Plato (left) and Aristotle in Raphael’s 1509 fresco, The School of Athens

Book I
Chapter I

All men by nature are actuated with the desire of knowledge, and an indication of this is the love of the senses; for even, irrespective of their utility, are they loved for their own sakes; and pre-eminently above the rest, the sense of sight. For not only for practical purposes, but also when not intent on doing anything, we choose the power of vision in preference, so to say, to all the rest of the senses. And a cause of this is the following, that this one of the senses particularly enables us to apprehend? whatever knowledge it is the inlet of, and that it makes many distinctive? qualities manifest.

By nature then, indeed, are animals formed endowed with sense; but in some of them memory is not innate from sense, and in others it is. And for this reason are these possessed of more foresight, as well as a greater aptitude for discipline, than those which are wanting in this faculty of memory. Those furnished with foresight, indeed, are yet without the capability of receiving instruction, whatever amongst them are unable to understand the sounds they hear; as, for instance, bees, and other similar tribes of animals; but those are capable of receiving instruction as many as, in addition to memory, are provided with this sense also.

The rest, indeed, subsist then through impressions and the operations of memory, but share experience in a slight degree; whereas the human race exists by means of art also and the powers of reasoning.

Now, experience accrues to men from memory for repeated acts of memory about the same thing done constitute the force of a single experience: and experience seems to be a thing almost similar to science and art.

But science and art result unto men by means of experience for experience, indeed, as Polus saith, and correctly so,’ has produced art, but inexperience, chance. But an art comes into being when, out of many conceptions of experience, one universal opinion is evolved with respect to similar cases. For, indeed, to entertain the opinion that this particular remedy has been of service to Callias, while labouring under this particular disease, as well as to Socrates, and so individually to many, this is an inference of experience; but that it has been conducive to the health of all, such as have been defined according to one species, while labouring under this disease, as, for instance, to the phlegmatic, or the choleric, or those sick of a burning fever, this belongs to the province of art.

As regards, indeed, practical purposes, therefore, experience seems in no wise to differ from art; nay, even we see the experienced compassing their objects more effectually than those who possess a theory without the experience. But a cause of this is the following that experience, indeed, is a knowledge of singulars, whereas art, of universals; but all things in the doing, and all generations, are concerned about the singular: for he whose profession it is to practise medicine, does not restore man to health save by accident, but Callias, or Socrates, or any of the rest so designated, to whom it happens to be a man. If, therefore, any one without the experience is furnished with the principle, and is acquainted with the universal, but is ignorant of the singular that is involved therein, he will frequently fall into error in the case of his medical treatment; for that which is capable of cure is rather the singular.

But, nevertheless, we are of opinion that, at least, knowledge and understanding appertain to art rather than experience; and we reckon artists more wise than the experienced, inasmuch as wisdom is the concomitant of all philosophers rather in proportion to their knowledge.

But this is so because some, indeed, are aware of the cause, and some are not. For the experienced, indeed, know that a thing is so, but they do not know wherefore it is so; but others I mean the scientific are acquainted with the wherefore and the cause. Therefore, also, we reckon the chief artificers in each ease to be entitled to more dignity, and to the reputation of superior knowledge, and to be more wise than the handicraftsmen, because the former are acquainted with the causes of the things that are being constructed; whereas the latter produce things, as certain inanimate things do, indeed; yet these perform their functions unconsciously, as the fire when it burns. Things indeed, therefore, that are inanimate, by a certain constitution of nature, perform each of these their functions, but the handicraftsmen through habit; inasmuch as it is not according as men are practical that they are more wise, but according as they possess the reason of a thing, and understand causes.

And, upon the whole, a proof of a person’s having knowledge is even the ability to teach; and for this reason we consider art, rather than experience, to be a science; for artists can, whereas the handicraftsmen cannot, convey instruction.

And further, we regard none of the senses to be wisdom, although, at least, these are the most decisive sources of knowledge about singulars; but they make no affirmation of the wherefore in regard of anything, as, for example, why fire is hot, but only the fact that it is hot.

Therefore, indeed, is it natural for the person who first discovers any art whatsoever, beyond the ordinary power of the senses, to be the object of human admiration, not only on account of something of the things that have been discovered being useful, but as one that is wise and superior to the rest of men. But when more arts are being discovered both some, indeed, in relation to things that are necessary, and others for pastime we invariably regard such more wise than those,’ on account of their sciences not being for bare utility. Whence all things of such a sort having been already, procured, those sciences have been invented which were pursued neither for purposes of pleasure nor necessity, and first in those places where the inhabitants enjoyed leisure: wherefore, in the neighbourhood of Egypt the mathematical arts were first established; for there leisure was spared unto the sacerdotal caste. It has then, indeed, been declared in the Ethics what is the difference between an art and a science, and the rest of the things of the same description.

But, at present, the reason of our producing this treatise is the fact, that all consider what is termed wisdom to be conversant about first causes and principles; so that as has been said on a former occasion the experienced seem to be more wise than those possessing any sense whatsoever, and the artificer than the experienced, and the master-artist than the handicraftsman, and the speculative rather than those that are productive. That, indeed, wisdom, therefore, is a science conversant about certain causes and first principles is obvious.

Chapter II

Now, since we are engaged in investigating this science, the following must form a subject for our consideration; namely, about what kind of causes, and what kind of first principles, is this science I mean wisdom conversant. If, doubtless, one would receive the opinions which we entertain concerning the wise man, perhaps from this our proposed inquiry would be evident the more.

Now, in the first place, indeed, we go on the supposition that the wise man, especially, is acquainted with all things scientifically, as far as this is possible, not, however, having a scientific knowledge of them singly. In the next place, a person who is capable of knowing things that are difficult, and not easy for a man to understand, such a one we deem wise (for perception by the senses is common to all, wherefore it is a thing that is easy, and by no means wise). Further, one who is more accurate, and more competent to give instruction in the causes of things, we regard more wise about every science. And of the sciences, also, that which is desirable for its own account, and for the sake of knowledge, we consider to be wisdom in preference to that which is eligible on account of its probable results, and that which is more qualified for preeminence we regard as wisdom, rather than that which is subordinate, for that the wise man ought not to be dictated to, but should dictate unto others; and that this person ought not to be swayed in his opinions by another, but one less wise by this man. Respecting this wisdom and wise men do we entertain such and so many suppositions.

But of these characteristics the scientific knowledge of all things must needs be found in him most especially who possesses the universal science for this person, in a manner, knows all things that are subjects of it. But, also, the most difficult nearly for men to know are the things that are especially universal, for they are most remote from the senses. But the most accurate of the sciences are those respecting things that are primary, in the most eminent sense of the word; for those from fewer principles are more accu- rate than those said to be from addition, as arithmetic than geometry. But, also, that science, without doubt, is more adapted towards giving instruction, at least, which speculates about causes; for those do afford instruction who assign the causes in regard of each individual thing. Now, understanding and scientific knowledge, for their own sakes, most especially reside in the science of that which is most particularly fitted for being scientifically known. For he who selects scientific knowledge, for its own sake, will especially choose that which is preeminently science; but such is that which is the science of that which is particularly fitting as an object of scientific knowledge, and particularly fitting as objects of scientific knowledge are first principles and causes; for on account of these, and by means of these, are the other objects of knowledge capable of being made known: but not these by means of those things that are subordinate to them. Most fit for preeminence likewise amongst the sciences, and fit for preeminence in preference to that which is subservient, is the science which communicates the knowledge of that on account of which each thing is to be done; but this constitutes the good in each particular, but, in general, that which is the best in every nature.

From all, therefore, that has been stated, the sought-for appellation lights upon the same science; for it is necessary that this be a science speculative of first principles and of causes, for the good, also, viewed as a final cause, is one from amongst our classified list of causes.

But that the science under investigation is not a science employed in producing,’ is evident from the case of those who formed stems of philosophy in the earliest ages. For from wonder men, both now and at the first, began to philosophize, having felt astonishment originally at the things which were more obvious, indeed, amongst those that were doubtful; then, by degrees, in this way having advanced onwards and, in process of time, having started difficulties about more important subjects, as, for example, respecting the passive conditions of the moon, and those brought to pass about the sun and stars, and respecting the generation of the universe. But he that labours under perplexity and wonder thinks that he is involved in ignorance. Therefore, also, the philosopher that is, the lover of wisdom is somehow a lover of fables, for the fable is made up of the things that are marvellous. Wherefore, it for the avoidance of ignorance; men from time to time have been induced to form systems of philosophy, it is manifest that they went in pursuit of scientific knowledge for the sake of understanding it, and not on account of any utility that it might possess. But the event itself also bears witness to the truth of this statement; for on the supposition of almost all those things being in existence that are requisite towards both ease and the management of life, prudence of such a sort as this began to be in requisition. Therefore is it evident that we seek scientific knowledge from no other actual ground of utility save what springs from itself.

But as we say a free man exists who is such for his own sake, and not for the sake of another, so, also, this alone of the sciences is free, for this alone subsists for its own sake.

Wherefore, also, the acquisition of this science in may be justly regarded as not human, for, in many instances, human nature is servile.’ So that, according to Simonides, the Deity only should enjoy this prerogative; yet that it is unworthy for a man not to investigate the knowledge that is in conformity with his own condition. But if, in reality, the poets make any such assertion, and if the Godhead is in its nature constituted so as to envy, in this respect it is especially natural that it should happen, and that all those that are over-subtle should be unfortunate: but neither does the Divine essence admit of being affected by envy, but according to the proverb the bards utter many falsehoods. Nor ought we to consider any other science more entitled to honour than such as that under investigation at present. For that which is most divine is also most worthy of honour. But such will be so in only two ways; for that which the Deity would especially possess is a divine one amongst the sciences; and if there is any such science, this would be the case with the science of things divine. But this science, such as we have described it, alone is possessed of both of these characteristics; for to all speculators doth the Deity appear as a cause, and a certain first principle and such a science as this, either God alone, or he principally, would possess. Therefore, indeed, may all sciences else be more requisite than this one; but none is more excellent.

It is, indeed, necessary, in a manner, to establish the order of this science, in its development, in a direction contrary to the speculations hat have been carried on from the beginning. For, indeed as we have remarked all men commence their inquiries from wonder whether a thing be so, as in the case of the spontaneous movements of jugglers’ figures to those who have not as yet speculated into their cause; or respecting the solstices, or the incommensurability of the diameter; for it seems to be a thing astonishing to all, if any quantity of those that are the smallest is not capable of being measured. But it is necessary to draw our inquiry to a close in a direction the contrary to this, and towards what is better, according to the proverb. As also happens in the case of these, when they succeed in learning those points; for nothing ‘would a geometrician so wonder at, as if the diameter of a square should be commensurable with its side. What, therefore, is the nature of the science under investigation has been declared; as, also, what the aim should be which the present inquiry and the entire treatise should strive and attain.

Chapter III

BUT since it is manifest that one ought to be in possession of a science of primary causes (for then we say that we know each individual thing when we think that we are acquainted with the first cause); and since causes are denominated under four different heads, the first of which we assert to be the substance and the essence of a thing (for the inquiry of the wherefore, in the first instance of a thing, is referred to the last reason, but the first wherefore of a thing is a cause and first principle); and the second cause we affirm to be the matter and the subject; and the third is the source of the first principle of motion; and the fourth, the cause that is in opposition to this, namely, both the final cause and the good; for such is an end of every generation;

Therefore, although there has been a sufficient amount of speculation concerning these in our treatise on Physics let us, however, bring forward those who before our time have approached to an examination of entities, and have formed systems of philosophy respecting truth. For it is obvious that they also affirm that there are in existence certain first principles and causes; therefore will it, at any rate, be of service to our present treatise should we take a review of these philosophers; for either we shall thereby discover a certain different description of cause, or we shall, in preference, repose our confidence in those that have been already enumerated.

Now, the majority of those who first formed systems of philosophy consider those that subsist in a form of matter to be alone! the principles of all things; for wherefrom all entities arise, and wherefrom they are generated, as from an original, and whereto they are corrupted, ultimately the substance, indeed, remaining permanent, but in its passive states undergoing a change, this they assert to be an element, and this a first principle of all things.

And for this reason they are of opinion that nothing is either produced or destroyed, in as much as such a constitution of nature is always in a state of conservation; as we say, that Socrates neither is absolutely brought into being when he may become handsome or musical, nor that he is destroyed when he may throw aside these habits on account of the fact of the subject, namely, Socrates himself remaining permanent; so neither is it the case with anything else that it is either generated or corrupted anew. For it is necessary that there should be a certain Nature either one or more than one from which the other entities are produced, that remaining in a state of conservation. The plurality, indeed, and the species of such a first principle, all do not affirm to be the same.

But Thales, indeed, the founder of this kind of philosophy, affirms the nature just mentioned to be water,(wherefore, also, he declared the earth to be superimposed upon water) probably deriving his opinion from observing that the nutriment of all things is moist, and that even actual heat is therefrom generated, and that animal life is sustained by this (but that wherefrom a thing is produced, this is a first principle of all things); and doubtless for this reason, likewise, holding such a theory, both from the fact of the seeds of all things possessing a moist nature, and of water being a first principle of their nature to things that are humid.

But there are some who suppose those who lived in the most ancient times, and far previous to the present generation, and who first formed schemes of theology, to have also entertained opinions after this manner concerning Nature; for these philosophers constituted both Oceanus and Tethys as the parents of generation, and water as the object of adjuration amongst the gods, called Styx by the poets themselves; for most entitled to respect is that which is most ancient, now an object of adjuration is a thing most entitled to respect. Whether, therefore, there is this certain early and ancient opinion concerning Nature, in all likelihood would be an obscure point to decide. Thales, indeed, is said to have declared his sentiments in this manner concerning the first cause; for no one would deign to place Hippo along with these, on account of the meanness of his intellect.

But Anaximenes and Diogenes placed air before water, and especially as a cause of simple bodies; whereas, Hippasus of Metapontum, and Heraclitus of Ephesus, fire; but Empedocles introduced four bodies, that is, one in addition to those three already mentioned, adding earth as a fourth; for that these ever continued permanent; and further, that they are not produced, save that, either in plurality or in paucity, they are compounded together, or dissolved into one and from one component element.

But Anaxagoras of Clazomente in age, indeed, being prior to this speculator, but in his works subsequent to him maintains that first principles are infinite. For he asserts that almost all things being homogeneous as water or fire in this way are produced and destroyed by concretion and dissolution merely; but that, in other respects, no entities were either brought into existence, or caused to cease to exist, but continued as things that are everlasting.

