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BOOK I
SURVEY OF CAUSESLesson 4
The four causes, & three characteristics of final cause
70. Accordingly, he says, first, that since it is evident that wisdom speculates about causes, we ought to begin by acquiring knowledge from the causes of things. This also seems to be in keeping with the intelligible structure of science, because we say that we know each thing scientifically when we think we are not ignorant of its cause. Now causes are spoken of in four ways. (1) One of these is the formal cause, which is the very substance of a thing by which we know what each thing is. For it is well known, as is stated in Book II of the Physics, that we do not say that anything has a nature before it has received a form. Now it is clear that a form is a cause, because the question “Why is something so?” we reduce to its formal cause as its ultimate explanation, beginning with proximate forms and proceeding to the ultimate form. But evidently the “why?” asks about a cause and principle. Hence it is evident that a form is a cause. (2) A second cause is the material cause. (3) A third is the efficient cause, which is the source of motion. (4) A fourth is the final cause, which is opposite to the efficient cause as a goal is to a starting-point; for motion begins with the efficient cause and terminates with the final cause. This flatter] cause is also that for the sake of which a thing comes to be, and the good of each nature.
71. He makes the final cause known by three considerations: (1) It is the goal of motion, and thus is opposite to the source of motion, which is the efficient cause. (2) It is first in intention, and for this reason is said to be that for the sake of which [something is done]. (3) It is desirable of itself, and for this reason is called a good; for the good is what all desire.
Hence, in explaining how the final cause is opposite to the efficient cause, he says that it is the goal [or end] of every process of generation and motion, whose starting-point is the efficient cause. By these two types of change he seems to imply that there is a twofold goal: (1) For the goal of a process of generation is the form itself, which is a part of a thing. (2) But the goal of motion is something sought for outside the thing moved. He says that he has treated these causes at sufficient length in the Physics, lest he should be asked to make a more extensive treatment of them.
OPINIONS OF THOSE WHO GAVE ONLY MATERIAL CAUSE
Four characteristics of matter
74. Accordingly he says, first (36), that most of those who first philosophized about the natural world held that the principles of all things are merely those which are referred to the class of material cause. In regard to this it must be said that they took the four conditions of matter which seem to belong to the notion of a principle. For, (1) that of which a thing is composed seems to be a principle of that thing. But matter is such a thing; for we say that a thing that has matter is of its matter, as a knife is of iron. (2) That from which a thing comes to be, being also a principle of the process of generation of that thing, seems to be one of its causes, because a thing comes into being by way of generation. But a thing first comes to be from matter, because the matter of things precedes their production. And a thing does not come from matter in an accidental way; for a thing is generated in an accidental way from its contrary or privation, as when we say that white comes from black. (3) Third, that into which all things are ultimately dissolved by corruption seems to be a principle of things. For just as principles are first in the process of generation, in a similar way they are last in the process of dissolution; and obviously this too pertains to matter. (4) Fourth, since a principle must remain in existence, then that which remains throughout the process of generation and corruption seems to be a principle. Now the matter which they said is the substance of a thing remains throughout every transmutation, although its attributes, such as its form and everything that accrues to it over and above its material substance, are changed. From all these considerations they concluded that matter is the element and principle of all beings.
Without material cause, no generation or corruption
75. Then he gives, as a secondary point, what they held as following from the above, namely, that in the world nothing is generated or corrupted in an absolute sense. For when some change occurs with regard to a thing’s attributes, and its substance remains unchanged, we do not say that it is generated or corrupted in an absolute sense, but only in a qualified one; for example, when Socrates becomes good or musical, we do not say that he simply comes to be, but comes to be this. And similarly when he loses a state of this kind, we do not say that he is corrupted in an absolute sense, but only in a qualified one. But matter, which is the substance of things according to them, always remains; and every change affects some of a thing’s accidents, such as its attributes. From this they concluded that nothing is generated or corrupted in an absolute sense, but only in a qualified one.
Opinions of pre-Socratics on material cause (76-92): Give modern equivalents.
Lesson 5
OPINIONS ON EFFICIENT CAUSE: intellect or love
100. Here he gives in detail the opinions about the aforesaid principle. First, he gives the opinions of those who held that there is one [efficient] cause; and second (104), the opinions of those who held that there are two such causes (“But since there would seem”).
In regard to the first he does two things. First, he gives the views of those who held that the first efficient cause is an intellect; and second (101), the opinions of those who held that it is love (“Now someone might”).
He says, then, that after the foregoing doctrine someone appeared who said that there is an intellect present in nature at large, just as there is in animals, and that this is the cause of the world and the order of the whole, i.e., of the universe, in which order the good of the entire universe and that of every single part consists. And this man atoned for the first philosophers by reducing to pure truth those who said unreasonable things and did not mention this kind of cause. Now Anaxagoras clearly stated this doctrine, although another philosopher —Hermotimus of Clazomenae—first gave him the idea of proposing this opinion. Hence it is evident that those who held this opinion claimed at the same time that the principle by which things are well disposed and the one which is the source of motion in things, are one and the same.
