Parmenides, however, seems to speak with rather more insight. For holding as he does that Not-being, as contrasted with Being, is nothing, he necessarily supposes that Being is one and that there is nothing else (we have discussed this point in greater detail in the Physics Aristot. Phys. 1.3 ); but being compelled to accord with phenomena, and assuming that Being is one in definition but many in respect of sensation, he posits in his turn two causes, i.e. two first principles, Hot and Cold; or in other words, Fire and Earth. Of these he ranks Hot under Being and the other under Not-being. Cf. note on Aristot. Met.
3.13. From the account just given, and from a consideration of those thinkers who have already debated this question, we have acquired the following information. From the earliest philosophers we have learned that the first principle is corporeal (since water and fire and the like are bodies); some of them assume one and others more than one corporeal principle, but both parties agree in making these principles material. Others assume in addition to this cause the source of motion, which some hold to be one and others two. Thus down to and apart from the Italian The Pythagoreans; so called because Pythagoras founded his society at Croton.
philosophers the other thinkers have expressed themselves vaguely on the subject, except that, as we have said, they actually employ two causes, and one of these—the source of motion —some regard as one and others as two. The Pythagoreans, while they likewise spoke of two principles, made this further addition, which is peculiar to them: they believed, not that the Limited and the Unlimited are separate entities, like fire or water or some other such thing, but that the Unlimited itself and the One itself are the essence of those things of which they are predicated, and hence that number is the essence of all things. Such is the nature of their pronouncements on this subject. They also began to discuss and define the "what" of things; but their procedure was far too simple. They defined superficially, and supposed that the essence of a thing is that to which the term under consideration first applies—e.g. as if it were to be thought that "double" and "2" are the same, because 2 is the first number which is double another. But presumably "to be double a number" is not the same as "to be the number 2." Otherwise, one thing will be many—a consequence which actually followed in their system. i.e., the same number might be the first to which each of several definitions applied; then that number would be each of the concepts so defined. This much, then, can be learned from other and earlier schools of thought. The philosophies described above were succeeded by the system of Plato, Compare Aristot. Met.
12.4.2-5. which in most respects accorded with them, but contained also certain peculiar features distinct from the philosophy of the Italians. In his youth Plato first became acquainted with Cratylus Cf. Aristot. Met.
4.5.18. and the Heraclitean doctrines—that the whole sensible world is always in a state of flux, Plat. Crat.
402a (fr. 41 Bywater). and that there is no scientific knowledge of it—and in after years he still held these opinions. And when Socrates, disregarding the physical universe and confining his study to moral questions, sought in this sphere for the universal and was the first to concentrate upon definition, Plato followed him and assumed that the problem of definition is concerned not with any sensible thing but with entities of another kind; for the reason that there can be no general definition of sensible things which are always changing. These entities he called "Ideas," I have translated i)de/a by Idea and ei)=dos by Form wherever Aristotle uses the words with reference to the Platonic theory.
Plato apparently uses them indifferently, and so does Aristotle in this particular connection, but he also uses ei)=dos in the sense of form in general. For a discussion of the two words see Taylor, Varia Socratica, 178-267, and Gillespie, Classical Quarterly, 6.179-203. and held that all sensible things are named after For this interpretation of para\ tau=ta see Ross's note ad loc. them sensible and in virtue of their relation to them; for the plurality of things which bear the same name as the Forms exist by participation in them. (With regard to the "participation," it was only the term that he changed; for whereas the Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by participation—merely a change of term. As to what this "participation" or "imitation" may be, they left this an open question.) Further, he states that besides sensible things and the Forms there exists an intermediate class, the objects of mathematics, i.e. arithmetical numbers and geometrical figures. which differ from sensible things in being eternal and immutable, and from the Forms in that there are many similar objects of mathematics, whereas each Form is itself unique. Now since the Forms are the causes of everything else, he supposed that their elements are the elements of all things. Accordingly the material principle is the "Great and Small," and the essence <or formal principle> is the One, since the numbers are derived from the "Great and Small" by participation in the the One. In treating the One as a substance instead of a predicate of some other entity, his teaching resembles that of the Pythagoreans, and also agrees with it in stating that the numbers are the causes of Being in everything else; but it is peculiar to him to posit a duality instead of the single Unlimited, and to make the Unlimited consist of the "Great and Small." He is also peculiar in regarding the numbers as distinct from sensible things, whereas they hold that things themselves are numbers, nor do they posit an intermediate class of mathematical objects. His distinction of the One and the numbers from ordinary things (in which he differed from the Pythagoreans) and his introduction of the Forms were due to his investigation of logic (the earlier thinkers were strangers to Dialectic) See Aristot. Met. 4.2.19-20, and cf. Aristot. Met. 8.4.4.; his conception of the other principle as a duality to the belief that numbers other than primes e)/cw tw=n prw/twn is very difficult, but it can hardly be a gloss, and no convincing emendation has been suggested. Whatever the statement means, it is probably (as the criticism which follows is certainly) based upon a misunderstanding. From Plat. Parm.
