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"If the units, then, are differentiated, each from each, these results and others similar to these follow of necessity. But (3) if those in different numbers are differentiated, but those in the same number are alone undifferentiated from one another, even so the difficulties that follow are no less. E.g. in the 10-its... |
"Again, as to the 2 being an entity apart from its two units, and the 3 an entity apart from its three units, how is this possible? Either by one's sharing in the other, as 'pale man' is different from 'pale' and 'man' (for it shares in these), or when one is a differentia of the other, as 'man' is different from 'anim... |
"Again, some things are one by contact, some by intermixture, some by position; none of which can belong to the units of which the 2 or the 3 consists; but as two men are not a unity apart from both, so must it be with the units. And their being indivisible will make no difference to them; for points too are indivisibl... |
"But this consequence also we must not forget, that it follows that there are prior and posterior 2 and similarly with the other numbers. For let the 2's in the 4 be simultaneous; yet these are prior to those in the 8 and as the 2 generated them, they generated the 4's in the 8-itself. Therefore if the first 2 is an Id... |
"In general, to differentiate the units in any way is an absurdity and a fiction; and by a fiction I mean a forced statement made to suit a hypothesis. For neither in quantity nor in quality do we see unit differing from unit, and number must be either equal or unequal-all number but especially that which consists of a... |
"Again, if every unit + another unit makes two, a unit from the 2-itself and one from the 3-itself will make a 2. Now (a) this will consist of differentiated units; and will it be prior to the 3 or posterior? It rather seems that it must be prior; for one of the units is simultaneous with the 3 and the other is simulta... |
"If the number of the 3-itself is not greater than that of the 2, this is surprising; and if it is greater, clearly there is also a number in it equal to the 2, so that this is not different from the 2-itself. But this is not possible, if there is a first and a second number. |
"Nor will the Ideas be numbers. For in this particular point they are right who claim that the units must be different, if there are to be Ideas; as has been said before. For the Form is unique; but if the units are not different, the 2's and the 3's also will not be different. This is also the reason why they must say... |
Part 8 " "First of all it is well to determine what is the differentia of a number-and of a unit, if it has a differentia. Units must differ either in quantity or in quality; and neither of these seems to be possible. But number qua number differs in quantity. And if the units also did differ in quantity, number would ... |
"Evidently then, if the Ideas are numbers, the units cannot all be associable, nor can they be inassociable in either of the two ways. But neither is the way in which some others speak about numbers correct. These are those who do not think there are Ideas, either without qualification or as identified with certain num... |
"It is evident, also, from this that the third version is the worst,-the view ideal and mathematical number is the same. For two mistakes must then meet in the one opinion. (1) Mathematical number cannot be of this sort, but the holder of this view has to spin it out by making suppositions peculiar to himself. And (2) ... |
"The Pythagorean version in one way affords fewer difficulties than those before named, but in another way has others peculiar to itself. For not thinking of number as capable of existing separately removes many of the impossible consequences; but that bodies should be composed of numbers, and that this should be mathe... |
"If, then, it is necessary, if number is a self-subsistent real thing, that it should exist in one of these ways which have been mentioned, and if it cannot exist in any of these, evidently number has no such nature as those who make it separable set up for it. |
"Again, does each unit come from the great and the small, equalized, or one from the small, another from the great? (a) If the latter, neither does each thing contain all the elements, nor are the units without difference; for in one there is the great and in another the small, which is contrary in its nature to the gr... |
"Again, number must be either infinite or finite; for these thinkers think of number as capable of existing separately, so that it is not possible that neither of those alternatives should be true. Clearly it cannot be infinite; for infinite number is neither odd nor even, but the generation of numbers is always the ge... |
"But if number is finite, how far does it go? With regard to this not only the fact but the reason should be stated. But if number goes only up to 10 as some say, firstly the Forms will soon run short; e.g. if 3 is man-himself, what number will be the horse-itself? The series of the numbers which are the several things... |
Again, spatial magnitudes and all such things are explained without going beyond a definite number; e.g. the first, the indivisible, line, then the 2 &c.; these entities also extend only up to 10. |
"Again, if number can exist separately, one might ask which is prior- 1, or 3 or 2? Inasmuch as the number is composite, 1 is prior, but inasmuch as the universal and the form is prior, the number is prior; for each of the units is part of the number as its matter, and the number acts as form. And in a sense the right ... |
They put things together out of the smallest parts, as some others also have done. Therefore the unit becomes the matter of numbers and at the same time prior to 2; and again posterior, 2 being treated as a whole, a unity, and a form. But (2) because they were seeking the universal they treated the unity which can be p... |