101. Here he gives the opinion of those who claimed that love is the first principle, although they did not hold this very explicitly or clearly. Accordingly, he says that some suspected that Hesiod had sought for such a principle to account for the good disposition of things, or anyone else who posited love or desire in nature. For when Parmenides attempted to explain the generation of the universe, he said that in the establishing of the universe “Love, the first of all the gods, was made.” Nor is this opposed to his doctrine that there is one immobile being, of which Aristotle speaks here; because this man held that there are many things according to the senses, although there is only one thing according to reason, as was stated above and will be stated below. Moreover, he called the celestial bodies, or perhaps certain separate substances, gods.
102. But Hesiod said that first of all there was chaos, and then broad earth was made, to be the receptacle of everything else; for it is evident that the receptacle [or void] and place are principles, as is stated in Book IV of the Physics. And he also held that love, which instructs all the immortals, is a principle of things. He did this because the communication of goodness seems to spring from love, for a good deed is a sign and effect of love. Hence, since corruptible things derive their being and every good disposition from immortal beings of this kind, this must be attributed to the love of the immortals. Furthermore, he held that the immortals are either the celestial bodies themselves, or material principles themselves. Thus he posited chaos and love as though there had to be in existing things not only a material cause of their motions, but also an efficient cause which moves and unites them, which seems to be the office of love. For love moves us to act, because it is the source of all the emotions, since fear, sadness and hope proceed only from love. That love unites things is clear from this, that love itself is a certain union between the lover and the thing loved, seeing that the lover regards the beloved as himself. This man Hesiod is to be numbered among the poets who lived before the time of the philosophers.
Lesson 7
STRANGE AND OBSCURE VIEWS ABOUT THE PRINCIPLES OF THINGS
Hidden principles: numbers
121. Here he gives the second reason which motivated them. For they thought of the attributes of harmonies, musical consonants and their ratios, i.e., proportions, in terms of the nature of numbers. Hence, since harmonious sounds are certain sensible things, they attempted by the same reasoning to liken all other sensible things, both in their intelligible structure and in their whole nature, to numbers, so that numbers are the first things in the whole of nature.
122. For this reason too they thought that the principles of numbers are the principles of all existing things, and they said that the whole heaven is merely a kind of nature and harmony of numbers, i.e., a kind of numerical proportion similar to the proportion found in harmonies. Hence, whatever they had “revealed,” i.e., had shown, which they could adapt to numbers and harmonies, they also adapted both to the changes undergone by the heavens, as its motion, eclipses and the like; and to its parts, as the different orbs; and to the whole arrangement of the heavens, as the different stars and different figures in the constellations.
Lesson 9
Unitarians
134. ...He says, then, that there were certain philosophers, other than those just mentioned, who spoke “of the whole,” i.e,, of the universe, as if it were of one nature, i.e., as if the whole universe were a single being or a single nature. However, not all maintained this position in the same way, as he will make clear below (138-49). Yet in the way in which they differ their statements are neither acceptable nor in conformity with nature. None of their statements are in conformity with nature, because they did away with motion in things. And none of them are acceptable, because they held an impossible position and used sophistical arguments, as is clear in Book I of the Physics.
135. Here he shows how a consideration of this position pertains to the present investigation and how it does not. He shows, first, that it has no bearing on this investigation if we consider their position itself; and, second (137), that it does have a bearing on this investigation if the reasoning or method behind their position is considered (“Yet their opinion”).
He says, then, that since these philosophers held that there is only one being, and a single thing cannot be its own cause, it is clear that they could not discover the causes. For the position that there is a plurality of things demands a diversity of causes in the world. Hence, a consideration of their statements is of no value for the purposes of the present study, which deals with causes. But the situation is different in the case of the ancient philosophers of nature, who held that there is only one being, and whose statements must be considered here. For they generated many things from that one principle as matter, and thus posited both cause and effect. But these men with whom we are now dealing speak of this in a different way. For they do not say that all things are one materially, so that all things are generated from one matter, but that all things are one in an absolute sense.
136. The reason for this difference is that the ancient philosophers of nature added motion to the view of those who posited one being and one principle, and said that this one being is mobile; and therefore different things could be generated from that one principle by a certain kind of motion, i.e., by rarefaction and condensation. And they said that the whole universe with respect to the diversity found in its parts is generated in this way. Yet since they held that the only change affecting substance is accidental, as was stated above (75), the conclusion then followed that the whole universe is one thing substantially but many things accidentally. But these thinkers [i.e., the Eleatics], said that the one being which they posited is immobile in an absolute sense; and therefore a diversity of things could not be produced from that one being. For since this being is immobile they could not posit any plurality in the world, either substantial or accidental.