143c, it might be inferred that the Great and Small (the Indeterminate Dyad) played no part in the generation of numbers; but there the numbers are not Ideal, as here they must be. In any case Aristotle is obsessed with the notion that the Dyad is a duplicative principle ( Aristot. Met.
13.8.14 ), which if true would imply that it could generate no odd number. Hence Heinze proposed reading perittw=n (odd) for prw/twn (which may be right, although the corruption is improbable) and Alexander tried to extract the meaning of "odd" from prw/twn by understanding it as "prime to 2."
However, as Ross points out (note ad loc.), we may keep prw/twn in the sense of "prime" if we suppose Aristotle to be referring either (a) to the numbers within the decad ( Aristot. Met. 13.8.17 ) and forgetting 9—the other odd numbers being primes; or (b) to numbers in general, and forgetting the entire class of compound odd numbers. Neither of these alternatives is very satisfactory, but it seems better to keep the traditional text. can be readily generated from it, as from a matrix. For a similar use of the word e)kmagei=on cf. Plat.
Tim. 50c.
The fact, however, is just the reverse, and the theory is illogical; for whereas the Platonists derive multiplicity from matter although their Form generates only once, Aristotle's objection is that it is unreasonable that a single operation of the formal upon the material principle should result in more than one product; i.e. that the material principle should be in itself duplicative. it is obvious that only one table can be made from one piece of timber, and yet he who imposes the form upon it, although he is but one, can make many tables. Such too is the relation of male to female: the female is impregnated in one coition, but one male can impregnate many females.
And these relations are analogues of the principles referred to. This, then, is Plato's verdict upon the question which we are investigating. From this account it is clear that he only employed two causes Plato refers several times in the dialogues to an efficient cause (e.g. the Demiurgus, Plat. Soph. 265b-d, Plat. Tim. 28c ff. ) and a final cause (e.g. Plat. Phil. 20d, 53e, Plat.
Tim. 29d ff. ); but Aristotle does not seem to take these allusions seriously.: that of the essence, and the material cause; for the Forms are the cause of the essence in everything else, and the One is the cause of it in the Forms. He also tells us what the material substrate is of which the Forms are predicated in the case of sensible things, and the One in that of the Forms—that it is this the duality, the "Great and Small."
Further, he assigned to these two elements respectively the causation of good Cf. Plat.
Phil. 25e-26b. and of evil; a problem which, as we have said, Aristot. Met. 3.17; 4.3. had also been considered by some of the earlier philosophers, e.g. Empedocles and Anaxagoras. We have given only a concise and summary account of those thinkers who have expressed views about the causes and reality, and of their doctrines. Nevertheless we have learned thus much from them: that not one of those who discuss principle or cause has mentioned any other type than those which we we have distinguished in the Physics.
Aristot. Phys. 2.3 Clearly it is after these types that they are groping, however uncertainly. Some speak of the first principle as material, whether they regard it as one or several, as corporeal or incorporeal: e.g. Plato speaks of the "Great and Small"; the Italians See note on Aristot. Met.
5.15. of the Unlimited; Empedocles of Fire, Earth, Water and Air; Anaxagoras of the infinity of homoeomeries. All these have apprehended this type of cause; and all those too who make their first principle air or water or "something denser than fire but rarer than air" The various references in Aristotle to material principles intermediate between certain pairs of "elements" have been generally regarded as applying to Indeterminate; but the references are so vague (cf. Aristot. Met. 7.6, Aristot. Phys.187a 14, better to connect them with later and minor members of the Milesian school. Cf. Ross's note ad loc. (for some have so described the primary element). These, then, apprehended this cause only, but others apprehended the source of motion —e.g. all such as make Love and Strife, or Mind, or Desire a first principle. As for the essence or essential nature, nobody has definitely introduced it; but the inventors of the Forms express it most nearly. For they do not conceive of the Forms as the matter of sensible things (and the One as the matter of the Forms), nor as producing the source of motion (for they hold that they are rather the cause of immobility and tranquillity); but they adduce the Forms as the essential nature of all other things, and the One as that of the Forms. The end towards which actions, changes and motions tend they do in a way treat as a cause, but not in this sense, i.e. not in the sense in which it is naturally a cause. Those who speak of Mind or Love assume these causes as being something good; but nevertheless they do not profess that anything exists or is generated for the sake of them, but only that motions originate from them. Cf. Aristot. Met.
