by Aristotle
Once more, it has in no sense been determined in which way numbers are the causes of substances and of being—whether as limits (as points are of magnitudes). [10] This is how Eurytus decided what was the number of what (e.g. of man, or of horse), viz. by imitating the figures of living things with pebbles, as some people bring numbers into the forms of triangle and square. Or is it because harmony is a ratio of [15] numbers, and so is man and everything else? But how are the attributes—white and sweet and hot—numbers? Evidently the numbers are not the substance nor causes of the form; for the ratio is the substance, while the number is the matter. E.g. the substance of flesh or bone is number only in this way, ‘three parts of fire and two of earth.’ And a number, whatever it is, is always a number of certain things, either [20] of fire or earth or of units; but the substance is that there is so much of one thing to so much of another in the mixture; and this is no longer a number but a ratio of mixture of numbers, whether these are corporeal or of any other kind.
Number, then, whether number in general or the number which consists of abstract units, is neither the cause as agent, nor the matter, nor the formula and form of things. Nor, of course, is it that for the sake of which. [25]
6 · One might also raise the question what the good is that things get from numbers because their composition is expressible by a number, either by one which is easily calculable or by an odd number. For in fact honey-water is no more wholesome if it is mixed in the proportion of three times three, but it would do more good if it were in no particular ratio but well diluted than if it were numerically [30] expressible but strong. Again, the ratios of mixtures are expressed by the adding of numbers, not by mere numbers, e.g. it is three parts to two, not three times two. For the same genus must underlie things that are multiplied together; therefore the product 1 × 2 × 3 must be measurable by 1, and 4 × 5 × 7 by 4, and therefore all products into which the same factor enters must be measurable by that factor. The number of fire, then, cannot be 2 × 5 × 3 × 7, and at the same time that of water [1093a1] 2 × 3.
If all things must share in number, it must follow that many things are the same, and the same number must belong to one thing and to another. Is number the cause, then, and does the thing exist because of its number, or is this not certain? E.g. the motions of the sun have a number, and again those of the moon, and so do [5] the life and prime of each animal. Why, then, should not some of these numbers be squares, some cubes, and some equal, others double? There is no reason why they should not, and indeed they must be comprised within these descriptions, since all things were assumed to share in number and things that differed might fall under [10] the same number. Therefore if the same number had belonged to certain things, these would have been the same as one another, since they would have had the same form of number; e.g. sun and moon would have been the same. But why are these numbers causes? There are seven vowels, the scale has seven strings, the Pleiades are seven, at seven animals lose their teeth (at least some, though some do not), and [15] the champions who fought against Thebes were seven. Is it then because the number is what it is, that the champions were seven or the Pleias consists of seven stars? Surely the champions were seven because there were seven gates or for some other reason, and the Pleias we count as seven, as we count the Bear as twelve, while other peoples count more stars in both. They even say that Ξ and Ψ Z are concords, and [20] because there are three concords, the double consonants also are three. They quite neglect the fact that there might be a thousand such letters; for one sign might be attached to ГP. But if they say that each of these three is equal to two of the other letters, and no other is so, and if the cause is that there are three parts of the mouth and one letter is applied to Σ in each, it is for this reason that there are only three, not because the concords are three; since as a matter of fact the concords are more [25] than three, but of double consonants there cannot be more. These people are like the old Homeric scholars, who see small resemblances but neglect great ones. Some say that there are many such cases, e.g. that the middle strings are represented by nine and eight, and that the epic verse has seventeen syllables, which is equal in number to the two strings; and the scansion is, in the right half of the line nine syllables, and [1093b1] in the left eight. And they say that the distance in the letters from alpha to omega is equal to that from the lowest note of the flute to the highest, and that the number of this note is equal to that of the whole system of the heavens. We must observe that [5] no one could find difficulty either in stating such analogies or in finding them in eternal things, since they can be found even in perishable things.
But the celebrated characteristics of numbers and their contraries, and generally the mathematical relations, if we view them as some do, making them [10] causes of nature, seem to escape us; for none of them is a cause in any of the senses that have been distinguished in reference to the first principles. Yet if mathematical objects be conceived as these thinkers conceive them, evidently goodness is predicable of them, and the odd, the straight, the equal-by-equal, and the powers of certain numbers, are in the column of the beautiful. For the seasons and a particular [15] number go together; and the other agreements that they collect from the theorems of mathematics all have this meaning. Hence they are like coincidences. For they are accidents, but appropriate to one another, and one by analogy. For in each category of being an analogous term is found—as the straight line is in length, so is [20] the plane in surface, perhaps the odd in number, and the white in colour.
Again, it is not the ideal numbers that are the causes of musical phenomena and the like (for equal ideal numbers differ from one another in form; for even the units do); so that we need not assume Ideas for this reason at least.