137. Here he shows how their opinion is relevant to the present inquiry. First, he deals with all of these thinkers in general; and second (142), with Parmenides in particular.
He says, first, that although they did away with diversity in the world, and consequently with causality, nevertheless their opinion is relevant to the present study to this extent, let us say: as regards the method by which they establish their position and the reason for their position.
138. Parmenides, who was a member of this group, seems to touch on unity according to intelligible structure) i.e., according to form; for he argued as follows: besides being there is only non-being, and non-being is nothing. Therefore besides being there is nothing. But being is one. Therefore, besides the one there is nothing.
In this argument he clearly considered the intelligible structure itself of being, which seems to be one, because nothing can be understood to be added to the concept of being by which it might be diversified. For whatever is added to being must be other than being. But anything such as this is nothing. Hence it does not seem that this can diversify being; just as we also see that differences added to a genus diversify it, even though these differences are outside the substance of that genus. For differences do not participate in a genus, as is stated in the Topics, Book IV, otherwise a genus would have the substance of a difference. And definitions would be nonsense if when a genus is given the difference were added, granted that the genus were the substance of the difference, just as it would be nonsense if the species were added. Moreover a difference would not differ in any way from a species. But those things which are outside the substance of being must be non-being, and thus cannot diversify being.
139. But they were mistaken in this matter, because they used being as if it were one in intelligible structure and in nature, like the nature of any genus. But this is impossible. For being is not a genus but is predicated of different things in many ways. Therefore in Book I of the Physics it is said that the statement “Being is one” is false. For being does not have one nature like one genus or one species.
140. But Melissus considered being in terms of matter. For he argued that being is one by reason of the fact that being is not generated from something prior, and this characteristic pertains properly to matter, which is ungenerated. For he argued in this way: whatever is generated has a starting-point. But being is not generated and therefore does not have a starting-point. But whatever lacks a starting-point lacks an end and therefore is unlimited. And if it is unlimited, it is immobile, because what is unlimited has nothing outside itself by which it is moved.
That being is not generated he proves thus. If being were generated, it would be generated either from being or from non-being. But it is not generated from non-being, because non-being is nothing and from nothing nothing comes. Nor is it generated from being, because then a thing would be before it came to be. Therefore it is not generated in any way.
In this argument he obviously treats being as matter, because it is of the very nature of matter not to be generated from something prior. And since limitation pertains to form, and unlimitedness to matter, Melissus, who considered being under the aspect of matter, said that there is one unlimited being. But Parmenides, who considered being under the aspect of form, said that being is limited. Hence, insofar as being is considered under the aspect of form and matter, a study of these men is relevant to the present investigation; because matter and form are included among the causes.
141. But Xenophanes, who was the first of those to say that everything is one (and therefore Parmenides was his disciple), did not explain by what reasoning he maintained that all things are one, either by arguing from the viewpoint of matter, or from that of form. Hence, with respect to neither nature, i.e., neither matter nor form, does he seem “to come up to these men,” that is, to reach and equal them in their irrational manner of arguing.
But concerning the whole heaven he says that the one is God. For the ancients said that the world itself is God. Hence, seeing that all parts of the universe are alike insofar as they are bodies, he came to think of them as if they were all one. And just as the foregoing philosophers held that beings are one by considering those things which pertain either to matter or to form, in a similar way these philosophers maintained this position regarding the composite itself.
142. His aim here is to explain in a special way how the opinion of Parmenides pertains to the present investigation. He concludes from the foregoing that, since these men did away with (~) diversity in the world and therefore with (~) causality, all of them must be disregarded so far as the present study is concerned. Two of them—Xenophanes and Melissus—must be disregarded altogether, because they are a little too “rustic,” i.e., they proceeded with less accuracy. But Parmenides seems to have expressed his views “with more insight,” i.e., with greater understanding. For he employs the following argument: besides being there is only non-being, and whatever is non-being “is thought to be nothing”; i.e., he considers it worthy to be nothing. Hence he thought that it necessarily followed that being is one, and that whatever is other than being is nothing. This argument has been treated more clearly in the Physics, Book I.
143. But even though Parmenides was compelled by this argument to hold that all things are one, yet, because there appeared to the senses to be many things in reality, and because he was compelled to accept what appeared to the senses, it was his aim to make his position conform to both of these, i.e., to what is apprehended both by the senses and by reason. Hence he said that all things are one according to reason but many according to the senses.