From these things, indeed, therefore, one would suppose that the only cause with these philosophers was that said to exist in a form of matter. But as these speculators advanced in this way, the thing itself guided them, and constrained them to investigate further for though every possible corruption and generation is from something subsisting, as one or more, yet why does this happen, and what is the cause of this, for undoubtedly the subject, at least, itself is in no wise instrumental in making itself undergo a change Now, I say, for example, that neither the wood nor the brass is the cause of either of these bodies undergoing a change; neither does the wood, indeed, produce a bed, and the brass a statue; but there is something else that is a cause of change. But the investigation of this is the investigation of a different principle, that is, the second cause, as we have stated, the principle of the origin of motion.

Those, indeed, therefore, who from the earliest times have altogether adopted such a method as this, and affirm the subject to be one, have created no difficulty for themselves; but some of these, at least, who say that it is one, as if overpowered by this investigation, assert that the one is immoveable, and the entire of nature, not only according to generation and corruption, for this is an ancient dogma, and one which all acknowledge, but also according to every other change, whatever; and this a tenet peculiar to themselves. Of those, indeed, therefore, who affirm the universe to be one merely, to none has it occurred to see clearly into a cause of such a kind, unless, perhaps, to Parmenides, and to him so far as that he lays down not one merely, but, somehow, even two causes to exist. And for those, truly, who make them more numerous is it allowable rather to assert the existence of such a cause as the efficient cause, I mean those who make causes to be the hot and the cold or fire and earth; for they employ the fire as possessing a motive nature, but water and earth, and such like, as something that is contrary to this.

But after these philosophers, and after the assertion of principles of this sort, as if on the grounds of their insufficiency to generate the nature of entities, again constrained by actual truth, as we have said, they investigated the principle next following, in the way of a consequence. For of the excellent and beautiful order of some things, and of the production of others of the entities, it is not natural to assign, perhaps, either earth or anything of this kind as a cause; nor is it natural that they should think that it is; nor was it seemly, on the other hand, attribute so important a part to chance and fortune.

Now, whosoever affirmed mind, as in animals so also in nature, to be the cause of the system of the world, and of the entire harmony of it, the same appeared, as it were, of sober temperament, in comparison with the vain theorists of the earlier ages. Indeed, then, we know that Anaxagoras openly adopted these principles. Hermotimus of Clazomenea, however, has the credit assigned him of having put forward a similar theory of causation at an earlier period.

Those, indeed, therefore, who have entertained these opinions have laid down as a first principle of entities, at the same time the cause of their orderly arrangement, with such a one as that of the origin of motion in things.

Chapter IV

SOME one, however, might indulge in the surmise that Hesiod was the first to broach such description of cause as the above; and that this is the case with whatsoever other speculator, if any, that may have placed love or desire as a first principle in entities; as, for instance, also Parmenides: for this philosopher, likewise, in drawing up his scheme of the generation of the universe, says, “The first thing of all the gods, indeed, plann’d he Love.”
But Hesiod’s words are,
“First, indeed, of all was Chaos; but next in order,
Earth with her spacious bosom. Then
Love, who is pre-eminent amongst all the Immortals;”
just as if it were necessary that in entities there should subsist some cause which will impart motion, and hold bodies in union together. How, indeed, then, in regard of these, one ought to distribute them, as to their order of priority, can be decided afterwards.

But, also, since things contrary to those that are good appeared inherent in Nature, and not only order and the beautiful, but also disorder and what is base; and since the evil things were more numerous than the good, and the worthless than the fair, accordingly, some one else introduced harmony and discord, as a cause severally of each of these. For if any one would follow the subject up, and form his opinion according to the faculty of thought, and not according to the obscure assertions of Empedocles, he will find harmony, indeed, to be a cause of the things that are good, and discord of those that are evil. Wherefore, if any should say that Empedocles both, in a certain sense, affirms, and that he was the first to affirm, that the evil and the good are first principles, perhaps he would make such an assertion correctly, if the cause of all things that are good be the good itself, and of those that are evil the evil.

These persons, indeed, therefore, as we have said, even thus far have adopted into their Systems two causes, as we have defined them in our Physics, I mean the material cause, and the principle of the origin of motion; that is, the efficient cause: obscurely, no doubt, and by no means clearly, but, in a manner, like the conduct of those who are unexercised in battles; for these latter, also, advancing forwards against their adversaries, strike frequently skillful blows: but neither do those combatants act thus from a scientific system, nor do these early speculators appear like men who understand that they are making the assertions which they actually are; for in no respect, almost, do they appear to employ these first principles, save to a small extent.

For Anaxagoras, also, employs mind as a machine’ for the production of the orderly system of the world; and when he finds himself in perplexity as to the cause of its being necessarily so, he then drags it in by force to his assistance; but, in the other instances, he assigns, as a cause of the things that are being produced, everything else in preference to mind.

And Empedocles, to an extent further than this last-named philosopher, employs his causes, however, neither adequately, nor does he discover in them that which confessedly is involved in them. Frequently, at least, in his system the harmony indeed separates, and the discord unites things together. For when the universe may be dissolved into its component elements, by reason of discord, then fire is commingled into one and each of the rest of the elements; but when all things, by reason of harmony, may unite into one, it is necessary that the parts from each undergo separation again. Empedocles then, indeed, in contradistinction to the early speculators, first introduced this cause, having divided it, not having constituted, as single, the first principle of motion, but first principles thereof which are different and opposite. But, moreover, the reputed elements, in form of matter, he was the first to assert the existence of as being four in number; he did not, doubtless, employ at least four, but regarded them as if there were only two; fire by itself; and those things that are opposed to this, as one nature, namely, both earth, and air, and water. But one may acquire this information by drawing the speculation itself from his poetry. This philosopher, indeed, therefore, as we have stated, enumerated his first principles in this way, and affirmed them to be so many in number.

But Leucippus, and his companion Democritus, assert that the full and the empty are elements; terming, for instance, the one, indeed, an entity, and the other a nonentity; and of these, the full and solid they call an entity, and the empty and the attenuated, a nonentity. Wherefore, they say that entity, in no respect less than nonentity, has, an existence, because neither has the vacuum a being more than corporeity, and that these are the causes of entities as material causes.

And as they who make the substance, which is the subject, one, generate all things else by means of the passive conditions of this substance, assigning the rare and the dense as first principles these affections, in the same manner these also affirm that differences are causes of the other things. They, indeed, say that these are three, even figure, and order, and position; for they affirm that entity differs merely in rhythm, and diathege, and trope;’ out of these the rhythm is figure, and the diathege order, and the trope position. For, indeed, the letter A differs from the letter N in figure, and AN from NA in order, and Z from N in position. But respecting motion, whence or how it exists in entities, in like manner, with the rest of the early speculators, have these carelessly neglected such inquiries. Respecting, then, two causes of the four, according to the statements we have just made, so fax has it appeared that an inquiry has been prosecuted by our predecessors.

Chapter V

BUT amongst these, and prior to them, those called Pythagoreans, applying themselves to the study of the mathematical sciences, first advanced these views; and having been nurtured therein, they considered the first principles of these to be the first principles of all entities. But since, among these, numbers by nature are the first, and in numbers they fancied they beheld many resemblances for entities and things that are being produced, rather than in fire, and earth, and water; because, to give an instance, such a particular property of numbers is justice, and such soul and mind; and another different one is opportunity; and it is the case, so to speak, in like manner with each of the other things; Moreover, also, in numbers discerning the passive conditions and reasons of harmonies, since it was apparent that, indeed, other things in their nature were in all points assimilated unto numbers, and that the numbers were the first of the entire of Nature, hence they supposed the elements of numbers to be the elements of all entities, and the whole heaven to be an harmony and number. And as many phenomena as they could demonstrate to be conformable, both in their numbers and harmonies, with the passive conditions and parts of the heaven, and with its entire arrangement, these they collected and adapted to their philosophy: and if there was any interval left anywhere, they supplied the deficiency, in order that there might he a chain of connexion running through their entire system? Now, I say, as an illustration, since the decade seems to be a thing that is perfect, and to have comprised the entire nature of numbers, hence they also assert that the bodies that are borne through the heaven are truly ten in number; and whereas nine only are apparent, on this account they constitute the confronting earth tenth. But respecting these theorists, we have arrived at more accurate decisions in other parts of our works. But the reason why we have gone in review through these philosophers is this, in order that we may receive also from them what they have already laid down as being first principles, and in what manner they fall in with the causes just enumerated. Undoubtedly do these appear to consider number to be a first principle, and, as it were, a material cause of entities, and as both their passive conditions and habits, and that the even and the odd are elements of number; and of these, that the one is finite and the other infinite, and that unity, doubtless, is composed of both of these, for that it is both even and odd, and that number is composed of unity, and that, as has been stated, the entire heaven is composed of numbers.

But others. of these very philosophers affirm that first principles are ten in number, denominated in accordance with the following co-ordinate series, namely:
Bound.| Infinity.
Odd.| Even.
Unity.| Plurality.
Right.| Left.
Male.| Female.
Rest.| Motion.
Straight.| Crooked.
Light.| Darkness.
Good.| Bad.
Square.| Oblong.

In the same manner seems Alcmeon of Crotona to have formed his opinion; and this philosopher certainly, either from those just named, or they from this person, have derived this their theory for Alcmceon had reached the age of manhood when Pythagoras was an old man; but he enumerated his sentiments in a manner similar with the Pythagoreans. For he affirms that the greater portion of things human may be reduced to two classes, calling them contrarieties; not distinguished as these had distinguished them, but such as were of any casual sort whatever, as for example:
White.| Black.
Sweet.| Bitter.
Good.| Bad.
Small.| Great

This philosopher, indeed, then, has indefinitely thrown out his opinions about the rest; but the Pythagoreans have declared both how numerous, and which these contrarieties are.

From both of these, therefore, it is possible to acquire thus much information, that contraries are first principles of entities; but how numerous, and which these are, may be ascertained only from other speculators. How, indeed, in respect of the causes enumerated, it is possible to draw up a compendious application of their principles has not, in distinct terms, been clearly declared by them; but they seem to arrange the elements as in a form of matter: for of these, as inherent, they say that the substance consists, and has been moulded.

Of the ancients, therefore, indeed, even of those who assert the elements of Nature to be many, it is sufficient from these statements to examine into their intention.

But there are some who have declared their opinions about the universe as though it were one Nature; but all have not put forward their theories in the same manner, either in regard of that which is constituted in an orderly way, or of that which is in accordance with the course of Nature. With, indeed, then, the present investigation of causes does this theory regarding them by no means adapt itself. For they do not, as some of the physiologers who supposed entity to be one, nevertheless, generate them from unity as from matter; but these, who say that entity and unity are the same, assert their production to take place after a different manner; for those, indeed, have added motion, at least, in their generation of the universe; but these say that it is immovable.

Of a truth, however, so far at least the theory of this school is akin to our present investigation; for Parmenides, indeed, appears to adopt a system of unity in accordance with reason: whereas Melissus, a theory of it according to matter. Wherefore, also, indeed, one says that the universe is finite, and the other that it is infinite. Xenophanes, first of these, however, having introduced this system of unity,(for Parmenides is said to have been his pupil,) made nothing plain, neither did he seem to have apprehended the nature of either of these; but looking wistfully upon the whole heaven, he affirms that unity is God.

These, indeed, therefore, as we have stated, must be omitted in regard of our present investigation, two of them entirely, even as being a little too uncivilized; namely, Xenophanes and Melissus. Parmenides, however, appears to express himself, in some passages, with more circumspection; for, with the exception of entity considering nonentity to have no existence he thinks entity to be necessarily one, and nothing else. Concerning which philosopher, we have spoken with more clearness in our Physics. Yet, compelled to follow the phenomena, and supposing unity to subsist according to reason, but plurality according to sense, he again lays down two causes, and two first principles, heat and cold; as, for example, in other words, he means fire and earth; but of these he arranges the one under the category of entity, that is, the hot, and the other under that of nonentity, viz, the cold.

From the statements, indeed, therefore, that have been made, and from those who have already devoted themselves to rational speculations, and are wise men, we have derived these views; from the earliest philosophers have we appropriated, indeed, both the corporeal first principle,(for water and fire, and such like, are bodies,) and from some of these one such, and from others many corporeal principles; both, however, agreeing in classing them as forms of matter. But from certain amongst these early speculators, who at the same time establish both this cause, and along with this that of the origin of motion, we have appropriated even this very efficient cause; from some, indeed, as a single principle, but from others, as one that is twofold. Up to the period of the Italic sects, and independent of them, the rest of the investigators have spoken with more moderation regarding these first principles, except, as we have said, in the case of those who happen to have employed two causes; and one of these, the second cause namely, the origin of motion some, indeed, make single, and others twofold.

But the Pythagoreans, in the same manner, have spoken of two first principles; but thus much have they added, which, also, is peculiar to themselves, namely, that they do not regard the finite, and the infinite, and the, one, to be certain different natures; as, for instance, fire, or earth, or any other such thing: but that the infinite itself, and the one itself, constitute the substance of those things of which they are predicated. Wherefore, also, they affirmed that number is the substance of all things. Respecting, then, these pointer likewise in this manner have they declared their opinions; and respecting quiddity they began, indeed, to make assertions and to frame definitions; but they treated of matters with great simplicity. For they both framed their definitions superficially, and in whatever first an alleged definition should be inherent, this they considered to be the substance of the thing; as if any one should think that twofold is the same thing with the duad, since the twofold first is inherent in the two; yet perhaps the being in what is twofold is not the same thing as being in a duad; but if not, unity will be plurality, which also was the result with them.

From our predecessors, indeed, therefore, and from the rest, it is possible for us to acquire thus much information.

Chapter VI

AFTER the schools of philosophy enumerated, supervenes the system of Plato in most points treading on the heels of these Pythagoreans: but also having peculiar temets of its own, differing from the philosophy of the Italics. For from a young man having at the first been associated with Cratylus, and being conversant with the opinions of Heraclitus, that all sensible objects are in a state of continual flux, and that scientific knowledge concerning them had no existence, he, indeed, subsequently in this way came to entertain these suppositions. But while Socrates was engaged about the formation of systems of Ethics, indeed, and that he broached no theory as regards the entire of Nature, seeing that he was searching, doubtless, In morals for the universal, and that he was.the first to apply his understanding to the subject of definitions, Plato, having applauded him on account of this his investigation of universals, was led to entertain thus much of his supposition, as that this took place in regard of other things, and not in regard of certain of the objects that are cognisant by the senses; for it is impossible, in his opinion, that there should be a common definition of any of the sensible natures, seeing that they are continually in a state of undergoing a change. This philosopher indeed, therefore, termed such things amongst entities, ideas; and asserted that all things are styled sensible according as they were different from these, or as they subsisted in accordance with these: for his theory was this, that, according to participation, the most of things synonymous are homonymous with the forms. Employing, however, the import of the term participation, he changed the name merely; for the Pythagoreans, indeed, affirm that entities subsist by an imitation of numbers: but Plato, by a participation of them, changing the name. At all events, as to participation at least, or imitation, what it may be, in the case of forms, they both in common omitted to investigate.

