translated by Benjamin Jowett
actual meeting of Socrates and Parmenides ca. 450 B.C. per Francis Cornford
These, Socrates, said Parmenides, are a few, and only a few of the difficulties in which we are involved if ideas really are and we determine each one of them to be an absolute unity. He who hears what may be said against them will deny the very existence of them—and even if they do exist, he will say that they must of necessity be unknown to man; and he will seem to have reason on his side, and as we were remarking just now, will be very difficult to convince; a man must be gifted with very considerable ability before he can learn that everything has a class and an absolute essence; and still more remarkable will he be who discovers all these things for himself, and having thoroughly investigated them is able to teach them to others.
I agree with you, Parmenides, said Socrates; and what you say is very much to my mind.
And yet, Socrates, said Parmenides, if a man, fixing his attention on these and the like difficulties, does away with ideas of things and will not admit that every individual thing has its own determinate idea which is always one and the same, he will have nothing on which his mind can rest; and so he will utterly destroy the power of reasoning, as you seem to me to have particularly noted.
Very true, he said.
But, then, what is to become of philosophy? Whither shall we turn, if the ideas are unknown?
I certainly do not see my way at present.
Yes, said Parmenides; and I think that this arises, Socrates, out of your attempting to define the beautiful, the just, the good, and the ideas generally, without sufficient previous training. I noticed your deficiency, when I heard you talking here with your friend Aristoteles, the day before yesterday. The impulse that carries you towards philosophy is assuredly noble and divine; but there is an art which is called by the vulgar idle talking, and which is often imagined to be useless; in that you must train and exercise yourself, now that you are young, or truth will elude your grasp.
And what is the nature of this exercise, Parmenides, which you would recommend?
That which you heard Zeno practising; at the same time, I give you credit for saying to him that you did not care to examine the perplexity in reference to visible things, or to consider the question that way; but only in reference to objects of thought, and to what may be called ideas.
Why, yes, he said, there appears to me to be no difficulty in showing by this method that visible things are like and unlike and may experience anything.
Quite true, said Parmenides; but I think that you should go a step further, and consider not only the consequences which flow from a given hypothesis, but also the consequences which flow from denying the hypothesis; and that will be still better training for you.
What do you mean? he said.
I mean, for example, that in the case of this very hypothesis of Zeno's about the many, you should inquire not only what will be the consequences to the many in relation to themselves and to the one, and to the one in relation to itself and the many, on the hypothesis of the being of the many, but also what will be the consequences to the one and the many in their relation to themselves and to each other, on the opposite hypothesis. Or, again, if likeness is or is not, what will be the consequences in either of these cases to the subjects of the hypothesis, and to other things, in relation both to themselves and to one another, and so of unlikeness; and the same holds good of motion and rest, of generation and destruction, and even of being and not-being. In a word, when you suppose anything to be or not to be, or to be in any way affected, you must look at the consequences in relation to the thing itself, and to any other things which you choose,—to each of them singly, to more than one, and to all; and so of other things, you must look at them in relation to themselves and to anything else which you suppose either to be or not to be, if you would train yourself perfectly and see the real truth.
That, Parmenides, is a tremendous business of which you speak, and I do not quite understand you; will you take some hypothesis and go through the steps?—then I shall apprehend you better.
That, Socrates, is a serious task to impose on a man of my years.
Then will you, Zeno? said Socrates.
Zeno answered with a smile:—Let us make our petition to Parmenides himself, who is quite right in saying that you are hardly aware of the extent of the task which you are imposing on him; and if there were more of us I should not ask him, for these are not subjects which any one, especially at his age, can well speak of before a large audience; most people are not aware that this roundabout progress through all things is the only way in which the mind can attain truth and wisdom. And therefore, Parmenides, I join in the request of Socrates, that I may hear the process again which I have not heard for a long time.
When Zeno had thus spoken, Pythodorus, according to Antiphon's report of him, said, that he himself and Aristoteles and the whole company entreated Parmenides to give an example of the process. I cannot refuse, said Parmenides; and yet I feel rather like Ibycus, who, when in his old age, against his will, he fell in love, compared himself to an old racehorse, who was about to run in a chariot race, shaking with fear at the course he knew so well—this was his simile of himself. And I also experience a trembling when I remember through what an ocean of words I have to wade at my time of life. But I must indulge you, as Zeno says that I ought, and we are alone. Where shall I begin? And what shall be our first hypothesis, if I am to attempt this laborious pastime? Shall I begin with myself, and take my own hypothesis the one? and consider the consequences which follow on the supposition either of the being or of the not-being of one?
By all means, said Zeno.
And who will answer me? he said. Shall I propose the youngest? He will not make difficulties and will be the most likely to say what he thinks; and his answers will give me time to breathe.
I am the one whom you mean, Parmenides, said Aristoteles; for I am the youngest and at your service. Ask, and I will answer....
ca. 345–325 B.C. per W. D. Ross
translated by W. D. Ross
All men by nature desire to know. An indication of this is the delight we take in our senses; for even apart from their usefulness they are loved for themselves; and above all others the sense of sight. For not only with a view to action, but even when we are not going to do anything, we prefer seeing (one might say) to everything else. The reason is that this, most of all the senses, makes us know and brings to light many differences between things.
By nature animals are born with the faculty of sensation, and from sensation memory is produced in some of them, though not in others. And therefore the former are more intelligent and apt at learning than those which cannot remember; those which are incapable of hearing sounds are intelligent though they cannot be taught, e.g. the bee, and any other race of animals that may be like it; and those which besides memory have this sense of hearing can be taught.
The animals other than man live by appearances and memories, and have but little of connected experience; but the human race lives also by art and reasonings. Now from memory experience is produced in men; for the several memories of the same thing produce finally the capacity for a single experience. And experience seems pretty much like science and art, but really science and art come to men through experience; for 'experience made art', as Polus says, 'but inexperience luck.' Now art arises when from many notions gained by experience one universal judgement about a class of objects is produced. For to have a judgement that when Callias was ill of this disease this did him good, and similarly in the case of Socrates and in many individual cases, is a matter of experience; but to judge that it has done good to all persons of a certain constitution, marked off in one class, when they were ill of this disease, e.g. to phlegmatic or bilious people when burning with fevers―this is a matter of art.