And inasmuch as he held that there is a plurality of things according to the senses, he was able to hold that there is in the world both cause and effect. Hence he posited two causes, namely, the hot and the cold, one of which he ascribed to fire, and the other to earth. And one of these—the hot or fire—seemed to pertain to the efficient cause, and the other—cold or earth—to the material cause. And lest his position should seem to contradict the conclusion of his own argument that whatever is besides being is nothing, he said that one of these causes—the hot—is being, and that the other cause—the one besides being, or the cold—is non-being, according to. both reason and the truth of the thing itself, and is a being only according to sensory perception.
144. Now in this matter he comes very close to the truth; for the material principle, which he held to be earth, is not an actual being.
And in a similar way, too, one of two contraries is a privation, as is said in Book I of the Physics. But privation does not belong to the intelligible constitution of being. Hence in a sense cold is the privation of heat, and thus is non-being.
145. Here he summarizes the remarks which have been made about the doctrines of the ancient philosophers; and in regard to this he does two things. First, he summarizes the remarks made about the doctrines of the ancient philosophers of nature; and second (147), those made about the doctrines of the Pythagoreans, who introduced mathematics.
Therefore from the above remarks he concludes, first, that from the foregoing philosophers, who adopted the same opinion, namely, that the material cause is the substance of things, and who were already beginning by the use of reason to know the causes of things by investigating them, we learn the causes which have been mentioned. For from the first philosophers it was learned that the principle of all things is corporeal. This is evident from the fact that water and the like, which are given as the principles of things, are bodies. However, they differed in this respect, that some, such as Thales, Diogenes and similar thinkers, claimed that there is only one corporeal principle, whereas others, such as Anaxagoras, Democritus and Leucippus, held that there are several corporeal principles. Yet both groups, i.e., both those who posited one principle and those who posited many, placed such corporeal principles in the class of material cause. And some of them not only posited a material cause but added to this the cause from which motion begins: some holding it to be one, as Anaxagoras did in positing intellect, and Parmenides, love, and others to be two, as Empedocles did in positing love and hate.
146. Hence, it is clear that these philosophers who lived down to the time of the Italians, or Pythagoreans, “and [were] independent of them,” i.e., who had their own opinions about reality and were unaware of those of the Pythagoreans, spoke obscurely about the principles of things; for they did not designate to what class of cause such principles might be reduced. Yet they made use of two causes, i.e., the source from which motion begins and matter: some saying that the former—the source from which motion begins—is one, and others two; as has been pointed out (145).
147. Here he summarizes the opinions expressed by the Pythagoreans, both what they held in common with the foregoing philosophers, and what was peculiar to themselves. Now the opinion common to some of the foregoing philosophers and to the Pythagoreans was this that they posited, in a sense, two principles in the same way as the foregoing philosophers did. For Empedocles held that there are two contrary principles, one being the principle of good things, and the other the principle of evil things, and the Pythagoreans did the same thing, as is clear from the co-ordination of contrary principles which they posited.
148. However, they did not do this in the same way; because Empedocles placed these contrary principles in the class of material cause, as was stated above (111), whereas the Pythagoreans added their own opinion to that of the other thinkers. The first thing that they added is this: they said that what I call the one, the limited and the unlimited are not (~) accidents of any other natures, such as fire or earth or the like, but claimed that what I call the one, the limited and the unlimited constitute the (+) substance of the same things of which they are predicated. From this they concluded that number, which is constituted of units, is the substance of all things. But while the other philosophers of nature posited the one, the limited and the unlimited, they nevertheless attributed these to another nature, as accidents are attributed to a subject, for example, to fire or water or something of this kind.
149. The second addition which they made to the views of the other philosophers is this: they began to discuss and to define “the whatness itself,” i.e., the substance and quiddity of things, although they treated this far too simply by defining things superficially. For in giving definitions they paid attention only to one thing; because they said that, if any given definition were to apply primarily to some thing, this would be the substance of that thing; just as if one were to suppose that the ratio “double” is the substance of the number two, because such a ratio is found first in the number two. And since being was found first in the one rather than in the many (for the many is composed of ones), they therefore said that being is the substance itself of the one.
But this conclusion of theirs is not acceptable; for although the number two is double, the essence of twoness is not the same as that of the double in such a way that they are the same conceptually, as the definition and the thing defined. But even if their statements were true, it would follow that the many would be one. For some plurality can belong primarily to something one; for example, evenness and the ratio double belong first to the number two. Hence [according to them] it would follow that the even and the double are the same. And it would likewise follow that that to which the double belongs is the same as the number two, so long as the double is the substance of the number two. This, indeed, is also the conclusion which the Pythagoreans drew; for they attributed plurality and diversity to things as if they were one, just as they said that the properties of numbers are the same as the properties of natural beings.
150. Hence, Aristotle concludes that it is possible to learn this much from the early philosophers, who posited only one material principle, and from the later philosophers, who posited many principles.
