2-2
BOOK III
METAPHYSICAL PROBLEMSLesson 1
338. Having indicated in Book II (331) the method of considering the truth, the Philosopher now proceeds with his study of the truth. First he proceeds disputatively, indicating those points which are open to question so far as the truth of things is concerned. Second (529), he begins to establish what is true, and he does this in Book IV, which begins: "There is a certain science."
The first part is divided into two sections. In the first, he states what he intends to do. In the second (346), he proceeds to do it ("The first problem").
In regard to the first he does two things. First, he states what he intends to do. Second (339), he gives the reasons for this ("Now for those").
He says first, then, that with a view to this science which we are seeking about first principles and what is universally true of things, we must attack, first of all, those subjects about which it is necessary to raise questions before the truth is established. Now there are disputed points of this kind for two reasons, either because the ancient philosophers entertained a different opinion about these things than is really true, or because they completely neglected to consider them.
339. Here he gives four arguments in support of this thesis:
First, he says that for those who wish to investigate the truth it is "worth the while," i.e., worth the effort, "to ponder these difficulties well," i.e., to examine carefully those matters which are open to question. This is necessary because the subsequent study of truth is nothing else than the solution of earlier difficulties. Now in loosening a physical knot it is evident that one who is unacquainted with this knot cannot loosen it. But a difficulty about some subject is related to the mind as a physical knot is to the body, and manifests the same effect. For insofar as the mind is puzzled about some subject, it experiences something similar to those who are tightly bound. For just as one whose feet are tied cannot move forward on an earthly road, in a similar way one who is puzzled, and whose mind is bound, as it were, cannot move forward on the road of speculative knowledge. Therefore, just as one who wishes to loosen a physical knot must first of all inspect the knot and the way in which it is tied, in a similar way one who wants to solve a problem must first survey all the difficulties and the reasons for them.
340. Here he gives the second argument. He says that those who wish to investigate the truth without first considering the problem are like those who do not know where they are going. This is true for this reason, that, just as the terminus of a journey is the goal intended by one who travels on foot, in a similar way the solution of a problem is the goal intended by one who is seeking the truth. But it is evident that one who does not know where he is going cannot go there directly, except perhaps by chance. Therefore, neither can one seek the truth directly unless he first sees the problem.
341. Here he gives the third argument. He says that, just as one who is ignorant of where he is going does not know whether he should stop or go further when he reaches his appointed goal, in a similar way one who does not know beforehand the problem whose solution marks the terminus of his search cannot know when he finds the truth which he is seeking and when not. For he does not know what the goal of his investigations is, but this is evident to one who knew the problem beforehand.
342. He gives the fourth argument, which is taken from the viewpoint of a judge. For a judge must pass judgment on the things which he hears. But just as one can pass judgment in a lawsuit only if he hears the arguments on both sides, in a similar way one who has to pass judgment on a philosophy is necessarily in a better position to do so if he will hear all the arguments, as it were, of the disputants.
343. Now it must be noted that it was for these reasons that Aristotle was accustomed, in nearly all his works, to set forth the problems which emerge before investigating and establishing what is true. But while in other works Aristotle sets down the problems one at a time in order to establish the truth about each one, in this work he sets forth all the problems at once, and afterwards in the proper order establishes the things that are true. The reason for this is that other sciences consider the truth in a particular way, and therefore it belongs to them to raise problems of a particular kind about individual truths. But just as it belongs to this science to make a universal study of truth, so also does it belong to it to discuss all the problems which pertain to the truth. Therefore it does not discuss its problems one at a time but all at once.
344. There can also be another reason [why Aristotle proceeds in this way], namely, that those problems on which he touches are chiefly those about which the philosophers have held different opinions. However, he does not proceed to investigate the truth in the same order as the other philosophers did. For he begins with things which are sensible and evident and proceeds to those which are separate from matter, as is evident below in Book VII (1566), whereas the other philosophers wanted to apply intelligible and abstract principles to sensible things. Hence, because he did not intend to establish the truth in the same order as that followed by the other philosophers, and from whose views these problems arise, he therefore decided to give first all the problems in a separate section, and afterwards to solve these problems in their proper order.
345. Averroes gives another reason [for Aristotle's procedure]. He says that Aristotle proceeds in this way because of the relationship of this science to logic, which will be touched on below in Book IV (588); and therefore he made dialectical discussion a principal part of this science.
Lesson 2
Q. 1: Does this science make use of all four causes?
346. Following out his announced plan, the Philosopher begins to set down the problems which are encountered in establishing the truth; and he divides this into two parts. In the first, he gives these problems; and in the second (369), he gives the reasons for these problems, by indicating the arguments on either side of the question ("Therefore let us discuss").
Now it was stated in Book II (335) that it is necessary to seek the method of a science before seeking the science itself. Therefore he gives, first, the problems which pertain to this science's method of investigation. Second (355), he gives the problems which pertain to the first principles with which this science deals, as has been stated in Book I (36) ("And we must inquire").
