Further, is it the business of one science, or of more than one, to examine the first principles of demonstration? If of one, (25) why of this rather than of any other? If of more, what sort of sciences must these be said to be?3
Further, does Wisdom investigate all substances or not? If not all, it is hard to say which; but if, being one, it investigates them all, it is doubtful how the same science can embrace several subject-matters.4
Further, does it deal with substances only or also with their attributes? If in the case of attributes demonstration is possible, (30) in that of substances it is not. But if the two sciences are different, what is each of them and which is Wisdom? If we think of it as demonstrative, the science of the attributes is Wisdom, but if as dealing with what is primary, the science of substances claim the title.5
But again the science we are looking for must not be supposed to deal with the causes which have been mentioned in the Physics.6 For (A) it does not deal with the final cause (for that is the nature of the good, (35) and this is found in the field of action and movement; and it is the first mover—for that is the nature of the end—but in the case of things unmovable there is nothing that moved them first),7 and (B) in general it is hard to say whether perchance the science we are now looking for deals with perceptible substances or not with them, but with certain others. [1059b] If with others, it must deal either with the Forms or with the objects of mathematics. Now (a) evidently the Forms do not exist. (But it is hard to say, even if one suppose them to exist, why in the world the same is not true of the other things of which there are Forms, as of the objects of mathematics. I mean that these thinkers place the objects of mathematics between the Forms and perceptible things, (5) as a kind of third set of things apart both from the Forms and from the things in this world; but there is not a third man or horse besides the ideal and the individuals. If on the other hand it is not as they say, with what sort of things must the mathematician be supposed to deal? Certainly not with the things in this world; for none of these is the sort of thing which the mathematical sciences demand. (10)) Nor (b) does the science which we are now seeking treat of the objects of mathematics; for none of them can exist separately. But again it does not deal with perceptible substances; for they are perishable.8
In general one might raise the question, to what kind of science it belongs to discuss the difficulties about the matter of the objects of mathematics. (15) Neither to physics (because the whole inquiry of the physicist is about the things that have in themselves a principle of movement and rest), nor yet to the science which inquires into demonstration and science; for this is just the subject which it investigates. It remains then that it is the philosophy which we have set before ourselves that treats of those subjects. (20)
One might discuss the question whether the science we are seeking should be said to deal with the principles which are by some called elements; all men suppose these to be present in composite things. But it might be thought that the science we seek should treat rather of universals; for every definition and every science is of universals and not of infimae species,9 (25) so that as far as this goes it would deal with the highest genera. These would turn out to be being and unity; for these might most of all be supposed to contain all things that are, and to be most like principles because they are first by nature; for if they perish all other things are destroyed with them; for everything is and is one. (30) But inasmuch as, if one is to suppose them to be genera, they must be predicable of their differentiae, and no genus is predicable of any of its differentiae, in this way it would seem that we should not make them genera nor principles. Further, if the simpler is more of a principle than the less simple, (35) and the ultimate members of the genus are simpler than the genera (for they are indivisible, but the genera are divided into many and differing species), the species might seem to be the principles, rather than the genera. But inasmuch as the species are involved in the destruction of the genera, the genera are more like principles; for that which involves another in its destruction is a principle of it.10 These and others of the kind are the subjects that involve difficulties. [1060a]
2 Further, must we suppose something apart from individual things, or is it these that the science we are seeking treats of? But these are infinite in number. (5) Yet the things that are apart from the individuals are genera or species; but the science we now seek treats of neither of these. The reason why this is impossible has been stated.11 Indeed, it is in general hard to say whether one must assume that there is a separable substance besides the sensible substances (i. e. the substances in this world), or that these are the real things and Wisdom is concerned with them. (10) For we seem to seek another kind of substance, and this is our problem, i. e. to see if there is something which can exist apart by itself and belongs to no sensible thing.—Further, if there is another substance apart from and corresponding to sensible substances, which kinds of sensible substance must be supposed to have this corresponding to them? Why should one suppose men or horses to have it, (15) more than either the other animals or even all lifeless things? On the other hand to set up other and eternal substances equal in number to the sensible and perishable substances would seem to fall beyond the bounds of probability.—But if the principle we now seek is not separable from corporeal things, what has a better claim to the name than matter? This, (20) however, does not exist in actuality, but exists in potency. And it would seem rather that the form or shape is a more important principle than this; but the form is perishable,12 so that there is no eternal substance at all which can exist apart and independent. But this is paradoxical; for such a principle and substance seems to exist and is sought by nearly all the most refined thinkers as something that exists; for how is there to be order unless there is something eternal and independent and permanent?13
Further, (25) if there is a substance or principle of such a nature as that which we are now seeking, and if this is one for all things, and the same for eternal and for perishable things, it is hard to say why in the world, if there is the same principle, some of the things that fall under the principle are eternal, and others are not eternal; this is paradoxical. (30) But if there is one principle of perishable and another of eternal things, we shall be in a like difficulty if the principle of perishable things, as well as that of eternal, is eternal; for why, if the principle is eternal, are not the things that fall under the principle also eternal? But if it is perishable another principle is involved to account for it, and another to account for that, and this will go on to infinity.14