Lesson 10
Plato and form
151. Having given the opinion of the ancient philosophers about the material and efficient cause, he gives a third opinion, that of Plato, who was the first to clearly introduce the formal cause. This is divided into two parts. First, he gives Plato’s opinion. Second (171), from all of the foregoing remarks he makes a summary of the opinions which the other philosophers expressed about the four classes of causes (“We have examined”).
In regard to the first he does two things. First, he gives Plato’s opinion about the substances of things; and second (159), his opinion about the principles of things (“And since the Forms”).
In regard to the first he does two things. First, he gives Plato’s opinion insofar as he posited Ideas; and second (157), insofar as he posited intermediate substances, namely, the separate mathematical entities (“Further, he says”).
He says, first, that after all the foregoing philosophers came the system of Plato, who immediately preceded Aristotle; for Aristotle is considered to have been his disciple. And even if Plato followed in many respects the natural philosophers who preceded him, such as Empedocles, Anaxagoras and the like, he nevertheless had certain other doctrines of his own in addition to those of the preceding philosophers, because of the philosophy of the Italians, or Pythagoreans. For insofar as he was devoted to the study of truth he sought out the philosophers of all lands in order to learn their teachings. Hence he came to Tarenturn in Italy, and was instructed in the teachings of the Pythagoreans by Archytas of Tarenturn, a disciple of Pythagoras.
152. Now Plato would seem to follow the natural philosophers who lived in Greece; and of this group some of the later members held that all sensible things are always in a state of flux, and that there can be no scientific knowledge of them (which was the position of Heraclitus and Cratylus). And since Plato became accustomed to positions of this kind from the very beginning, and agreed with these men in this position, which he acknowledged to be true in later years, he therefore said that scientific knowledge of particular sensible things must be abandoned. And Socrates (who was Plato’s master and the disciple of Archelaus, a pupil of Anaxagoras), because of this position, which arose in his time, that there can be no science of sensible things, was unwilling to make any investigation into the nature of physical things, but only busied himself with moral matters. And in this field he first began to investigate what the universal is, and to insist upon the need for definition.
153. Hence, Plato, being Socrates’ pupil, “accepted Socrates,” i.e., followed him, and adopted this method for the purpose of investigating natural beings. He did so believing that in their case the universal in them could successfully be grasped and a definition be assigned to it, with no definition being given for any sensible thing; because, since sensible things are always “changing,” i.e., being changed, no common intelligible structure can be assigned to any of them. For every definition must conform to each thing defined and must always do so, and thus requires some kind of immutability. Hence universal entities of this kind, which are separate from sensible things and that to which definitions are assigned, he called the Ideas or Forms of sensible things. He called them Ideas, or exemplars, inasmuch as sensible things are made in likeness to them; and he called them Forms inasmuch as [sensible things] have substantial being by participating in them. Or he called them Ideas inasmuch as they are principles of being, and Forms inasmuch as they are principles of knowledge. Hence all sensible things have being because of them and in conformity with them. They have being because of the Ideas insofar as the Ideas are the causes of the being of sensible things, and “in conformity with them” insofar as they are the exemplars of sensible things.
154. The truth of this is clear from the fact that “many individuals of the same name” are attributed to one Form alone, i.e., there are many individuals which have the same Form predicated of them, and predicated by participation. For the Form or Idea [of man] is the specific nature itself by which there exists man essentially. But an individual is man by participation inasmuch as the specific nature [man] is participated in by this designated matter. For that which is something in its entirety does not participate in it but is essentially identical with it, whereas that which is not something in its entirety but has this other thing joined to it, is said properly to participate in that thing. Thus, if heat were a self-subsistent heat, it would not be said to participate in heat, because it would contain nothing but heat. But since fire is something other than heat, it is said to participate in heat.
155. In a similar way , since the separate Idea of man contains nothing but the specific nature itself, it is man essentially; and for this reason it was called by him man-in-itself. But since Socrates and Plato have in addition to their specific nature an individuating principle, which is designated matter, they are therefore said to participate in a Form, according to Plato.
156. Now Plato took this term participation from Pythagoras, although [in doing so] he made a change in the term. For the Pythagoreans said that numbers are the causes of things, just as the Platonists said that the Ideas are, and claimed that sensible things of this kind exist as certain imitations of numbers. For inasmuch as numbers, which have no position of themselves, received positions, they caused bodies. But because Plato held that the Ideas are unchangeable in order that there might be scientific knowledge of them, he did not agree that the term imitation could be used of the Ideas, but in place of it he used the term participation. However, it must be noted that, even though the Pythagoreans posited participation or imitation, they still did not investigate the way in which a common Form is participated in by individual sensible things or imitated by them. But the Platonists have treated this.