Now a science is concerned with two things, as was said in Book II (336), namely, a study of the causes by which it demonstrates and the things with which it deals. Hence in regard to the first point he does two things. First, he presents a problem concerning the investigation of causes. Second (347), he presents several problems concerning the things with which this science deals ("And there is also the problem")
He says, then, that the first problem is one which we proposed in the issues raised at the end of Book II (336), which is, so to speak, the prologue to the whole of science, i.e., whether a study of the four causes in their four classes belongs to one science or to many different sciences And this is to ask whether it belongs to one science, and especially to this science, to demonstrate by means of all the causes, or rather whether some sciences demonstrate by one cause and some by another.
Q. 2: Does it consider both principles of substance and principles of knowledge?
347. Here he raises problems about the things which this science considers. First, he inquires about the things which this science considers about substances; and second (350), about substances themselves ("It is also necessary"). In regard to the first he raises three questions. For if it is supposed, from what was said in Book I (35), that this science considers first principles, the first question here will be whether it belongs to this science to know only the first principles of substances, or also to consider the first principles of demonstration, by means of which all sciences demonstrate. For example, should this science consider whether it is possible to affirm and deny one and the same thing at the same time or not? And the same thing applies to the other first and self-evident principles of demonstration.
Q. 3: Is its subject all substances, or do different sciences consider different substances?
348. And if this science considers substance as the primary kind of being, the second question is whether there is one science which considers all substances, or whether there are many sciences which consider different substances. For it seems that there should be many sciences which consider many substances.
Q. 4: Is it distinct from other sciences?
349. And if there are many sciences which consider many substances, the third question is whether all are "cognate," i.e., whether all belong to one class, as geometry and arithmetic belong to the class of mathematical science, or whether they do not, but some to the class of wisdom and some to another class, for example, to the class of natural philosophy or to that of mathematical science. For according to the first point of view it seems that they do not belong to one class, since material and immaterial substances are not known by the same method.
Q. 5. Are there immaterial substances, and of what kind?
350. Here he adds to the number of questions about substance; and he does this by raising two questions. The first question is whether sensible substances alone must be held to exist, as the philosophers of nature claimed, or whether there are in addition to sensible substances other immaterial and intelligible substances, as Plato claimed.
351. And if there are some substances separate from sensible things, the second question is whether "they are unique," i.e., whether they belong only to one class, or whether there are many classes of such substances. For certain men, understanding that there is a twofold abstraction, namely, of the universal from the particular, and of the mathematical form from sensible matter, held that each class is self-subsistent. Thus they held that there are separate substances which are subsisting abstract universals, and between these and particular sensible substances they placed the objects of mathematics-numbers, continuous quantities, and figures-which they regarded as separate subsisting things. Concerning the questions which have now been raised, then, it is necessary to investigate them below. He does this, first, by arguing both sides of the question, and, second, by determining its truth.
Q. 6: Does this science consider accidents or properties of substance?
352. Here he asks whether this science's investigations extend to accidents; and he raises three questions. The first is whether this science, seeing that it is called the philosophy of substance, speculates about substance alone, or whether it also speculates about the proper accidents of substance; for it seems to be the office of the same science to consider a subject and the proper accidents of that subject.
Q. 7: How does it differ from logic in considering these things?
353. The second question is whether this science considers certain things which seem to be proper accidents of being and which belong to all beings, namely, sameness and difference, likeness and unlikeness, contrariety, priority, and posteriority, and all others of this kind which are treated by the dialecticians, who deal with all things. However, they do not examine such things according to necessary premises but according to probable ones. For from one point of view it seems that, since these accidents are common ones, they pertain to first-philosophy; but from another point of view it seems that, since they are considered by the dialecticians, whose office it is to argue from Probabilities, an examination of them does not belong to the consideration of the philosopher, whose office it is to demonstrate.
Q. 8: Does it consider how these accidents are inter-related?
354. And since certain proper attributes naturally flow from these common accidents of being, the third question is whether it is the function of the philosopher to consider in regard to the common accidents only their quiddity or also their properties; for example, whether there is one opposite for each one.
Lesson 3
Q. 9: How are substances to be analysed, into elements or into genera?
355. Having raised questions pertaining to the method of investigation which this science uses, the Philosopher now raises questions pertaining to the things which this science considers. And since this science considers first principles, as has been stated in Book I (35), he therefore raises here questions pertaining to the principles of things.
Now both the Forms and the objects of mathematics were held to be the first principles of things. Therefore, first, he raises questions concerning the Forms; and second (366), concerning the objects of mathematics ("And in addition to these").
In regard to the first he does two things. First, he asks what things are principles; and second (361), what sort of beings they are ("Further, we must inquire").
