Nor, again, is the Broad the genus of which the Deep is a species; for then body would be a kind of plane. Further, how will it be possible for figures to contain points? Lines, planes, and solids are generated from varieties of the Great and Small, but points cannot be, having no magnitude; how, then, can the latter be present in the former? Plato steadily rejected this class of objects as a geometrical fiction, but he recognized "the beginning of a line," and he frequently assumed this latter class, i.e. the " indivisible lines." That Plato denied the existence of the point and asserted that of indivisible lines is not directly stated elsewhere, but the same views are ascribed to Xenocrates, and were attacked in the treatise Xenocrates De lineis insecabilibus.
See Ross ad loc.
But these must have some limit; and so by the same argument which proves the existence of the line, the point also exists. Sc. if the point is the limit of the line. In general, although Wisdom is concerned with the cause of visible things, we have ignored this question (for we have no account to give of the cause from which change arises), Cf. Aristot. Met. 7.5 and Aristot. Met. 1.9. and in the belief that we are accounting for their substance we assert the existence of other substances; but as to how the latter are the substances of the former, our explanation is worthless—for "participation," as we have said before, Aristot. Met. 1.12. means nothing. And as for that which we can see to be the cause in the sciences, and through which all mind and all nature works—this cause The final cause. Cf. Aristot. Met. 1.6.9-10. which we hold to be one of the first principles—the Forms have not the slightest bearing upon it either. Philosophy has become mathematics for modern thinkers, e.g.
Speusippus, for whom see Aristot. Met.
7.2.4. although they profess Cf. Plat. Rep.531c-d that mathematics is only to be studied as a means to some other end.
Further, one might regard the substance which they make the material substrate as too mathematical, and as being a predicate and differentia of substance or matter rather than as matter itself, I mean the "Great and Small," which is like the "Rare and Dense" of which the physicists speak, Cf. iv. 10. holding that they are the primary differentiae of the substrate; because these qualities are a species of excess and defect. Also with regard to motion, if the "Great and Small" is to constitute motion, obviously the Forms will be moved; if not, whence did it come? On this view the whole study of physics is abolished. And what is supposed to be easy, to prove that everything is One, does not follow; because from their exposition The word e)/kqesis has various technical meanings. The process referred to here apparently consisted in taking, e.g., particular men, and reducing them with reference to their common nature to a single unit or universal, "man"; then taking "man," "horse," "dog," etc. and treating them in the same way, until a unit is reached which embraces everything (Alexander). it does not follow, even if you grant them all their assumptions that everything is One, but only that there is an absolute One— and not even this, unless you grant that the universal is a class; which is impossible in some cases. Probably those of relative or negative terms. Cf. Aristot. Met. 1.3. Nor is there any explanation of the lines, planes and solids which "come after" the Numbers See note on Aristot. Met.
1.23.: neither as to how they exist or can exist, nor as to what their importance is. They cannot be Forms (since they are not numbers) or Intermediates (which are the objects of mathematics) or perishables; clearly they form yet another fourth class. In general, to investigate the elements of existing things without distinguishing the various senses in which things are said to exist is a hopeless task; especially when one inquires along these lines into the nature of the elements of which things are composed. For (a) we cannot surely conceive of the elements of activity or passivity or straightness; this is possible, if at all, only in the case of substances. Hence to look for, or to suppose that one has found, the elements of everything that exists, is a mistake. (b) How can one apprehend the elements of everything? Obviously one could not have any previous knowledge of anything; because just as a man who is beginning to learn geometry can have previous knowledge of other facts, but no previous knowledge of the principles of that science or of the things about which he is to learn, so it is in the case of all other branches of knowledge. Hence if there is a science which embraces everything e.g. Plato's Dialectic. (as some say), the student of it can have no previous knowledge at all.
