995aIt is necessary, with a view to the science which we are investigating, that we first describe the questions which should first be discussed. These consist of all the divergent views which are held about the first principles; and also of any other view apart from these which happens to have been overlooked. Now for those who wish to get rid of perplexities it is a good plan to go into them thoroughly; for the subsequent certainty is a release from the previous perplexities, and release is impossible when we do not know the knot. The perplexity of the mind shows that there is a “knot” in the subject; for in its perplexity it is in much the same condition as men who are fettered: in both cases it is impossible to make any progress. Hence we should first have studied all the difficulties, both for the reasons given and also because those who start an inquiry without first considering the difficulties are like people who do not know where they are going; besides, one does not even know whether the thing required has been found or not. 995bTo such a man the end is not clear; but it is clear to one who has already faced the difficulties. Further, one who has heard all the conflicting theories, like one who has heard both sides in a lawsuit, is necessarily more competent to judge. The first difficulty is concerned with the subjects¹ which we discussed in our prefatory remarks. (1.) Does the study of the causes belong to one science or to more than one?²(2.) Has that science only to contemplate the first principles of substance, or is it also concerned with the principles which all use for demonstration—e.g. whether it is possible at the same time to assert and deny one and the same thing, and other similar principles?³ And if it is concerned with substance, (3.) is there one science which deals with all substances, or more than one; and if more than one, are they all cognate, or should we call some of them “kinds of Wisdom” and others something different?⁴ This too is a question which demands inquiry: (iv.) should we hold that only sensible substances exist, or that there are other besides? And should we hold that there is only one class of non-sensible substances, or more than one (as do those who posit the Forms and the mathematical objects as intermediate between the Forms and sensible things)?⁵ These questions, then, as I say, must be considered; and also (v.) whether our study is concerned only with substances, or also with the essential attributes of substance; and further, with regard to Same and Other, and Like and Unlike and Contrariety, and Prior and Posterior, and all other such terms which dialecticians try to investigate, basing their inquiry merely upon popular opinions; we must consider whose province it is to study all of these. Further, we must consider all the essential attributes of these same things, and not merely what each one of them is, but also whether each one has one opposite⁶; and (vi.) whether the first principles and elements of things are the genera under which they fall or the pre-existent parts into which each thing is divided; and if the genera, whether they are those which are predicated ultimately of individuals, or the primary genera—e.g., whether “animal” or “man” is the first principle and the more independent of the individual.⁷ Above all we must consider and apply ourselves to the question (7.) whether there is any other cause per se besides matter, and if so whether it is dissociable from matter, and whether it is numerically one or several; and whether there is anything apart from the concrete thing (by the concrete thing I mean matter together with whatever is predicated of it) or nothing; or whether there is in some cases but not in others; and what these cases are.⁸ 996aFurther, (8.) we must ask whether the first principles are limited in number or in kind⁹—both those in the definitions and those in the substrate—and (ix.) whether the principles of perishable and of imperishable things are the same or different; and whether all are imperishable, or those of perishable things are perishable.¹⁰ Further, there is the hardest and most perplexing question of all: (x.) whether Unity and Being (as the Pythagoreans and Plato maintained) are not distinct, but are the substance of things; or whether this is not so, and the substrate is something distinct¹¹(as Empedocles holds of Love,¹² another thinker¹³ of fire, and another¹⁴ of water or air¹⁵); and (xi.) whether the first principles are universal or like individual things¹⁶; and (12.) whether they exist potentially or actually; and further whether their potentiality or actuality depends upon anything other than motion¹⁷; for these questions may involve considerable difficulty. Moreover we must ask (13.) whether numbers and lines and figures and points are substances in any sense, or not; and if they are, whether they are separate from sensible things or inherent in them.¹⁸ With regard to these problems not only is it difficult to attain to the truth, but it is not even easy to state all the difficulties adequately.¹⁹