With a view to action experience seems in no respect inferior to art, and men of experience succeed even better than those who have theory without experience. (The reason is that experience is knowledge of individuals, art of universals, and actions and productions are all concerned with the individual; for the physician does not cure man, except in an incidental way, but Callias or Socrates or some other called by some such individual name, who happens to be a man. If, then, a man has the theory without the experience, and recognizes the universal but does not know the individual included in this, he will often fail to cure; for it is the individual that is to be cured.) But yet we think that knowledge and understanding belong to art rather than to experience, and we suppose artists to be wiser than men of experience (which implies that Wisdom depends in all cases rather on knowledge); and this because the former know the cause, but the latter do not. For men of experience know that the thing is so, but do not know why, while the others know the 'why' and the cause. Hence we think also that the masterworkers in each craft are more honourable and know in a truer sense and are wiser than the manual workers, because they know the causes of the things that are done (we think the manual workers are like certain lifeless things which act indeed, but act without knowing what they do, as fire burns,-but while the lifeless things perform each of their functions by a natural tendency, the labourers perform them through habit); thus we view them as being wiser not in virtue of being able to act, but of having the theory for themselves and knowing the causes. And in general it is a sign of the man who knows and of the man who does not know, that the former can teach, and therefore we think art more truly knowledge than experience is; for artists can teach, and men of mere experience cannot. Again, we do not regard any of the senses as Wisdom; yet surely these give the most authoritative knowledge of particulars. But they do not tell us the 'why' of anything―e.g. why fire is hot; they only say that it is hot.
At first he who invented any art whatever that went beyond the common perceptions of man was naturally admired by men, not only because there was something useful in the inventions, but because he was thought wise and superior to the rest. But as more arts were invented, and some were directed to the necessities of life, others to recreation, the inventors of the latter were naturally always regarded as wiser than the inventors of the former, because their branches of knowledge did not aim at utility. Hence when all such inventions were already established, the sciences which do not aim at giving pleasure or at the necessities of life were discovered, and first in the places where men first began to have leisure. This is why the mathematical arts were founded in Egypt; for there the priestly caste was allowed to be at leisure.
We have said in the Ethics what the difference is between art and science and the other kindred faculties; but the point of our present discussion is this, that all men suppose what is called Wisdom to deal with the first causes and the principles of things; so that, as has been said before, the man of experience is thought to be wiser than the possessors of any sense-perception whatever, the artist wiser than the men of experience, the masterworker than the mechanic, and the theoretical kinds of knowledge to be more of the nature of Wisdom than the productive. Clearly then Wisdom is knowledge about certain principles and causes.
Since we are seeking this knowledge, we must inquire of what kind are the causes and the principles, the knowledge of which is Wisdom. If one were to take the notions we have about the wise man, this might perhaps make the answer more evident. We suppose first, then, that the wise man knows all things, as far as possible, although he has not knowledge of each of them in detail; secondly, that he who can learn things that are difficult, and not easy for man to know, is wise (sense-perception is common to all, and therefore easy and no mark of Wisdom); again, that he who is more exact and more capable of teaching the causes is wiser, in every branch of knowledge; and that of the sciences, also, that which is desirable on its own account and for the sake of knowing it is more of the nature of Wisdom than that which is desirable on account of its results, and the superior science is more of the nature of Wisdom than the ancillary; for the wise man must not be ordered but must order, and he must not obey another, but the less wise must obey him.
Such and so many are the notions, then, which we have about Wisdom and the wise. Now of these characteristics that of knowing all things must belong to him who has in the highest degree universal knowledge; for he knows in a sense all the instances that fall under the universal. And these things, the most universal, are on the whole the hardest for men to know; for they are farthest from the senses. And the most exact of the sciences are those which deal most with first principles; for those which involve fewer principles are more exact than those which involve additional principles, e.g. arithmetic than geometry. But the science which investigates causes is also instructive, in a higher degree, for the people who instruct us are those who tell the causes of each thing. And understanding and knowledge pursued for their own sake are found most in the knowledge of that which is most knowable (for he who chooses to know for the sake of knowing will choose most readily that which is most truly knowledge, and such is the knowledge of that which is most knowable); and the first principles and the causes are most knowable; for by reason of these, and from these, all other things come to be known, and not these by means of the things subordinate to them. And the science which knows to what end each thing must be done is the most authoritative of the sciences, and more authoritative than any ancillary science; and this end is the good of that thing, and in general the supreme good in the whole of nature. Judged by all the tests we have mentioned, then, the name in question falls to the same science; this must be a science that investigates the first principles and causes; for the good, i.e. the end, is one of the causes.
That it is not a science of production is clear even from the history of the earliest philosophers. For it is owing to their wonder that men both now begin and at first began to philosophize; they wondered originally at the obvious difficulties, then advanced little by little and stated difficulties about the greater matters, e.g. about the phenomena of the moon and those of the sun and of the stars, and about the genesis of the universe. And a man who is puzzled and wonders thinks himself ignorant (whence even the lover of myth is in a sense a lover of Wisdom, for the myth is composed of wonders); therefore since they philosophized order to escape from ignorance, evidently they were pursuing science in order to know, and not for any utilitarian end. And this is confirmed by the facts; for it was when almost all the necessities of life and the things that make for comfort and recreation had been secured, that such knowledge began to be sought. Evidently then we do not seek it for the sake of any other advantage; but as the man is free, we say, who exists for his own sake and not for another's, so we pursue this as the only free science, for it alone exists for its own sake.
Hence also the possession of it might be justly regarded as beyond human power; for in many ways human nature is in bondage, so that according to Simonides 'God alone can have this privilege', and it is unfitting that man should not be content to seek the knowledge that is suited to him. If, then, there is something in what the poets say, and jealousy is natural to the divine power, it would probably occur in this case above all, and all who excelled in this knowledge would be unfortunate. But the divine power cannot be jealous (nay, according to the proverb, 'bards tell a lie'), nor should any other science be thought more honourable than one of this sort. For the most divine science is also most honourable; and this science alone must be, in two ways, most divine. For the science which it would be most meet for God to have is a divine science, and so is any science that deals with divine objects; and this science alone has both these qualities; for (1) God is thought to be among the causes of all things and to be a first principle, and (2) such a science either God alone can have, or God above all others. All the sciences, indeed, are more necessary than this, but none is better.