157. Here he gives Plato’s opinion about the mathematical substances. He says that Plato posited other substances—the objects of mathematics—in addition to the Forms and sensible things. Moreover, he said that beings of this kind were an intermediate class among the three kinds of substances; or that they were above sensible substances and below the Forms, and differed from both. The mathematical substances differed from sensible substances, because sensible substances are corruptible and changeable, whereas the mathematical substances are eternal and immobile. The PIatonists got this idea from the way in which mathematical science conceives its objects; for mathematical science abstracts from motion. The mathematical substances also differed from the Forms, because the objects of mathematics are found to be numerically different and specifically the same, otherwise the demonstrations of mathematics would prove nothing. For unless two triangles belonged to the same class, geometry would attempt in vain to demonstrate that some triangles are alike; and the same thing is true of other figures. But this does not happen in the case of the Forms. For, since a Form is just the specific nature itself of a thing, each Form can only be unique. For even though the Form of man is one thing, and the Form of ass another thing, nevertheless the Form of man is unique, and so is the Form of ass; and the same thing is true of other things.
158. Now to one who carefully examines Plato’s arguments it is evident that Plato’s opinion was false, because he believed that the mode of being which the thing known has in reality is the same as the one which it has in the act of being known. Therefore, since he found that our intellect understands abstractions in two ways: in one way as we understand universals abstracted from singulars, and in another way as we understand the objects of mathematics abstracted from sensible things, he claimed that for each abstraction of the intellect there is a corresponding abstraction in the essences of things. Hence he held that both the objects of mathematics and the Forms are separate.
But this is not necessary. For even though the intellect understands things insofar as it becomes assimilated to them through the intelligible form by which it is put into act, it still is not necessary that a form should have the same mode of being in the intellect that it has in the thing known; for everything that exists in something else exists there according to the mode of the recipient. Therefore, considering the nature of the intellect, which is other than the nature of the thing known, the mode of understanding, by which the intellect understands, must be one kind of mode, and the mode of being, by which things exist, must be another. For although the object which the intellect understands must exist in reality, it does not exist there according to the same mode [which it has in the intellect]. Hence, even though the intellect understands mathematical entities without simultaneously understanding sensible substances, and understands universals without understanding particulars, it is not therefore necessary that the objects of mathematics should exist apart from sensible things, or that universals should exist apart from particulars. For we also see that sight perceives color apart from flavor, even though flavor and color are found together in sensible substances.
159. Here he gives Plato’s opinion concerning the principles of things; and in regard to this he does two things. First, he states the principles which Plato assigned to things; and second (169), the class of cause to which they are reduced (“From the foregoing”).
In regard to the first he does two things. First, he tells us what kind of principles Plato had assigned to things. Second (160), he shows in what respect Plato agreed with the Pythagoreans, and in what respect he differed from them (“Yet Plato”).
He says, first, that, since the Forms are the causes of all other beings according to Plato, the Platonists therefore thought that the elements of the Forms are the elements of all beings. Hence, they assigned as the material principle of things the great and small, and said that “the substance of things,” i.e., their form, is the one. They did this because they held these to be the principles of the Forms. For they said that just as the Forms are the formal principles of sensible things, in a similar way the one is the formal principle of the Forms. Therefore, just as sensible things are constituted of universal principles by participation in the Forms, in a similar way the Forms, which he said are numbers, are constituted “of these,” i.e., of the great and small. For the unit constitutes different species of numbers by addition and subtraction, in which the notion of the great and small consists. Hence, since the one was thought to be the substance of being (because he did not distinguish between the one which is the principle of number, and the one which is convertible with being), it seemed to him that a plurality of different Forms might be produced from the one, which is their common substance, in the same way that a plurality of different species of numbers is produced from the unit.
160. Here he compares the position of Plato with that of Pythagoras. First, he shows in what respect they agreed; and second (160), in what respect they differed (“But to posit”).
Now they agreed in two positions; (1) and the first is that the one is the substance of things. For the Platonists, like the Pythagoreans, said that what I call the one is not predicated’ of some other being as an accident is of a subject, but signifies a thing’s substance. They said this, as we have pointed out (159), because they did not distinguish between the one which is convertible with being and the one which is the principle of number.
161. (2) The second position follows from the first; for the Platonists, like the Pythagoreans, said that numbers are the causes of the substance of all beings; and they held this because [in their opinion] number is just a collection of units. Hence if the one is substance, number must also be such.
162. Here he shows in what respect they differed; and in regard to this he does two things. First, he states how they differed. Second (164), he gives the reason for this difference (“Therefore, his making”).
Now this difference involves two things. First, the Pythagoreans, as has already been stated, posited two principles of which things are constituted, namely, the limited and the unlimited, of which one, i.e., the unlimited, has the character of matter. But in place of this one principle—the unlimited— which the Pythagoreans posited, Plato created a dyad, holding that the great and small have the character of matter. Hence the unlimited, which Pythagoras claimed to be one principle, Plato claimed to consist of the great and small. This is his own opinion in contrast with that of Pythagoras.