If on the other hand we are to set up what are thought to be the most unchangeable principles, (35) being and unity, firstly, if each of these does not indicate a ‘this’ or substance, how will they be separable and independent? Yet we expect the eternal and primary principles to be so. [1060b] But if each of them does signify a ‘this’ or substance, all things that are are substances; for being is predicated of all things (and unity also of some); but that all things that are are substance is false. (5) Further, how can they15 be right who say that the first principle is unity and this is substance, and generate number as the first product from unity and from matter, (10) and assert that number is substance? How are we to think of ‘two’, and each of the other numbers composed of units, as one? On this point neither do they say anything nor is it easy to say anything. But if we are to suppose lines or what comes after these (I mean the primary surfaces) to be principles, these at least are not separable substances, but sections and divisions—the former of surfaces, the latter of bodies (while points are sections and divisions of lines); and further they are limits of these same things; and all these are in other things and none is separable. (15) Further, how are we to suppose that there is a substance of unity and the point? Every substance comes into being by a gradual process, but a point does not; for the point is a division.16
A further difficulty is raised by the fact that all knowledge is of universals and of the ‘such’, (20) but substance is not a un
iversal, but is rather a ‘this’—a separable thing, so that if there is knowledge about the first principles, the question arises, how are we to suppose the first principle to be substance?17
Further, is there anything apart from the concrete thing (by which I mean the matter and that which is joined with it), or not? If not, (25) we are met by the objection that all things that are in matter are perishable. But if there is something, it must be the form or shape. Now it is hard to determine in which cases this exists apart and in which it does not; for in some cases the form is evidently not separable, e. g. in the case of a house.18
Further, are the principles the same in kind or in number? If they are one in number, (30) all things will be the same.19
3 Since the science of the philosopher treats of being qua being universally and not in respect of a part of it, and ‘being’ has many senses and is not used in one only, it follows that if the word is used equivocally and in virtue of nothing common to its various uses, being does not fall under one science (for the meanings of an equivocal term do not form one genus); but if the word is used in virtue of something common, (35) being will fall under one science. The term seems to be used in the way we have mentioned, like ‘medical’ and ‘healthy’. For each of these also we use in many senses. [1061a] Terms are used in this way by virtue of some kind of reference, in the one case to medical science, in the other to health, in others to something else, but in each case to one identical concept. For a discussion and a knife are called medical because the former proceeds from medical science, (5) and the latter is useful to it. And a thing is called healthy in a similar way; one thing because it is indicative of health, another because it is productive of it. And the same is true in the other cases. Everything that is, then, is said to ‘be’ in this same way; each thing that is is said to ‘be’ because it is a modification of being qua being or a permanent or a transient state or a movement of it, (10) or something else of the sort. And since everything that is may be referred to something single and common, each of the contrarieties also may be referred to the first differences and contrarieties of being, whether the first differences of being are plurality and unity, or likeness and unlikeness, or some other differences; let these be taken as already discussed. It makes no difference whether that which is be referred to being or to unity. (15) For even if they are not the same but different, at least they are convertible; for that which is one is also somehow being, and that which is being is one.
But since every pair of contraries falls to be examined by one and the same science, and in each pair one term is the privative of the other—though one might regarding some contraries raise the question, (20) how they can be privately related, viz. those which have an intermediate, e. g. unjust and just—in all such cases one must maintain that the privation is not of the whole definition, but of the infima species. e. g. if the just man is ‘by virtue of some permanent disposition obedient to the laws’, the unjust man will not in every case have the whole definition denied of him, (25) but may be merely ‘in some respect deficient in obedience to the laws’, and in this respect the privation will attach to him; and similarly in all other cases.
As the mathematician investigates abstractions (for before beginning his investigation he strips off all the sensible qualities, e. g. (30) weight and lightness, hardness and its contrary, and also heat and cold and the other sensible contrarieties, and leaves only the quantitative and continuous, sometimes in one, sometimes in two, sometimes in three dimensions, and the attributes of these qua quantitative and continuous, (35) and does not consider them in any other respect, and examines the relative positions of some and the attributes of these, and the commensurabilities and incommensurabilities of others, and the ratios of others; but yet we posit one and the same science of all these things—geometry)—the same is true with regard to being. [1061b] For the attributes of this in so far as it is being, (5) and the contrarieties in it qua being, it is the business of no other science than philosophy to investigate; for to physics one would assign the study of things not qua being, but rather qua sharing in movement; while dialectic and sophistic deal with the attributes of things that are, but not of things qua being, and not with being itself in so far as it is being; therefore it remains that it is the philosopher who studies the things we have named, (10) in so far as they are being. Since all that is is said to ‘be’ in virtue of something single and common, though the term has many meanings, and contraries are in the same case (for they are referred to the first contrarieties and differences of being), and things of this sort can fall under one science, (15) the difficulty we stated at the beginning20 appears to be solved—I mean the question how there can be a single science of things which are many and different in genus.