(1.) Firstly, then, with respect to the first point raised: whether it is the province of one science or of more than one to study all the kinds of causes. How can one science comprehend the first principles unless they are contraries? Again, in many things they are not all present. How can a principle of motion be in immovable things? or the “nature of the Good”? for everything which is good in itself and of its own nature is an end and thus a cause, because for its sake other things come to be and exist; and the end and purpose is the end of some action, and all actions involve motion; thus it would be impossible either for this principle to exist in motionless things or for there to be any absolute Good. Hence in mathematics too nothing is proved by means of this cause, nor is there any demonstration of the kind “because it is better or worse”; indeed no one takes any such consideration into account. And so for this reason some of the sophists, e.g. Aristippus,²⁰ spurned mathematics, on the ground that in the other arts, even the mechanical ones such as carpentry and cobbling, all explanation is of the kind “because it is better or worse,” while mathematics takes no account of good and bad.²¹ 996bOn the other hand if there are several sciences of the causes, and a different one for each different principle, which of them shall we consider to be the one which we are seeking, or whom of the masters of these sciences shall we consider to be most learned in the subject which we are investigating? For it is possible for all the kinds of cause to apply to the same object; e.g. in the case of a house the source of motion is the art and the architect; the final cause is the function; the matter is earth and stones, and the form is the definition. Now to judge from our discussion some time ago²² as to which of the sciences should be called Wisdom, there is some case for applying the name to each of them. Inasmuch as Wisdom is the most sovereign and authoritative kind of knowledge, which the other sciences, like slaves, may not contradict, the knowledge of the end and of the Good resembles Wisdom (since everything else is for the sake of the end ); but inasmuch as it has been defined as knowledge of the first principles and of the most knowable, the knowledge of the essence will resemble Wisdom. For while there are many ways of understanding the same thing, we say that the man who recognizes a thing by its being something knows more than he who recognizes it by its not being something; and even in the former case one knows more than another, and most of all he who knows what it is, and not he who knows its size or quality or natural capacity for acting or being acted upon. Further, in all other cases too, even in such as admit of demonstration, we consider that we know a particular thing when we know what it is (e.g. what is the squaring of a rectangle? answer, the finding of a mean proportional to its sides; and similarly in other instances); but in the case of generations and actions and all kinds of change, when we know the source of motion. This is distinct from and opposite to the end . Hence it might be supposed that the study of each of these causes pertained to a different science.²³ (2.) Again, with respect to the demonstrative principles as well, it may be disputed whether they too are the objects of one science²⁴ or of several.²⁵ By demonstrative I mean the axioms from which all demonstration proceeds, e.g. “everything must be either affirmed or denied,” and “it is impossible at once to be and not to be,” and all other such premisses. Is there one science both of these principles and of substance, or two distinct sciences? and if there is not one, which of the two should we consider to be the one which we are now seeking? It is not probable that both subjects belong to one science; for why should the claim to understand these principles be peculiar to geometry rather than to any other science? Then if it pertains equally to any science, and yet cannot pertain to all, 997acomprehension of these principles is no more peculiar to the science which investigates substances than to any other science. Besides, in what sense can there in be a science of these principles? We know already just what each of them is; at any rate other sciences employ them as being known to us.²⁶ If, however there is a demonstrative science of them, there will have to be some underlying genus, and some of the principles will be derived from axioms, and others will be unproved (for there cannot be demonstration of everything), since demonstration must proceed from something, and have some subject matter, and prove something. Thus it follows that there is some one genus of demonstrable things; for all the demonstrative sciences employ axioms. On the other hand, if the science of substance is distinct from the science of these principles, which is of its own nature the more authoritative and ultimate? The axioms are most universal, and are the first principles of everything. And whose province will it be, if not the philosopher’s, to study truth and error with respect to them?²⁷ (3.) And in general, is there one science of all substances, or more than one?