Yet the acquisition of it must in a sense end in something which is the opposite of our original inquiries. For all men begin, as we said, by wondering that things are as they are, as they do about self-moving marionettes, or about the solstices or the incommensurability of the diagonal of a square with the side; for it seems wonderful to all who have not yet seen the reason, that there is a thing which cannot be measured even by the smallest unit. But we must end in the contrary and, according to the proverb, the better state, as is the case in these instances too when men learn the cause; for there is nothing which would surprise a geometer so much as if the diagonal turned out to be commensurable.
We have stated, then, what is the nature of the science we are searching for, and what is the mark which our search and our whole investigation must reach.
Evidently we have to acquire knowledge of the original causes (for we say we know each thing only when we think we recognize its first cause), and causes are spoken of in four senses. In one of these we mean the substance, i.e. the essence (for the 'why' is reducible finally to the definition, and the ultimate 'why' is a cause and principle); in another the matter or substratum, in a third the source of the change, and in a fourth the cause opposed to this, the purpose and the good (for this is the end of all generation and change). We have studied these causes sufficiently in our work on nature, but yet let us call to our aid those who have attacked the investigation of being and philosophized about reality before us. For obviously they too speak of certain principles and causes; to go over their views, then, will be of profit to the present inquiry, for we shall either find another kind of cause, or be more convinced of the correctness of those which we now maintain....
CRITIQUE OF PURE REASON
translated by Norman Kemp Smith
Preface to First Edition
Human reason has this peculiar fate that in one species of its knowledge it is burdened by questions which, as prescribed by the very nature of reason itself, it is not able to ignore, but which, as transcending all its powers, it is also not able to answer. The perplexity into which it thus falls is not due to any fault of its own. It begins with principles which it has no option save to employ in the course of experience, and which this experience at the same time abundantly justifies it in using. Rising with their aid (since it is determined to this also by its own nature) to ever higher, ever more remote, conditions, it soon becomes aware that in this way―the questions never ceasing―its work must always remain incomplete; and it therefore finds itself compelled to resort to principles which overstep all possible empirical employment, and which yet seem so unobjectionable that even ordinary consciousness readily accepts them. But by this procedure human reason precipitates itself into darkness and contradictions; and while it may indeed conjecture that these must be in some way due to concealed errors, it is not in a position to be able to detect them. For since the principles of which it is making use transcend the limits of experience, they are no longer subject to any empirical test. The battle-field of these endless controversies is called metaphysics. Time was when metaphysics was entitled the Queen of all the sciences; and if the will be taken for the deed, the pre-eminent importance of her accepted tasks gives her every right to this title of honour. Now, however, the changed fashion of the time brings her only scorn; a matron outcast and forsaken, she mourns like Hecuba: Modo maxima rerum, tot generis natisque potens―nunc trahor exul, inops.
Her government, under the administration of the dogmatists, was at first despotic. But inasmuch as the legislation still bore traces of the ancient barbarism, her empire gradually through intestine wars gave way to complete anarchy; and the sceptics, a species of nomads, despising all settled modes of life, broke up from time to time all civil society. Happily they were few in number, and were unable to prevent its being established ever anew, although on no uniform and self-consistent plan. In more recent times, it has seemed as if an end might be put to all these controversies and the claims of metaphysics receive final judgment, through a certain physiology of the human understanding ―that of the celebrated Locke. But it has turned out quite otherwise. For however the attempt be made to cast doubt upon the pretensions of the supposed Queen by tracing her lineage to vulgar origins in common experience, this genealogy has, as a matter of fact, been fictitiously invented, and she has still continued to uphold her claims. Metaphysics has accordingly lapsed back into the ancient time-worn dogmatism, and so again suffers that depreciation from which it was to have been rescued. And now, after all methods, so it is believed, have been tried and found wanting, the prevailing mood is that of weariness and complete indifferentism -- the mother, in all sciences, of chaos and night, but happily in this case the source, or at least the prelude, of their approaching reform and restoration. For it at least puts an end to that ill-applied industry which has rendered them thus dark, confused, and unserviceable.
But it is idle to feign indifference to such enquiries, the object of which can never be indifferent to our human nature. Indeed these pretended indifferentists, however they may try to disguise themselves by substituting a popular tone for the language of the Schools, inevitably fall back, in so far as they think at all, into those very metaphysical assertions which they profess so greatly to despise. None the less this indifference, showing itself in the midst of flourishing sciences, and affecting precisely those sciences, the knowledge of which, if attainable, we should least of all care to dispense with, is a phenomenon that calls for attention and reflection. It is obviously the effect not of levity but of the matured judgment of the age, which refuses to be any longer put off with illusory knowledge. It is a call to reason to undertake anew the most difficult of all its tasks, namely, that of self-knowledge, and to institute a tribunal which will assure to reason its lawful claims, and dismiss all groundless pretensions, not by despotic decrees, but in accordance with its own eternal and unalterable laws. This tribunal is no other than the critique of pure reason.
I do not mean by this a critique of books and systems, but of the faculty of reason in general, in respect of all knowledge after which it may strive independently of all experience. It will therefore decide as to the possibility or impossibility of metaphysics in general, and determine its sources, its extent, and its limits -- all in accordance with principles.
I have entered upon this path―the only one that has remained unexplored ―and flatter myself that in following it I have found a way of guarding against all those errors which have hitherto set reason, in its non-empirical employment, at variance with itself. We often hear complaints of shallowness of thought in our age and of the consequent decline of sound science. But I do not see that the sciences which rest upon a secure foundation, such as mathematics, physics, etc. , in the least deserve this reproach. On the contrary, they merit their old reputation for solidity, and, in the case of physics, even surpass it. The same spirit would have become active in other kinds of knowledge, if only attention had first been directed to the determination of their principles. Till this is done, indifference, doubt, and, in the final issue, severe criticism, are themselves proofs of a profound habit of thought. Our age is, in especial degree, the age of criticism, and to criticism everything must submit. Religion through its sanctity, and law-giving through its majesty, may seek to exempt themselves from it. But they then awaken just suspicion, and cannot claim the sincere respect which reason accords only to that which has been able to sustain the test of free and open examination....