3.17. Similarly also those who hold that Unity or Being is an entity of this kind state that it is the cause of existence, but not that things exist or are generated for the sake of it. So it follows that in a sense they both assert and deny that the Good is a cause; for they treat it as such not absolutely, but incidentally. It appears, then, that all these thinkers too (being unable to arrive at any other cause) testify that we have classified the causes rightly, as regards both number and nature. Further, it is clear that all the principles must be sought either along these lines or in some similar way. Let us next examine the possible difficulties arising out of the statements of each of these thinkers, and out of his attitude to the first principles. All those who regard the universe as a unity, and assume as its matter some one nature, and that corporeal and extended, are clearly mistaken in many respects. They only assume elements of corporeal things, and not of incorporeal ones, which also exist. They attempt to state the causes of generation and destruction, and investigate the nature of everything; and at the same time do away with the cause of motion. Then there is their failure to regard the essence or formula as a cause of anything; and further their readiness to call any one of the simple bodies—except earth—a first principle, without inquiring how their reciprocal generation is effected. I refer to fire, water, earth and air. Of these some are generated from each other by combination and others by differentiation; and this difference is of the greatest importance in deciding their relative priority. In one way it might seem that the most elementary body is that from which first other bodies are produced by combination; and this will be that body which is rarest and composed of the finest particles. Hence all who posit Fire as first principle will be in the closest agreement with this theory. However, even among the other thinkers everyone agrees that the primary corporeal element is of this kind. At any rate none of the Monists thought earth likely to be an element—obviously on account of the size of its particles— but each of the other three has had an advocate; for some name fire as the primary element, others water, and others air. Cf. Aristot. Met.
3.5, 8. And yet why do they not suggest earth too, as common opinion does? for people say "Everything is earth." And Hesiod too says Cf. Aristot. Met. 4.1.
that earth was generated first of corporeal things—so ancient and popular is the conception found to be. Thus according to this theory anyone who suggests any of these bodies other than fire, or who assumes something "denser than air but rarer than water," Cf. Aristot. Met.
7.3 n. will be wrong. On the other hand if what is posterior in generation is prior in nature, and that which is developed and combined is posterior in generation, then the reverse will be the case; water will be prior to air, and earth to water. So much for those who posit one cause such as we have described. The same will apply too if anyone posits more than one, as e.g. Empedocles says that matter consists of four bodies; objections must occur in his case also, some the same as before, and some peculiar to him. First, we can see things being generated from each other in a way which shows that fire and earth do not persist as the same corporeal entity. (This subject has been treated in my works on Natural Science. Aristot. De Caelo, 3.7; Aristot. De Gen. et Corr.
2.6. ) Again with regard to the cause of motion in things, whether one or two should be assumed, it must not be thought that his account is entirely correct or even reasonable. Cf. Aristot. Met.