And since separate universals were held to be the principles of things, he asks, first, whether universals are the principles of things; and second (357), whether separate entities are the principles of things ("But most of all").
Concerning the first he asks two questions. The first is whether genera constitute the principles and elements of things, or the ultimate parts into which each individual thing is dissolved. This question arises because an element is that of which a thing is first composed and into which it is ultimately dissolved. Now we find a twofold mode of composition and dissolution. One has to do with the intelligible constitution, in which species are resolved into genera, and according to this mode genera seem to be the principles and elements of things, as Plato claimed. The other mode of composition and dissolution has to do with the real order; for example, natural bodies are composed of fire, air, water and earth, and are dissolved into these. It was for this reason that the natural philosophers claimed that the elements constitute the first principles of things.
356. And assuming that genera are the principles of things, the second question is whether the principles of things are to be identified with the universals which are predicated of individual things, i.e., the lowest species, which he calls genera after the usage of the Platonists, because the lowest species contain under themselves many individuals just as genera contain many species; or whether it is rather the first and most common genera that constitute principles, for example, which of the two is more of a principle, animal or man; for man is a principle according to the Platonists, and is more real than any singular man. Now this problem arises because of two divisions which reason makes. One of these is that whereby we divide genera into species, and the other is that whereby we resolve species into genera. For it seems that whatever is the last term in a process of division is always the first principle and element in a process of composition.
Q. 10: Is there an immaterial principle? Is it one or many?
357. Here he inquires whether separate entities are the principles of things; and he raises four questions. For since the first philosophers of nature posited only a material cause, the first question is whether besides matter there is anything else that is a cause in the proper sense or not.
358. And granted that there is some other cause besides matter, the second question is whether it is separable from matter, as Plato held, or as Pythagoras held.
359. And if there is something separable from matter, the third question is whether it is a single thing, as Anaxagoras claimed, or many, as Plato and Aristotle himself claimed.
Q. 11: Is individuality distinct from the specific form?
360. The fourth question is whether there is anything "besides the synolon," i.e., the concrete whole, or nothing; or whether there is something in certain cases and not in others; and what kind of things they are in those cases in which there is something else, and what kind of things they are in those in which there is not. And he explains what a synolon or concrete whole is; i.e., it is matter when something is predicated of it. Now in order to understand this we must note that Plato claimed that man and horse, and universals which are predicated in this way, are certain separate Forms; and that man is predicated of Socrates or Plato by reason of the fact that sensible matter participates in a separate Form. Hence Socrates or Plato is called a synolon or concrete whole, because each is constituted as a result of matter participating in a separate form. And each is, as it were, a kind of predicate of matter. Hence the Philosopher asks here whether the whatness of the individual thing is something else in addition to the individual thing itself, or not; or also whether it is something rise in the case of some things and not in that of others. The Philosopher will answer this question in Book VII (7356).
361. Here he raises questions about the way in which principles exist. And since being is divided by the one and many, and by act and potency, he asks, first, whether these principles are one or many; and second (365), whether they are actual or potential ("Again, we must inquire"). In regard to the first he asks four questions:
Q. 12 The first is whether the principles of things are limited in number or in kind; as we say, for example, that there are three principles of nature. Now the statement that they are limited in number can mean that the principle of nature is numerically a single form and a single matter and privation. And the statement that they are limited in kind can mean that there are many material principles which have in common the specific nature of material principle, and so on for the rest. And since some of the philosophers, such as the Platonists, attributed formal causes to things, while others, such as the ancient natural philosophers, attributed only material causes to things, he adds that this question is applicable both "in the intelligible structures," i.e., in formal causes, "and in the underlying subject," i.e., in material causes.
Q. 13: Are the principles of corruptible and incorruptible things the same or different?
362. (2) The second question is whether the principles of corruptible and of incorruptible things are the same or different. And if they are different, whether all are incorruptible, or whether the principles of corruptible things are corruptible and those of incorruptible things are incorruptible.
Q. 14: Are "one" and "being" the same as or distinct from specific natures?
363. (3) The third question is whether unity and being signify the very substance of things and not something added to the substance of things, as the Pythagoreans and Platonists claimed; or whether they do not signify the substance of things, but something else is the subject of unity and being, for example, fire or air or something else of this kind, as the ancient philosophers of nature held. Now he says that this question is the most difficult and most puzzling one, because on this question depends the entire thought of Plato and Pythagoras, who held that numbers are the substance of things.
Lesson 4: Answers
Q 1: Can one science consider many causes?
369. Having raised the questions which cause difficulty in this science, Aristotle begins here to treat them dialectically. This is divided into three parts. In the first part, he treats the questions which pertain to the method of investigation of this science. In the second (403), he treats the questions which pertain to substances ("Furthermore, there is"). In the third (423), he treats the questions which pertain to the principles of substances ("Concerning the principles").