But, moreover, besides sensibles and forms, he affirms that mathematical entities are things of an intermediate nature; differing, on the one hand, from sensibles in being eternal and immovable; but, on the other, from forms, in the fact that the most of such are similar, but that every form itself constituted one thing merely.

But since the forms are causes of other things, the elements of all these he supposed to be elements of entities. Therefore, indeed, he regarded the great and the little to be first principles as matter, but unity as substance; for from these, by participation of unity, that the forms are numbers. That, doubtless, unity at least is as substance, and that not any other entity is denominated so, Plato affirmed, similarly with the Pythagorics; and the dogma, that numbers are causes to other things of their substance, he in like manner asserted with them. But, in place of the infinite considered as one, the having made a duad, and the having made the infinite, out of the great and the small, this was peculiar to him: and, moreover, Plato affirmed the existence of numbers independent of sensibles; whereas the Pythagoreans say that numbers constitute the things themselves, and they do not set down mathematical entities as intermediate between these.

The principle of his having made unity, therefore, and numbers, as different from things, and not as the Pythagoreans, who regarded them as well as the introduction of forms, ensued on account of his logical investigations; for his predecessors took no share in dialectical science. But the constituting, a duad, as a different nature from the one, arose from the fact that the numbers, with the exception of those that are first, are suitably generates from this as from, a certain express image.

And yet it happens in a contrary way; for it would not be reasonable that it should take place thus: for, indeed, at present, from matter they make many things, whereas form generates only once. And from one matter there appears to be produced one table; but he who introduces form, though being one, makes many tables.

In like manner, also, the male stands in relation to the female for the one is impregnated from a single copulation, whereas the male impregnates many. These, however, are imitations of those first principles. Plato, indeed, therefore, respecting these objects of investigation, laid down distinctions in this way.

But it is manifest, from the things that have been stated, that Plato only employed two causes; namely, both the formal cause and the material cause: for, according to him, forms are the causes of what anything is to the rest of the entities, and unity to the forms; and that there is a certain cause which subsists according to matter, which is that subject through which the forms have a subsistence that are resident in sensibles, and through which unity is said to be in the forms, because the actual duad constitutes the great and the small. Further, the cause of “the well and the ill” he ascribed severally to the several elements; which particular point we affirm certain philosophers such as Empedocles and Anaxagoras to have investigated more elaborately than the early speculators.

Chapter VII

CONCISELY, indeed, therefore, and by way of summary,’ we have recounted both who they are that have declared their opinions and in what manner they happen to have spoken concerning both first principles and truth. Nevertheless, however, we have received thus much information from them, that no one of those who have declared their sentiments, concerning a first principle and a cause, has made any assertion beyond those definitions that have been set down in our Physics; but notwithstanding that all of them have unfolded their views with obscurity, indeed, yet in a manner they appear as persons engaged in cursorily treating those four causes enumerated above and elsewhere.

For, indeed, some speculators speak of the first principle as matter, whether they may suppose one principle or more to exist, and whether they consider it as body, and whether as a thing that is incorporeal: as, for instance, Plato, indeed, in his mention of the great and the small; and the Italics, in their theory of the infinite; and Empedocles, in that of fire, and earth, and water, and air; and Anaxagoras, in his system of the infinity of homogeneous things. Now, truly, all these touched upon a cause of this kind: and, further, as many as affirmed the existence, as a first principle, of air, or fire, or water, or a substance of greater density than fire, but of greater rarity than air; for certain philosophers have also declared a thing of this sort to be the first element. All these, indeed, therefore, adopted this cause merely in a superficial way.

But certain others introduce the second cause; namely, the origin of the principle of motion as, for instance, as many as make a first principle of harmony and discord, or mind or love. But of the essence and the substance that is, of the formal cause not one, indeed, has rendered a clear account: most especially do those make assertions respecting it who adopt the hypothesis of forms, and the things inherent in forms; for neither do they suppose that forms, and the things inherent in forms, subsist as matter to sensibles; nor, as though from thence were derived the principle of motion;(for, in preference, they assert them to be causes of immobility, and of things being in a state of rest;) but, in regard of the essence, to each of the other things do forms supply this, and unity imparts it to the forms.

But the final cause of actions, and changes, and motions, in a certain manner, they assert to be a cause: yet in this way they do not assert it to be a cause; nor do they speak of it in a way conformably to what it naturally is. For they, indeed, who assign mind or harmony as such, have laid down these causes as, doubtless, a something that is good; they do not, however, affirm that from these, as final causes, anything amongst entities either is in existence, or is being produced, but that, as it were, from these the Emotions of these things were derived. So, also, in like manner, they who say that either unity or entity is such a nature of this kind, affirm it to be a cause of substance, indeed; yet they do not, for a certainty, affirm that anything either exists or is produced from this as a final cause. Wherefore, it happens unto them, in a manner, both to affirm, and not to affirm, that the good is a cause of this sort; for they do not make the assertion absolutely, but by accident.

That, therefore, our distinctions have been laid down correctly respecting causes, both as to how numerous and what sort they are, do even all these early philosophers appear to us to bear witness, in not being able to fix upon any other cause. And, in addition to the testimony of these speculators, it is evident that first principles must be investigated, either all in this way, or in some such mode as has been adopted by these philosophers. Now, how each of these has declared his opinions, and how the case stands, in regard of the possible doubts respecting first principles, let us, after this, proceed to pass through a review of such points.

Chapter VIII

As many, indeed, therefore, as set down the universe as both one and a certain single nature, as matter, and this such as is corporeal and involving magnitude, it is obvious that they labour under manifold errors. For they have established the elements of bodies merely, but not of incorporeals, when even there are in existence, I mean, things that are incorporeal. And in endeavouring to assign causes of generation and corruption, and drawing up, concerning all bodies in nature, systems of physiology, they take way the cause of motion. Further, the not positing also the substance as a cause of anything, nor as such the formal principle, or the very essence of a thing, this was erroneous.

And, in addition to the foregoing, the assertion that anything whatsoever might readily be a first principle of simple bodies, except earth, but at the same time not examining into their mode of generation one from another, how they are produced, now I mean fire and water, and earth and air, for partly by concretion, and partly by separation, are things produced from one another, this was an error of theirs. But this, in regard of the being prior and posterior, will involve the greatest difference; for, indeed, earth would appear to he a thing most elementary of all, from which, as a first principle, elements are produced by concretion: but a thing of this kind would be most minute in its parts, and a thing most refined amongst bodies. Wherefore, as many as establish fire as a first principle would make assertions particularly in consonance with this theory. But each philosopher also acknowledges something of this sort to be an element of other things, I mean an element of bodies.

No one, at least of subsequent speculators, even of those who assert the universe to be one has thought fit to maintain earth to be an element, doubtless, on account of the size of the component particles, but each of the three elements has obtained a certain umpire; for, indeed, some assert fire to be this, but others, water, and some, air. Although why, pray, do they not assert this of earth, as the majority of men do for they say that earth constitutes all things. ‘But Hesiod, also, says that earth was the first produced amongst bodies: thus it has happened that the supposition is an ancient and vulgar one. According, indeed, therefore, to this account,if one affirms to be this either any one thing belonging to these save fire, or if one lays down, as such, a thing denser than air, indeed, but more refined than water, he would not make such an assertion as this correctly. But if that which is subsequent in generation be prior in Nature, and if that which has been digested and compounded together be a thing that is subsequent in its production, there would take place that which is the contrary of these, water, for instance, would be a thing prior to air, and earth, to water. With regard to those who are for establishing one such cause as we have declared, let these remarks be sufficient.

But the same assertion may be made even if any one posites these corporeal principles as being many in number; as, for example, Empedocles, who says that four bodies elementally, constitute matter. For, likewise, to this philosopher partly, indeed, the same consequences, but partly those that are peculiar to his own system, must needs happen. For, also, we see, in the case of things that are being produced one from another, that the fire and earth do not always continue as of the same body. But we have spoken on these subjects in our Physics. And respecting the cause of things that are being moved, whether we must assign one or two such, we should be inclined to think that we have not expressed ourselves either correctly or altogether irrationally. And, in short, must the principle of alteration be overturned by those who make assertions in this way; for not from heat will arise cold, nor from cold, heat. For what change the contraries themselves would undergo, and what would be the one nature which should become fire and water, that very philosopher (I mean Empedocles) does not declare.

But if any one should suppose that Anaxagoras mentions two elements, he would form his opinion most especially in accordance with a theory which, although that philosopher himself did not enunciate distinctly, yet, indeed, would, as necessary consequence, follow in the footsteps of those who introduced this dogma. For, otherwise, would even the assertion be absurd, that all things from the beginning have been in a state of mixture; both on account of its happening that all things prior to this should pre-exist in an unmixed state, and on account of its not being consonant to Nature, that anything at random should be mingled with anything at random too; and, in addition to these reasons, we may add, that, according to this doctrine, their passive states and accidents would be separated from substances,(for to the same things belong mixture and separation.) If any one, however, follows up the subject, arranging into clauses together those statements which he wishes to make, he would, in all probability, utter assertions that would assume an air of novelty. For when there was nothing in existence that has been separated, it is obvious that no true assertion could be put forward in regard of that substance now, I say, for instance, that it would not necessarily be a thing either white, or black, or darkish, or any other colour, but a thing necessarily colourless, for otherwise it would possess some one of these colours. In like manner would it be with that which is insipid, according to this same mode of reasoning: nor could it be so with anything else of those things that are similar; for neither is it possible that it could possess any actual thing of a certain quality or quantity, or that anything else be so. For therein would be inherent something of those termed partial forms; yet this is impossible when all things have been in his system mingled together, for already it would subsist in a state of separation: but, with the exception of mind, he affirms all things to be mingled, and that mind only is unmixed and pure. Now, from these statements it is consequential with him that he should denominate, as the first principles, both unity (for this is simple and unmixed) and another thing, as if it were an entity such as we are for establishing viz., the indefinite prior to its having been defined, and to partaking of a certain form. Therefore, the assertion is made neither correctly nor clearly, notwithstanding that he intends something similar with both those who subsequently make statements to this effect, and more in harmony with the present phenomena. For these, however, happen only to be familiar with the theories appertaining to generation, and corruption, and motion for, also, with regard to such a substance, they investigate almost only both the first principles and the causes.

But as many as frame their speculation respecting all entities, but of entities have set down some, indeed, as being cognisant by sense, and others as not being sensibles, it is manifest that they institute for themselves an inquiry concerning both kinds.

Wherefore, one might be induced, in preference, to linger upon an investigation respecting these, as to what they say, well or not well, in regard of the examination of those speculations now proposed by us.

Those, indeed, called Pythagoreans, in a far more outlandish manner employ their first principles and elements than the physiologists. But the cause is, because they have not derived them from sensibles; for those natures that are mathematical amongst entities are without motion, except those pertaining to astrology. They, however, discuss and treat of all points concerning Nature; for they both generate the heaven, and respecting the parts thereof, and the passive conditions and the operations thereof, they closely observe that which takes place; and upon these they lavish their first principles and causes, as if acknowledging to the rest of the natural philosophers that whatsoever thing is such as is cognisant by the senses, that this constitutes entity, and such as that which is called heaven comprises. But the causes and the first principles as we have said they affirm are sufficient both to secure a transition even to a higher order of entities, and that they are more sufficient than those that are in harmony with physical theories.

From what mode, however, there will be motion, merely on the supposition of the existence of the subjects of finite and infinite, and odd and even, they in no wise declare; or how it may be possible, without motion and change, that there should be generation and corruption, or the operations of those bodies that are whirled along the heaven.

But further, whether one grants to them that from these results magnitude, or whether this should require to be demonstrated, nevertheless, in a certain manner, some bodies will be light, indeed, and some involving weight; for the things from which they adopt for themselves their theories, and make assertions, they in no respect affirm in regard of sensibles in preference to mathematical bodies. Therefore, concerning fire or earth, or the other bodies of such a kind, they have declared nothing whatsoever, inasmuch as affirming, in my opinion, nothing that is peculiar to them concerning sensible natures.

But further, how must we receive as causes the passive conditions of number, and the number itself as the cause of entities which subsist in heaven, and of things that are being produced there both from the beginning and at present, and at the same time allow that there is no other number save this number from which the order of the universe consists? For since, indeed, in this portion of the creation (according to these philosophers) there may be in existence opinion and opportunity, but a little above, or a little below, injustice and separation, or mixture; and since they may adduce a demonstration that each one of these is number, and it happens, from this mode of reasoning in this place, that there subsists already a multitude of constituted magnitudes, from the fact of these affections following each of these places respectively, on the supposition of the foregoing we may ask whether, therefore, is this owing to the same number as that which is in the heaven, and which we ought to receive because that each of these exists, or, besides this, is there another number? For Plato says, indeed, that there is a different number: he, however, also thinks both these, and the causes of these, to be numbers, but numbers that are, indeed, intelligible causes; whereas those are merely sensible, according to Plato. Respecting then, indeed, the Pythagoreans, let us leave off our present discussions; for it is sufficient thus far to have touched upon their system.

Chapter IX

BUT they who put forward ideas as causes, in their early investigations, indeed, to acquire the causes of these entities, in the first place have adduced other things equal in number to these; as if one, desiring to have reckoned certain things, when these were less numerous, would consider this impossible, but, by creating a greater number, should succeed in counting them; for almost equal, or not less numerous, are the forms than those things respecting which, in investigating their causes, they have advanced from these to those: for, according to each individual thing, there is a certain homonymous form, and, in addition to the substances, also, of other things, there is the unity involved in the notion of plurality, both in the case of these and of things that are eternal.

Moreover, in the ways in which it is demonstrated that there are forms according to none of these doth the subsistence of forms become apparent for, indeed from some there is no necessity, in the sequence of the reasoning, that a syllogism arise: but from other things, also, not of such as we should expect to find forms, of these are there forms generated. For according to the rational principles deducible from the sciences will there be forms of all things, of as many as there are sciences; and in accordance with the argument for ideas founded on the notion of unity involved in plurality, will there also be forms or ideas of negations: and according to the ability to understand something of what has been destroyed of things liable to decay will there also be forms, for of these there is a certain phantasm.