4.6. And in general those who hold such views as these must of necessity do away with qualitative alteration; for on such a theory cold will not come from hot nor hot from cold, because to effect this there must be something which actually takes on these contrary qualities: some single element which becomes both fire and water—which Empedocles denies. If one were to infer that Anaxagoras recognized two Mind, and the "mixture" of homoeomerous particles. elements, the inference would accord closely with a view which, although he did not articulate it himself, he must have accepted as developed by others. To say that originally everything was a mixture is absurd for various reasons, but especially since (a) it follows that things must have existed previously in an unmixed state; (b) it is contrary to nature for anything to mix with anything; (c) moreover affections and attributes would then be separable from their substances (because what is mixed can also be separated). At the same time, if one were to follow his doctrine carefully and interpret its meaning, perhaps it would be seen to be more up-to-date; because when nothing was yet differentiated, obviously nothing could be truly predicated of that substance—e.g. that it was white or black or buff or any other color. It must necessarily have been colorless, since otherwise it would have had one of these colors. Similarly by the same argument it had no taste or any other such attribute; for it cannot have had any quality or magnitude or individuality. Otherwise some particular form would have belonged to it; but this is impossible on the assumption that everything was mixed together, for then the form would have been already differentiated, whereas he says that everything was mixed together except Mind, which alone was pure and unmixed. Anaxagoras. Fr. 12 (Diels). It follows from this that he recognizes as principles the One (which is simple and unmixed) and the Other, which is such as we suppose the Indeterminate to be before it is determined and partakes of some form. Thus his account is neither correct nor clear, but his meaning approximates to more recent theories and what is now more obviously true. However, these thinkers are really concerned only with the theories of generation and destruction and motion (for in general it is only with reference to this aspect of reality that they look for their principles and causes). Those, however, who make their study cover the whole of reality, and who distinguish between sensible and non-sensible objects, clearly give their attention to both kinds; hence in their case we may consider at greater length what contributions, valuable or otherwise, they make to the inquiry which is now before us. The so-called Pythagoreans employ abstruser principles and elements than the physicists. The reason is that they did not draw them from the sensible world; for mathematical objects, apart from those which are connected with astronomy, are devoid of motion. Nevertheless all their discussions and investigations are concerned with the physical world. They account for the generation of the sensible universe, and observe what happens in respect of its parts and affections and activities, and they use up their principles and causes in this connection, as though they agreed with the others—the physicists—that reality is just so much as is sensible and is contained in the so-called "heavens." All the same, as we have said, Aristot. Met. 1.8.17. the causes and principles which they describe are capable of application to the remoter class of realities as well, and indeed are better fitted to these than to their physical theories. But as to how there is to be motion, if all that is premissed is Limit and the Unlimited, and Odd and Even, they do not even hint; nor how, without motion and change, there can be generation and destruction, or the activities of the bodies which traverse the heavens. And further, assuming that it be granted to them or proved by them that magnitude Aristotle uses the word me/geqos both of magnitude in general and of spatial magnitude or extension. Here the meaning seems to be the former.
Numbers obviously have magnitude, and might be regarded as causing it; but (except on the Number-Atomism theory,) they are no more the cause of extension than that of gravity. is composed of these factors, yet how is it to be explained that some bodies are light, and others have weight? For in their premisses and statements they are speaking just as much about sensible as about mathematical objects; and this is why they have made no mention of fire or earth or other similar bodies, because, I presume, they have no separate explanation of sensible things. Again, how are we to understand that number and the modifications of number are the causes of all being and generation, both in the beginning and now, and at the same time that there is no other number than the number of which the universe is composed? i.e., how can number be both reality and the cause of reality? Because when they make out that Opinion and Opportunity are in such and such a region, and a little above or below them Injustice and Separation or Mixture, and when they state as proof of this that each of these abstractions is a number; and that also in this region there is already a plurality of the magnitudes composed of number, inasmuch as these modifications of number correspond to these several regions,—is the number which we must understand each of these abstractions to be the same number which is present in the sensible universe, or another kind of number? The point seems to be this. The Pythagoreans say that Opinion is a number, 3 (or 2, according to another version), and is located in a certain region of the universe because that region is proper to a corporeal magnitude composed of the number 3 (air was so composed according to Syrianus). Are we to understand, says Aristotle, that the abstract number identified with Opinion is the same as the concrete number of which air consists? The difficulty is probably due to an attempt to combine two different Pythagorean views of number. Plato at least says that it is another. It is true that he too supposes that numbers are both these magnitudes and their causes; but in his view the causative numbers are intelligible and the others sensible. The Pythagoreans, then, may be dismissed for the present, for it is enough to touch upon them thus briefly. As for those who posit the Forms as causes, For a discussion of the Ideal theory and Aristotle's conception of it see Introduction; and with the whole contents of Aristot. Met. 9.1-15 cf. Aristot. Met. 13.4.6-5. in the first place in their attempt to find the causes of things in our sensible world, they introduced an equal number of other entities—as though a man who wishes to count things should suppose that it would be impossible when they are few, and should attempt to count them when he has added to them. For the Forms are as many as, or not fewer than, the things in search of whose causes these thinkers were led to the Forms; because corresponding to each thing there is a synonymous entity apart from the substances (and in the case of non-substantial things there is a One over the Many An Idea which represents their common denominator. ), both in our everyday world and in the realm of eternal entities. The heavenly bodies. Again, not one of the arguments by which we Aristotle is here speaking as a Platonist. Contrast the language of Aristot. Met. 13.4.7ff., and see Introduction. try to prove that the Forms exist demonstrates our point: from some of them no necessary conclusion follows, and from others it follows that there are Forms of things of which we hold that there are no Forms. For according to the arguments from the sciences Scientific knowledge must have a permanent object (cf. Aristot. Met. 1.4.2. there will be Forms of all things of which there are sciences Including artificial products; cf. Aristot. Met.