In regard to the first he does three things. First, he argues dialectically about this science's method of investigation, with reference to the causes by means of which it demonstrates; second (387), with reference to the first principles of demonstration ("But insofar"); and third (393), with reference to substances themselves ("And there is the problem").
In regard to the first he does two things. First, he takes up again the question about which he plans to argue dialectically, concluding from the order in which the questions have been listed that it is necessary first to debate those issues which were stated first in the list of questions, namely, whether it is the function of one science or of many to investigate all the classes of causes; so that in this way the order of argument corresponds to the order in which the questions have been raised.
384. However, we do not find that Aristotle explicitly solves this question later on, though his solution can be ascertained from the things which he establishes below in different places. For in Book IV (533) he establishes that this science considers being as being, and therefore that it also belongs to it, and not to the philosophy of nature, to consider first substances; for there are other substances besides mobile ones.
But every substance is either a being of itself, granted that it is only a form; or it is a being by its form, granted that it is composed of matter and form. Hence inasmuch as this science considers being, it considers the formal cause before all the rest. But the first substances are not known by us in such a way that we know what they are, as can be understood in some way from the things established in Book IX (1904); and thus in our knowledge of them the formal cause has no place.
But even though they are immobile in themselves, they are nevertheless the cause of motion in other things after the manner of an end. Hence inasmuch as this science considers first substances, it belongs to it especially to consider the final cause and also in a way the efficient cause.
But to consider the material cause in itself does not belong to it in any way, because matter is not properly a cause of being but of some definite kind of being, namely, mobile substance. However, such causes belong to the consideration of the particular sciences, unless perhaps they are considered by this science inasmuch as they are contained under being; for it extends its analysis to all things in this way.
385. Now when these things are seen it is easy to answer the arguments which have been raised. For, first, nothing prevents the different causes in this science from belonging to a single existing thing, even though they are not contraries, because they are reducible to one thing-being in general-as has been stated (384).
And in a similar way, even though not every science considers all of the causes, still nothing prevents one science from being able to consider all of the causes or several of them insofar as they are reducible to some one thing. But to be more specific, it must be said that in the case of immobile things nothing prevents the source of motion and the end or good from being investigated. By immobile things I mean here those which are still causes of motion, as the first substances. However, in the case of those things which are neither moved cause motion there is no investigation of the source of motion, or of the end in the sense of the end of motion, although an end can be considered as the goal of some operation which does not involve motion. For if there are held to be intellectual substances which do not cause motion, as the Platonists claimed, still insofar as they have an intellect and will it is necessary to hold that they have an end and a good which is the object of their will. However, the objects of mathematics neither are moved nor cause motion nor have a will. Hence in their case the good is not considered under the name of good and end, although in them we do consider what is good, namely, their being and what they are. Hence the statement that the good is not found in the objects of mathematics is false, as he proves below in Book IX (1888) .
386. The reply to the second question is already clear; for a study of the three causes, about which he argued dialectically, belongs to this science.
Lesson 5
Q. 2: Is the science of substance also that of first principles?
387. Having debated the first question which had to do with the study of causes, Aristotle's intention here is to argue dialectically about the science which is concerned with the study of the first principles of demonstration; and in regard to this he does three things. First, he raises the question. Second (388), he argues one side of the question. Third (391), he argues on the other side of the question.
Accordingly, he states, first, the problem relating to the first principles of demonstration, namely, whether the study of these principles belongs to one science or to many. Further, he explains what the principles of demonstration are, saying that they are the common conceptions of all men on which all demonstrations are based, i.e., inasmuch as the particular principles of the proper demonstrated conclusions derive their stability from these common principles. And he gives an example of first principles, especially this one, that everything must either be affirmed or denied [of some subject]. Another principle which he mentions is that it is impossible for the same thing both to be and not to be at the same time. Hence the question arises whether these principles and similar ones pertain to one science or to many. And if they pertain to one science, whether they pertain to the science which investigates substance or to another science. And if to another science, then which of these must be called wisdom, or first philosophy, which we now seek.
392. The Philosopher answers this question in Book IV (590) of this work. He says that the study of the axioms belongs chiefly to the [first] philosopher inasmuch as it pertains to him to consider being in general, to which first principles of this kind essentially belong, as is most evident in the case of the very first principle: it is impossible for the same thing both to be and not to be [at the same time]. Hence all the particular sciences use principles of this kind just as they use being itself, although it is the first philosopher who is chiefly concerned with this. And the first argument is solved in this way.
But the second argument is solved thus: the [first] philosopher does not consider principles of this kind in such a way as to make them known by defining them or by demonstrating them in an absolute sense, but by refutation, i.e., by arguing disputatively against those who deny them, as is stated in Book IV (608).
Lesson 6
Qq. 3 & 6: Does the science of substance consider all substances as well as accidents?