"If the 1-itself must be unitary (for it differs in nothing from other 1's except that it is the starting-point), and the 2 is divisible but the unit is not, the unit must be liker the 1-itself than the 2 is. But if the unit is liker it, it must be liker to the unit than to the 2; therefore each of the units in 2 must ... |
Part 9 "Since there is not contact in numbers, but succession, viz. between the units between which there is nothing, e.g. between those in 2 or in 3 one might ask whether these succeed the 1-itself or not, and whether, of the terms that succeed it, 2 or either of the units in 2 is prior. |
"Similar difficulties occur with regard to the classes of things posterior to number,-the line, the plane, and the solid. For some construct these out of the species of the 'great and small'; e.g. lines from the 'long and short', planes from the 'broad and narrow', masses from the 'deep and shallow'; which are species ... |
"(All these views share a difficulty which occurs with regard to species-of-a-genus, when one posits the universals, viz. whether it is animal-itself or something other than animal-itself that is in the particular animal. True, if the universal is not separable from sensible things, this will present no difficulty; but... |
"Some, then, generate spatial magnitudes from matter of this sort, others from the point -and the point is thought by them to be not 1 but something like 1-and from other matter like plurality, but not identical with it; about which principles none the less the same difficulties occur. For if the matter is one, line an... |
"Again, how number can consist of the one and plurality, they make no attempt to explain; but however they express themselves, the same objections arise as confront those who construct number out of the one and the indefinite dyad. For the one view generates number from the universally predicated plurality, and not fro... |
Nor again can there be indivisible parts of a distance, as the elements out of which the units are said to be made are indivisible parts of plurality; for number consists of indivisibles, but spatial magnitudes do not. |
"All these objections, then, and others of the sort make it evident that number and spatial magnitudes cannot exist apart from things. Again, the discord about numbers between the various versions is a sign that it is the incorrectness of the alleged facts themselves that brings confusion into the theories. For those w... |
"But regarding numbers the questions we have raised and the conclusions we have reached are sufficient (for while he who is already convinced might be further convinced by a longer discussion, one not yet convinced would not come any nearer to conviction); regarding the first principles and the first causes and element... |
"Those who posit numbers only, and these mathematical, must be considered later; but as regards those who believe in the Ideas one might survey at the same time their way of thinking and the difficulty into which they fall. For they at the same time make the Ideas universal and again treat them as separable and as indi... |
Part 10 " "Let us now mention a point which presents a certain difficulty both to those who believe in the Ideas and to those who do not, and which was stated before, at the beginning, among the problems. If we do not suppose substances to be separate, and in the way in which individual things are said to be separate, ... |
"If they are individual and not universal, (a) real things will be just of the same number as the elements, and (b) the elements will not be knowable. For (a) let the syllables in speech be substances, and their elements elements of substances; then there must be only one 'ba' and one of each of the syllables, since th... |
"(b) Again, the elements will not be even knowable; for they are not universal, and knowledge is of universals. This is clear from demonstrations and from definitions; for we do not conclude that this triangle has its angles equal to two right angles, unless every triangle has its angles equal to two right angles, nor ... |
"But if the principles are universal, either the substances composed of them are also universal, or non-substance will be prior to substance; for the universal is not a substance, but the element or principle is universal, and the element or principle is prior to the things of which it is the principle or element. |
"All these difficulties follow naturally, when they make the Ideas out of elements and at the same time claim that apart from the substances which have the same form there are Ideas, a single separate entity. But if, e.g. in the case of the elements of speech, the a's and the b's may quite well be many and there need b... |
BOOK XIV Part 1 "REGARDING this kind of substance, what we have said must be taken as sufficient. All philosophers make the first principles contraries: as in natural things, so also in the case of unchangeable substances. But since there cannot be anything prior to the first principle of all things, the principle cann... |
"But these thinkers make one of the contraries matter, some making the unequal which they take to be the essence of plurality-matter for the One, and others making plurality matter for the One. (The former generate numbers out of the dyad of the unequal, i.e. of the great and small, and the other thinker we have referr... |
But if, as they claim, things consist of contraries, and to the One either there is nothing contrary, or if there is to be anything it is plurality, and the unequal is contrary to the equal, and the different to the same, and the other to the thing itself, those who oppose the One to plurality have most claim to plausi... |
"'The one' evidently means a measure. And in every case there is some underlying thing with a distinct nature of its own, e.g. in the scale a quarter-tone, in spatial magnitude a finger or a foot or something of the sort, in rhythms a beat or a syllable; and similarly in gravity it is a definite weight; and in the same... |