But further, as regards the most accurate of the arguments for the ideal theory, some of them, indeed, frame ideas of things relative, of which they do not say that there is an essential genus whereas others speak of there being a third man.

And, upon the whole, the theories respecting forms overturn the things which they who affirm the existence of forms would wish should have a subsistence in preference to the subsistence of the ideas; for it happens that the duad is not, the first, but that the number is, and that the relative is, before the essentral. And all those consequences ensue, as many as certain, who have followed up the opinions respecting forms have set in contrariety to first principles. Further, also, according to the supposition in virtue of which we speak of the existence of the ideas, not only will there be forms of substances, but of many other things also; for, also, there is the one conception not only respecting substances, but also in the case of other substances; and there are sciences not only of substance, but of different things also, and innumerable other things of this sort occur: but according to necessity, and the opinions respecting forms, it follows, on the supposition that forms are things capable of participation, that there should be ideas of substances only; for not according to accident, are they participated in, but things must participate in this respect in each idea, so far forth as each idea is not predicated about the subject. Now,I mean, for example, that if anything participates in the twofold itself, this also is a participant in what is eternal, but according to accident, for it is accidental for the twofold to be eternal. Therefore, the forms will to substance.

For the same things, both here and there, signify substance; or what will be the meaning of the assertion of the existence of a something that is independent of sensibles, drawn from the argument founded on unity, involved in the notion of plurality; and if there be the same form of the ideas, and of things that are participants of them, there will be something in common; for, by no means, in the case of perishable duads and, indeed, most duads, but such as are eternal is the dual said to be rather one and the same, than in the case of this and one of some particular thing. But if there be not the same form there would be an homonymy; and it will bejust like as if one should call both Callias and a piece of wood a man, discerning no community whatever between them.

But most of all would one feel perplexed as to what at all the forms contribute, either to hose things that are eternal amongst sensibles, or to things that are being produced and being corrupted. For neither are they to them a cause of any motion or exchange whatever. But, truly, neither are they of any assistance towards the science of other things (for neither are those the substance of these, for in such a case they would be in these), nor do they contribute towards the existence of other things, inasmuch as they are not inherent in things that are their participants, at least; for so, indeed, they would perhaps be supposed as causes, just as if the white were mixed with the white it might be called the cause of a white body. But, indeed, this theory is very easily overthrown, which Anaxagoras, indeed, first, and Eudoxus subsequently, and certain others, advanced; for it would be easy to collect together, also, many impossibilities in reference to such an opinion: but, truly, neither do other things subsist from forms in accordance with any mode of existence of those that are want to be mentioned.

But the assertion that these forms are exemplars, and that the rest of entities participate in them, is to speak vain words, and to utter poetic metaphors. For in what respect, may I ask does that which operates look towards the ideas as a model for it is possible that anything whatever that is similar both should exist and be produced, and yet that it be not made like in reference to that to which it is similar. Wherefore, also, on the supposition of the existence and non-existence of Socrates, just such another one as Socrates is would be produced. And, in like manner, is it evident that this would follow, even though Socrates were eternal; and, besides, there will be many exemplars of the same thing; wherefore also, the forms for instance, of man, such as animal and biped, and at the same time, also, ideal man will have a subsistence. Further, not only of things sensible are forms the exemplars, but also of forms themselves; as, for example, the genus as a genus will be an exemplar of species; wherefore, at exemplar and an image will be the same thing.

Further, it would seem impossible for the substance to be separate from that of which it is the substance; therefore, in what way can the ideas; when they are substances of things, exist separately from them?

But in the Phædo an assertion is made to this effect, that the forms are causes of existence and of production. On the supposition, however, of the existence of forms, nevertheless, those things that are participants will not be produced, if there be not in existence that which is likely to he the origin of motion; and many other things are produced, such as a house and a ring, of which we do not say that there are forms. Wherefore, it is evident that it is possible, also, for other things both to exist and be produced from such causes, likewise, on account of which, also, arise those entities mentioned just now.

Moreover, if forms are numbers, how willthey be causes? whether is it because entities are different numbers, as, for instance, this particular man is this particular number, indeed, and Socrates another, and Callias another, different from both, in what respect are those, therefore, the causes of these? for neither will it make any difference whether those may be eternal, and these not so. But if it is because the things here are proportions or ratios of numbers, as, for instance, a symphony, it is obvious that there will be a certain one thing, at least, amongst those of which there are ratios or proportions. Now, if this is one thing say matter it is palpable that the actual numbers, also, will be certain proportions of one thing with another; but I say, for example, if Callias is a proportion in numbers of fire, and earth, and water, and air, to certain other subjects will belong the same man likewise; and if the idea constitute a number, the ideal man, also, whether the idea may be a certain number or not, nevertheless, will be a ratio in numbers of certain things without being himself a number; nor will there be a certain particular number on account of these things.

Further, out of many numbers, one number results but from forms how is one form producedandifformsare not produced from forms, but from the units that are in numbers as, for instance, in the myriad how is it with the subsistence of the monads? for if they are of the same species, many absurdities will ensue; but if they are not of the same species, neither will they be the same with one another, nor all the rest the same with all: for wherein will they differ, since they are impassive? for such statements as these are neither rational nor consonant with the understanding. And, moreover, it is necessary to establish a certain other description of number, regarding which arithmetic is conversant, and all such things as are termed media by some; and how, or from what principles, will these arise? or why will they be media between the things here and these?

Further, the monads which are in each duad are from some prior duad, although such is impossible. Further, why is there an aggregated number, as one thing and further, in addition to the things that have been stated, if the monads are different, they ought to declare their opinions in this same way as those do, even as many as affirm the elements to be fourfold or twofold; for, also, each one of these mentions not what is common as an element for example, body but fire and earth, whether body is anything that is common or not. But now, an assertion is made just as if the one were in existence as homogeneous fire or water; but if this be the case, numbers will not be substances; it is, however, evident, that if unity itself be anything, and if this be a first principle, that unity is expressed in many ways, for that it should be otherwise is impossible.

But they who wish to refer substances to first principles set down lengths, indeed, as consisting from the long and the short, from something small and large, and a superficies as from what is broad and narrow, and a body from what is deep and low. In what way, however, will the superficies involve a line, or the solid a line and surface, for the wide and the narrow are a different genus from deep and low? As, therefore, neither number is inherent in these, because the much and the few are different from these, so it is manifest that neither will anything else of those superior natures be inherent in those that are inferior. But, truly, neither is the wide a genus of the deep; for body would be a certain surface in this case. Further, may I ask from what will points be compounded? This genus, indeed, then, did Plato also oppose, as being a geometric dogma; but he used to call it the first principle of a line: and this he often set down,(I mean the existence of indivisible lines,) although of necessity there must be some limit to these; wherefore, from whatever principle a line is, therefrom also is a point.

And upon the whole, seeing that wisdom investigates into the cause, in respect of things that are manifest, this consideration, indeed, have we omitted; for we say nothing regarding the cause of the origin of the principle of change: but, thinking to mention the substance of these, we say that there are different substances; but in what manner those may be substances of these we ineffectually describe, for as to such being accomplished by participation as also we have stated on a former occasion there is no advantage gained in saying this Neither, truly, are ideas such causes as we see to be a cause to the sciences, on account of which both every mind and every nature operate; nor that cause which we affirm to be one of the first principles do forms in anywise touch upon but to men, in the present age, mathematics have become the philosophy; although they say that persons ought to cultivate these sciences for the sake of other sciences.

But, further, one may suppose the subject-substance to be as matter that is more mathematical, and rather to be converted into a predicable, and to constitute a difference of substance and of matter, as, for instance, the great and the small,just as, also, the natural philosophers mention the rare and the dense, saying that there are these primary differences of the subject, for these are a certain excess and defect. And respecting motion, if, indeed, these will constitute motion, it is evident that the forms will be moved; but if they are not, whence has motion originated? for thereby the entire investigation about Nature has been abolished.

And what seems to be easy namely; the demonstration that all things are one does not turn out to be so; for, according to the interpretation, all things lo not become one, but a certain thing itself is one, if any one would grant that all things are so: and neither would he allow this, unless one would admit the existence of a universal as a genus; but this, in some cases, is impossible.

But neither have those things that are after the numbers any grounds in reason, namely, both lengths, and surfaces, and solids; nor is it so in regard of the mode of how they are, or shall be, or whether they involve any capacity; for these cannot possibly be either forms (for numbers they are not), or media (for those are mathematical), or things that are corruptible: but these, again, appear as this certain other fourth genus different from those other three.

But, upon the whole, the investigation of the elements of entities, seeing that they are expressed multifariously, it is impossible for any persons to discover a solution of who have not divided them; and, especially, if they investigate in this manner from what sort of elements they are compounded. For action, or passion, or the wide, it is not, doubtless, possible to receive from some things of which these consist; but, if this were the case, it would be possible to receive them as subsisting from substances only. Wherefore, either to investigate or to think that you possess the elements of all entities is not true.

But how can any one learn the elements of all things? for it is evident that it is not possible that he should be previously a person having prior knowledge thereof. For, as to one learning geometry, it is, indeed, possible to see beforehand other things; but of such things as the science consists of, and concerning which he is about to receive instruction, he can have no prior knowledge, so, also, is it in the case of other things. Wherefore, if there is a certain science of all things, as some affirm, nothing could this person know beforehand. Every system of learning, however, subsists, or is attainable by means of previous knowledge, either of all things, or of certain particular things: and either by demonstration is this accomplished, or by definitions; for those things whereof the definition consists it is requisite to understand beforehand, and that they be known. In like manner is it the case with knowledge by induction. But, truly, if also it happens that there is in our possession a congenital knowledge of things, it is astonishing how we, in possession of the most excellent of the sciences, are unconscious of such a treasure. Further, how will any one know from what particulars all things consist, and bow will this be manifest? for this also involves perplexity; for one would feel a doubt, just as also concerning some syllable: for certain affirm that S M A is composed of S and M and A, but others say that it possesses a different sound from its components, and none of those that are known.

Moreover, those things of which there is perception by sense, how could any one know if he were not furnished with the capacity of perceiving by sense? although one ought, if these are the elements of all things whereof they consist just as the compound sounds arise from their own proper elements.

That, therefore, all seem to seek the causes mentioned in our Physics, and, besides these, that we have no other to adduce, is likewise from the foregoing statements evident. But the early philosophers, I admit, have treated of these causes, obscurely, however; and, indeed, in a certain manner, all such four causes have been enumerated by speculators of an age prior to ours: and, in a certain manner, by no means has this been the case; for the earliest system of philosophy concerning all things was like unto one articulating with a stammer, inasmuch as it was new as regards first principles, and a thing the first in its kind. For Empedocles says that a bone exists from form by the principle of composition; but this is the essence and the substance of that thing. But, truly, if this be admitted, in like manner, also, is it necessary that of both flesh, and everything else of the other things, there should subsist this principle of concretion, or that it should not subsist as a principle of anything at all; for on account of this are both flesh and bone, and each of the other things, in existence, and not on account of the matter, which he says is fire, and earth, and water, and air. But, also, with any other, indeed, who would make these assertions, he would of necessity concur; but he has not expressed himself with clearness respecting them. The case regarding such points, therefore, has been made evident on a former occasion; but as many doubts as any one might indulge in respecting these same, we will a second time enumerate; for perhaps we shall thereby acquire a facility for having our difficulties resolved in reference to subsequent questions on doubt.

Book I. The Less

Chapter I

SPECULATION respecting truth is partly difficult and partly easy. And a proof is the following, that, in the pursuit of truth, neither is any one philosopher, in a way worthy of the dignity of the subject, able to attain this; nor can all investigators fail in reaching it, but that each says something to the point concerning Nature: and individually that, indeed, they add nothing or but little, to this speculation respecting truth, but from all these collected together that there ensues something of magnitude. Wherefore, if, indeed, it so seems to be the case, as we happen to say in the proverb, “Who will miss the door?” in this way, truly, would the speculation of truth be easy.

But for philosophers to have a certain whole and not to be able to have each some portion, indicates the difficulty of it: and perhaps, also, from the fact that the difficulty arises in two ways, the cause of this may not be so much in things themselves as in us; for as the eyes of bats are to the light that follows the dawn of day, so also is the mind of our soul to those things which, above all, are naturally the most splendid. But not only is it just to return thanks to those whose opinions one may have fellowship with, but also to those, moreover, who have enunciated their sentiments more superficially; for even these, likewise contribute something, for they have previously exercised our speculative habit. For if there had not been a Timotheus, we would not have had much melody; and unless there had been a Phrynis, there would not have been such a person as Timotheus. But, in the same manner, also, it is in the case of those who have declared their sentiments concerning truth; for, indeed, from some of them we have inherited certain opinions: but others have been the causes of these becoming opinions of theirs.

But it is correct, also, that philosophy should be styled a science, speculative of truth. For speculative science the end is truth, but of practical science, a work; for even though they may examine how a thing is, practical men do not investigate into the cause of that thing in itself, but in relation to something else, and as connected with the present time: but we do not know the truth without the knowledge of cause. But, especially, is each thing that amongst other things according to which, also, there subsists in other things that which is synonymous, as, for example, fire is a thing most hot; for also in the rest of entities is this a cause of their heat Wherefore, also, most true is that which is a cause to posterior natures of their being true. Wherefore, is it necessary that the first principles ofthingsalways existing should always be most true; for not sometimes are they true, neither is anything the cause of being to those, but those are the causes of being in other things. Wherefore, as each thing is disposed in regard of existence, so, also, is it in regard of the truth.

Chapter II

BUT, truly, that there is, at least, some first principle, and that the causes of entities are not infinite, either in a progress in a straight forward direction, or according to form, is evident. For neither, as of matter, is it possible that this particular entity proceed from this to infinity; for instance, flesh, indeed, from earth, and earth from air, and air from fire, and this without over coming to a stand-still. Nor can there an infinite progression take place with the origin of the principle of motion; as, for instance, that man should have been moved by the air, and this by the sun, and the sun by discord; and of the, that there should be no end. Nor, in like manner, can this infinite progression take place with the final cause, that walking, for instance, should be gone through for the sake of health, and this for the sake of enjoyment, and this enjoyment for the sake of something else; and, similarly, that one thing invariably should subsist on account of another. And, in like manner, is it the case with the formal cause. For of media, to which externally there is something last and first, it is necessary that what is first should be a cause of those things which are subsequent to it. For if we must declare what is the cause of three things, we will assert that it is the first of the three; for, doubtless, it is not the last, at least, for that is not, at any rate, at the extremity of anything as a cause: but, truly, neither is it the middle, for this is the cause of one thing only. But it makes no difference whether one or many media be assumed, nor whether they are things infinite or finite; but in this way all the portions of things infinite, and of the infinite in general, are similarly media up to the extremity; so that if there is nothing that is the first, there is, in short, no cause.