393. Having debated the questions the third question, which pertains to which pertain to the scope of investigation of this science, he now treats the study of substances and accidents. This is divided into two parts inasmuch as he discusses two questions on this point. The second (403) begins where he says, "Furthermore, there is."
In regard to the first he does three things. First, he raises the question whether there is one science that considers all substances, or whether there are many sciences that consider different substances.
394. Second, he argues the first side of the question with a view to showing that there is one science of all substances. For if there were not one science of all substances, then apparently it would be impossible to designate the substance which this science considers, because substance as substance is the primary kind of being. Hence it does not seem that one substance rather than another belongs to the consideration of the basic science.
395. Third, he argues the other side of the question, saying that it is unreasonable to hold that there is one science of all substances. For it would follow that there would be one demonstrative science of all essential accidents. And this is true because every science which demonstrates certain accidents speculates about the essential accidents of some particular subject, and it does this from certain common conceptions. Therefore, since a demonstrative science considers the accidents only of some particular subject, it follows that the study of some subject-genus belongs to the same science that is concerned with the study of the essential accidents of that genus and vice versa, so long as demonstrations proceed from the same principles.
396. But sometimes it happens to be the function of some science to demonstrate from certain principles that a thing is so, and sometimes it happens to be the function of some science to demonstrate the principles from which it was demonstrated that a thing is so, sometimes to the same science and sometimes to a different one.
An example of its being the function of the same science is seen in the case of geometry, which demonstrates that a triangle has three angles equal to two right angles in virtue of the principle that the exterior angle of a triangle is equal to the two interior angles opposite to it; for to demonstrate this belongs to geometry alone. And an example of its being the function of a different science is seen in the case of music, which proves that a tone is not divided into two equal semitones by reason of the fact that a ratio of 9 to 8, which is superparticular, cannot be divided into two equal parts. But to prove this does not pertain to the musician but to the arithmetician. It is evident, then, that sometimes sciences differ because their principles differ, so long as one science demonstrates the principles of another science by means of certain higher principles.
397. But if it is assumed that the principles are identical, sciences could not differ so long as the accidents are the same and the subject-genus is the same, as if one science considered the subject and another its accidents. Hence it follows that that science which considers a substance will also consider its accidents, so that if there are many sciences which consider substances, there will be many sciences which consider accidents. But if there is only one science which considers substances, there will be only one science which considers accidents. But this is impossible, because it would then follow that there would be only one science, since there is no science which does not demonstrate the accidents of some subject. Therefore it is not the function of one science to consider all substances.
398. This is treated in Book IV (546) of this work, where it is shown that the examination of substance as substance belongs to the first science, whose province it is to consider being as being; and thus it considers all substances according to the common aspect of substance. Therefore it belongs to this science to consider the common accidents of substance. But it belongs to the particular sciences, which deal with particular substances, to consider the particular accidents of substances, just as it belongs to the science of nature to consider the accidents of mobile substance. However, among substances there is also a hierarchy, for the first substances are immaterial ones. Hence the study of them belongs properly to first-philosophy, just as the philosophy of nature would be first philosophy if there were no other substances prior to mobile corporeal substances, as is stated below in Book VI (1170).
399. Here he raises another question regarding the study of substance and accidents. Concerning this he does three things. First, he raises the question whether the investigation of this science is concerned with substance alone or also with the attributes that are accidents of substances. For example, if we say that lines, surfaces and solids are substances of some sort, as some held, the question arises whether it belongs to the same science to consider such things and also their proper accidents, which are demonstrated in the mathematical sciences, or whether it belongs to another science.
402. The Philosopher answers this question in Book IV (570) of this work, saying that it is also the office of that science which is concerned with the study of substance and being to consider the proper accidents of substance and being. Yet it does not follow that it would consider each in the same way, i.e., by demonstrating substance as it demonstrates accidents, but by defining substance and by demonstrating that accidents either belong to or do not belong to it, as is explained more fully at the end of Book IX (1895) of this work.
Lesson 7
Q. 5: Are there substances besides sensible ones?
403. Having debated the questions which pertain to the scope of this science, the Philosopher now treats dialectically the questions which pertain to the substances themselves with which this science is chiefly concerned. In regard to this he does three things. First, he raises the questions. Second (406), he indicates the source from which arguments can be drawn in support of one side of the question ("Now the way"). Third (407), he argues on the other side of the question ("But while they involve").
In regard to the first part of this division he raises two questions. The first question is whether sensible substances alone are found in the universe, as certain of the ancient philosophers of nature claimed, or whether besides sensible substances there are certain others, as the Platonists claimed.
404. And assuming that besides sensible substances there are certain others, the second question is whether these substances belong to one genus, or whether there are many genera of substances. For he considers both opinions. For some thinkers held, that in addition to sensible substances there are only separate Forms, i.e., an immaterial man-in-himself and horse-in itself and so on for the other classes of things, whereas others held that there are certain other substances midway between the Forms and sensible things, namely, the objects of mathematics, with which they said the mathematical sciences deal.
