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, Footnote 1For 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 Footnote 2An Idea which represents their common denominator. ), both in our everyday world and in the realm of eternal entities. Footnote 3The heavenly bodies.
Again, not one of the arguments by which we Footnote 4Aristotle 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 Footnote 5Scientific knowledge must have a permanent object (cf. Aristot. Met. 1.4.2. there will be Forms of all things of which there are sciences Footnote 6Including artificial products; cf. Aristot. Met. 1.15. ; and according to the One-over-Many
argument, Footnote 7The 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. Footnote 8The 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, Footnote 9Plat. Phaedo 74a-77a, Plat. Rep. 479a-480a. which we do not hold to form a separate genus;
and others state the Third Man.
Footnote 10Several 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 Footnote 11The 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 Footnote 12This 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 a subject.
I mean, e.g., 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. Footnote 13Sensible 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
Footnote 14i.e. pairs of sensible objects. and the twos
which are many but eternal, Footnote 15i.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. Footnote 16The 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 Footnote 17This 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 Footnote 18Anaxagoras Fr. 12ad fin. and later by Eudoxus Footnote 19See 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 Footnote 20Plato 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. Footnote 21Why 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. Footnote 22The 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? Footnote 23Cf. Aristot. Met. 1.10. It is stated in the Phaedo Footnote 24Plat. 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. Footnote 25The 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). Footnote 26That 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. Footnote 27Cf. 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. Footnote 28i.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. Footnote 29In the Aristot. De Gen. et Corr. 320b 23Aristotle 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. Footnote 30This 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 Footnote 31The 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. Nor, again, is the Broad the genus of which the Deep is a species; for then body would be a kind of plane.
Further, how will it be possible for figures to contain points? Footnote 32Lines, planes, and solids are generated from varieties of the Great and Small, but points cannot be, having no magnitude; how, then, can the latter be present in the former? Plato steadily rejected this class of objects as a geometrical fiction, but he recognized the beginning of a line,
and he frequently assumed this latter class, i.e. the indivisible lines.
Footnote 33That Plato denied the existence of the point and asserted that of indivisible lines is not directly stated elsewhere, but the same views are ascribed to Xenocrates, and were attacked in the treatise Xenocrates De lineis insecabilibus. See Ross ad loc. But these must have some limit; and so by the same argument which proves the existence of the line, the point also exists. Footnote 34Sc. if the point is the limit of the line.
In general, although Wisdom is concerned with the cause of visible things, we have ignored this question (for we have no account to give of the cause from which change arises), Footnote 35Cf. Aristot. Met. 7.5 and Aristot. Met. 1.9. and in the belief that we are accounting for their substance we assert the existence of other substances; but as to how the latter are the substances of the former, our explanation is worthless—for participation,
as we have said before, Footnote 36Aristot. Met. 1.12. means nothing.
And as for that which we can see to be the cause in the sciences, and through which all mind and all nature works—this cause Footnote 37The final cause. Cf. Aristot. Met. 1.6.9-10. which we hold to be one of the first principles—the Forms have not the slightest bearing upon it either. Philosophy has become mathematics for modern thinkers, Footnote 38e.g. Speusippus, for whom see Aristot. Met. 7.2.4. although they profess Footnote 39Cf. Plat. Rep.531c-d that mathematics is only to be studied as a means to some other end.
Further, one might regard the substance which they make the material substrate as too mathematical, and as being a predicate and differentia of substance or matter rather than as matter itself, I mean the Great and Small,
which is like the Rare and Dense
of which the physicists speak, Footnote 40Cf. iv. 10. holding that they are the primary differentiae of the substrate; because these qualities are a species of excess and defect.
Also with regard to motion, if the Great and Small
is to constitute motion, obviously the Forms will be moved; if not, whence did it come? On this view the whole study of physics is abolished. And what is supposed to be easy, to prove that everything is One, does not follow; because from their exposition Footnote 41The word ἔκθεσις has various technical meanings. The process referred to here apparently consisted in taking, e.g., particular men, and reducing them with reference to their common nature to a single unit or universal, man
; then taking man,
horse,
dog,
etc. and treating them in the same way, until a unit is reached which embraces everything (Alexander). it does not follow, even if you grant them all their assumptions that everything is One, but only that there is an absolute One—
and not even this, unless you grant that the universal is a class; which is impossible in some cases. Footnote 42Probably those of relative or negative terms. Cf. Aristot. Met. 1.3. Nor is there any explanation of the lines, planes and solids which come after
the Numbers Footnote 43See note on Aristot. Met. 1.23. : neither as to how they exist or can exist, nor as to what their importance is. They cannot be Forms (since they are not numbers) or Intermediates (which are the objects of mathematics) or perishables; clearly they form yet another fourth class.
In general, to investigate the elements of existing things without distinguishing the various senses in which things are said to exist is a hopeless task; especially when one inquires along these lines into the nature of the elements of which things are composed. For (a) we cannot surely conceive of the elements of activity or passivity or straightness; this is possible, if at all, only in the case of substances. Hence to look for, or to suppose that one has found, the elements of everything that exists, is a mistake.
(b) How can one apprehend the elements of everything ? Obviously one could not have any previous knowledge of anything; because just as a man who is beginning to learn geometry can have previous knowledge of other facts, but no previous knowledge of the principles of that science or of the things about which he is to learn, so it is in the case of all other branches of knowledge.
Hence if there is a science which embraces everything Footnote 44e.g. Plato’s Dialectic. (as some say), the student of it can have no previous knowledge at all. But all learning proceeds, wholly or in part, from what is already known; whether it is through demonstration or through definition—since the parts of the definition must be already known and familiar. The same is true of induction.
On the other hand, assuming that this knowledge should turn out to be innate, Footnote 45Cf. the doctrine of ἀνάμνησις (recollection), Plat. Meno 81c, Plat. Phaedo 72e. it is astonishing that we should possess unawares the most important of the sciences. Further, how is one to know of what elements things consist? how is it to be established?
Even this presents a difficulty, because the facts might be disputed, as happens in the case of certain syllables—for some say that ZA is composed of S, D and A, while others say that it is a distinct sound and not any one of those which are familiar to us. Footnote 46στοιχεῖον means both an element
and a letter of the alphabet
; hence letters are often used as analogues of the material elements. The point here is: Is Z or rather the Greek ζ) a στοιχεῖον, or is it further analyzable? Since this can be disputed, we must expect differences of opinion about the elements in general.
Further, how can one gain knowledge of the objects of a particular sense-perception without possessing that sense? Yet it should be possible, that if the elements of which all things consist, as composite sounds consist of their peculiar Footnote 47Peculiar to them as sounds, not as individual sounds. If sights and sounds had the same elements, sight, which knows those elements as composing sights, would know them as composing sounds; i.e., we could see sounds. elements, are the same.