PHENOMENOLOGY OF THE SPIRIT
G. W. F. Hegel
translated by J. B. Baillie
Preface to First Edition
In the case of a philosophical work it seems not only superfluous, but, in view of the nature of philosophy, even inappropriate and misleading to begin, as writers usually do in a preface, by explaining the end the author had in mind, the circumstances which gave rise to the work, and the relation in which the writer takes it to stand to other treatises on the same subject, written by his predecessors or his contemporaries. For whatever it might be suitable to state about philosophy in a preface―say, an historical sketch of the main drift and point of view, the general content and results, a string of desultory assertions and assurances about the truth―this cannot be accepted as the form and manner in which to expound philosophical truth.
Moreover, because philosophy has its being essentially in the element of that universality which encloses the particular within it, the end or final result seems, in the case of philosophy more than in that of other sciences, to have absolutely expressed the complete fact itself in its very nature; contrasted with that the mere process of bringing it to light would seem, properly speaking, to have no essential significance. On the other hand, in the general idea of e.g. anatomy―the knowledge of the parts of the body regarded as lifeless―we are quite sure we do not possess the objective concrete fact, the actual content of the science, but must, over and above, be concerned with particulars. Further, in the case of such a collection of items of knowledge, which has no real right to the name of science, any talk about purpose and suchlike generalities is not commonly very different from the descriptive and superficial way in which the contents of the science these nerves and muscles, etc.―are themselves spoken of. In philosophy, on the other hand, it would at once be felt incongruous were such a method made use of and yet shown by philosophy itself to be incapable of grasping the truth.
In the same way too, by determining the relation which a philosophical work professes to have to other treatises on the same subject, an extraneous interest is introduced, and obscurity is thrown over the point at issue in the knowledge of the truth. The more the ordinary mind takes the opposition between true and false to be fixed, the more is it accustomed to expect either agreement or contradiction with a given philosophical system, and only to see reason for the one or the other in any explanatory statement concerning such a system. It does not conceive the diversity of philosophical systems as the progressive evolution of truth; rather, it sees only contradiction in that variety. The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant’s existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another. But the ceaseless activity of their own inherent nature makes them at the same time moments of an organic unity, where they not merely do not contradict one another, but where one is as necessary as the other; and this equal necessity of all moments constitutes alone and thereby the life of the whole. But contradiction as between philosophical systems is not wont to be conceived in this way; on the other hand, the mind perceiving the contradiction does not commonly know how to relieve it or keep it free from its one-sidedness, and to recognise in what seems conflicting and inherently antagonistic the presence of mutually necessary moments.
The demand for such explanations, as also the attempts to satisfy this demand, very easily pass for the essential business philosophy has to undertake. Where could the inmost truth of a philosophical work be found better expressed than in its purposes and results? and in what way could these be more definitely known than through their distinction from what is produced during the same period by others working in the same field? If, however, such procedure is to pass for more than the beginning of knowledge, if it is to pass for actually knowing, then we must, in point of fact, look on it as a device for avoiding the real business at issue, an attempt to combine the appearance of being in earnest and taking trouble about the subject with an actual neglect of the subject altogether. For the real subject-matter is not exhausted in its purpose, but in working the matter out; nor is the mere result attained the concrete whole itself, but the result along with the process of arriving at it. The purpose of itself is a lifeless universal, just as the general drift is a mere activity in a certain direction, which is still without its concrete realisation; and the naked result is the corpse of the system which has left its guiding tendency behind it. Similarly, the distinctive difference of anything is rather the boundary, the limit, of the subject; it is found at that point where the subject-matter stops, or it is what this subject-matter is not. To trouble oneself in this fashion with the purpose and results, and again with the differences, the positions taken up and judgments passed by one thinker and another, is therefore an easier task than perhaps it seems. For instead of laying hold of the matter in hand, a procedure of that kind is all the while away from the subject altogether. Instead of dwelling within it and becoming absorbed by it, knowledge of that sort is always grasping at something else; such knowledge, instead keeping to the subject-matter and giving itself up to it, never gets away from itself. The easiest thing of all is to pass judgments on what has a solid substantial content; it is more difficult to grasp it, and most of all difficult to do both together and produce the systematic exposition of it.
The beginning of culture and of the struggle to pass out of the unbroken immediacy of naive psychical life has always to be made by acquiring knowledge of universal principles and points of view, by striving, in the first instance, to work up simply to the thought of the subject-matter in general, not forgetting at the same time to give reasons for supporting it or refuting it, to apprehend the concrete riches and fullness contained in its various determinate qualities, and to know how to furnish a coherent, orderly account of it and a responsible judgment upon it. This beginning of mental cultivation will, however, very soon make way for the earnestness of actual life in all its fullness, which leads to a living experience of the subject-matter itself; and when, in addition, conceptual thought strenuously penetrates to the very depths of its meaning, such knowledge and style of judgment will keep their due place in everyday thought and conversation.
The systematic development of truth in scientific form can alone be the true shape in which truth exists. To help to bring philosophy nearer to the form of science―that goal where it can lay aside the name of love of knowledge and be actual knowledge―that is what I have set before me. The inner necessity that knowledge should be science lies in its very nature; and the adequate and sufficient explanation for this lies simply and solely in the systematic exposition of philosophy itself. The external necessity, however, so far as this is apprehended in a universal way, and apart from the accident of the personal element and the particular occasioning influences affecting the individual, is the same as the internal: it lies in the form and shape in which the process of time presents the existence of its moments. To show that the time process does raise philosophy to the level of scientific system would, therefore, be the only true justification of the attempts which aim at proving that philosophy must assume this character; because the temporal process would thus bring out and lay bare the necessity of it, nay, more, would at the same time be carrying out that very aim itself.
When we state the true form of truth to be its scientific character―or, what is the same thing, when it is maintained that truth finds the medium of its existence in notions or conceptions alone―know that this seems to contradict an idea with all its consequences which makes great pretensions and has gained widespread acceptance and conviction at the present time. A word of explanation concerning this contradiction seems, therefore, not out of place, even though at this stage it can amount to no more than a dogmatic assurance exactly like the view we are opposing. If, that is to say, truth exists merely in what, or rather exists merely as what, is called at one time intuition, at another immediate knowledge of the Absolute, Religion, Being―not being in the centre of divine love, but the very Being of this centre, of the Absolute itself―from that point of view it is rather the opposite of the notional or conceptual form which would be required for systematic philosophical exposition. The Absolute on this view is not to be grasped in conceptual form, but felt, intuited; it is not its conception, but the feeling of it and intuition of it that are to have the say and find expression.