But neither, truly, is it possible, as regards a progression downwards, to proceedonto infinity, in case that which is in a progression upwards involves, a first principle as, for example, that from fire, indeed, water should be produced, but from this earth, and so invariably that a certain different genus be produced. For, in a twofold manner, is one thing produced from another, not as this particular thing is said to take place after that; for example, the Olympic games from the Isthmæan, either as a man is produced from a boy undergoing a change, or air from water.

As, indeed, then, we say that a man is produced from a boy as a thing that has been from that which is in a process of formation, or that which has been finished from that which is being finished, or tends towards perfection, for always is there a certain medium; as production is a medium between existence and non-existence, so also is the thing that is being produced between entity and nonentity: and a person receiving instruction is one becoming scientifically learned. And this is the meaning of what is affirmed, that from a person learning is produced one that is scientifically learned; and just as water is generated from air on account of the air having undergone corruption. Wherefore, in the former instance, the things adduced, indeed, do not revert into one another, nor is a child produced from a man; for that which is being produced does not arise from the act of generation, but is subsequent to generation: for so, also, the day is generated from the dawn, because it is posterior to this; wherefore, neither is the dawn generated from the day: but the other instances revert into each other.

In both these cases, however, it is impossible to pursue the progress on to infinity; for, in the one case, of those that are media there must needs be an end, and, in the other case, the things adduced revert into one another, for the destruction of one is the generationof the other. But at the same time, also, it is impossible, that what is first, seeing that it is eternal, should be subject to corruption; for since generation is not infinite in an ascending progression, that nature must needs not be eternal from which anything has been produced as from that which is primary, and has been subject to corruption; but this is impossible.

Further, the final cause is an end; but a thing of this sort is that which does not subsist on account of another, but other things on account of that. Wherefore, if that which is last be a thing of this sort, there will not be a progression to infinity; but if there is no such thing I mean that which is last the final cause will have no existence. But they who introduce this infinite progression forget that they destroy the nature of the good. Although no one would undertake entering on any course of action not intending to go on to a termination of his undertaking; nor would there be design in such things: for one who is possessed of mind always does a thing for some purpose or other,(for this is a termination for it,) for the end proposed is a termination. But, indeed, neither can the formal cause admit of being referred to another definition more copious in reason. For the prior definition is invariably more the definition of a thing; but the subsequent is not so. But to that of which there is no first, neither has that which is next in order any existence, Further, they destroy scientific knowledge who make assertions in this way; for it is not even possible to understand anything before we come to individual things; and scientific knowledge has no existence in this case: for things infinite, in this manner, how is it possible to apprehend? for the infinite here is not a thing similar to infinity in the case of a line, which, as regards its divisions, indeed, does not come to a stand-still, but is indivisible; nor is it possible for one to apprehend these divisions, except he imposes some limit to their divisibility. Wherefore, he will not reckon the divisions or sections who goes through the infinite in detail, But also, as regards the matter, so far as it is such, in what it being moved,’ it is necessary to understand it thus far; and for nothing that is infinite is there any possibility of existence: but, if this is not the case, not infinite, at any rate, is that by which we may know the infinite. But, doubtless, if the species of causes were infinite in number, neihther in such a case would the perception of our knowledge be possible; for then we think we know when we may make known to causes: but the infinite according to addition, it is not in finite duration possible to exhaust.

Chapter III

BUT lectures on philosophic subjects fall out according to our habits; for as we have been accustomed, so we deem it right a thing should be expressed; and whatever things are besides these do not appear similar: but, from the fact of our not being habituated thereto, they seem more unknown and strange, for the habitual is more known. And how great force the habitual possesses, the laws make manifest, in which fabulous and puerile things have greater force from usage than the reality of our knowledge concerning them.

But some persons, indeed, do not admit those making assertions, unless one speaks with mathematical precision; but others do not approve of what is said, unless they express themselves by means of an exemplar; and others think it right to adduce a poet as a witness. And some require all things to be expressed with accuracy; whereas accuracy is troublesome to others, either on account of their not being able to carry on a train of reasoning, or on account of their considering such as mere quibbling about verbal niceties, for the precise involves some such thing. Wherefore, as in the case of contracts, so also in that of philosophic discourses, precision seems to be a thing to some persons that is illiberal.

Wherefore, it is necessary that one should have been instructed what way we must admit each and all points of inquiry, as it would be absurd at the same time to seek for scientific knowledge and the mode of attaining such knowledge: but it is not easy to acquire either of these. Now, mathematical accuracy of language is not to be required in all things, but in those things that do not involve any connexion with matter. Wherefore, such is not the natural mode of discovering truth; for perhaps the whole of Nature involves matter: therefore, first must we investigate what Nature is. For in this way, also, will it be evident about what only natural science is conversant, and whether it is the province of one science, or of many, to speculate into causes and first principles.

Book II
Chapter I

FOR the advancement of the science under investigation it is necessary for us, first, to take a review of those points respecting which one ought to doubt in the first instance; but these are whatsoever subjects some speculators have entertained opinions of after a different mode, and whatever beyond these may happen to have been overlooked. For it will contribute towards one’s object, who wishes to acquire a facility in the gaining of knowledge, to doubt judiciously, for a subsequent acquisition in the way of knowledge is the solution of previous doubts; but when one is ignorant of the bond of a thing, it is not possible for such to loose it. But the perplexity of the intellect makes manifest this assertion respecting the matter in hand; for so far forth as the dianoetic faculty doubts, so far does it undergo something similar to persons loaded with chains; for it is impossible, in both cases, to advance further. Wherefore, it is necessary, in the first instance, to speculate into all the difficulties involved in the present subject, both on account of these things, and also from the fact, that they who carry on an investigation, without doubting first, are similar to persons ignorant where they ought to walk; and, in addition to these things, neither can such know whether he has discovered the object of his speculation or not; for the end is not manifest to this speculator: but to one who has previously doubted, in a judicious way, it is manifest. But, further, there is a necessity that a person should be better qualified for forming a judgment who has heard all the reasons, as it were, of adversaries and opposing disputants.

Now, the first source of perplexity is concerning those things which we have expressed doubts of in our Preface; namely, whether to speculate into causes be the province of one or many sciences? and whether it be the province of this science to discover merely the primary principles of substance, or also to speculate concerning the first principles from which all derive their demonstrations? as, for instance, whether it is possible to affirm and deny one and the same thing, at the same time, or not, and concerning the other things of such a kind? And, if it is the province of this science to be conversant about substance, whether one may be about all, or whether there be many such in existence? and, if many, whether all are akin to each other, or it may be proper to style some of them sciences of “wisdom,” and others of them, something else?

And this very thing is amongst the necessary points of investigation, whether it should be affirmed that sensible substances exist only, or whether others also subsist in addition to these? and whether there is a genus singly, or a number of genera of substances according to the opinion of those we introduce both forms and mathematical entities as things intermediate between these and sensibles? Concerning these, therefore, as we have said, an examination must be made; and also concerning substances, whether the speculation extend only to them, or to the essential accidents of these substances? But, in addition to these points, we might inquire in regard of sameness and diversity, and similarity and dissimilarity, and identity and contrariety, and concerning priority and subsequence, and all the rest of such things, concerning as many as the Dialecticians endeavour to examine, instituting their inquiries from matters merely of opinion, we might, I say, investigate whose province it is to speculate into all of these. Further, may one investigate whatsoever things are essential accidents in these very things, both not only what each of them is, but also whether, in truth, one be contrary to one?

And whether genera are first principles and elements, or those things into which, as being inherent, each thing is divided, and if the genera are so, whether they are such things as are predicated last or the first concerning individuals? as, for example, whether animal or man be a first principle, and be so rather than a singular But most especially must we investigate and examine, with pains, as to whether besides matter there is any absolute cause or not, and whether this is separate or not, and whether it be one, or such causes may be many in number? And whether there is anything beside entirety,’ (but I mean by entirety when anything has been predicated of matter,) or nothing, or whether this is the case with some things, indeed, but not so with others, and what sort of entities such are? Moreover, whether first principles are limited in number or in species, both those that subsist in formal causes and those that are in the subject and whether of things corruptible and incorruptible the principles be the same or different? and whether all are incorruptible, or whether of corruptible things there are corruptible principles? Moreover, also, the most difficult of all, and involving the greatest perplexity, is the inquiry, whether unity and entity, as the Pythagoreans and Plato used to affirm, be not anything else but the substance of entities; or this be not the case, but that there be some other subject, as Empedocles says harmony is, and a certain other philosopher, fire, and another, water or air? And whether first principles are universal or are as the singulars of things? and whether they subsist in capacity or in energy? Further, whether they subsist otherwise than according to motion for also these speculations would furnish much perplexity. But, in addition to these points, there remains the inquiry, whether numbers and dimensions, and figures and points, be certain substances or not and, if they are substances, whether they are capable of being separated from sensibles or be inherent in them? for, concerning all of these questions, not only is it difficult successfully to attain unto the truth, but neither is a judicious doubting easy for the reasoning faculties.

Chapter II

IN the first place, indeed, therefore, let us institute an inquiry concerning the first assertions which we have made; namely, whether to speculate concerning all kinds of causes be the province of one or many sciences. For how would it be the province of a single science to take cognisance of existing first principles when they are not contrary to each other. But, further, in the case of many of the entities all do not exist in all of them. For in what way is it possible for the principle of motion to be found in things incapable of motion; or that the nature of the good should, if everything which may be essentially good, and by reason of its own nature, is an end, and so a cause, inasmuch as on account of that other things are both produced and exist? But the end and the final cause are an end of any action. And all things in the act of doing are attended with motion; therefore, in things incapable of motion it would not be possible that this should exist as the first principle, or that there be therein any essential good. Wherefore, also, in mathematics nothing is demonstrated through this cause; nor is there any demonstration for the reason that a thing is better or worse: but neither does any mathematician make mention at all of any such thing whatsoever. Therefore, for this reason, certain of the Sophists, as, for example, Aristippus, regarded these sciences with disdain; for in the other arts, even the mechanical ones themselves, as in those of carpentry and shoe-making, he said that wherefore a thing is better or worse could be declared in every respect, but that the mathematical sciences make no account concerning things good and evil. But, truly, if there are, at least, many sciences of causes, and different sciences of a different first principle, which of these must be said to be the one under investigation; or whom of those that are in possession of them shall we pronounce scientifically informed, particularly in the matter tinder inquiry for in the same subject is it possible that all the modes of causes exist; as, for example, of a house, the origin of the principle of motion is from art and the builder, and the final cause is the work, but the matter is earth and stones, and the form is the definition.

From the distinctions, therefore, laid down by us originally, as to which of the sciences we ought to denominate wisdom, is involved a reason for further styling each thus. For as far as a science is most qualified for the pre-eminence and for superiority over the rest, and so far as it is just that, as servants, the rest of the sciences should not contradict, so far such is a science of the end and of the good, for the rest of things are, on account of this; but as far as wisdom has been defined a science of first causes, and of that which is especially capable of being scientifically known, so far such would be a science of substance. For seeing that persons may acquire the same knowledge by many methods, we say that he rather understands a thing who makes known by its being what that thing is than by its not-being; and of these themselves one in preference to another, and particularly he who knows what a thing is, and not he who knows the quantity or the quality of a thing, or what it is by nature fitted far in the way of action or of passion. Further, in the case of other things, the understanding each of those subjects concerning which there are demonstrations, we think then to have an existence when we.may understand what a thing is for instance, what the squaring of a right-lined figure is: that it is the finding of a mean proportional. In like manner, is it in the case of the rest. But with regard to generations, and actions, and every kind of change, we are in a way of understanding each when we understand the first principle of motion; and this is different and in opposition to the end. Wherefore, it would appear to belong to the department of a different science’ to investigate each of these causes.

But, truly, also, with regard to demonstrative first principles, whether they belong to one science or more is a question open to doubt. But I term demonstrative even those common opinions from which all derive their demonstrations; for instance, that everything must needs be either an affirmation or negation, and that it is impossible for the same thing to be and not to be at the same time, and whatsoever other such propositions there are. It is I say, a (question open to doubt, whether there be one science of these and of substance or a different one, and if not one whether it is necessary to denominate as such the science under investigation? Therefore it would not then appear reasonable, indeed, that it should be the province of one science for why, in preference, should the perception concerning these peculiarly belong to geometry rather than to any other science whatsoever? If, therefore, in like manner, truly it belongs to any whatsoever, but it does not admit of belonging to all the sciences, as neither is it the peculiarity of the rest, so neither is it the province of that science which makes known the substances to investigate concerning these. But, at the same time, also, in what way will it be the science of these? For what each of these happens to be we also now know; the rest of the arts, therefore, employ them as things known. But if there be a demonstrative science concerning them, it would be necessary that there be a certain subject-genus, and that some of these, indeed, should be passive properties and other axioms: for concerning all things it is impossible thatthere should be a demonstration; for demonstration must needs be composed of certain principles, and be conversant respecting some thing, and the demonstration of some things. Wherefore, it happens that there is one particular genus of all things that are being demonstrated, for all the demonstrative sciences employ axioms. But, truly, if there be a science on substance different from the one concerning these, which them is by nature fitted to be more sovereign and prior, for especially and universally the principles of all things are the axioms? And if this is not the part of the philosopher whose else will it be to speculate into the truth and falsehood regarding these.

And, upon the whole, whether of all substance is there one science or more? if indeed, therefore, there is not one science of such, what so of substance must we consider as the subject-matter of this science of ontology? But that there should be one science all substances is not reasonable; for there would be on demonstrative science concerning all things that are essential accidents, if every demonstrative science, in respect of a certain subject, speculates into essential accidents from general opinions. Respecting, then, the same genus it is the province of the same science to investigate the essentif accidents from these same general opinions: for an examination respecting the wherefore belongs to one science, and to one respecting those elements whereof a thing consist whether both investigations belong to the same or a different science? Wherefore, the like will take place in regard of accidents, whether these will investigate them or one of those But, further, might we examine whether the speculation is confined only to substances, or is also concerning the accidents in these? but I say, for example, if a solid be a certain substance, and lines, and surfaces, whether it be the province of the same science to take cognisance of these things, and of the accidents of each genus about which the mathematical sciences demonstrate, or if it be the province of a different one? For if, indeed, of the same, there would be a certain demonstrative science, and that the science of substance; but of the essence or formal cause there does not appear to be a demonstration: but, if of a different science, what will be the science that speculates about the accidents -of substance? for this would be altogether difficult to render an account of Further, also whether must we say that there are sensible substances only, or, also,. besides these, others? and whether do the genera of these substances happen to subsist singly, or are they more numerous, as, for instance, they who speak both of forms and media between forms, and things sensible, concerning which, they say, are conversant the mathematical sciences?