163. The second difference is that Plato held that numbers are separate from sensible things, and this in two ways. For he said that the Forms themselves are numbers, as was pointed out above (159); and he also held, as was stated above (157), that the objects of mathematics are an intermediate class between the Forms and sensible things, and that they are numbers by their very essence. But the Pythagoreans said that sensible things themselves are numbers, and did not make the objects of mathematics an intermediate class between the Forms and sensible things; nor again did they hold that the Forms are separate from things.
164. Here he gives the reason for the difference. First, he gives the reason for the second difference; and then (165), the reason for the first difference.
He says, then, that the Platonists adopted the position that both the one and numbers exist apart from sensible things and not in sensible things, as the Pythagoreans claimed; and they also introduced separate Forms because of the investigation “which was made into the intelligible structures of things,” i.e., because of their investigation of the definitions of things, which they thought could not be attributed to sensible substances, as has been stated (150). This is the reason they were compelled to hold that there are certain things to which definitions are assigned. But the Pythagoreans, who came before Plato, were ignorant of dialectic, whose office it is to investigate definitions and universals of this kind, the study of which led to the introduction of the Ideas.
165. Here he gives the reason for the other difference, that is, the one concerning matter. First, he gives the reason for such a difference. Second (166), he shows that Plato was not reasonably motivated.
He accordingly says that the Platonists made the dyad [or duality] to be a number of a different nature than the Forms, because all numbers with the exception of prime numbers are produced from it. They called prime numbers those which are not measured by any other number, such as three, five, seven, eleven, and so on; for these are produced immediately from unity alone. But numbers which are measured by some other number are not called prime numbers but composite ones, for example, the number four, which is measured by the number two; and in general every even number is measured by the number two. Hence even numbers are attributed to matter, since unlimitedness, which belongs to matter, is attributed to them, as has been stated above (125). This is why he posited the dyad, from which as “a matrix,” or exemplar, all other even numbers are produced.
166. Here he proves that Plato made unreasonable assumptions; and in regard to this he does two things. For, first, he proves this by an argument from nature. Second (167), he gives the argument based on the nature of things, which led Plato to adopt this position (“And from one matter”).
He says that, although Plato posited a dyad on the part of matter, still what happens is the contrary of this, as the opinions of all the other natural philosophers testify; for they claimed that contrariety pertains to form and unity to matter, as is clear in Book I of the Physics. For they held that the material principle of things is air or water or something of this kind, from which the diversity of things is produced by rarefaction and condensation, which they regarded as formal principles; for Plato’s position is not a reasonable one. Now the natural philosophers adopted this position because they saw that many things are generated from matter as a result of a succession of forms in matter. For that matter which now supports one form may afterwards support rnany forms as a result of one form being corrupted and another being generated. But one specifying principle or form “generates only once,” i.e., constitutes the thing which is generated. For when something is generated it receives a form, and the same form numerically cannot become the form of another thing that is generated, but ceases to be when that which was generated undergoes corruption. In this argument it is clearly apparent that one matter is related to many forms, and not the reverse, i.e., one form to many matters. Thus it seems more reasonable to hold that unity pertains to matter but duality or contrariety to form, as the philosophers of nature claimed. This is the opposite of what Plato held.
167. Here he gives an opposite argument taken from sensible things according to the opinion of Plato. For Plato saw that each thing is received in something else according to the measure of the recipient. Hence receptions seem to differ according as the capacities of recipients differ. But one matter is one capacity for reception. And Plato also saw that the agent who induces the form, although he is one, causes many things to have this form; and this comes about because of diversity on the part of matter. An example of this is evident in the case of male and female; for a male is related to a female as an agent and one who impresses a form on matter. But a female is impregnated by one act of a male, whereas one male can impregnate many females. This is why he held that unity pertains to form and duality to matter.
168. Now we must note that this difference between Plato and the philosophers of nature is a result of the fact that they considered things from different points of view. For the philosophers of nature considered sensible things only insofar as they are subject to change, in which one subject successively acquires contrary qualities.
Hence they attributed unity to matter and contrariety to form. But Plato, because of his investigation of universals, went on to give the principles of sensible things. Therefore, since the cause of the diversity of the many singular things which come under one universal is the division of matter, he held that diversity pertains to matter and unity to form. “And such are the changes of those principles” which Plato posited, i.e., participations, or, as I may say, influences in the things generated. For Pythagoras understands the word change in this way. Or Aristotle says “changes” inasmuch as Plato changed the opinion which the first philosophers of nature had about principles, as is evident from the foregoing. Hence it is evident from the foregoing that Plato dealt thus with the causes which we are investigating.