If we consider the appearance of a claim like this in its more general setting, and look at the level which the self-conscious mind at present occupies, we shall find that self-consciousness has got beyond the substantial fullness of life, which it used to carry on in the element of thought―beyond the state of immediacy of belief, beyond the satisfaction and security arising from the assurance which consciousness possessed of being reconciled with ultimate reality and with its all-pervading presence, within as well as without. Self-conscious mind has not merely passed beyond that to the opposite extreme of insubstantial reflection of self into self, but beyond this too. It has not merely lost its essential and concrete life, it is also conscious of this loss and of the transitory finitude characteristic of its content. Turning away from the husks it has to feed on, and confessing that it lies in wickedness and sin, it reviles itself for so doing, and now desires from philosophy not so much to bring it to a knowledge of what it is, as to obtain once again through philosophy the restoration of that sense of solidity and substantiality of existence it has lost. Philosophy is thus expected not so much to meet this want by opening up the compact solidity of substantial existence, and bringing this to the light and level of self-consciousness is not so much to bring chaotic conscious life back to the orderly ways of thought, and the simplicity of the notion, as to run together what thought has divided asunder suppress the notion with its distinctions, and restore the feeling of existence. What it wants from philosophy is not so much insight as edification. The beautiful, the holy, the eternal, religion, love―these are the bait required to awaken the desire to bite: not the notion, but ecstasy, not the march of cold necessity in the subject-matter, but ferment and enthusiasm―these are to be the ways by which the wealth of the concrete substance is to be stored and increasingly extended.
With this demand there goes the strenuous effort, almost perfervidly zealous in its activity, to rescue mankind from being sunken in what is sensuous, vulgar, and of fleeting importance, and to raise men’s eyes to the stars; as if men had quite forgotten the divine, and were on the verge of finding satisfaction, like worms, in mud and water. Time was when man had a heaven, decked and fitted out with endless wealth of thoughts and pictures. The significance of all that is, lay in the thread of light by which it was attached to heaven; instead of dwelling in the present as it is here and now, the eye glanced away over the present to the Divine, away, so to say, to a present that lies beyond. The mind’s gaze had to be directed under compulsion to what is earthly, and kept fixed there; and it has needed a long time to introduce that clearness, which only celestial realities had, into the crassness and confusion shrouding the sense of things earthly, and to make attention to the immediate present as such, which was called Experience, of interest and of value. Now we have apparently the need for the opposite of all this; man’s mind and interest are so deeply rooted in the earthly that we require a like power to have them raised above that level. His spirit shows such poverty of nature that it seems to long for the mere pitiful feeling of the divine in the abstract, and to get refreshment from that, like a wanderer in the desert craving for the merest mouthful of water. By the little which can thus satisfy the needs of the human spirit we can measure the extent of its loss.
This easy contentment in receiving, or stinginess in giving, does not suit the character of science. The man who only seeks edification, who wants to envelop in mist the manifold diversity of his earthly existence and thought, and craves after the vague enjoyment of this vague and indeterminate Divinity―he may look where he likes to find this: he will easily find for himself the means to procure something he can rave over and puff himself up withal. But philosophy must beware of wishing to be edifying.
Still less must this kind of contentment, which holds science in contempt, take upon itself to claim that raving obscurantism of this sort is something higher than science. These apocalyptic utterances pretend to occupy the very centre and the deepest depths; they look askance at all definiteness and preciseness meaning; and they deliberately hold back from conceptual thinking and the constraining necessities of thought, as being the sort of reflection which, they say, can only feel at home in the sphere of finitude. But just as there is a breadth which is emptiness, there is a depth which is empty too: as we may have an extension of substance which overflows into finite multiplicity without the power of keeping the manifold together, in the same way we may have an insubstantial intensity which, keeping itself in as mere force without actual expression, is no better than superficiality. The force of mind is only as great as its expression; its depth only as deep as its power to expand and lose itself when spending and giving out its substance. Moreover, when this unreflective emotional knowledge makes a pretence of having immersed its own very self in the depths of the absolute Being, and of philosophizing in all holiness and truth, it hides from itself the fact that instead of devotion to God, it rather, by this contempt for all measurable precision and definiteness, simply attests in its own case the fortuitous character of its content, and in the other endows God with its own caprice. When such minds commit themselves to the unrestrained ferment of sheer emotion, they think that, by putting a veil over self-consciousness, and surrendering all understanding, they are thus God’s beloved ones to whom He gives His wisdom in sleep. This is the reason, too, that in point of fact, what they do conceive and bring forth in sleep is dreams.
For the rest it is not difficult to see that our epoch is a birth-time, and a period of transition. The spirit of man has broken with the old order of things hitherto prevailing, and with the old ways of thinking, and is in the mind to let them all sink into the depths of the past and to set about its own transformation. It is indeed never at rest, but carried along the stream of progress ever onward. But it is here as in the case of the birth of a child; after a long period of nutrition in silence, the continuity of the gradual growth in size, of quantitative change, is suddenly cut short by the first breath drawn―there is a break in the process, a qualitative change and the child is born. In like manner the spirit of the time, growing slowly and quietly ripe for the new form it is to assume, disintegrates one fragment after another of the structure of its previous world. That it is tottering to its fall is indicated only by symptoms here and there. Frivolity and again ennui, which are spreading in the established order of things, the undefined foreboding of something unknown―all these betoken that there is something else approaching. This gradual crumbling to pieces, which did not alter the general look and aspect of the whole, is interrupted by the sunrise, which, in a flash and at a single stroke, brings to view the form and structure of the new world.
But this new world is perfectly realised just as little as the new-born child; and it is essential to bear this in mind. It comes on the stage to begin with in its immediacy, in its bare generality. A building is not finished when its foundation is laid; and just as little, is the attainment of a general notion of a whole the whole itself. When we want to see an oak with all its vigour of trunk, its spreading branches, and mass of foliage, we are not satisfied to be shown an acorn instead. In the same way science, the crowning glory of a spiritual world, is not found complete in its initial stages. The beginning of the new spirit is the outcome of a widespread revolution in manifold forms of spiritual culture; it is the reward which comes after a chequered and devious course of development, and after much struggle and effort. It is a whole which, after running its course and laying bare all its content, returns again to itself; it is the resultant abstract notion of the whole. But the actual realisation of this abstract whole is only found when those previous shapes and forms, which are now reduced to ideal moments of the whole, are developed anew again, but developed and shaped within this new medium, and with the meaning they have thereby acquired....