"Those who treat the unequal as one thing, and the dyad as an indefinite compound of great and small, say what is very far from being probable or possible. For (a) these are modifications and accidents, rather than substrata, of numbers and magnitudes-the many and few of number, and the great and small of magnitude-lik... |
Again, (d) elements are not predicated of the things of which they are elements, but many and few are predicated both apart and together of number, and long and short of the line, and both broad and narrow apply to the plane. If there is a plurality, then, of which the one term, viz. few, is always predicated, e.g. 2 (... |
Part 2 " "We must inquire generally, whether eternal things can consist of elements. If they do, they will have matter; for everything that consists of elements is composite. Since, then, even if a thing exists for ever, out of that of which it consists it would necessarily also, if it had come into being, have come in... |
"There are some who describe the element which acts with the One as an indefinite dyad, and object to 'the unequal', reasonably enough, because of the ensuing difficulties; but they have got rid only of those objections which inevitably arise from the treatment of the unequal, i.e. the relative, as an element; those wh... |
"There are many causes which led them off into these explanations, and especially the fact that they framed the difficulty in an obsolete form. For they thought that all things that are would be one (viz. Being itself), if one did not join issue with and refute the saying of Parmenides: " |
"'For never will this he proved, that things that are not are.' "They thought it necessary to prove that that which is not is; for only thus-of that which is and something else-could the things that are be composed, if they are many. |
"But, first, if 'being' has many senses (for it means sometimes substance, sometimes that it is of a certain quality, sometimes that it is of a certain quantity, and at other times the other categories), what sort of 'one', then, are all the things that are, if non-being is to be supposed not to be? Is it the substance... |
"Secondly, of what sort of non-being and being do the things that are consist? For 'nonbeing' also has many senses, since 'being' has; and 'not being a man' means not being a certain substance, 'not being straight' not being of a certain quality, 'not being three cubits long' not being of a certain quantity. What sort ... |
"The question evidently is, how being, in the sense of 'the substances', is many; for the things that are generated are numbers and lines and bodies. Now it is strange to inquire how being in the sense of the 'what' is many, and not how either qualities or quantities are many. For surely the indefinite dyad or 'the gre... |
"They should have asked this question also, how relative terms are many and not one. But as it is, they inquire how there are many units besides the first 1, but do not go on to inquire how there are many unequals besides the unequal. Yet they use them and speak of great and small, many and few (from which proceed numb... |
"It is necessary, then, as we say, to presuppose for each thing that which is it potentially; and the holder of these views further declared what that is which is potentially a 'this' and a substance but is not in itself being-viz. that it is the relative (as if he had said 'the qualitative'), which is neither potentia... |
"But further, if the 'this' and the quantitative are not the same, we are not told how and why the things that are are many, but how quantities are many. For all 'number' means a quantity, and so does the 'unit', unless it means a measure or the quantitatively indivisible. If, then, the quantitative and the 'what' are ... |
"One might fix one's attention also on the question, regarding the numbers, what justifies the belief that they exist. To the believer in Ideas they provide some sort of cause for existing things, since each number is an Idea, and the Idea is to other things somehow or other the cause of their being; for let this suppo... |
Part 3 " "As for those, then, who suppose the Ideas to exist and to be numbers, by their assumption in virtue of the method of setting out each term apart from its instances-of the unity of each general term they try at least to explain somehow why number must exist. Since their reasons, however, are neither conclusive... |
"There are some who, because the point is the limit and extreme of the line, the line of the plane, and the plane of the solid, think there must be real things of this sort. We must therefore examine this argument too, and see whether it is not remarkably weak. For (i) extremes are not substances, but rather all these ... |
"Again, if we are not too easily satisfied, we may, regarding all number and the objects of mathematics, press this difficulty, that they contribute nothing to one another, the prior to the posterior; for if number did not exist, none the less spatial magnitudes would exist for those who maintain the existence of the o... |
"All this is absurd, and conflicts both with itself and with the probabilities, and we seem to see in it Simonides 'long rigmarole' for the long rigmarole comes into play, like those of slaves, when men have nothing sound to say. And the very elements-the great and the small-seem to cry out against the violence that is... |
"It is strange also to attribute generation to things that are eternal, or rather this is one of the things that are impossible. There need be no doubt whether the Pythagoreans attribute generation to them or not; for they say plainly that when the one had been constructed, whether out of planes or of surface or of see... |
Part 4 "These thinkers say there is no generation of the odd number, which evidently implies that there is generation of the even; and some present the even as produced first from unequals-the great and the small-when these are equalized. The inequality, then, must belong to them before they are equalized. If they had ... |