4 Since even the mathematician uses the common axioms only in a special application, it must be the business of first philosophy to examine the principles of mathematics also. That when equals are taken from equals the remainders are equal, is common to all quantities, (20) but mathematics studies a part of its proper matter which it has detached, e. g. lines or angles or numbers or some other kind of quantity—not, however, qua being but in so far as each of them is continuous in one or two or three dimensions; but philosophy does not inquire about particular subjects in so far as each of them has some attribute or other, (25) but speculates about being, in so far as each particular thing is.—Physics is in the same position as mathematics; for physics studies the attributes and the principles of the things that are, (30) qua moving and not qua being (whereas the primary science, we have said, deals with these, only in so far as the underlying subjects are existent, and not in virtue of any other character); and so both physics and mathematics must be classed as parts of Wisdom.21
5 There is a principle in things, about which we cannot be deceived, (35) but must always, on the contrary, recognize the truth—viz. that the same thing cannot at one and the same time be and not be, or admit any other similar pair of opposites.22 [1062a] About such matters there is no proof in the full sense, though there is proof ad hominem. For it is not possible to infer this truth itself from a more certain principle, yet this is necessary if there is to be completed proof of it in the full sense.23 (5) But he who wants to prove to the asserter of opposites that he is wrong must get from him an admission which shall be identical with the principle that the same thing cannot be and not be at one and the same time, but shall not seem to be identical; for thus alone can his thesis be demonstrated to the man who asserts that opposite statements can be truly made about the same subject. (10) Those, then, who are to join in argument with one another must to some extent understand one another; for if this does not happen how are they to join in argument with one another? Therefore every word must be intelligible and indicate something, and not many things but only one; and if it signifies more than one thing, (15) it must be made plain to which of these the word is being applied. He, then, who says ‘this is and is not’ denies what he affirms, so that what the word signifies, he says it does not signify; and this is impossible. Therefore if ‘this is’ signifies something, one cannot truly assert its contradictory.24
Further, if the word signifies something and this is asserted truly,25 this connexion must be necessary; and it is not possible that that which necessarily is should ever not be; it is not possible therefore to make the opposed affirmations and negations truly of the same subject.26 (20) Further, if the affirmation is no more true than the negation, he who says ‘man’ will be no more right than he who says ‘not-man’. It would seem also that in saying the man is not a horse one would be either more or not less right than in saying he is not a man, (25) so that one will also be right in saying that the same person is a horse; for it was assumed to be possible to make opposite statements equally truly. It follows then that the same person is a man and a horse, or any other animal.27
While, then, there is no proof of these things in the full sense, (30) there is a proof which may suffice against one who will make the
se suppositions. And perhaps if one had questioned Heraclitus himself in this way one might have forced him to confess that opposite statements can never be true of the same subjects. But, as it is, he adopted this opinion without understanding what his statement involves.28 But in any case if what is said by him is true, (35) not even this itself will be true—viz. that the same thing can at one and the same time both be and not be. [1062b] For as, when the statements are separated, the affirmation is no more true than the negation, in the same way—the combined and complex statement being like a single affirmation—the whole taken as an affirmation will be no more true than the negation.29 (5) Further, if it is not possible to affirm anything truly, this itself will be false—the assertion that there is no true affirmation.30 But if a true affirmation exists, this appears to refute what is said by those who raise such objections and utterly destroy rational discourse. (10)
6 The saying of Protagoras is like the views we have mentioned; he said that man is the measure of all things, meaning simply that that which seems to each man also assuredly is. If this is so, (15) it follows that the same thing both is and is not, and is bad and good, and that the contents of all other opposite statements are true, because often a particular thing appears beautiful to some and the contrary of beautiful to others, and that which appears to each man is the measure. (20) This difficulty may be solved by considering the source of this opinion. It seems to have arisen in some cases from the doctrine of the natural philosophers, and in others from the fact that all men have not the same views about the same things, but a particular thing appears pleasant to some and the contrary of pleasant to others.31
That nothing comes to be out of that which is not, (25) but everything out of that which is, is a dogma common to nearly all the natural philosophers. Since, then, white cannot come to be if the perfectly white and in no respect not-white existed before, that which becomes white must come from that which is not white; so that it must come to be out of that which is not (so they argue), (30) unless the same thing was at the beginning white and not-white. But it is not hard to solve this difficulty; for we have said in our works on physics32 in what sense things that come to be come to be from that which is not, and in what sense from that which is.33
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