²⁸ if there is not one, with what sort of substance must we assume that this science is concerned? On the other hand, it is not probable that there is one science of all substances; for then there would be one demonstrative of all attributes—assuming that every demonstrative science proceeds from accepted beliefs and studies the essential attributes concerned with some definite subject matter. Thus to study the essential attributes connected with the same genus is the province of the same science proceeding from the same beliefs. For the subject matter belongs to one science, and so do the axioms, whether to the same science or to a different one; hence so do the attributes, whether they are studied by these sciences themselves or by one derived from them.²⁹ (v.) Further, is this study concerned only with substances, or with their attributes as well?³⁰ I mean, e.g., if the solid is a kind of substance, and so too lines and planes, is it the province of the same science to investigate both these and their attributes, in every class of objects about which mathematics demonstrates anything, or of a different science? If of the same, then the science of substance too would be in some sense demonstrative; but it does not seem that there is any demonstration of the “what is it?” And if of a different science, what will be the science which studies the attributes of substance? This is a very difficult question to answer.³¹ (iv.) Further, are we to say that only sensible substances exist, or that others do as well? and is there really only one kind of substance, or more than one 997b(as they hold who speak of the Forms and the Intermediates, which they maintain to be the objects of the mathematical sciences)? In what sense we Platonists hold the Forms to be both causes and independent substances has been stated³² in our original discussion on this subject. But while they involve difficulty in many respects, not the least absurdity is the doctrine that there are certain entities apart from those in the sensible universe, and that these are the same as sensible things except in that the former are eternal and the latter perishable.³³ For Platonists say nothing more or less than that there is an absolute Man, and Horse, and Health; in which they closely resemble those who state that there are Gods, but of human form; for as the latter invented nothing more or less than eternal men, so the former simply make the Forms eternal sensibles. Again, if anyone posits Intermediates distinct from Forms and sensible things, he will have many difficulties; because obviously not only will there be lines apart from both Ideal and sensible lines, but it will be the same with each of the other classes.³⁴ Thus since astronomy is one of the mathematical sciences, there will have to be a heaven besides the sensible heaven, and a sun and moon, and all the other heavenly bodies. But how are we to believe this? Nor is it reasonable that the heaven should be immovable; but that it should move is utterly impossible.³⁵ It is the same with the objects of optics and the mathematical theory of harmony; these too, for the same reasons, cannot exist apart from sensible objects. Because if there are intermediate objects of sense and sensations, clearly there will also be animals intermediate between the Ideal animals and the perishable animals.³⁶ One might also raise the question with respect to what kind of objects we are to look for these sciences. For if we are to take it that the only difference between mensuration and geometry is that the one is concerned with things which we can perceive and the other with things which we cannot, clearly there will be a science parallel to medicine (and to each of the other sciences), intermediate between Ideal medicine and the medicine which we know. Yet how is this possible? for then there would be a class of healthy things apart from those which are sensible and from the Ideally healthy. Nor, at the same time, is it true that mensuration is concerned with sensible and perishable magnitudes; for then it would perish as they do. Nor, again, can astronomy be concerned with sensible magnitudes or with this heaven of ours; 998afor as sensible lines are not like those of which the geometrician speaks (since there is nothing sensible which is straight or curved in that sense; the circle³⁷ touches the ruler not at a point, but 〈along a line〉 as Protagoras used to say in refuting the geometricians), so the paths and orbits of our heaven are not like those which astronomy discusses, nor have the symbols of the astronomer the same nature as the stars. Some, however, say that these so-called Intermediates between Forms and sensibles do exist: not indeed separately from the sensibles, but in them. It would take too long to consider in detail all the impossible consequences of this theory, but it will be sufficient to observe the following. On this view it is not logical that only this should be so; in clearly it would be possible for the Forms also to be in sensible things; for the same argument applies to both. Further, it follows necessarily that two solids must occupy the same space; and that the Forms cannot be immovable, being present in sensible things, which move. And in general, what is the object of assuming that Intermediates exist, but only in sensible things? The same absurdities as before will result: there will be a heaven besides the sensible one, only not apart from it, but in the same place; which is still more impossible.³⁸