1.15.; and according to the "One-over-Many" argument, The fact that several particulars can have a common quality or nature implies a single Idea of which they all partake ( Plat. Rep.
596a ). of negations too; and according to the argument that "we have some conception of what has perished," of perishable things; because we have a mental picture of these things. The theory always admitted Ideas of perishable things, e.g. "man." The objection here is that if the memory of dead men establishes the Idea of "man," the memory of a dead individual establishes an Idea of that (perishable) individual. Again, of Plato's more exact arguments some establish Ideas of relations, Plat. Phaedo 74a-77a, Plat. Rep.
479a-480a. which we do not hold to form a separate genus; and others state the "Third Man." Several arguments bore this name. Here the reference is probably to the following: If X is a man because he resembles the Idea of Man, there must be a third "man" in whom the humanity of these two is united. Cf. Plat. Parm. 132a-133a. And in general the arguments for the Forms do away with things which are more important to us exponents of the Forms than the existence of the Ideas; for they imply that it is not the Dyad that is primary, but Number The Indeterminate Dyad, being to Aristotle a glorified 2, falls under the Idea of Number, which is therefore prior to it.; and that the relative is prior to the absolute This seems to be a development of the same objection. Number, which is relative, becomes prior to the supposedly self-subsistent Dyad.; and all the other conclusions in respect of which certain persons, by following up the views held about the Ideas, have gone against the principles of the theory. Again, according to the assumption by which we hold that the Ideas exist, there will be Forms not only of substances but of many other things (since the concept is one not only in the case of substances, but also in the case of all other things; and there are sciences not only of substances but of other things as well; and there are a thousand other similar consequences); but according to logical necessity, and from the views generally held about them, it follows that if the Forms are participated in, then there can only be Ideas of substances. For they are not participated in qua accidents; each Form can only be participated in in so far as it is not predicated of that if anything participates in "absolute Doubleness" it participates also in "eternal," but only accidentally; because it is an accident of Doubleness to be eternal. Sensible double things are not eternal; therefore they do not, in the proper sense of "participation," participate in the Idea of Doubleness qua having the accidental attribute "eternal." Therefore Ideas, qua participated in, are not attributes but substances. Thus the Forms must be substance. But the same names denote substance in the sensible as in the Ideal world; otherwise what meaning will there be in saying that something exists beside the particulars, i.e. the unity comprising their multiplicity? If the form of the Ideas and of the things which participate in them is the same, they will have something in common (for why should Duality mean one and the same thing in the case of perishable "twos" i.e. pairs of sensible objects. and the "twos" which are many but eternal, i.e. mathematical 2s.
and not in the case of the Idea of Duality and a particular "two"?); but if the form is not the same, they will simply be homonyms; just as though one were to call both Callias and a piece of wood "man," without remarking any property common to them. The argument of 7-8 is: Ideas are substances. The common name which an idea shares with its particulars must mean the same of both; otherwise "participation" is merely homonymy.
But as applied to Ideas it denotes substance; therefore particulars must be substances. Above all we might examine the question what on earth the Forms contribute to sensible things, whether eternal or subject to generation and decay; for they are not the cause of any motion or change in them. Again, they are no help towards the knowledge of other things This objection, like the next, is chiefly directed against the transcendence of the Ideas. It is anticipated by Plato in Plat.
Parm. 134d. (for they are not the substance of things, otherwise they would be in things), nor to their existence, since they are not present in the things which partake of them. If they were, it might perhaps seem that they are causes, in the sense in which the admixture of white causes a thing to be white; but this theory, which was first stated by Anaxagoras Anaxagoras Fr. 12 ad fin. and later by Eudoxus See note on Aristot. Met. 12.8.9. Apparently he was a Platonist who regarded the Ideas as immanent in particulars. and others, is very readily refutable, for it is easy to adduce plenty of impossibilities against such a view.
Again, other things are not in any accepted sense derived from the Forms. To say that the Forms are patterns, and that other things participate in them, is to use empty phrases and poetical metaphors; for what is it that fashions things on the model of the Ideas Plato says "the Demiurgus"? Plat. Tim. 28c, Plat. Tim. 29a. Besides, anything may both be and become like something else without being imitated from it; thus a man may become just like Socrates whether Socrates exists or not, and even if Socrates were eternal, clearly the case would be the same. Also there will be several "patterns," and hence Forms, of the same thing; e.g. "animal" and "two-footed" will be patterns of "man," and so too will the Idea of Man. Why this consequence is objectionable is not quite clear. Perhaps it is on the ground that to "account for appearances" in this way is not economical. Further, the Forms will be patterns not only of sensible things but of themselves (e.g. genus in the sense of genus of species), and thus the same thing will be both pattern and copy. The species will be the "pattern" of individuals, and the genus of the species.