As to the assertion, then, indeed, that we have made, namely, that forms are causes, and substances absolutely subsisting, it has been declared in the earliest of our disquisitions concerning these: but as these inquiries in many ways are clogged with difficulties, it would be no less absurd the assertion that there are, indeed, certain natures besides those which are in the heavens, and that these are the same with things sensible, except that the former are, indeed, eternal, and the latter, corruptible. For they speak of the existence of ideal man, and ideal horse, and ideal health, but say nothing else in regard of these; acting, in a way, similar to those who affirm the existence of the gods, no doubt, but in the shape of men; for neither did these latter constitute aught save eternal men, nor do the former make species anything else but eternal sensibles.

But, further, if in addition, also, to forms and sensibles anywill set down things intermediate, he will be involved in many doubts. For it is evident that, in like manner, there will be lines, and each of the other genera, besides also them that are sensible. Wherefore, since astrology is one of these, there will also be a certain heaven besides the sensible heaven, and a certain other sun and moon; and so with the rest, in like manner, of the bodies that are situated in the heavens. Although, how need one place confidence in such statements as these? for neither is it reasonable that this ideal heaven should be incapable of motion; but, also, that it should be capable of motion is altogether impossible. In like manner, also, is it the case concerning the objects whereof optical science treats, and that of harmonics in mathematics for, also, it is impossible that these should have a subsistence different from sensibles through the same causes: for if things sensible and senses have an intermediate subsistence, it is manifest, also, that there will be animals which will be media between them and think corruptible. But one would doubt, also, concerning what sort of entities it is necessary for these sciences to investigate. For if geodesy will differ from geometry in this only, that one is conversant about things which we perceive by the senses, but the other, about things that are not cognisant by sense, it is manifest that besides the medicinal science, and besides each of the rest, there will be a certain science intermediate between the healing art itself and this particular art of medicine. Although, indeed, how is this possible? for, also, would there be, in such a case, certain salubrious qualities in addition to those that are sensible, and to the salubrious itself: but, at the same time, neither is this true that geodesy is conversant about sensible magnitudes and those that are corruptible; for it would fall into decay when they were in process of being destroyed. But, truly, neither will astronomy be conversant about sensible magnitude nor about yon heaven.For neither are the lines that fall under the cognisance of the senses the same as the geometrician, describes them; for nought of the things that are perceived by the senses is in this way strictly straight or round, for the circle touches the rule not in a point, but as Protagoras was accustomed to say in his refutation of the geometricians. Neither are the motions and the evolutions of the heaven similar to those about which astrology has formed its systems; nor have the symbols the same nature with the stars.

But there are some persons who say that these reputed media between forms and sensibles are not, indeed, separable from sensibles, at least, but inherent in them and to enumerate all the impossibilities attendant upon these statements would require a more copious discourse but even it will be sufficient to speculate thus much on this point. For neither is it reasonable that this should be so in the case of these merely; but it is evident that it would be possible, also, for forms to subsist in sensibles: for both of these are results of the same process of reasoning. But, further, must there needs be two solids in the same place; and these mathematical entities must needs not be things incapable of motion, seeing that they, at least, subsist in sensibles that are being moved and, in short, on what account will any one lay down their having a subsistence, indeed, and a subsistence in sensibles for the same absurdities with the things that have been previously spoken will ensue; for there will be a certain heaven in addition to the heaven we see, except that it will not be separate, but in the same place, which is still more absurd.

Chapter III

Now, respecting these points much doubt, therefore prevails; namely, how it is necessary by forming one’s opinion thereupon to attain unto the truth: and, likewise, respecting first principles, whether it is requisite to consider the genera as elements and first principles or in preference, those things from which, as inherent, each first thing consists? as, for example, the elements and first principles of voice appear to be those things from which all voices are composed primarily, but not the voice in common; and we say that those things are elements of figures the demonstrations of which are inherent in the demonstrations either of all or of the greater part of other things. But, further, both some in affirming that there are many elements of bodies, and others that there is one, of which they are composed, and from which they consist, assert these to be the first principles; as, for example, Empedocles asserts that fire and water, and the elements subsisting along with these, are those from which, as being inherent, entities derive their existence: but he does not speak of these as the genera of entities. And, in addition to these statements, we may subjoin the remark, that if any one wishes to contemplate the nature of the rest of things as, for example, a bed, of what parts it consists, and how those parts are put together in that case he is acquainted with the nature of it. From these reasons, therefore, it would appear that first principles would not be the genera of entities. But so far forth as we obtain a knowledge of each thing by means of the definitions, and so far as first principles are the genera of definitions, it is necessary, also, that first principles be the genera of things capable of definition. And, likewise, if to acquire the science of the forms according to which entities are denominated is to acquire the science of entities themselves, in this case the genera of the forms are first principles. But those, also, who affirm that the elements of entities are unity or entity,’ or the great and the little, appear to employ these as genera. But neither, truly, in both cases is it possible, at least, to affirm, also, that they are first principles. For indeed, of substance there is one reason or formal principle; different, however, will be the definition through the genera, and that which declares the entities whereof, as inherent; a thing consists. If, also, most especially, in addition to these things, the genera are first principles, whether is it necessary to regard the first of the genera to be principles, or the lowest that are predicated of individuals? for this, also, is involved in doubt. For if, indeed, it is requisite that universals are first principles in a more eminent degree, it is evident that the topmost genera will be first principles; for these are predicated of all things. Therefore, the first principles of entities will be as numerous as the first genera; so that unity and entity will be first principles and substances: for these especially are predicated of all entities. But it is not possible that there should be one genus of entities, or that unity or entity should be such; for it is necessary, indeed, that the differences of each genus both exist, and that each should be one: but it is impossible either for the species to be predicated about the proper differences of the genus, or for the genus to subsist, independent of the species of itself. Wherefore, if unity or entity be a genus, neither will entity or unity constitute any difference. But, doubtless, unless there De genera there will not be first principles, since genera are first principles. Further, also, media that are comprehended along with the differences will be genera as far as to individuals; but now this appears to be the case with some, and not with others. And further, in addition to these things, we may add that the differences are rather first principles than the genera; but if these, also, are first principles, first principles become infinite, so to speak: and this is especially the case if one should constitute the first genus a first principle.

But truly, if, also, the one rather be that which is principal, and if one be a thing that is indivisible, and everything that is indivisible is so, either according to quantity or according to species, and if that which is according to species have a prior subsistence, and the genera are more divisible into species, one would be predicated last, for man is not a genus of certain particular men. Further, of those things wherein the prior and subsequent are inherent, it is not possible that what is predicated of them would be anything different from these; for instance, if a duad be the first of numbers there will not be any number different from the species of numbers: and, in like manner, rather will there be figures in addition to the species of figures. But if this is not the case in regard of these, hardly, at least, will there be genera of other things in addition to the species, for of these there seem especially to be genera. But in individuals there is not one thing that is prior, and another that is subsequent. Further, where one thing is better and another worse, that which is better always is prior; so that none of these could be a genus. From these statements, indeed, therefore, it appears that those things that are predicated of individuals are first principles, rather than the genera. But, again, how, on the other hand, it is necessary to regard these as first principles, it would not be easy to express. For it is requisite that there should be a first principle and a cause exclusive of the things of which there is a first principle, and that it should be capable of subsisting in a condition of separation therefrom; but, as to the existence of some such thing besides the singular,’ why should one make a supposition to this effect, except that it is predicated universally, and of all things But if, indeed, this is done on this account, in such a case universals are to be set down as first principles in a more eminent degree, so that the first genera would be principles.

Chapter IV

But a doubt closely connected with the foregoing is one which of all is both the most difficult and the most requisite to examine into, concerning which our treatise, at present, is immediately occupied. For if there is not anything besides singulars, and if singulars are infinite, how is it possible to be in possession of a science of things that are infinite for, as far as there is something that is one and the same, and as far as there is something that is universal, so far do we attain a knowledge of all things. But, doubtless, if this be necessary, and if there must needs be something in addition to singulars, it would be requisite that there be genera in addition to singulars, whether they are the lowest or the highest; but that this is impossible we have ourselves just now expressed a doubt.

But, further, if most especially there is something besides the entire when anything has been predicated concerning matter, whether, if there be a certain form, must there needs be something universal in addition to some, and not in addition to other things, or is there nothing universal besides singulars? If, then, there is nothing universal besides singulars, there would not be anything that is cognisable by the mind; but all things would fall beneath the notice of the senses, and there would not be a scientific knowledge of anything, unless one would assert the exercise of the senses to be science. Further, would there be nothing eternal or immovable; for all things sensible are in a process of corruption, and are in motion. But, truly, if there is, at least, nothing that is eternal, neither is it a thing possible that there should be generation; for there must needs be something, namely, that which is being produced, and wherefrom it is produced: and of these the last must be ingenerable if both the progress of successive productions is to stop at all, and if generation from non-entity should be a thing that is impossible. But, moreover, on the supposition of such things being in existence ab generation and motion, there must needs be a limit likewise, for neither is any motion infinite; but of every motion is there an end: but that cannot be produced which it is impossible could have been produced; but that which has been produced must needs exist when first it has been produced. But, further, if matter be an existence from the fact of its being ingenerable, still it is much more reasonable that substance should have a subsistence when that is generated so as to have a being; for if neither substance nor matter shall have an existence, neither will there he anything at all in existence: but, if this be impossible, there must needs be something in addition to the entire, namely, the form and species; yet, it on the other hand, any one will establish this dogma, a doubt presents itself, both in the case of what things one should make this assertion, and in the case of what one should not. For that this is not possible, in the case of all, is evident; for we would not posite existence of any particular house in addition to certain houses.

But, in addition to the foregoing points, we may subjoin the inquiry, whether will there be one substance of all things, for instance, of men. Now, this is absurd, for all things are not one of which the substance is one, but are many, and different; this, however, also, is an unreasonable statement. And, at the same time, also, how would matter become each of these and how is the entire both of these But, further, respecting first principles we would also entertain this particular doubt. For if, indeed, they are one in species, nought will there be that is one in number; nor will actual unity or entity have any existence; and how would scientific knowledge be in existence, unless there was a certain one in all things? But, truly, if they are one in number, each of the first principles also will be one; and not, as in the case of sensibles, one principle of one thing, and another of another; as, for instance, of this syllable when it is the same in species, the first principles, also, are the same in species, for these, likewise, are different in number: and if this be not the case, but if the first principles of entities are one in number, there will not be in existence anything else besides the elements; for to speak of one in number, or of the singular, makes no difference, for so we speak of the singular as one in number, and of the universal as that which is common to these. Just, therefore, does the case stand as if the elements of voice should be limited in number, all the letters necessarily must be in number as many as the elements, since neither two, nor more than two, of them would be the same.

But a doubt of no less difficulty has been overlooked, both by modern investigators and by our predecessors, namely, as to whether the first principles of things corruptible and of things incorruptible be the same or different. For if, indeed, they are the same, how is it the case that some things are incorruptible and others corruptible, and from what cause does this difference arise?

Those of the Hesiodic school, and all as many as are theologians, fixed their thoughts only upon probable, as it appeared to themselves; but they have treated us with disdain. For, seeing that they make the first principles gods, and to have been produced from gods, whatsoever did not taste of the nectar and ambrosia they say are mortal; palpably speaking of these denominations as expressive of things that are known to themselves.

Respecting, however, the actual adducing of these causes, they have spoken beyond our comprehension. For if, indeed, the immortals partake of these for the sake of pleasure, the nectar and ambrosia are, in no respect, the causes of their existence; and if these are the causes of their existence, how would they be eternal when thus requiring sustenance. But, respecting those fabulous systems of philosophy, it is not worth one’s while considering them with seriousness.

But from those who make assertions by demonstration, it is necessary to ascertain in our inquiries, why, forsooth, if entities are from the same source, some of them are in their nature eternal and why others of these entities are subject to decay But, inasmuch as they neither mention a cause of this, and as it is not reasonable that the case should be so, it is manifest that the first principles of these would not be the same, nor would there be the same causes of them. For, also, one whom any person would suppose to speak particularly consistent with himself, namely, Empedocles,’ has, likewise, experienced the same difficulty. For he, indeed, is for establishing discord which is a first principle in his system as a certain cause of corruption. Nevertheless, this would seem, however, also, to produce entities that are beyond the one; for from this are produced all the other works of creation, except the Deity. The following, at least, are the words of Empedocles: “From which are all things, as many as were, and are, and shall be after; And trees therefrom have blossomed, and men and women, And beasts and birds, and water-fed fishes, And even the long-lived gods.”

And the subsistence of all things independent of these is manifest; for, unless discord were inherent in things, all things would have been one, as he says: for when they would have come together, then last in the conglomeration would stand discord. Wherefore, also, it happens to him, in his system, that the Deity, who is supremely happy, should be less prudent than the rest of beings, for he does not know all the elements, for he is not in possession of discord; but the knowledge of the like is through the like. “For, indeed, says he, by earth we see earth, and by water, water, And ether divine by ether, and through fire the ruinous fire, And by concord, concord, and by gloomy discord, discord.”

But, to return to the point from whence our discourse digressed. This, at all events, is evident, hat it happens, according to the theory of Empedocles, that discord is no more the cause of corruption than of existence; and, in like manner, that neither is harmony a cause of existence more than of corruption, for while collecting things into unity it is a cause of corruption to other things. And, at the same time, also, he mentions no cause of the actual transmutation, save that the thing is thus constituted by nature to take place. Mark his words: “But when mighty discord was nourished in the members, And rose up to the honours of deified Time, who, holding. The sway over them alternately, had, in the end, Surpassed the ample objects of God’s adjuration.”

As if, indeed, it were a thing necessary that a change should take place; but he does not bring to light any necessary cause. But, nevertheless, thus much, at least, he only asserts consistently, for he does not constitute some entities corruptible and others incorruptible, but all corruptible, except the elements. But the source of perplexity now mentioned it this: why, if entities spring from the same source, some of them are incorruptible and some of them are not so. That, therefore, the first principles of things would not be the same, let this much suffice to have been spoken.