422. Now the Philosopher treats these questions below in Books XII, XIII and XIV of this work, where he shows that there are neither separate mathematical substances nor Forms. The reasoning which moved those who posited the objects of mathematics and the Forms, which are derived from an abstraction of the intellect, is given at the beginning of Book XIII. For nothing prevents a thing which has some particular attribute from being considered by the intellect without its being viewed under this aspect and yet be considered truly, just as a white man can be considered without white being considered. Thus the intellect can consider sensible things not inasmuch as they are mobile and material but inasmuch as they are substances or continuous quantities; and this is to abstract the thing known from matter and motion. However, so far as the thing known is concerned, the intellect does not abstract in such a way that it understands continuous quantities and forms to exist without matter and motion. For then it would follow either that the intellect of the one abstracting is false, or that the things which the intellect abstracts are separate in reality.
Lesson 8
Q. 9: What is the difference between genera and elements?
423. Having debated the questions which were raised about substances, the Philosopher now treats dialectically the questions which were raised about principles. This is divided into two parts. In the first he discusses the questions which asked what the principles of things are; and in the second (456), the questions which asked what kind of things the principles are ("Again, there is the problem").
In the first part of this division he discusses two questions: first, whether universals are the principles of things; and second (443), whether any principles are separate from matter ("But there is a problem").
In regard to the first he discusses two questions, of which the first is whether genera are the principles of things. The second (431) asks which genera these are, whether the first genera or the others ("Again, if genera").
In regard to the first he does two things: first, he raises the question; and second (424), he treats it dialectically ("Just as the elements").
The first question has to do with the principles of things: whether it is necessary to accept or believe that those genera which are predicated of many things are the elements and principles of things, or rather that those parts of which every single thing is composed must be called the elements and principles of things. But he adds two conditions, one of which is "inasmuch as they are intrinsic," which is given in order to distinguish these parts from a contrary and a privation. For white is said to come from black, or the non-white, although these are not intrinsic to white. Hence they are not its elements. The other condition is what he calls "the first things," which is given in order to distinguish them from secondary components. For the bodies of animals are composed of flesh and nerves, which exist within the animal; yet these are not called the elements of animals, because they are not the first things of which an animal is composed, but rather fire, air, water and earth, from which flesh and nerves derive their being.
431. Then he treats the second question dialectically. First, he raises the question; and second (432), he brings up arguments relative to this question ("For if universals").
Accordingly, he says that if we hold that genera are the principles of things in the fullest sense which of these genera should be considered to be the principles of things to a greater degree? Must we consider those "genera" which are first in number, namely, the most common, or also the lowest genera, which are proximately predicated of the individual, i.e., the lowest species. For this is open to question, as is clear from what follows.
442. Now the solution to these questions is implied in this last argument. For according to this argument genera or species are held to be universal principles inasmuch as they are held to be separate. But the fact that they are not separate and self-subsistent is shown in Book VII (1592) of this work. Hence the Commentator also shows, in Book VIII, that the principles of things are matter and form, to which genus and species bear some likeness. For a genus is derived from matter and difference from form, as will be shown in the same book (720). Hence, since form is more of a principle than matter, species will consequently be principles more than genera. But the objection which is raised against this, on the grounds that genera are the principles of knowing a species and its definitions, is answered in the same way the objection raised about their separateness. For, since a genus is understood separately by the mind without understanding its species, it is a principle of knowing. And in the same way it would be a principle of being, supposing that it had a separate being.
Lesson 9
Q. 10: Is there anything separate from sensible things, which is their principle?
443. Having debated the question whether universals are the principles of things, the Philosopher now raises a question about their separability, namely, whether there is anything separate from sensible things as their principle. In regard to this he considers two questions. The first of these is whether universals are separate from singular things. The second (447) is whether there is any formal [principle] separate from things which are composed of matter and form.
In regard to the first he does three things. First, he describes the problem. Second (444), he argues one side of the question ("For if there is nothing"). Third (445), he argues the other side of the question.
Accordingly, this problem arises with regard to a point mentioned in the last argument of the preceding question, namely, whether a universal is separate from singular things, as the aforesaid argument supposed. He describes this problem as "the one with which our analysis is now concerned (235)," i.e., the one which immediately preceded the foregoing argument. And he speaks of it in this way: first, that "it is connected with," i.e., is a consequence of, the foregoing one, because, as has already been stated, the consideration of the preceding question depends on this. For if universals are not separate, they are not principles; but if they are separate, they are principles. Second, he speaks of this problem as the most difficult of all the problems in this science. This is shown by the f act that the most eminent philosophers have held different opinions about it. For the Platonists held that universals are separate, whereas the other philosophers held the contrary. Third, he says that this problem is one which it is most necessary to consider, because the entire knowledge of substances, both sensible and immaterial, depends on it.