But all learning proceeds, wholly or in part, from what is already known; whether it is through demonstration or through definition—since the parts of the definition must be already known and familiar. The same is true of induction. On the other hand, assuming that this knowledge should turn out to be innate, Cf. the doctrine of a)na/mnhsis (recollection), Plat. Meno 81c, Plat. Phaedo 72e. it is astonishing that we should possess unawares the most important of the sciences. Further, how is one to know of what elements things consist? how is it to be established? Even this presents a difficulty, because the facts might be disputed, as happens in the case of certain syllables—for some say that ZA is composed of S, D and A, while others say that it is a distinct sound and not any one of those which are familiar to us. stoixei=on means both "an element" and "a letter of the alphabet"; hence letters are often used as analogues of the material elements. The point here is: Is Z or rather the Greek z ) a stoixei=on, or is it further analyzable? Since this can be disputed, we must expect differences of opinion about the elements in general. Further, how can one gain knowledge of the objects of a particular sense-perception without possessing that sense? Yet it should be possible, that if the elements of which all things consist, as composite sounds consist of their peculiar Peculiar to them as sounds, not as individual sounds. If sights and sounds had the same elements, sight, which knows those elements as composing sights, would know them as composing sounds; i.e., we could see sounds. elements, are the same. Thus it is obvious, from the statements of earlier thinkers also, that all inquiry is apparently directed towards the causes described in the Physics, Aristot. Phys. 2.3, 7. and that we cannot suggest any other cause apart from these. They were, however, only vaguely conceived; and although in one sense they have all been stated before, in another they have not been stated at all. For the earliest philosophy speaks falteringly, as it were, on all subjects; being new and in its infancy. Even Empedocles says that bone exists by virtue of its ratio, Empedocles Fr. 96, 98 (Diels), Ritter and Preller 175. Aristotle says that Empedocles had some idea of the essence or formal cause, but did not apply it generally.
which is the definition or essence of a thing. But by similar reasoning both flesh and every other thing, or else nothing at all, must be ratio; for it must be because of this, and not because of their matter—which he calls fire, earth, water and air—that flesh and bone and every other thing exists. If anyone else had stated this, he would necessarily have agreed, but his own statement was not clear. These and similar points have been explained already. We will now return to the difficulties which might be raised about these same questions, for they may throw some light upon subsequent difficulties. The reference is to Book 3. See Introduction.
The study of Truth is in one sense difficult, in another easy. This is shown by the fact that whereas no one person can obtain an adequate grasp of it, we cannot all fail in the attempt; each thinker makes some statement about the natural world, and as an individual contributes little or nothing to the inquiry; but a combination of all conjectures results in something considerable. Thus in so far as it seems that Truth is like the proverbial door which no one can miss, Leutsch and Schneidewin, Paroemiographi, 2.678. in this sense our study will be easy; but the fact that we cannot, although having some grasp of the whole, grasp a particular part, shows its difficulty. However, since difficulty also can be accounted for in two ways, its cause may exist not in the objects of our study but in ourselves: just as it is with bats' eyes in respect of daylight, so it is with our mental intelligence in respect of those things which are by nature most obvious. It is only fair to be grateful not only to those whose views we can share but also to those who have expressed rather superficial opinions. They too have contributed something; by their preliminary work they have formed our mental experience. If there had been no Timotheus, Of Miletus, 446 (?)— 357 B.C. we should not possess much of our music; and if there had been no Phrynis, Of Mytilene; he is referred to as still alive in Aristoph. Cl. 971. Both Phrynis and Timotheus are criticized in the fragment of Pherecrates Chiron translated by Rogers in the appendix to his ed. of the Clouds. there would have been no Timotheus. It is just the same in the case of those who have theorized about reality: we have derived certain views from some of them, and they in turn were indebted to others. Moreover, philosophy is rightly called a knowledge of Truth. The object of theoretic knowledge is truth, while that of practical knowledge is action; for even when they are investigating how a thing is so, practical men study not the eternal principle but the relative and immediate application. But we cannot know the truth apart from the cause. Now every thing through which a common quality is communicated to other things is itself of all those things in the highest degree possessed of that quality (e.g.
fire is hottest, because it is the cause of heat in everything else); hence that also is most true which causes all subsequent things to be true. Therefore in every case the first principles of things must necessarily be true above everything else—since they are not merely sometimes true, nor is anything the cause of their existence, but they are the cause of the existence of other things,—and so as each thing is in respect of existence, so it is in respect of truth. Moreover, it is obvious that there is some first principle, and that the causes of things are not infinitely many either in a direct sequence or in kind. For the material generation of one thing from another cannot go on in an infinite progression (e.g. flesh from earth, earth from air, air from fire, and so on without a stop); nor can the source of motion (e.g. man be moved by air, air by the sun, the sun by Strife, Aristotle is evidently thinking of Empedocles' system. with no limit to the series). In the same way neither can the Final Cause recede to infinity—walking having health for its object, and health happiness, and happiness something else: one thing always being done for the sake of another. And it is just the same with the Formal Cause. For in the case of all intermediate terms of a series which are contained between a first and last term, the prior term is necessarily the cause of those which follow it; because if we had to say which of the three is the cause, we should say "the first." At any rate it is not the last term, because what comes at the end is not the cause of anything. Neither, again, is the intermediate term, which is only the cause of one (and it makes no difference whether there is one intermediate term or several, nor whether they are infinite or limited in number). But of series which are infinite in this way, and in general of the infinite, all the parts are equally intermediate, down to the present moment. Thus if there is no first term, there is no cause at all. On the other hand there can be no infinite progression downwards (where there is a beginning in the upper direction) such that from fire comes water, and from water earth, and in this way some other kind of thing is always being produced. There are two senses in which one thing "comes from" another—apart from that in which one thing is said to come after another, e.g. the Olympian "from" e)k means not only "from" but "after"; Aristotle dismisses this latter meaning. The Isthmian fell alternatively in the same year as the Olympian festival; when this happened the former was held in the spring and the latter in the summer.