169. Here he shows to what class of cause the principles given by Plato are referred. He says that it is evident from the foregoing that Plato used only two kinds of causes. For he used as “one” cause of a thing the cause of its “whatness,” i.e., its quiddity, or its formal cause, which determines its quiddity; and he also used matter itself. This is also evident from the fact that the Forms which he posited “are the causes of other things,” i.e., the causes of the whatness of sensible things, namely, their formal causes, whereas the formal cause of the Forms themselves is what I call the one, which seems to be the substance of which the Forms are composed. And just as he holds that the one is the formal cause of the Forms, in a similar fashion he holds that the great and small are their material cause, as was stated above (159). And these causes—the formal and the material cause—are referred not only to the Forms but also to sensible substances, because [there is some subject of which] the one is predicated in the case of the Forms. That is to say, that which is related to sensible substances in the same way as the one is to the Forms is itself a Form, because that duality which relates to sensible things as their matter is the great and small.
170. Furthermore, Plato indicated the cause of good and evil in the world, and he did this with reference to each of the elements which he posited. For he made Form the cause of good and matter the cause of evil.
However, some of the first philosophers attempted to investigate the cause of good and evil, namely, Anaxagoras and Empedocles, who established certain causes in the world with this special end in view that by means of these causes they might be able to give the principles of good and evil. And in touching upon these causes of good and evil they came very close to positing the final cause, although they did not posit this cause directly but only indirectly, as is stated below (177).
Lesson 11
All the foregoing weak on FINAL cause
177. Here he gives the opinions of certain thinkers about the final cause. He says that in one sense the philosophers say that the goal for the sake of which motions, changes and activities occur is a cause, and in another sense they do not. And they neither speak of it in the same way, nor in the way in which it is a true cause. For those who affirm that intellect or love is a cause, posit these causes as good. For they said that things of this kind are the causes of things being well disposed, since the cause of good can only be good. Hence it follows that they could make intellect and love to be causes, just as the good is a cause. But good can be understood in two ways: (1) in one way as a final cause, in the sense that something comes to be for the sake of some good; and (2) in another way as an efficient cause, as we say that the good man does good.
Now these philosophers did not say that the foregoing causes are good in the sense that they are the reason for the existence or coming to be of some beings, which pertains to the intelligibility of the final cause, but in the sense that there proceeds from these causes—intellect and will—a kind of motion toward the being and coming-to-be of things; and this pertains to the intelligibility of the efficient cause.
178. In a similar way the Pythagoreans and Platonists, who said that the substance of things is the one itself or being, also attributed goodness to the one or being. Thus they said that such a reality, i.e., the good, is the cause of the substance of sensible things, either in the manner of a formal cause, as the Platonists maintained, or in the manner of a material cause, as the Pythagoreans claimed.
However, they did not say that the being and coming-to-be of things exists for the sake of this, i.e., the one or being; and this is something that pertains to the intelligibility of the final cause.
Hence, just as the philosophers of nature claimed that the good is a cause in the manner of an (+) efficient cause and not in that of a (~) formal cause, in a similar way the Platonists claimed that the good is a cause in the manner of a (+) formal cause, and not in that of a (~) final cause. The Pythagoreans, on the other hand, considered it to be a cause in the manner of a (+) material cause.
179. It is evident, then, that in one sense they happened to speak of the good as a cause and in another not. For they did not speak of it as a cause in its principal aspect but in a secondary one; because according to its proper intelligible structure the good is a cause in the manner of a final cause. This is clear from the fact that the good is what all desire. Now that to which an appetite tends is a goal. Therefore according to its proper intelligible structure the good is a cause in the manner of a goal.
Hence those who make the good a cause in its principal aspect claim that it is a final cause. But those who attribute a different mode of causality to the good claim that the good is a cause but only in a secondary way; because they do not hold that it is such by reason of being good, but by reason of that to which good happens to belong by reason of its being active or perfective.
Hence it is clear that those philosophers posited a final cause only incidentally, because they posited as a cause something that is fitting to be an end, namely, the good. However, they did not claim that it is a cause in the manner of a final cause, as has been stated.
Conclusion
180. Here he draws the conclusion at which he chiefly aims: that the things established about the causes, both as to their number and their kinds, are correct. For the foregoing philosophers seem to bear witness to this in being unable to add another class of cause to those discussed above. This is one of the useful pieces of information resulting from the account of the foregoing views.
Another is that evidently the principles of things must be investigated in this science, either all those which the ancient philosophers posited, and which have been established above, or some of them. For this science considers chiefly the formal and final cause, and also in a sense the efficient cause.
Now it is not only necessary that the above views be discussed, but after this examination it is also necessary to describe the way in which each of these men has spoken (both in what sense their statements are acceptable and in what sense not), and how the statements which have been made about the principles of things contain a problem.