SCIENCE OF LOGIC
G. W. F. Hegel
translated by A. V. Miller
Preface to First Edition
The complete transformation which philosophical thought in Germany has undergone in the last twenty-five years and the higher standpoint reached by spirit in its awareness of itself, have had but little influence as yet on the structure of logic.
That which, prior to this period, was called metaphysics has been, so to speak, extirpated root and branch and has vanished from the ranks of the sciences. The ontology, rational psychology, cosmology, yes even natural theology, of former times―where is now to be heard any mention of them, or who would venture to mention them? Inquiries, for instance, into the immateriality of the soul, into efficient and final causes, where should these still arouse any interest? Even the former proofs of the existence of God are cited only for their historical interest or for purposes of edification and uplifting the emotions. The fact is that there no longer exists any interest either in the form or the content of metaphysics or in both together. If it is remarkable when a nation has become indifferent to its constitutional theory, to its national sentiments, its ethical customs and virtues, it is certainly no less remarkable when a nation loses its metaphysics, when the spirit which contemplates its own pure essence is no longer a present reality in the life of the nation.
The exoteric teaching of the Kantian philosophy―that the understanding ought not to go beyond experience, else the cognitive faculty will become a theoretical reason which itself generates nothing but fantasies of the brain―this was a justification from a philosophical quarter for the renunciation of speculative thought. In support of this popular teaching came the cry of modern educationists that the needs of the time demanded attention to immediate requirements, that just as experience was the primary factor for knowledge, so for skill in public and private life, practice and practical training generally were essential and alone necessary, theoretical insight being harmful even. Philosophy [Wissenschaft] and ordinary common sense thus co-operating to bring about the downfall of metaphysics, there was seen the strange spectacle of a cultured nation without metaphysics―like a temple richly ornamented in other respects but without a holy of holies. Theology, which in former times was the guardian of the speculative mysteries and of metaphysics (although this was subordinate to it) had given up this science in exchange for feelings, for what was popularly matter-of-fact, and for historical erudition. In keeping with this change, there vanished from the world those solitary souls who were sacrificed by their people and exiled from the world to the end that the eternal should be contemplated and served by lives devoted solely thereto―not for any practical gain but for the sake of blessedness; a disappearance which, in another context, can be regarded as essentially the same phenomenon as that previously mentioned. So that having got rid of the dark utterances of metaphysics, of the colourless communion of the spirit with itself, outer existence seemed to be transformed into the bright world of flowers―and there are no black flowers, as we know.
Logic did not fare quite so badly as metaphysics. That one learns from logic how to think (the usefulness of logic and hence its purpose, were held to consist in this―just as if one could only learn how to digest and move about by studying anatomy and physiology) this prejudice has long since vanished, and the spirit of practicality certainly did not intend for logic a better fate than was suffered by the sister science. Nevertheless, probably for the sake of a certain formal utility, it was still left a place among the sciences, and indeed was even retained as a subject of public instruction. However, this better lot concerns only the outer fate of logic, for its structure and contents have remained the same throughout a long inherited tradition, although in the course of being passed on the contents have become ever more diluted and attenuated; logic shows no traces so far of the new spirit which has arisen in the sciences no less than in the world of actuality. However, once the substantial form of the spirit has inwardly reconstituted itself, all attempts to preserve the forms of an earlier culture are utterly in vain; like withered leaves they are pushed off by the new buds already growing at their roots.
Even in the philosophical sphere this ignoring of the general change is beginning gradually to come to an end. Imperceptibly, even those who are opposed to the new ideas have become familiar with them and have appropriated them, and if they continue to speak slightingly of the source and principles of those ideas and to dispute them, still they have accepted their consequences and have been unable to defend themselves from their influence; the only way in which they can give a positive significance and a content to their negative attitude which is becoming less and less important, is to fall in with the new ways of thinking.
On the other hand, it seems that the period of fermentation with which a new creative idea begins is past. In its first manifestation, such an idea usually displays a fanatical hostility toward the entrenched systematisation of the older principle; usually too, it is fearful of losing itself in the ramifications of the particular and again it shuns the labour required for a scientific elaboration of the new principle and in its need for such, it grasps to begin with at an empty formalism. The challenge to elaborate and systematise the material now becomes all the more pressing. There is a period in the culture of an epoch as in the culture of the individual, when the primary concern is the acquisition and assertion of the principle in its undeveloped intensity. But the higher demand is that it should become systematised knowledge.
Now whatever may have been accomplished for the form and content of philosophy in other directions, the science of logic which constitutes metaphysics proper or purely speculative philosophy, has hitherto still been much neglected. What it is exactly that I understand by this science and its standpoint, I have stated provisionally in the Introduction. The fact that it has been necessary to make a completely fresh start with this science, the very nature of the subject matter and the absence of any previous works which might have been utilised for the projected reconstruction of logic, may be taken into account by fair-minded critics, even though a labour covering many years has been unable to give this effort a greater perfection. The essential point of view is that what is involved is an altogether new concept of scientific procedure. Philosophy, if it would be a science, cannot, as I have remarked elsewhere, borrow its method from a subordinate science like mathematics, any more than it can remain satisfied with categorical assurances of inner intuition, or employ arguments based on grounds adduced by external reflection. On the contrary, it can be only the nature of the content itself which spontaneously develops itself in a scientific method of knowing, since it is at the same time the reflection of the content itself which first posits and generates its determinate character.
The understanding determines, and holds the determinations fixed; reason is negative and dialectical, because it resolves the determinations of the understanding into nothing; it is positive because it generates the universal and comprehends the particular therein. Just as the understanding is usually taken to be something separate from reason as such, so too dialectical reason is usually taken to be something distinct from positive reason. But reason in its truth is spirit which is higher than either merely positive reason, or merely intuitive understanding. It is the negative, that which constitutes the quality alike of dialectical reason and of understanding; it negates what is simple, thus positing the specific difference of the understanding; it equally resolves it and is thus dialectical. But it does not stay in the nothing of this result but in the result is no less positive, and in this way it has restored what was at first simple, but as a universal which is within itself concrete; a given particular is not subsumed under this universal but in this determining, this positing of a difference, and the resolving of it, the particular has at the same time already determined itself. This spiritual movement which, in its simple undifferentiatedness, gives itself its own determinateness and in its determinateness its equality with itself, which therefore is the immanent development of the Notion, this movement is the absolute method of knowing and at the same time is the immanent soul of the content itself. I maintain that it is this self-construing method alone which enables philosophy to be an objective, demonstrated science. It is in this way that I have tried to expound consciousness in the Phenomenology of Spirit. Consciousness is spirit as a concrete knowing, a knowing too, in which externality is involved; but the development of this object, like the development of all natural and spiritual life, rests solely on the nature of the pure essentialities which constitute the content of logic. Consciousness, as spirit in its manifestation which in its progress frees itself from its immediacy and external concretion, attains to the pure knowing which takes as its object those same pure essentialities as they are in and for themselves. They are pure thoughts, spirit thinking its own essential nature. Their self-movement is their spiritual life and is that through which philosophy constitutes itself and of which it is the exposition.