455. Now Aristotle solves this problem partly in Book XII (2488) of this work, where he shows that there are certain substances separate from sensible things and intelligible in themselves; and partly in Book VII (1503), where he shows that the forms or specifying principles of sensible things are not separate from matter. However, it does not follow that no science of sensible things can be had or that science is sensory perception. For it is not necessary that things have in themselves the same mode of being which they have in the intellect of one who knows them. For those things which are material in themselves are known in an immaterial way by the intellect, as has also been stated above (446). And even though a form is not separate from matter, it is not therefore necessary that it should be generated; for it is not forms that are generated but composites, as will be shown in Book VII (1417) of this work. It is clear, then, in what cases it is necessary to posit separate forms and in what not. For the forms of all things which are sensible by nature are not separate from matter, whereas the forms of things which are intelligible by nature are separate from matter. For the separate substances do not have the nature of sensible things, but are of a higher nature and belong to another order of existing things.
Lesson 10
Q. 11: Are there one or many forms and principles of things?
456... The problem (245), then, is whether all things that belong to the same species, for example, all men, have a single substance or form.
460. Here he raises a difficulty concerning the unity of principles in general: whether the principles of things are numerically the same, or only specifically the same and numerically distinct...
465. Now this question will be solved in Book XII (2464); for it will be shown there that the principles which things have, namely, matter and form or privation, are not numerically the same for all things but analogically or proportionally the same. But those principles which are separate, i.e., the intellectual substances, of which the highest is God, are each numerically one in themselves. Now that which is one in itself and being is God; and from Him is derived the numerical unity found in all things. And there is science of these, not because they are numerically one in all, but because in our conception there is a one in many. Moreover, the argument which is proposed in support of the opposite side of the question is true in the case of essential principles but not in that of separate ones, which is the class to which the agent and final cause belong. For many things can be produced by one agent or efficient cause, and can be directed to one end.
Lesson 11
Q. 13: Are the principles of corruptible and incorruptible things the same?
487. Now the solution to this problem is given in Book XII (2553), where the Philosopher shows that the first active or motive principles of all things are the same but in a certain sequence. For the first principles of things are unqualifiedly incorruptible and immobile, whereas the second are incorruptible and mobile, i.e., the celestial bodies, which cause generation and corruption in the world as a result of their motion. Now the intrinsic principles of corruptible and of incorruptible things are the same, not numerically but analogically. Still the intrinsic principles of corruptible things, which are matter and form, are not corruptible in themselves but only in reference to something else. For it is in this way that the matter and form of corruptible things are corrupted, as is stated in Book I of the Physics.
Lesson 12
Q. 14a: Are "one" and "being" substances or principles of things?
488. Having asked whether the principles of things are the same or different, the Philosopher now asks how unity itself could have the nature of a principle; and in regard to this he does three things. First, he asks whether unity itself is a principle; second (502), he asks whether numbers, which arise or follow from unity, are the principles of things; and third (515), whether the Forms, which are certain separate unities, are the principles of things.
In regard to the first he does three things. First, he raises the question. Second (489), he gives the opinions on both sides ("For some think"). Third (490), he advances arguments on both sides ("But if anyone").
He says, first (266), that of all the different questions which have been raised, one is more difficult to consider because of the weight of the arguments on both sides, and that this question is also one about which it is necessary to know the truth, because our decision about the substances of things depends on it. Now this question is whether unity and being are the substances of things, not so that either of them must be attributed to some other nature which would be informed, as it were, by unity and being, but rather so that the unity and being of a thing are its substance; or, in an opposite way, whether it is necessary to ask what that thing is to which unity and being properly belong, as though there were some other nature which is their subject.
501. The solution of this problem is treated by Aristotle in the following books. For the fact that there is something separate, which is itself one and being, he will prove below in Book XII (2553), when he establishes the oneness of the first principle which is separate in an absolute sense, although it is not the substance of all things which are one, as the Platonists thought, but is the cause and principle of the unity of all things. And insofar as unity is predicated of other things it is used in two ways. In one way it is interchangeable with being, and in this way each thing is one by its very essence, as is proved below in Book IV (548); and unity in this sense adds nothing to being except merely the notion of undividedness. Unity is used in another way insofar as it has the character of a first measure, either in an absolute sense or with respect to some genus. And this unity if it is both a minimum in the absolute sense and indivisible, is the one which is the principle and measure of number. But if it is not both a minimum in an absolute sense and indivisible, it will not be a unit and measure in an absolute sense, as a pound in the case of weights and a half-tone in the case of melodies, and a foot in the case of lengths. And nothing prevents continuous quantities from being composed of this kind of unity. He will establish this in Book X (1940) of this work. But because the Platonists thought that the one which is the principle of number and the one which is interchangeable with being are the same, they therefore held that the one which is the principle of number is the substance of each thing, and consequently that number, inasmuch as it is composed of many substantial principles, makes up or comprises the substance of composite things. But he will treat this question at greater length in Books XIII and XIV of this work.
