(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, Footnote 1Founder 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. Footnote 2For 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 Footnote 3Cf. 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. Footnote 4See 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 Footnote 5sc. the science which studies the four causes. or of several. Footnote 6Cf. 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. Footnote 7sc. 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? Footnote 8For the answer see Aristot. Met. 4.3.
(3.) And in general, is there one science of all substances, or more than one? Footnote 9Cf. 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. Footnote 10For 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? Footnote 11Cf. 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. Footnote 12This 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 Footnote 13Aristot. 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. Footnote 14As 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. Footnote 15sc. 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. Footnote 16The reference is to the supposed intermediate
heaven. A heaven
(including heavenly bodies) without motion is unthinkable; but a non-sensible heaven can have no motion. 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. Footnote 17If there are intermediate,
i.e. non-sensible, sights and sounds, there must be intermediate
faculties of sight and hearing, and intermediate
animals to exercise these faculties; which is absurd.
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;
for 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 circle Footnote 18i.e., the visible circle which we draw. Like the ruler, it is geometrically imperfect; thus they touch at more than one point. 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. Footnote 19The problem is dealt with partly in Aristot. Met. 12.6-10, where Aristotle describes the eternal moving principles, and partly in Books 13 and 14, where he argues against the Platonic non-sensible substances.