, are styled entities; but others, because they are affections of substance; but others, because they are a way to substance, either as corruptions, or privations, or qualities, or things formative or generative, of substance, or of those which are spoken of in reference to substance, or the negations of any of these or of substance. Wherefore, also, the nonentity we pronounce to be non-entity.

science.

As, then, there is one science of all things 2. Metaphysics one general pertaining to health, in like manner, also, is this so in the case of other things. For it is the province of one science to speculate concerning not only those things spoken of according to one, but also those spoken of in reference to a single nature. For these, also, in a certain manner, are spoken of in accordance with one. It is evident, therefore, that it is the province of a single science to speculate concerning entities, so far forth as they are entities. But in every respect is the science of ontology strictly a science of that which is first or elemental, both on which the other things depend and through which they are denominated. If, then, this is substance, the Philosopher or Metaphysician must needs be in possession of the first principles and causes of substances. Now, of every genus there is both one sense of each and one science; as, for instance, grammatical science is one, and speculates into all vocal sounds. Wherefore, to speculate into, also, the number of the species of entity, and the species of the species, belongs to a science one in kind.

1 The subject of entity is fully discussed in the next book chap. vii.