Further, it would seem impossible that the substance and the thing of which it is the substance exist in separation; hence how can the Ideas, if they are the substances of things, exist in separation from them? Cf. Aristot. Met.
1.10. It is stated in the Phaedo Plat. Phaedo 100d. that the Forms are the causes both of existence and of generation. Yet, assuming that the Forms exist, still the things which participate in them are not generated unless there is something to impart motion; while many other things are generated (e.g. house, ring) of which we hold that there are no Forms. Thus it is clearly possible that all other things may both exist and be generated for the same causes as the things just mentioned. Further, if the Forms are numbers, in what sense will they be causes? Is it because things are other numbers, e.g. such and such a number Man, such and such another Socrates, such and such another Callias? then why are those numbers the causes of these? Even if the one class is eternal and the other not, it will make no difference. And if it is because the things of our world are ratios of numbers (e.g. a musical concord), clearly there is some one class of things of which they are ratios. Now if there is this something, i.e. their matter, clearly the numbers themselves will be ratios of one thing to another. I mean, e.g., that if Callias is a numerical ratio of fire, earth, water and air, the corresponding Idea too will be a number of certain other things which are its substrate. The Idea of Man, too, whether it is in a sense a number or not, will yet be an arithmetical ratio of certain things, and not a mere number; nor, on these grounds, will any Idea be a number. The point, which is not very clearly expressed, is that the Ideas will not be pure numerical expressions or ratios, but will have a substrate just as particulars have. Again, one number can be composed of several numbers, but how can one Form be composed of several Forms? And if the one number is not composed of the other numbers themselves, but of their constituents (e.g. those of the number 10,000), what is the relation of the units? If they are specifically alike, many absurdities will result, and also if they are not (whether (a) the units in a given number are unlike, or (b) the units in each number are unlike those in every other number). That the words in brackets give the approximate sense seems clear from Aristot. Met.
13.6.2-3, Aristot. Met. 13.7.15; but it is difficult to get it out of the Greek. For in what can they differ, seeing that they have no qualities? Such a view is neither reasonable nor compatible with our conception of units. Further, it becomes necessary to set up another kind of number (with which calculation deals), and all the objects which are called "intermediate" by some thinkers. Cf. vi. 4. But how or from what principles can these be derived? or on what grounds are they to be considered intermediate between things here and Ideal numbers? Further, each of the units in the number 2 comes from a prior 2; but this is impossible. i.e., if 2 is derived from a prior 2 (the Indeterminate Dyad; Aristotle always regards this as a number 2), and at the same time consists of two units or 1s, 2 will be prior both to itself and to 1.
Further, why should a number <of units>, taken together, be one thing? And further, in addition to the above objections, if the units are unlike, they should be treated as the thinkers who assume two or four elements treat those elements; for not one of them applies the term "element" to the common substrate, e.g. body, but to fire and earth—whether there is a common substrate (i.e. body) or not. In the Aristot. De Gen. et Corr. 320b 23 Aristotle says that there is not. As it is, the One is spoken of as though it were homogeneous, like fire or water. But if this is so, the numbers will not be substances. And if there is an absolute One which is a principle, clearly the term "one" is ambiguous; otherwise this is impossible. This last sentence shows that in what goes before A. has been regarding the Platonic One as a unit. If this is so, he says, substance cannot be composed of it. If on the other hand the One is something different from the unit, they ought to make this clear. When we wish to refer substances to their principles we derive lines The lines, planes, and solids here discussed are probably the Ideal lines, etc., which are immediately posterior to the Idea-Numbers. Cf. 30, Aristot. Met.
13.6.10, Aristot. Met. 13.9.2, and see Introduction. from "Long and Short," a kind of "Great and Small"; and the plane from "Wide and Narrow," and the solid body from "Deep and Shallow." But in this case how can the plane contain a line, or the solid a line and a plane? for "Wide and Narrow" and "Deep and Shallow" are different genera. Nor is Number contained in these objects (because "Many and Few" is yet another class); and in the same way it is clear that none of the other higher genera will be contained in the lower.