Lesson 13
Q 14b: Are numbers and continuous quantities the substances or principles of sensible things?
502. Having inquired whether unity and being are the substances of sensible things, the Philosopher now asks whether numbers and continuous quantities are the substances of sensible things; and in regard to this he does three things. First (502), he presents the question. Second (503), he argues in support of one side of the question ("For if they are not"). Third (507), he argues on the other side ("But if it is admitted").
Accordingly he says, first, that "connected with these," i.e., following from the foregoing problem, there is the question whether numbers and continuous quantities, i.e., bodies, surfaces, and their extremities, such as points, are either substances that are separate from sensible things, or are the substances of sensible things themselves, or not. He says that this problem is a result of the foregoing one, because in the foregoing problem it was asked whether unity is the substance of things. Now unity is the principle of number. But number seems to be the substance of continuous quantity inasmuch as a point, which is a principle of continuous quantity, seems to be merely the number one having position, and a line to be the number two having position, and the primary kind of surface to be the number three having position, and a body the number four having position.
514. But the Philosopher will treat this question in Books XIII and XIV. And the truth of the matter is that mathematical entities of this kind are not the substances of things, but are accidents which accrue to substances. But this mistake about continuous quantities is due to the fact that no distinction is made between the sort of body which/belongs to the genus of substance and the sort which belongs to the genus of quantity. For body belongs to the genus of substance according as it is composed of matter and form; and dimensions are a natural consequence of these in corporeal matter. But dimensions themselves belong to the genus of quantity, and are not substances but accidents whose subject is a body composed of matter and form. The same thing too was said above (500) about those who held that numbers are the substances of things; for their mistake came from not distinguishing between the one which is the principle of number and that which is interchangeable with being.
Lesson 14
Q14c: Are forms substances or principles of things?
515. Having inquired whether the objects of mathematics are the principles of sensible substances, the Philosopher now inquires whether in addition to the objects of mathematics there are certain other principles, such as those which we call Forms, which are the substances and principles of sensible things. In regard to this he does three things. First, he presents the question. Second (516), he argues one side of the question ("For if it is because"). Third (518), he argues the other side ("But if we hold").
Accordingly, he says, first, that if one assumes that the objects of mathematics are not the principles of sensible things and their substances, one will next have the problem why, in addition to both sensible things and the objects of mathematics (which are an intermediate class between sensible things and the Forms), it is necessary to posit a third class of entities, namely, the specific essences, i.e., the Ideas or separate Forms.
518. Then he counters with an argument for the other side of the question. He says that, if we hold that there are separate Forms and that the principles of things are limited not only in species but also in number, certain impossible consequences will follow, which are touched on above in one of the questions (464).
But the Philosopher will deal with this problem in Book XII (2450) and Book XIV of this work. And the truth of the matter is that, just as the objects of mathematics do not exist apart from sensible things, neither do Forms exist apart from the objects of mathematics and from sensible substances. And while the efficient and moving principles of things are limited in number, the formal principles of things, of which there are many individuals in one species, are not limited in number but only in species.
Lesson 15
Q 14d: Are principles of substances actual or potential?
519. Having inquired what the principles are, the Philosopher now asks how they exist. First, he asks whether they exist potentially or actually; and second (523), whether they are universals or singulars ("And there is also the problem"). In regard to the first he does three things. First, he raises the question. Second (520), he argues one side ("If they exist"). Third (501), he argues the opposite side ("But if the elements").
His first question (287), then, is whether first principles exist potentially or "in some other way," i.e., actually. This problem is introduced because of the ancient philosophers of nature, who held that there are only material principles, which are in potency. But the Platonists, who posited separate Forms as formal principles, claimed that they exist actually.
522. This question will be answered in Book IX (1844) of this work, where it is shown that actuality is prior to potentiality in an unqualified sense, but that in anything moved from potentiality to actuality, potentiality is prior to actuality in time. Hence it is necessary that the first principle exist actually and not potentially, as is shown in Book XII (2500) of this work.
Q 14e: Are principles of substances universal or singular?
523. Here he asks whether the principles of things exist as universals or as singular things; and in regard to this he does three things. First, he presents the question. Second (524), he argues one side ("For if they are universals"). Third (527), he argues the other side ("However, if they are not universals"). The problem (290), then, is whether principles are universals or exist in the manner of singular things.
528. This question will be answered in Book VII (1584) of this work, where it is shown that universals are neither substances nor the principles of things. However, it does not follow for this reason that, if the principles and substances of things were singulars, there could be no science of them, both because immaterial things, even though they subsist as singulars, are nevertheless also intelligible, and also because there is science of singulars according to their universal concepts which are apprehended by the intellect.