"A difficulty, and a reproach to any one who finds it no difficulty, are contained in the question how the elements and the principles are related to the good and the beautiful; the difficulty is this, whether any of the elements is such a thing as we mean by the good itself and the best, or this is not so, but these a... |
"This, then, is the problem,-which of the two ways of speaking is right. It would be strange if to that which is primary and eternal and most self-sufficient this very quality--self-sufficiency and self-maintenance--belongs primarily in some other way than as a good. But indeed it can be for no other reason indestructi... |
"These absurdities follow, and it also follows that the contrary element, whether it is plurality or the unequal, i.e. the great and small, is the bad-itself. (Hence one thinker avoided attaching the good to the One, because it would necessarily follow, since generation is from contraries, that badness is the fundament... |
"All these objections, then, follow, partly because they make every principle an element, partly because they make contraries principles, partly because they make the One a principle, partly because they treat the numbers as the first substances, and as capable of existing apart, and as Forms. |
Part 5 " "If, then, it is equally impossible not to put the good among the first principles and to put it among them in this way, evidently the principles are not being correctly described, nor are the first substances. Nor does any one conceive the matter correctly if he compares the principles of the universe to that... |
"It is out of place, also, to generate place simultaneously with the mathematical solids (for place is peculiar to the individual things, and hence they are separate in place; but mathematical objects are nowhere), and to say that they must be somewhere, but not say what kind of thing their place is. |
"Those who say that existing things come from elements and that the first of existing things are the numbers, should have first distinguished the senses in which one thing comes from another, and then said in which sense number comes from its first principles. |
"By intermixture? But (1) not everything is capable of intermixture, and (2) that which is produced by it is different from its elements, and on this view the one will not remain separate or a distinct entity; but they want it to be so. |
"By juxtaposition, like a syllable? But then (1) the elements must have position; and (2) he who thinks of number will be able to think of the unity and the plurality apart; number then will be this-a unit and plurality, or the one and the unequal. |
"Again, coming from certain things means in one sense that these are still to be found in the product, and in another that they are not; which sense does number come from these elements? Only things that are generated can come from elements which are present in them. Does number come, then, from its elements as from se... |
"Once more, it has not been determined at all in which way numbers are the causes of substances and of being-whether (1) as boundaries (as points are of spatial magnitudes). This is how Eurytus decided what was the number of what (e.g. one of man and another of horse), viz. by imitating the figures of living things wit... |
"Number, then, whether it be number in general or the number which consists of abstract units, is neither the cause as agent, nor the matter, nor the ratio and form of things. Nor, of course, is it the final cause. |
Part 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 d... |
"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,-yes, ... |
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 in each applied to sigma, it is for this reason that there are only three, not because the concords are three; since as a matter of fact the co... |
"These people are like the old-fashioned 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 that th... |
"But the lauded characteristics of numbers, and the contraries of these, and generally the mathematical relations, as some describe them, making them causes of nature, seem, when we inspect them in this way, to vanish; for none of them is a cause in any of the senses that have been distinguished in reference to the fir... |
"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 together. The fact that our opponnts have much trouble with the generation of 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 a... |
The Nicomachean Ethics of Aristotle By Aristotle Introduction by J. A. Smith Contents INTRODUCTION ARISTOTLE’S ETHICS BOOK I BOOK II BOOK III BOOK IV BOOK V BOOK VI BOOK VII BOOK VIII BOOK IX BOOK X NOTES |
INTRODUCTION The _Ethics_ of Aristotle is one half of a single treatise of which his _Politics_ is the other half. Both deal with one and the same subject. This subject is what Aristotle calls in one place the “philosophy of human affairs;” but more frequently Political or Social Science. In the two works taken togethe... |
The principle of distribution of the subject-matter between the two works is far from obvious, and has been much debated. Not much can be gathered from their titles, which in any case were not given to them by their author. Nor do these titles suggest any very compact unity in the works to which they are applied: the p... |
Nevertheless each work aims at a relative completeness, and it is important to observe the relation of each to the other. The distinction is not that the one treats of Moral and the other of Political Philosophy, nor again that the one deals with the moral activity of the individual and the other with that of the State... |
We must, however, remember that the production of good character is not the end of either individual or state action: that is the aim of the one and the other because good character is the indispensable condition and chief determinant of happiness, itself the goal of all human doing. The end of all action, individual o... |