Cf. Aristot. Met. 5.24.5. the Isthmian games—either as a man comes from a child as it develops, or as air comes from water. Now we say that a man "comes from" a child in the sense that that which has become something comes from that which is becoming: i.e. the perfect from the imperfect. (For just as "becoming" is always intermediate between being and not-being, so is that which is becoming between what is and what is not. The learner is becoming informed, and that is the meaning of the statement that the informed person "comes from" the learner.) On the other hand A comes from B in the sense that water comes from air by the destruction of B. Hence the former class of process is not reversible (e.g.
a child cannot come from a man, for the result of the process of becoming is not the thing which is becoming, but that which exists after the process is complete. So day comes from early dawn, because it is after dawn; and hence dawn does not come from day). But the other class is reversible. In both cases progression to infinity is impossible; for in the former the intermediate terms must have an end, and in the second the process is reversible, for the destruction of one member of a pair is the generation of the other. At the same time the first cause, being eternal, cannot be destroyed; because, since the process of generation is not infinite in the upper direction, that cause which first, on its destruction, became something else, cannot possibly be eternal. The argument is elliptical and confused. The meaning is this: Since there is an upward limit, there is a first cause which is eternal, being independent of any other cause. Therefore this cause cannot cause other things by its destruction, in the manner just described. Further, the Final cause of a thing is an end, and is such that it does not happen for the sake of some thing else, but all other things happen for its sake.
So if there is to be a last term of this kind, the series will not be infinite; and if there is no such term, there will be no Final cause.
Those who introduce infinity do not realize that they are abolishing the nature of the Good (although no one would attempt to do anything if he were not likely to reach some limit); nor would there be any intelligence in the world, because the man who has intelligence always acts for the sake of something, and this is a limit, because the end is a limit. Nor again can the Formal cause be referred back to another fuller definition; for the prior definition is always closer, and the posterior is not; and where the original definition does not apply, neither does the subsequent one. Further, those who hold such a view do away with scientific knowledge, for on this view it is impossible to know anything until one comes to terms which cannot be analyzed. Understanding, too, is impossible; for how can one conceive of things which are infinite in this way? It is different in the case of the line, which, although in respect of divisibility it never stops, yet cannot be conceived of unless we make a stop (which is why, in examining an infinite i.e.
infinitely divisible. line, one cannot count the sections). It does not follow that we can apprehend that which is infinite because we can apprehend a line which is infinitely divisible. We can only really apprehend the line by setting a limit to its divisibility and regarding it simply as divisible into a very great (but not infinite) number of sections. An infinite number of sections can neither be apprehended nor counted. Even matter has to be conceived under the form of something which changes, Matter too, which is infinite in its varieties, can only be apprehended in the form of concrete sensible objects which are liable to change. This seems to be the meaning of the text, but Ross's reading and interpretation may be right: see his note ad loc. and there can be nothing which is infinite. i.e. not actually, but only potentially. In any case the concept of infinity is not infinite. Cf. the third note above. Again, if the kinds of causes were infinite in number it would still be impossible to acquire knowledge; for it is only when we have become acquainted with the causes that we assume that we know a thing; and we cannot, in a finite time, go completely through what is additively infinite. The effect of a lecture depends upon the habits of the listener; because we expect the language to which we are accustomed, and anything beyond this seems not to be on the same level, but somewhat strange and unintelligible on account of its unfamiliarity; for it is the familiar that is intelligible. The powerful effect of familiarity is clearly shown by the laws, in which the fanciful and puerile survivals prevail, through force of habit, against our recognition of them. Thus some people will not accept the statements of a speaker unless he gives a mathematical proof; others will not unless he makes use of illustrations; others expect to have a poet adduced as witness. Again, some require exactness in everything, while others are annoyed by it, either because they cannot follow the reasoning or because of its pettiness; for there is something about exactness which seems to some people to be mean, no less in an argument than in a business transaction. Hence one must have been already trained how to take each kind of argument, because it is absurd to seek simultaneously for knowledge and for the method of obtaining it; and neither is easy to acquire. Mathematical accuracy is not to be demanded in everything, but only in things which do not contain matter. Hence this method is not that of natural science, because presumably all nature is concerned with matter. Hence we should first inquire what nature is; for in this way it will become clear what the objects of natural science are [and whether it belongs to one science or more than one to study the causes and principles of things]. These words have evidently been inserted to form a kind of link with the subject matter of the Metaphysics. The book is almost certainly part of a quite independent treatise; see Introduction.