In the foregoing there is indicated the relation of the science which I call the Phenomenology of Spirit, to logic. As regards the external relation, it was intended that the first part of the System of Science which contains the Phenomenology should be followed by a second part containing logic and the two concrete [realen] sciences, the Philosophy of Nature and the Philosophy of Spirit, which would complete the System of Philosophy. But the necessary expansion which logic itself has demanded has induced me to have this part published separately; it thus forms the first sequel to the Phenomenology of Spirit in an expanded arrangement of the system. It will later be followed by an exposition of the two concrete philosophical sciences mentioned. This first volume of the Logic contains as Book One the Doctrine of Being; Book Two, the Doctrine of Essence, which forms the second part of the first volume, is already in the press; the second volume will contain Subjective Logic or the Doctrine of the Notion.
PRINCIPLES OF MATHEMATICS
Preface to First Edition
The present work has two main objects. One of these, the proof that all pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts, and that all its propositions are deducible from a very small number of fundamental logical principles, is undertaken in Parts I–VII of this Volume, and will be established by strict symbolic reasoning in Volume II. The demonstration of this thesis has, if I am not mistaken, all the certainty and precision of which mathematical demonstrations are capable. As the thesis is very recent among mathematicians, and is almost universally denied by philosophers, I have undertaken, in this volume, to defend its various parts as occasion arose, against such adverse theories as appeared most widely held or most difficult to disprove. I have also endeavoured to present, in language as untechnical as possible, the more important stages in the deductions by which the thesis is established.
The other object of this work, which occupies Part I, is the explanation of the fundamental concepts which mathematics accepts as indefinable. This is a purely philosophical task, and I cannot flatter myself that I have done more than indicate a vast field of inquiry, and give a sample of the methods by which the inquiry may be conducted. The discussion of indefinables―which forms the chief part of philosophical logic―is the endeavour to see clearly, and to make others see clearly, the entities concerned, in order that the mind may have that kind of acquaintance with them which it has with redness or the taste of a pineapple. Where, as in the present case, the indefinable, are obtained primarily as the necessary residue in a process of analysis, it is often easier to know that there must be such entities than actually to perceive them; there is a process analogous to that which resulted in the discovery of Neptune, with the difference that the final stage―the search with a mental telescope for the entity which has been inferred―is often the most difficult part of the undertaking. In the case of classes, I must confess, I have failed to perceive any concept fulfilling the conditions requisite for the notion of class. And the contradiction discussed in Chapter X proves that something is amiss, but what this is I have hitherto failed to discover.
The second volume, in which I have had the great good fortune to secure the collaboration of Mr. A. N. Whitehead, will be addressed exclusively to mathematicians; it will contain chains of deductions, from the premisses of symbolic logic through Arithmetic, finite and infinite, to Geometry, in an order similar to that adopted in the present volume; it will also contain various original developments, in which the method of Professor Peano, as supplemented by the Logic of Relations, has shown itself a powerful instrument of mathematical investigation.
The present volume, which may be regarded either as a commentary upon, or as an introduction to, the second volume, is addressed in equal measure to the philosopher and to the mathematician; but some parts will be more interesting to the one, others to the other. I should advise mathematicians, unless they are specially interested in Symbolic Logic, to begin with Part IV., and only to refer to earlier parts as occasion arises. The following portions are more specially philosophical: Part I (omitting Chapter II); Part II, Chapters XI, XV, XVI, XVII; Part III; Part IV, § 207, Chapters XXVI, XXVII, XXXI; Part V, Chapters LII, LIV, LV, LVII, LVIII; and the two Appendices, which belong to Part I, and should be read in connection with it. Professor Frege’s work, which largely anticipates my own, was for the most part unknown to me when the printing of the present work began; I had seen his Grundgesetze der Arithmetik, but, owing to the great difficulty of his symbolism, I had failed to grasp its importance or to understand its contents. The only method, at so late a stage, of doing justice to his work, was to devote an Appendix to it; and in some points the views contained in the Appendix differ from those in Chapter VI, especially in §§ 71, 73, 74. On questions discussed in these sections, I discovered errors after passing the sheets for the press; these errors, of which the chief are the denial of the null-class, and the identification of a term with the class whose only member it is, are rectified in the Appendices. The subjects treated are so difficult that I feel little confidence in my present opinions, and regard any conclusions which may be advocated as essentially hypotheses.
A few words as to the origin of the present work may serve to show the importance of the questions discussed. About six years ago, I began an investigation into the philosophy of Dynamics. I was met by the difficulty that, when a particle is subject to several forces, no one of the component accelerations actually occurs, but only the resultant acceleration, of which they are not parts; this fact rendered illusory such causation of particulars as is affirmed, at first sight, by the law of gravitation. It appeared also that the difficulty in regard to absolute motion is insoluble on a relational theory of space. From these two questions I was led to a re-examination of the principles of Geometry, thence to the philosophy of continuity and infinity, and thence, with a view to discovering the meaning of the word any, to Symbolic Logic. The final outcome, as regards the philosophy of Dynamics, is perhaps rather slender; the reason of this is, that almost all the problems of Dynamics appear to me empirical, and therefore outside the scope of such a work as the present. Many very interesting questions have had to be omitted, especially in Parts VI and VII, as not relevant to my purpose, which, for fear of misunderstandings, it may be well to explain at this stage.