These, then, are the results of the theory, and yet more might be brought [25] together. The fact that they have much trouble with the generation of ideal numbers and can in no way make a system of them, seems to indicate that the objects of mathematics are not separable from sensible things, as some say, and that they are not the first principles.
**TEXT: W. D. Ross, Aristotle’s Metaphysics, Clarendon Press, Oxford, 1924
1In the translation of the Metaphysics ‘formula’ (or ‘definitory formula’) renders ‘λόγoς’.
2Some authorities read: ‘For Alcmaeon lived during the old age of Pythagoras, and he expressed himself. . .’.
3Reading τò ὂν ἓν μέν.
4The MSS read τὰ εἴδη εἶναι τoὐς ἀριθμoὑς. ‘come the Forms, i.e. the numbers’.
1Retaining τὴν ὕλην ἐν κινoυμένῳ.
2Excised by Ross (see 995b6).
1Excised by Ross.
1Origin’ translates ‘ἀρχἡ’, elsewhere often ‘source’ or ‘(first) principle’. In Greek ‘ἀρχἡ’ also means ‘rule’ or ‘office’, whence the illustration under (5).
2Frag. 8 Diels-Kranz.
3Electra 256.
4I.e. a power.
1Excised by Ross.
1Excised by Jaeger.
2Excised by Ross.
1See V (Δ) 12, where ‘δὑναμις’ was translated ‘capacity’.
2Omitting πεσεῖν.
3Omitting ὅτι.
4Ross excises ‘in the strictest sense’.
1Retaining ἢ συνεχές.
1Physics I 8.
1Reading ἀλλ’ oὐ τoὑτων.
2Reading κινoῦν μέσoν, κινoῦν ἐστἱ.
3Physics VIII 8–9.
4Reading ἐννέα for έπτά.
5Iliad II 204.
1Reading πoτ’ for πότ’.
2Phaedo 100D.
3Omitting ἤ.
4Retaining ἔπειτα.
5Ross marks this clause as corrupt.
1Retaining τῷ ἴσῷ.
2Frag. 7 Diels-Kranz.
3Reading ὲξ ἄλλoυ δὲ τίνoς.
NICOMACHEAN ETHICS**
W. D. Ross
revis
ed by J. O. Urmson
BOOK I
1 · Every art and every inquiry, and similarly every action and choice, is [1094a1] thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim. But a certain difference is found among ends; some are activities, others are products apart from the activities that produce them. Where there are ends apart from the actions, it is the nature of the products to be [5] better than the activities. Now, as there are many actions, arts, and sciences, their ends also are many; the end of the medical art is health, that of shipbuilding a vessel, that of strategy victory, that of economics wealth. But where such arts fall under a single capacity—as bridle-making and the other arts concerned with the [10] equipment of horses fall under the art of riding, and this and every military action under strategy, in the same way other arts fall under yet others—in all of these the ends of the master arts are to be preferred to all the subordinate ends; for it is for the [15] sake of the former that the latter are pursued. It makes no difference whether the activities themselves are the ends of the actions, or something else apart from the activities, as in the case of the sciences just mentioned.
2 · If, then, there is some end of the things we do, which we desire for its own sake (everything else being desired for the sake of this), and if we do not choose everything for the sake of something else (for at that rate the process would go on to [20] infinity, so that our desire would be empty and vain), clearly this must be the good and the chief good. Will not the knowledge of it, then, have a great influence on life? Shall we not, like archers who have a mark to aim at, be more likely to hit upon what we should? If so, we must try, in outline at least, to determine what it is, and [25] of which of the sciences or capacities it is the object. It would seem to belong to the most authoritative art and that which is most truly the master art. And politics appears to be of this nature; for it is this that ordains which of the sciences should be studied in a state, and which each class of citizens should learn and up to what point [1094b1] they should learn them; and we see even the most highly esteemed of capacities to fall under this, e.g. strategy, economics, rhetoric; now, since politics uses the rest of [5] the sciences, and since, again, it legislates as to what we are to do and what we are to abstain from, the end of this science must include those of the others, so that this end must be the good for man. For even if the end is the same for a single man and for a state, that of the state seems at all events something greater and more complete both to attain and to preserve; for though it is worth while to attain the end [10] merely for one man, it is finer and more godlike to attain it for a nation or for city-states. These, then, are the ends at which our inquiry, being concerned with politics, aims.
3 · Our discussion will be adequate if it has as much clearness as the subject-matter admits of; for precision is not to be sought for alike in all discussions, any more than in all the products of the crafts. Now fine and just actions, which political [15] science investigates, exhibit much variety and fluctuation, so that they may be thought to exist only by convention, and not by nature. And goods also exhibit a similar fluctuation because they bring harm to many people; for before now men have been undone by reason of their wealth, and others by reason of their courage. We must be content, then, in speaking of such subjects and with such premisses to [20] indicate the truth roughly and in outline, and in speaking about things which are only for the most part true and with premisses of the same kind to reach conclusions that are no better. In the same spirit, therefore, should each of our statements be received; for it is the mark of an educated man to look for precision in each class of [25] things just so far as the nature of the subject admits: it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician demonstrative proofs.