But, if the first principles of things be different, one matter of doubt, indeed, is, whether these also will be incorruptible or corruptible? For if, indeed, they are corruptible, it is manifest that it is requisite that these, also, should spring from certain entities; for all things perish into those from whence they derive their being. Wherefore, it happens that to principles there are other first principles that are prior; but this is impossible, both on the supposition of the progression being stationary, at some stage of its progress, and on the supposition of its going on to infinity. And, moreover, how will things perishable subsist if the first principles will be destroyed? but if these principles are imperishable, why, indeed, from these that are things imperishable will arise those that are perishable, but from the others those that are imperishable for this is not reasonable, but either is impossible, or requires for its establishment much rational support. And, further, neither has any one attempted to enumerate different ones; but speculators assign the same first principles of all things the first subject of doubt, however, they entertain slightly, regarding it as something trifling.

But, also, the most difficult point of all to examine into, and the most necessary for the discovery of truth, is, whether entity and unity are substances of entities, and whether each of them not being anything else, this is unity and that is entity; or whether it is necessary to investigate what, at length, unity and entity are, as if another nature were the subject to these? For some, truly, in that way, and some in this, suppose their nature to be disposed. For Plato, indeed, and the Pythagoreans do not regard entity as anything different from unity, but that this is their nature that it should be the same thing for the substance to be one, and to be a certain entity. But amongst natural philosophers, Empedocles, for instance, as if conducting the inquiry to that which is more known, says that unity is entity. For he would seem to affirm that this is harmony at least, this is a cause in his system of unity being found in all things. But others say that fire, and some that air, is this unity and entity from whence that entities both arise and are produced. So, in like manner, is it the case, also, with those who lay down the existence of more elements than these; for it is, likewise, necessary for these to reckon unity and entity such things as whatever, at least, they affirm first principles to be. But it happens, unless one will set down the existence of unity and entity as a certain substance, that not any of the rest of the universals will have any subsistence, for these are universal pre-eminently above all. But, if unity itself be not some particular thing, nor entity itself, much less will there be any of the other things that will have a subsistence, except those denominated singulars. But, further, on the supposition of unity not being a substance, it is evident that neither would number have a subsistence, as a certain nature that has been separated from entities, for number constitutes the monad; but the monad is the same as some certain unit. But, truly, if, at least, actual unity and actual entity be a certain particular thing, it is necessary that the substance of that thing be entity and unity; for it is not any different thing that is universally predicated about them, but these very same things.

But, doubtless, if actual entity and actual unity, at least, shall have any existence, much doubt will arise how there will subsist anything different from these. Now, I mean how there will be more entities in existence than one. For anything different from entity has no existence. Wherefore, according to the theory of Parmenides, it must needs happen that all entities are one, and that this one constitutes entity. But in both cases there is a difficulty; for even on the supposition whether unity, doubtless, be not substance, or whether any actual unity have a subsistence, it is impossible for number to be substance: but if, indeed, then, it has not a subsistence, it bath been previously stated why; but if it has the same doubt presents itself respecting entity also: for from what will there be another one besides the one itself, for must not that necessarily be not one, for all entities are either one or many, each of which is one. Further, if unity itself be indivisible, according, indeed, to the axiom of Zeno, nothing would there be having a subsistence. For that which neither when added nor subtracted makes anything greater or less, he affirms this not to belong to the category of entities, because entity is manifestly magnitude; and if it is magnitude it is corporeal, for this, in every way, is entity. But the addition of such things, in one way, will make what is greater, and, in another, will not make anything so at all. As a surface and a line make that which is greater; but a point and a monad, by no means, have this effect. But since this philosopher speculates clumsily, and it happens that there is something that is indivisible, wherefore, even in this way, also, hath one for him a certain reply as follows, an addition of this sort will not make a thing greater, but will make it more; yet how, forsooth, from one, or more than one, of this kind will arise magnitude, for this is even like saying, that a line is made up of points! But, doubtless, if any one makes a supposition in this way, so that, as some say, from actual unity, and a something else that is not one, is composed number, not the less should it form a subject for investigation, why, and how, what is produced will one time be number, and another time, magnitude, if what is not one be inequality and the same nature. For neither is it manifest how from one and this nature, nor how from a certain number and this nature, magnitudes would arise.

Chapter V

BUT a doubt connected with these is, whether numbers and bodies, and surfaces and points, certain substances or not? For if they are not, it eludes our comprehension what being is, and what the substances of entities are. For passive properties, and motions, and relations, and dispositions, and ratios, do not appear to signify a substance of anything; for all these are predicated respecting a certain subject, and no one of them can be said to be this or that particular thing. But things which would seem particularly to signify substance, namely, water, and earth, and fire, from which compounded bodies consist, the heats and colds of these and such like qualities are affections, not substances; but all the while the body, which undergoes these passive conditions, alone sustains them as a certain entity, and as being a certain substance. But, truly, both body is less substance than a superficies, and this latter than a line, and this than the monad and the point, for by these is body defined. And these, indeed, seem capable of existence without body; but the existence of body, without these, seems impossible.

Wherefore, the majority of speculators and our predecessors considered substance and entity to be body, and the other things to be passive properties of this; so that, also, the first principles those of bodies are the first principles of entities. Subsequent investigators, however, and they, too, persons that appeared endowed with more wisdom than these, supposed such to be numbers. As, therefore, we have said, unless these are substance, there is, upon the whole, no substance in existence, nor no entity, for the accidents, at least, in these it would not; truly, be worthy to call entities.

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 ease 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 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

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 entities, there are certain others, such as some call the forms, there will not be a substance one 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, 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 whether elements subsist in potentiality, or in 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.

And these doubts, then, is it necessary to moot respecting first principles; and there remains, 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.

Book III

Chapter I

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, indeed, but in reference to one, and to one certain nature, and not equivocally; but, in like manner, also, as everything conducive to health is termed so in reference to 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 in 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, 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.

As, then, there is one science of all things 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 thing 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.

If, therefore, entity and unity are the same thing, and one nature, from the fact of their following each other as first principle and cause, yet they are not manifested by a single definition; there is, however, no difference, should we even make our suppositions in regard of them after a similar manner, nay, even rather is it for the advantage of the present inquiry. For it is the same thing, one man and the entity man and man; and not anything different does it make manifest, according to a repetition of the expression, to say man is, and man and one man: but it is evident that there is no separation of being either in the case of production or corruption. But in like manner, also, is it the case with unity. Wherefore, it is manifest that addition in these implies the same thing, and that nothing different is unity from entity And, further, the substance of each thing is one not according to accident; and in like manner, also, is it the case with any entity whatsoever. Therefore, as numerous as are the species of unity, so numerous, also, are those of entity, into the nature of which it is the province of the same science in kind to investigate: now I speak, for instance, of sameness and similarity, and of the other things of this sort, and of those that are in opposition to these. And almost all contraries are reduced to this first principle. These points, however, have formed the subject-matter of our inquiries in our treatise styled, “A Selection of Contraries.”

And so many portions of philosophy are there as there are, at least, substances. Wherefore, is it necessary that there should be a certain first philosophy, and one next in order belonging to these; for unity and entity are things straightway involving genera; wherefore, also, the sciences will follow upon these. For the Philosopher or Metaphysician is as one that is styled a Mathematician, for his science also has parts; and there is a certain first and second science, and another next in order, in mathematics. But whereas it is the province of one science to investigate things that are in opposition, and since plurality is opposed to unity,’ it is also the province of one science to speculate into negation and privation, on account of both kinds of inquiry being possible in the case of unity, of which there is the negation or the privation, either absolutely affirmed that such does not reside therein, or in a certain genus thereof. In this case, indeed, therefore, the difference is present in unity with the exception of that which is inherent in negation,(for negation is the absence of that.) And in privation, also, is there a certain subject nature of which the privation is predicated. Now, plurality is opposed to unity; wherefore, also, the things that are in opposition to those that have been mentioned namely, both diversity, and dissimilarity, and inequality, and as many other qualities as are denominated either according to the same, or according to plurality and unity it is the province of the science of metaphysics that we have alluded to, to examine into; among the number of which, also, a certain one is contrariety; for contrariety is a certain difference, but difference is diversity.

Wherefore, since unity is spoken of in various ways, these, also, shall in many ways be spoken of but, nevertheless, it is the province of one science to make known all such; for even though unity be spoken of in many ways, on that account it is not the province of a different science to investigate them: if, however, neither the definitions are capable of being reduced in accordance with one, nor in reference to one, then is it the province of a different science. But since all such are referred to what is first as, for example; as many things as are styled one are spoken of in reference to the first one in the same manner may the assertion be made, that this science is concerning sameness and diversity, and the rest of the contraries. Wherefore, in dividing how many modes each is expressed by, in this way must reference be made to what is first or original in each category, in order to ascertain how it is expressed in reference to that. For things will be denominated partly by reason of having those primaries, and partly that they are causes of them, and partly according to other such modes. Therefore, is it evident, as has been stated in the doubts, that it is the province of one science to institute an inquiry concerning these and concerning substance. But this was one of those inquiries that have been mentioned in the doubts.

And it is the part of the philosopher to be able to speculate about all the foregoing subjects of inquiry. For, if it be not the province of the philosopher, who shall there be that will be likely to examine whether he be the same person, Socrates, and Socrates sitting; or whether one be contrary to one, or what a contrary is, or in how many ways it is denominated? In like manner, also, is it in the case of the rest of such points for investigation. Since, therefore, these of themselves are affections of unity, so far forth as it is unity, and of entity, so far forth as it is entity, but, not so far forth as they are numbers; or lines, or fire, it is evident that it is the province of that science of ontology to make known both what these are, and the accidents that are inherent in them. And not in this respect do they err who examine concerning these, as not philosophising, but because substance, about which they understand nothing, is a thing prior in existence. Since, as there are peculiar affections of number, as far as it is number,(for instance, oddness, evenness, commensurability, equality, excess, defect,) and as these both absolutely and relatively to one another are inherent in numbers, and since in a similar way there are other peculiar qualities, in what is solid and incapable of motion, and in what is being moved, both that which is without weight, and that which has weight, so, also, in entity, so far forth as it is entity, are there certain peculiar properties; and these are they about the truth of which it is the province of the philosopher or ontologist to inquire.

Now, a proof of this is the following: for dialecticians and sophists assume, indeed, the same figure as the philosopher,(for sophistical is only apparent wisdom, and dialecticians dispute about all things) to all, however, is entity common. But they dispute concerning these, evidently, from the cause of these being proper subjects of inquiry for philosophy. For, in,deed, sophistry and dialectics are employed about the same genus as philosophy is; but philosophy differs from the one in the mode of power, and from the other in the choice of life. And again, dialectic science is merely tentative of the knowledge of those things that philosophy has already actually reached; but sophistic science is only apparent, and not real. And the same is further proved from the fact that a different co-ordination of contraries is privation, and all things are referred to entity and nonentity, and to unity and plurality: as, for instance, rest in its nature partakes of unity, and motion of plurality. But that entities and substance are compounded of contraries almost all men acknowledge all, at least, assert the first principles to be contraries: according to some, indeed, these principles being odd and even; and according to others, hot and cold; and according to others, finite and infinite; and others, harmony and discord. But all the rest of such are referred apparently to unity and plurality; for let this reduction be received by us as is done in the first book of our work “Concerning the Good.” Now, there it appears that first principles, both altogether and as is acknowledged by others, fall under these genera.

From these statements, therefore, is it also evident that to investigate entity, so far forth as it is entity, is the province of one science. For all things are either contraries or composed from contraries: but the first principles, also, of contraries are unity and plurality; and these are belonging to the department of one science, whether the predication be made according to one or not, as, perhaps, the truth is. But, nevertheless, even though unity be spoken of in many ways, to the first will the rest be reduced, and the contraries in like manner. And for this reason, even though entity and unity be not universal and the same, in the case of all things, or separable, as, perhaps, they are not, yet some things, no doubt, are referred to unity, but others to that next in order; and for this reason it is not the business of the geometer to investigate into what the contrary is, or the perfect, or unity, or entity, or identity, or diversity, save only from hypothesis.

That, therefore, it is the province of one science to investigate entity, so far forth as it is entity, and the things therein existing, so far forth as they constitute entity, is evident; and that the same science is speculative not only of substances, but also of things that are inherent in substances, and of the particulars enumerated, both concerning priority and subsequence, and genus and species, and whole and part, and the rest of each, this is evident also.

Chapter III

BUT we must determine whether it is the province of one science, or a different one, to speculate concerning axioms, as they are called, in mathematics and concerning substance, doubtless, it is manifest that it is belonging to one, and that the science of the philosopher, and the investigation of such inquirer is respecting these; for in all entities are they inherent, but not in any genus separate distinctly from the rest. And all investigators employ them, indeed, because they belong to entity, so far forth as it is entity; each genus, however, constitutes entity. And thus far do they employ them as is sufficient for their purpose, but that is as far as they comprise the genus about which they bring forward their demonstrations. Wherefore, since it is evident that they are inherent in all things, as far as they are entities,(for this is held by these in common,) the speculation of them belongs to the philosopher, whose business it is to make known the truth concerning entity, so far forth as it is entity, and concerning these. Therefore, no one of those who are partial inquirers attempts to say aught concerning these, whether they are true or not, neither, for instance, the geometer nor the arithmetician.

Some of the natural philosophers, however, in doing so, act reasonably; for they alone are accustomed to think that it is their province to examine concerning the whole of nature, and concerning entity. But since there is something of a higher order than the physical (for nature is merely one certain genus of entity,) the investigation in regard of these should belong to the universal, and to that which is speculative of the first substance. Now, I admit there is a certain wisdom, namely, even the physical; but it is not the first. As many things, however, as certain of those who speak concerning the truth of axioms attempt to lay down, in what way they ought to be admitted, they do this from ignorance of analytics; for they ought to approach such a subject who are instructed therein beforehand: but whilst hearers they should not be investigators. That, therefore, it is the part of the philosopher, and of the inquirer concerning substance in its entirety, so far forth as it is such by nature, to examine, also, in regard of syllogistic principles is evident.