When actual objects are counted, or when Geometry and Dynamics are applied to actual space or actual matter, or when, in any other way, mathematical reasoning is applied to what exists, the reasoning employed has a form not dependent upon the objects to which it is applied being just those objects that they are, but only upon their having certain general properties. In pure mathematics, actual objects in the world of existence will never be in question, but only hypothetical objects having those general properties upon which depends whatever deduction is being considered; and these general properties will always be expressible in terms of the fundamental concepts which I have called logical constants. Thus when space or motion is spoken of in pure mathematics, it is not actual space or actual motion, as we know them in experience, that are spoken of, but any entity possessing those abstract general properties of space or motion that are employed in the reasonings of geometry or dynamics. The question whether these properties belong, as a matter of fact, to actual space or actual motion, is irrelevant to pure mathematics, and therefore to the present work, being, in my opinion, a purely empirical question, to be investigated in the laboratory or observatory. Indirectly, it is true, the discussions connected with pure mathematics have a very important bearing upon such empirical questions, since mathematical space and motion are held by many, perhaps most, philosophers to be self-contradictory, and therefore necessarily different from actual space and motion, whereas, if the views advocated in the following pages be valid, no such self-contradictions are to be found in mathematical space and motion. But extra-mathematical considerations of this kind have been almost wholly excluded from the present work.
On fundamental questions of philosophy, my position, in all its chief features, is derived from Mr G. E. Moore. I have accepted from him the non-existential nature of propositions (except such as happen to assert existence) and their independence of any knowing mind; also the pluralism which regards the world, both that of existents and that of entities, as composed of an infinite number of mutually independent entities, with relations which are ultimate, and not reducible to adjectives of their terms or of the whole which these compose. Before learning these views from him, I found myself completely unable to construct any philosophy of arithmetic, whereas their acceptance brought about an immediate liberation from a large number of difficulties which I believe to be otherwise insuperable. The doctrines just mentioned are, in my opinion, quite indispensable to any even tolerably satisfactory philosophy of mathematics, as I hope the following pages will show. But I must leave it to my readers to judge how far the reasoning assumes these doctrines, and how far it supports them. Formally, my premises are simply assumed; but the fact that they allow mathematics to be true, which most current philosophies do not, is surely a powerful argument in their favour.
In Mathematics, my chief obligations, as is indeed evident, are to Georg Cantor and Professor Peano. If I had become acquainted sooner with the work of Professor Frege, I should have owed a great deal to him, but as it is I arrived independently at many results which he had already established. At every stage of my work, I have been assisted more than I can express by the suggestions, the criticisms, and the generous encouragement of Mr A. N. Whitehead; he also has kindly read my proofs, and greatly improved the final expression of a very large number of passages. Many useful hints I owe also to Mr W. E. Johnson; and in the more philosophical parts of the book I owe much to Mr G. E. Moore besides the general position which underlies the whole.
In the endeavour to cover so wide a field, it has been impossible to acquire an exhaustive knowledge of the literature. There are doubtless many important works with which I am unacquainted; but where the labour of thinking and writing necessarily absorbs so much time, such ignorance, however regrettable, seems not wholly avoidable.
Many words will be found, in the course of discussion, to be defined in senses apparently departing widely from common usage. Such departures, I must ask the reader to believe, are never wanton, but have been made with great reluctance. In philosophical matters, they have been necessitated mainly by two causes. First, it often happens that two cognate notions are both to be considered, and that language has two names for the one, but none for the other. It is then highly convenient to distinguish between the two names commonly used as synonyms, keeping one for the usual, the other for the hitherto nameless sense. The other cause arises from philosophical disagreement with received views. Where two qualities are commonly supposed inseparably conjoined, but are here regarded as separable, the name which has applied to their combination will usually have to be restricted to one or other. For example, propositions are commonly regarded as (1) true or false, (2) mental. Holding, as I do, that what is true or false is not in general mental, I require a name for the true or false as such, and this name can scarcely be other than proposition. In such a case, the departure from usage is in no degree arbitrary. As regards mathematical terms, the necessity for establishing the existence-theorem in each case―i.e. the proof that there are entities of the kind in question―has led to many definitions which appear widely different from the notions usually attached to the terms in question. Instances of this are the definitions of cardinal, ordinal, and complex numbers. In the two former of these, and in many other cases, the definition as a class, derived from the principle of abstraction, is mainly recommended by the fact that it leaves no doubt as to the existence-theorem. But in many instances of such apparent departure from usage, it may be doubted whether more has been done than to give precision to a notion which had hitherto been more or less vague.
For publishing a work containing so many unsolved difficulties, my apology is, that investigation revealed no near prospect of adequately resolving the contradiction discussed in Chapter X, or of acquiring a better insight into the nature of classes. The repeated discovery of errors in solutions which for a time had satisfied me caused these problems to appear such as would have been only concealed by any seemingly satisfactory theories which a slightly longer reflection might have produced; it seemed better, therefore, merely to state the difficulties, than to wait until I had become persuaded of the truth of some almost certainly erroneous doctrine.
translated by C.K. Ogden with the assistance of Ludwig Wittgenstein,
Bertrand Russell, and Frank Ramsey
This book will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in it—or similar thoughts. It is therefore not a textbook. Its object would be attained if it afforded pleasure to one who read it with understanding.
The book deals with the problems of philosophy and shows, as I believe, that the method of formulating these problems rests on the misunderstanding of the logic of our language. Its whole meaning could be summed up somewhat as follows: What can be said at all can be said clearly; and whereof one cannot speak thereof one must be silent.
The book will, therefore, draw a limit to thinking, or rather—not to thinking, but to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought).
The limit can, therefore, only be drawn in language and what lies on the other side of the limit will be simply nonsense.
How far my efforts agree with those of other philosophers I will not decide. Indeed what I have here written makes no claim to novelty in points of detail; and therefore I give no sources, because it is indifferent to me whether what I have thought has already been thought before my by another.
I will only mention that to the great works of Frege and the writings of my friend Bertrand Russell I owe in large measure the stimulation of my thoughts.
If this work has a value it consists in two things. First that in it thoughts are expressed, and this value will be the greater the better the thoughts are expressed. the more the nail has been hit on the head.—Here I am conscious that I have fallen far short of the possible. Simply because my powers are insufficient to cope with the task.—May others come and do it better.
On the other hand the truth of the thoughts communicated here seems to me unassailable and definitive. I am, therefore, of the opinion that the problems have in essentials been finally solved. And if I am not mistaken in this, then the value of this work secondly consists in the fact that it shows how little has been done when these problems have been solved.
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