Now each man judges well the things he knows, and of these he is a good judge. And so the man who has been educated in a subject is a good judge of that subject, [1095a1] and the man who has received an all-round education is a good judge in general. Hence a young man is not a proper hearer of lectures on political science; for he is inexperienced in the actions that occur in life, but its discussions start from these and are about these; and, further, since he tends to follow his passions, his study will [5] be vain and unprofitable, because the end aimed at is not knowledge but action. And it makes no difference whether he is young in years or youthful in character; the defect does not depend on time, but on his living and pursuing each successive object as passion directs. For to such persons, as to the incontinent, knowledge brings no [10] profit; but to those who desire and act in accordance with a rational principle knowledge about such matters will be of great benefit.
These remarks about the student, the way in which our statements should be received, and the purpose of the inquiry, may be taken as our preface.
4 · Let us resume our inquiry and state, in view of the fact that all knowledge [15] and choice aims at some good, what it is that we say political science aims at and what is the highest of all goods achievable by action. Verbally there is very general agreement; for both the general run of men and people of superior refinement say that it is happiness, and identify living well and faring well with being happy; but with regard to what happiness is they differ, and the many do not give the same [20] account as the wise. For the former think it is some plain and obvious thing, like pleasure, wealth, or honour; they differ, however, from one another—and often even the same man identifies it with different things, with health when he is ill, with wealth when he is poor; but, conscious of their ignorance, they admire those who [25] proclaim some great thing that is above their comprehension. Now some thought that apart from these many goods there is another which is good in itself and causes the goodness of all these as well. To examine all the opinions that have been held would no doubt be somewhat fruitless: it is enough to examine those that are most prevalent or that seem to have some reason in their favour. [30]
Let us not fail to notice, however, that there is a difference between arguments from and those to the first principles. For Plato, too, was right in raising this question and asking, as he used to do, ‘are we on the way from or to the first principles?’ There is a difference, as there is in a race-course between the course from the judges to the turning-point and the way back. For, while we must begin [1095b1] with what is familiar, things are so in two ways—some to us, some without qualification. Presumably, then, we must begin with things familiar to us. Hence any one who is to listen intelligently to lectures about what is noble and just and, generally, about the subjects of political science must have been brought up in good [5] habits. For the facts are the starting-point, and if they are sufficiently plain to him, he will not need the reason as well; and the man who has been well brought up has or can easily get starting-points. And as for him who neither has nor can get them, let him hear the words of Hesiod:1
Far best is he who knows all things himself; [10]
Good, he that hearkens when men counsel right;
But he who neither knows, nor lays to heart
Another’s wisdom, is a useless wight.
5 · Let us, however, resume our discussion from the point at which we digressed. To judge from the lives that men lead, most men, and men of the most vulgar type, seem (not without some reason) to identify the good, or happiness, with [15] pleasure; which is the reason why they love the life of enjoyment. For there are, we may say, three prominent types of life—that just mentioned, the political, and thirdly the contemplative life. Now the mass of mankind are evidently quite slavish in their tastes, preferring a life suitable to beasts, but they get some reason for their [20] view from the fact that many of those in high places share the tastes of Sardanapallus. But people of superior refinement and of active disposition identify happiness with honour; for this is, roughly speaking, the end of the political life. But it seems too superficial to be what we are looking for, since it is thought to depend on those who
bestow honour rather than on him who receives it, but the good we divine to [25] be something of one’s own and not easily taken from one. Further, men seem to pursue honour in order that they may be assured of their merit; at least it is by men of practical wisdom that they seek to be honoured, and among those who know them, and on the ground of their excellence; clearly, then, according to them, at any [30] rate, excellence is better. And perhaps one might even suppose this to be, rather than honour, the end of the political life. But even this appears somewhat incomplete; for possession of excellence seems actually compatible with being asleep, or with lifelong inactivity, and, further, with the greatest sufferings and [1096a1] misfortunes; but a man who was living so no one would call happy, unless he were maintaining a thesis at all costs. But enough of this; for the subject has been sufficiently treated even in ordinary discussions. Third comes the contemplative [5] life, which we shall consider later.
The life of money-making is one undertaken under compulsion, and wealth is evidently not the good we are seeking; for it is merely useful and for the sake of something else. And so one might rather take the aforenamed objects to be ends; for they are loved for themselves. But it is evident that not even these are ends—although [10] many arguments have been thrown away in support of them. Let us then dismiss them.