It 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. To 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 subjects The principles and causes referred to in Book I. which we discussed in our prefatory remarks. (1.) Does the study of the causes belong to one science or to more than one? The problem is discussed Aristot. Met. 3.2.1-10, and answered Aristot. Met. 4.1. (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? Discussed Aristot. Met. 3.2.10-15; answered Aristot. Met.
4.2. 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? Discussed Aristot. Met.
3.2.15-17; answered Aristot. Met.
4.2.9-10, Aristot. Met.
6.1. 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)? Discussed Aristot. Met. 3.2.20-30 answered Aristot. Met. 12.6-10, and also by the refutation of the Platonic Ideas and Intermediates in Books 13 and 14. 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 opposite Discussed Aristot. Met. 3.2.18-19; answered Aristot. Met. 4.2.8-25.; 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. Discussed Aristot. Met. 3.3; answered Aristot. Met. 7.10, 12-13 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. Discussed iv. 1-8. For answers to these questions see Aristot. Met. 7.8, 13-14; Aristot. Met. 12.6-10; Aristot. Met. 13.10.
Further, (8.) we must ask whether the first principles are limited in number or in kind Discussed Aristot. Met. 3.4.8-10; answered Aristot. Met. 12.4-5, Aristot. Met.
13.10. —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. Discussed Aristot. Met. 3.4.11-23; for Aristotle's general views on the subject see Aristot. Met. 7.7-10, Aristot. Met. 12.1-7. 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 distinct Discussed Aristot. Met. 3.4.24-34; answered Aristot. Met. 7.16.3-4, Aristot. Met.
10.2. (as Empedocles holds of Love, Actually Love was no more the universal substrate than was any other of Empedocles' elements; Aristotle appears to select it on account of its unifying function. another thinker Heraclitus. of fire, and another Thales. of water or air Anaximenes. ); and (xi.) whether the first principles are universal or like individual things Discussed Aristot. Met. 3.6.7-9; for the answer see Aristot. Met. 7.13-15, Aristot. Met.
13.10.; and (12.) whether they exist potentially or actually; and further whether their potentiality or actuality depends upon anything other than motion Discussed Aristot. Met. 3.6.5-6; for the relation of potentiality to actuality see Aristot.
Met. 9.1-9; for actuality and motion see Aristot. Met. 12.6-7.; 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. Discussed Aristot. Met. 3.5; answered Aristot. Met. 13.1-3, 6-9; Aristot. Met. 14.1-3, 5, 6. 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. For another statement of the problems sketched in this chapter see Aristot. Met. 9.1, 2. (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, Founder of the Cyrenaic school in the early fourth century. 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. For a defense of mathematics see Aristot. Met. 13.3.10-12.
On 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 ago Cf. Aristot. Met.
1.2.5-6. 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. See Aristot. Met. 4.1 (2.) Again, with respect to the demonstrative principles as well, it may be disputed whether they too are the objects of one science sc. the science which studies the four causes. or of several. Cf. Aristot. Met. 3.1.5. 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, comprehension 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. sc.
and so there can be no science which defines them. 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? For the answer see Aristot. Met.
4.3. (3.) And in general, is there one science of all substances, or more than one? Cf. Aristot. Met. 3.1.6. 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. For the answer see Aristot. Met. 4.2.9-10, Aristot. Met.
6.1. (v.) Further, is this study concerned only with substances, or with their attributes as well? Cf. Aristot. Met.
3.1.8-10. 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. This problem, together with the appendix to it stated in Aristot. Met. 3.1.9-10, is answered in Aristot. Met. 4.2.8-25. (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 (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 stated Aristot. Met.
1.6. 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. As it stands this is a gross misrepresentation; but Aristotle's objection is probably directed against the conception of Ideas existing independently of their particulars. See Introduction. 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. sc. of objects of mathematical sciences.
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. The reference is to the supposed "intermediate" heaven. A "heaven" (including heavenly bodies) without motion is unthinkable; but a