Looking forward, then, to the life of the State as that which aids support, and combines the efforts of the individual to obtain happiness, Aristotle draws no hard and fast distinction between the spheres of action of Man as individual and Man as citizen. Nor does the division of his discussion into the _Ethics_ and th... |
This is the kernel of the _Ethics_, and all the rest is subordinate to this main interest and purpose. Yet “the rest” is not irrelevant; the whole situation in which character grows and operates is concretely conceived. There is a basis of what we should call Psychology, sketched in firm outlines, the deeper presupposi... |
As was pointed out above, the proem (Book I., cc. i-iii.) is a prelude to the treatment of the whole subject covered by the _Ethics_ and the _Politics_ together. It sets forth the purpose of the enquiry, describes the spirit in which it is to be undertaken and what ought to be the expectation of the reader, and lastly ... |
It is characteristic of such knowledge that it should be deficient in “exactness,” in precision of statement, and closeness of logical concatenation. We must not look for a mathematics of conduct. The subject-matter of Human Conduct is not governed by necessary and uniform laws. But this does not mean that it is subjec... |
The _Ethics_ is addressed to students who are presumed both to have enough general education to appreciate these points, and also to have a solid foundation of good habits. More than that is not required for the profitable study of it. |
If the discussion of the nature and formation of character be regarded as the central topic of the _Ethics_, the contents of Book I., cc. iv.-xii. may be considered as still belonging to the introduction and setting, but these chapters contain matter of profound importance and have exercised an enormous influence upon ... |
But this end is not conceived as presented to him by a superior power nor even as something which _ought_ to be. The presentation of the Moral Ideal as Duty is almost absent. From the outset it is identified with the object of desire, of what we not merely judge desirable but actually do desire, or that which would, if... |
In what then does happiness consist? Aristotle summarily sets aside the more or less popular identifications of it with abundance of physical pleasures, with political power and honour, with the mere possession of such superior gifts or attainments as normally entitle men to these, with wealth. None of these can consti... |
It is interesting to compare this account of Happiness with Mill’s in _Utilitarianism_. Mill’s is much the less consistent: at times he distinguishes and at times he identifies, happiness, pleasure, contentment, and satisfaction. He wavers between belief in its general attainability and an absence of hopefulness. He mi... |
The main factor which determines success or failure in human life is the acquisition of certain powers, for Happiness is just the exercise or putting forth of these in actual living, everything else is secondary and subordinate. These powers arise from the due development of certain natural aptitudes which belong (in v... |
Perhaps the truest way of conceiving Aristotle’s meaning here is to regard a moral virtue as a form of obedience to a maxim or rule of conduct accepted by the agent as valid for a class of recurrent situations in human life. Such obedience requires knowledge of the rule and acceptance of it _as the rule_ of the agent’s... |
The “moral virtues and vices” make up what we call character, and the important questions arise: (1) What is character? and (2) How is it formed? (for character in this sense is not a natural endowment; it is formed or produced). Aristotle deals with these questions in the reverse order. His answers are peculiar and di... |
(1.) Character, good or bad, is produced by what Aristotle calls “habituation,” that is, it is the result of the repeated doing of acts which have a similar or common quality. Such repetition acting upon natural aptitudes or propensities gradually fixes them in one or other of two opposite directions, giving them a bia... |
But what are “right” acts? In the first place, they are those that conform to a rule—to the right rule, and ultimately to reason. The Greeks never waver from the conviction that in the end moral conduct is essentially reasonable conduct. But there is a more significant way of describing their “rightness,” and here for ... |
(2) What then is a “moral virtue,” the result of such a process duly directed? It is no mere mood of feeling, no mere liability to emotion, no mere natural aptitude or endowment, it is a permanent _state_ of the agent’s self, or, as we might in modern phrase put it, of his will, it consists in a steady self-imposed obe... |
The Doctrine of the Mean here takes a form in which it has impressed subsequent thinkers, but which has less importance than is usually ascribed to it. In the “Table of the Virtues and Vices,” each of the virtues is flanked by two opposite vices, which are respectively the excess and defect of that which in due measure... |
Books III-V are occupied with a survey of the moral virtues and vices. These seem to have been undertaken in order to verify in detail the general account, but this aim is not kept steadily in view. Nor is there any well-considered principle of classification. What we find is a sort of portrait-gallery of the various t... |
Aristotle is unable wholly to avoid allusion to the metaphysical difficulties and what he does here say upon them is obscure and unsatisfactory. But he insists upon the importance in moral action of the agent’s inner consent, and on the reality of his individual responsibility. For his present purpose the metaphysical ... |
The treatment of Justice in Book V has always been a source of great difficulty to students of the _Ethics_. Almost more than any other part of the work it has exercised influence upon mediaeval and modern thought upon the subject. The distinctions and divisions have become part of the stock-in-trade of would be philos... |
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