But it is becoming that one especially furnishing information about each genus should be competent to speak of the very surest principles of the thing; and, therefore, the same holds true of a person that is engaged in the investigation of entities, so far forth as they are entities I mean, that he should be able to adduce the most firm principles of all Now, this is the philosopher; and the most firm first principle of all is that concerning which there can be no possibility of deception, for such must needs be that which is most known; for those points respecting which men do not impart knowledge are all exposed to deception in; and it must needs, likewise, be a thing independent of hypothesis. For a principle which one must be in possession of who understands any entity whatsoever, this is not an hypothesis; but what one must make known, in the manifestation of anything whatsoever, he must also needs come forward furnished with this. That, therefore, indeed, such is the most firm first principle of all is evident. Now, what this principle is we shall after this declare. For the same thing to be present and not be present at the same time in the same subject, and according to the same, is impossible,(and whatsoever things we have further defined, let these be so defined in respect of their logical difficulties.) This, however, is the most firm of all first principles; for it involves the distinction spoken of above. For it is impossible to suppose that anything whatsoever is the same, and is not the same, as certain think that Heraclitus asserts; for it is not necessary, as far as concerns what one asserts to exist, to suppose that these also do exist. But if it is not admissible that contraries at the same time should subsist in the same subject,(now the usual definitions have been additionally made by us to this proposition,) and if an opinion contrary to an opinion be that of contradiction, it is evident that it is impossible for the same inquirer to suppose that at the same time the same thing should be and not be; for one labouring under deception in regard of this would entertain contrary opinions at the same time. Wherefore, all who employ demonstration reduce the matter to this last opinion; for by nature this, also, is the first principle of all the rest of the axioms.

Chapter IV

Now, there are certain philosophers who, as we have intimated, themselves both affirm that it is possible that the same thing may and may not be, and that they really think so. This principle, however, do many of the investigators of nature employ. But we just now have assumed it as a thing impossible, in the case of an entity, that it should be and not be at the same time; and by means of this have we demonstrated that this is the most firm of all first principles. Now, some also demand a demonstration of this, from ignorance; for it is ignorance the not knowing what things one ought to seek a demonstration of, and of what things he ought not. For, indeed, upon the whole, it is impossible that there should be a demonstration of all things; for one would go on in this case to infinity, so that there would not be any demonstration at all in this way. If, however, there be some things of which we should not seek a demonstration, what they in preference require such a first principle to be they have not the ability to affirm. But it is possible to demonstrate concerning this, by refutation, that it is impossible, if only he would affirm anything who doubts; but if he makes no assertion, it would be ridiculous the seeking an argument against him who had not a reason to put forward about anything, so far as he had no such reason; for an adversary of this sort, as far now as he is such, would be like unto a plant. Now, I say, demonstration by refutation differs from demonstration simply or properly so called, because he that employs demonstration would seem to require what is the principle in the beginning; but, on the supposition of the existence of another cause of such a kind, it would be a refutation, and not a demonstration.

Now, a commencement of a discussion in regard of all such points is, not the demanding the declaration that either a thing exists or doth not exist,(for this, one would imagine, perhaps, was the asking the principle assumed originally,) but the demanding the signification, at least, of a thing, both as for oneself and for another. For this also amounts to a necessity, if he is to say anything at all; for if he does not, there would be no possibility of a rational discussion with such a one, neither for himself relatively to himself, nor to another. If any one, however, would grant this, there willbe a demonstration in existence for now will there actually be in existence something that has been determined. But thecause is not the person demonstrating, but the person sustaining the argument; for, by overturning the discussion, he yet sustains the discussion. And further, he that acquiesces in this,hath acquiesced in the truth of something independent of demonstration; so that not everything would be so and not so.

In the first place, indeed, therefore, it is evident that this very assertion is true, because the name signifies the existence or the non existance of this particular thing; so that not everything would be so, and not so in this particular way. Further, if man signifies one thing, let this be a two-footed animal. Now, I say, that this signifies one thing; if this be man, whatever is a man, this, namely, the being a two-footed animal, is the being in man: but there is no difference should any one assert that more is thereby signified, provided only they have been reduced under proper definitions; for grant that upon each definition a different name may have been imposed. Now, I say, for example, if he would not assert that man signifies one, but many things, of one of which there is a single definition, namely, two-footed animal, yet, also, are there many others, but defined according to number; for its own proper denomination might be set down according to each of the definitions. But if its proper denomination should not be thus set down, but one would say that such signified an infinity of things, it is palpable that there would not be a definition of it at all; for the signifying not any one thing is the signifying nothing. And when the denominations are devoid of meaning, there is an end to mutual discussion, and, also, in reality, to discussion on the part of a man with himself. For it is not possible that a person should understand anything that is not capable of understanding one thing: but, if it were possible, one name would be imposed on this thing. Let it, doubtless, be granted, as has been stated in the commencement, that a name significant of something be significant of one thing also.

It is not, therefore, possible that being in man signifies the same particular thing as the not being in man, if man is significant not merely of what is predicated of one, but even one thing itself; for this we do not require that the one should signify that which is predicated of one: since, if the case stands in this way, at least, the musical, and the white, and the man, would signify one thing; so that all things would be one, for they would be synonymous; and it will not be possible that the same thing be and not be, save, by equivocation just as if we would call any one a man whom others would call a not-man. The subject of doubt, however, is not this, if it is possible that the same thing at the same time should be and not be the man nominally, but really. But if the name man, and the name not-man, do not signify anything different, it is evident that the not being man will not differ from the being man. Wherefore, the being man will be the not being man, for they will be one thing; for this signifies that they are one as a tunic and a cloak if there is one definition of each. And if they shall be one, the being man and the not being man signify one thing: but it has been demonstrated that they signify a different thing.

There is a necessity, therefore, of this consequence, if there be a particle of truth in the assertion, that man in signification is equipollent with being a two-footed animal; for this was what the expression man was assumed to signify. Now, if there exists a necessity that this be the case, it is not possible for this very thing not to be a two-footed animal then, for this doth the phrase, “the being a necessity,” signify, namely, the impossibility of its not being man. Accordingly, it is not possible to be true to say at the same time that the same thing is both a man and is not a man. But there prevails the same mode of reasoning in the case of the not being man also; for the being of a man and the not being of a man signify a different thing, if truly, both the being white and the being man are different; for much more is there opposition in this case to justify the difference of signification. But if, also, one would say that the white signifies one and the same thing with the being man, again will we make the same assertion, as has been declared on a former occasion, namely, that all things will be one, and not merely things in opposition. But, if this be not possible, that which has been declared will happen, if the question asked be answered.

If, however, when a simple question is put one subjoin negations also, the question actually put is not replied to: for nothing hinders the same thing being both man and white, and other things ten thousand in multitude; but, nevertheless, if the question be asked, if it is true to affirm man to be this, or not to be so, the reply should be, that it signifies one thing, and no addition should be made that it is both white and large. For, also, it is impossible to go through accidents when, at least, they are infinite; either, therefore, let one go through all or none. In like manner, therefore, if, also, ten thousand times over they are the same thing, namely, man and not man, the reply to the question, if man is, should not be that at the same time also not man is, unless the reply likewise states, in addition, the rest of whatsoever things are accidents, as many as are so, and as many as are not; if this, however, be not done by the person asked the question, there is nothing under discussion at all.

But, in general, they who make this assertion overturn substance and essence, or the formal cause and very nature of a thing; for they must themselves needs affirm all things to be accidents, and that the essence of man or animal, whatsoever it be, has no existence. For if there will exist the essential nature of anything whatsoever, such as is that which is to be man this will not be to be not man, or not to be man, although these are negations of this; for it was one thing which it signified, and this was the substance of a certain thing. But the signification of the substance of a thing is, that not anything else is the being of that thing: but if the being whatsoever man is will be found in this, being either whatsoever is not man, or whatsoever not is man, is a thing impossible; for it will be a something different. Wherefore, it will be necessary for them to say that a formal and substantial definition of this kind, and one invariably suited unto the subject, will be one of a nonentity: but all things, as we have supposed, are according to accident; for in this lies the distinction between substance and accident, for the white is an accident in man, because he is white, but not anything whatsoever that is white.

But, if all things are spoken of according to accident, there will be no primary universal, if an accident always signifies a predication about a certain subject. There is a necessity, then, of going on in a progression to infinity. But this is impossible,(for more than two of such are not connected together,) for accident is not a thing that is accidental to that which is an accident, unless that both are accidentalin the same subject. Now, I say this, for example, in the instance of the white being musical, and the latter being white, because both are accidents in man; but not on this account is Socrates musical, because it happens that both are accidents in a certain other subject. Since accidents, therefore, are spoken of some in this way and some in that, as many as are so expressed, as the white in Socrates, it is not possible should be infinite in an ascending series of productions in the case of man; as, for example, that in Socrates the white there should be some other different accident, for any one thing is not produced from all: nor, truly, in the white will be found any different accident; as, for instance, the musical: for, also, in no wise rather is this an accident in that, than that in this. And, at the same time, the distinction has been made that some things are accidents after this manner, but others, as the musical in Socrates. But as to as many things as are accidental in this way, such are accidents not in such a way as an accident in what is accidental; but this is the case with whatsoever is accidental in that other way. Wherefore, all things will not be spoken of according to accident; something, then, will there be significant, also, as of substance; and if this be so, it has been demonstrated that it is impossible that at the same time contradictions should be predicated of the same subject.

Further, if all contradictions are true at same time concerning the same thing, it is manifest that all things will be one. For the same thingwill it be, both a trireme, and a wall, and a man, if it is possible to affirm or deny anything of everything, as there is a necessity for those to do who assert the opinion of Protagoras. For if; also, to any one a man seems not to be a trireme, it is evident that he will not be a trireme: wherefore, also, he is, if the contradiction be true. And, doubtless, comes to pass a saying of Anaxagoras: “at the same time subsist together all things,” so that, in reality, nothing is one. The indefinite, therefore, they seem to speak of; and, thinking that they mention entity, they talk about nonentity; for an entity in capacity, and not in actuality, constitutes the indefinite. But, doubtless, must we say to the authors of this hypothesis, that of everything either an affirmation or a negation must be predicated; for it would be absurd if in each thing there will be inherent the negation of itself, but that the negation of what is different, and which is not inherent therein, will have no existence. Now, I say, for example, if it is true to assert of a man that he is not a man, it is manifest also that he is not a trireme; if, indeed, therefore, there is truth in the affirmation, there is a necessity that also there be truth in the negation: but if there is not truth in the affirmation, the negation, at least, of a trireme will more appertain to him than the negation of himself. If, therefore, that also be true, there will also be truth in the negation of the trireme; and if in the negation of this, in the affirmation also. And these consequences happen to those who make such a statement, even to the effect that it is not necessary to employ either affirmation or negation. For, if it is true that the same individual is man and not man, it is evident that such a one will be neither man nor not man; for of those two qualities there are two negations. But if that is one which is composed of both, this one would also be in opposition.

Further, indeed, respecting all things it is so and a thing will be white and not white, and entity and nonentity, and it will be so respecting the rest of the assertions and negations in a similar manner; or this will not be the case, but only so regarding some, and not regarding others. And it doubtless, it were not so respecting all, these would be indisputable; but if it be true concerning all, again, no doubt, in the case of whatsoever there is an assertion there will also be a negation; and in the case of whatsoever there is a negation there will likewise be an assertion; or in the case of whatsoever there is an assertion there will also be a negation; or of whatsoever, indeed, there is an assertion there is also a negation: but of whatsoever things there is a negation, of all such there will not be an assertion. And if this be so, there would be something indubitably a nonentity, and this will be a firm opinion; and if to be a nonentity be something both firm and known, more firm would be the opposite assertion. And if, in like manner, also, it is necessary that in the case of whatsoever things one employs a negation he should employ an affirmaton also, it would be true, undoubtedly, by dividing, to say either that a thing, for instance, is white, ‘and again that it is not white, or that this would not be true. And if, indeed, it is not true, by dividing, to say so,’ he does not affirm these things, and there is nothing in existence; but how can one speak of non-entities, or understand anything respecting them, or thus move forward in the paths of knowledge? And all things would be one, as it has been said heretofore, and both man and god, and trireme, and the contradictions of them, will be the same. But if, in like manner, this be so in the case of each thing, in no wise will one thing differ from another; for if there will be a difference, this will be true, and a peculiarity of this. In like manner, also, if it is possible that he who makes the division should speak the truth, there happens that which has been declared. And to this reason we may subjoin the following: that all would speak the truth, and all would speak falsely, and one would acknowledge himself to be speaking what is false. At the same time, however, it is evident that the investigation with such a person is concerning nothing; for he affirms nothing. For neither in this manner nor in that is the assertion made with such a one, but in this manner and not in this manner. And again, at least, with respect to these points he makes a negation of both, because the assertion is made that they are neither so in this manner nor not in this manner, but both in this manner and not in this manner; for, if this were not the case, there would now be in existence something that has been defined. Further, if when an assertion be true the negation be false, and if when the latter itself be true the affirmation be false, it would not be possible at the same time to assert and deny the same thing with truth. But, perhaps, persons will say that this is what has been laid down from the commencement.

Further, does one who supposes that ina manner a thing either is so and so, or that it not so, labour under a misapprehension but he who thinks that it is both, does he speak truth, or can he verify his assertion for if he affirms truth, what is the assertion, save that such is the nature of entities and if he does not affirm the truth, but rather he speaks truth who makes a supposition in that way, entities, in such a case, would, in a certain manner, be now disposed thus; and would this be true and not so at the same time, and yet, in reality not true? But if, in like manner, all both speak falsehood and speak truth, it is not possible for such either to utter or to declare anything, for at the same time he says the same things and not the same things. But if he makes no supposition, but in the same way thinks and does not think, in what way will he be disposed differently from plants?

Whence, also, it is especially manifest that no one either of the rest of the sceptics, or of those making this statement, is so affected. For why, may I ask, does he walk towards Megara, but not remain still, thinking that he is actually walking! nor straightway, at dawn, does he proceed to a well or a precipice! if he may chance to meet with such, he, however, appears cautious, as not considering the falling into it to be not good and to be good in the same sense. It is evident, accordingly, that the one he considers preferable, but the other as not preferable. And, if this be the case, both the one he must needs consider a man and the other not a man; and the one thing sweet, and the other not sweet. For not as of equal importance doth be investigate and regard all things, inasmuch as he thinks it better to drink water and to visit a certain person, and then seeks, in point of fact, for those very things. Although he ought to seek for all things with equal zest, if, in like manner, it were the same thing I mean to say, both man and not man. But, as has been declared, there is no one who does not appear cautious in regard of the one set of things and not so in regard of the other. Wherefore, as it appears all men suppose that the case is absolutely so, if not concerning all things, at least, concerning what is better and worse. Now, if they do so not