Pythagoras, however, disliked his government, and therefore left Samos. It is said, and is not improbable, that Pythagoras visited Egypt, and learnt much of his wisdom there; however that may be, it is certain that he ultimately established himself at Croton, in southern Italy.
He soon became a mythical figure, credited with miracles and magic powers, but he was also the founder of a school of mathematicians.II Thus two opposing traditions disputed his memory, and the truth is hard to disentangle. Pythagoras is one of the most interesting and puzzling men in history. Not only are the traditions concerning him an almost inextricable mixture of truth and falsehood, but even in their barest and least disputable form they present us with a very curious psychology. He may be described, briefly, as a combination of Einstein and Mrs. Eddy. He founded a religion, of which the main tenets were the transmigration of soulsIII and the sinfulness of eating beans.
Some of the rules of the Pythagorean order were: 1. To abstain from beans. 2. Not to pick up what has fallen. 3. Not to touch a white cock. 4. Not to break bread. 5. Not to step over a crossbar. 6. Not to stir the fire with iron. 7. Not to eat from a whole loaf. 8. Not to pluck a garland. 9. Not to sit on a quart measure. 10. Not to eat the heart. 11. Not to walk on highways. 12. Not to let swallows share one’s roof. 13. When the pot is taken off the fire, not to leave the mark of it in the ashes, but to stir them together. 14. Do not look in a mirror beside a light. 15. When you rise from the bedclothes, roll them together and smooth out the impress of the body.IV
mysticism, though his mysticism was of a peculiarly intellectual sort. He attributed to himself a semi-divine character, and appears to have said: “There are men and gods, and beings like Pythagoras.” All the systems that he inspired, Cornford says, “tend to be otherworldly, putting all value in the unseen unity of God, and condemning the visible world as false and illusive, a turbid medium in which the rays of heavenly light are broken and obscured, in mist and darkness.”
Pythagoras taught “first, that the soul is an immortal thing, and that it is transformed into other kinds of living things; further, that whatever comes into existence is born again in the revolutions of a certain cycle, nothing being absolutely new; and that all things that are born with life in them ought to be treated as kindred.”V It is said that Pythagoras, like Saint Francis, preached to animals.
“We are strangers in this world, and the body is the tomb of the soul, and yet we must not seek to escape by self-murder; for we are the chattels of God who is our herdsman, and without his command we have no right to make our escape. In this life, there are three kinds of men, just as there are three sorts of people who come to the Olympic Games. The lowest class is made up of those who come to buy and sell, the next above them are those who compete. Best of all, however, are those who come simply to look on. The greatest purification of all is, therefore, disinterested science, and it is the man who devotes himself to that, the true philosopher, who has most effectually released himself from the ‘wheel of birth.’ ”VI
I spoke above about the word “orgy”; now I want to speak about the word “theory.” This was originally an Orphic word, which Cornford interprets as “passionate sympathetic contemplation.” In this state, he says, “The spectator is identified with the suffering God, dies in his death, and rises again in his new birth.” For Pythagoras, the “passionate sympathetic contemplation” was intellectual, and issued in mathematical knowledge. In this way, through Pythagoreanism, “theory” gradually acquired its modern meaning; but for all who were inspired by Pythagoras it retained an element of ecstatic revelation. To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural even if untrue. It might seem that the empirical philosopher is the slave of his material, but that the pure mathematician, like the musician, is a free creator of his world of ordered beauty.
Pythagoras, as everyone knows, said that “all things are numbers.” This statement, interpreted in a modern way, is logically nonsense, but what he meant was not exactly nonsense. He discovered the importance of numbers in music, and the connection which he established between music and arithmetic survives in the mathematical terms “ harmonic mean” and “harmonic progression.” He thought of numbers as shapes, as they appear on dice or playing cards. We still speak of squares and cubes of numbers, which are terms that we owe to him. He also spoke of oblong numbers, triangular numbers, pyramidal numbers, and so on. These were the numbers of pebbles (or, as we should more naturally say, shot) required to make the shapes in question. He presumably thought of the world as atomic, and of bodies as built up of molecules composed of atoms arranged in various shapes. In this way he hoped to make arithmetic the fundamental study in physics as in aesthetics.
The influence of geometry upon philosophy and scientific method has been profound. Geometry, as established by the Greeks, starts with axioms which are (or are deemed to be) self-evident, and proceeds, by deductive reasoning, to arrive at theorems that are very far from self-evident. The axioms and theorems are held to be true of actual space, which is something given in experience. It thus appeared to be possible to discover things about the actual world by first noticing what is self-evident and then using deduction. This view influenced Plato and Kant, and most of the intermediate philosophers. When the Declaration of Independence says “we hold these truths to be self-evident,” it is modelling itself on Euclid. The eighteenth-century doctrine of natural rights is a search for Euclidean axioms in politics.VIII The form of Newton’s Principia, in spite of its admittedly empirical material, is entirely dominated by Euclid. Theology, in its exact scholastic forms, takes its style from the same source. Personal religion is derived from ecstasy, theology from mathematics; and both are to be found in Pythagoras.
Geometry deals with exact circles, but no sensible object is exactly circular; however carefully we may use our compasses, there will be some imperfections and irregularities. This suggests the view that all exact reasoning applies to ideal as opposed to sensible objects; it is natural to go further, and to argue that thought is nobler than sense, and the objects of thought more real than those of sense-perception. Mystical doctrines as to the relation of time to eternity are also reinforced by pure mathematics, for mathematical objects, such as numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God’s thoughts. Hence Plato’s doctrine that God is a geometer, and Sir James Jeans’ belief that He is addicted to arithmetic. Rationalistic as opposed to apocalyptic religion has been, ever since Pythagoras, and notably ever since Plato, very completely dominated by mathematics and mathematical method.
what appears as Platonism is, when analysed, found to be in essence Pythagoreanism. The whole conception of an eternal world, revealed to the intellect but not to the senses, is derived from him.
From his early interest in mysticism he retained a belief in the unreality of separateness; the world, in his view, was not a collection of hard units, whether atoms or souls, each completely self-subsistent. The apparent self-subsistence of finite things appeared to him to be an illusion; nothing, he held, is ultimately and completely real except the whole. But he differed from Parmenides and Spinoza in conceiving the whole, not as a simple substance, but as a complex system, of the sort that we should call an organism. The apparently separate things of which the world seems to be composed are not simply an illusion; each has a greater or lesser degree of reality, and its reality consists in an aspect of the whole, which is what it is seen to be when viewed truly. With this view goes naturally a disbelief in the reality of time and space as such, for these, if taken as completely real, involve separateness and multiplicity.
The whole, in all its complexity, is called by Hegel “the Absolute.” The Absolute is spiritual; Spinoza’s view, that it has the attribute of extension as well as that of thought, is rejected.
Logic, as Hegel understands the word, is declared by him to be the same thing as metaphysics; it is something quite different from what is commonly called logic. His view is that any ordinary predicate, if taken as qualifying the whole of Reality, turns out to be self-contradictory. One might take as a crude example the theory of Parmenides, that the One, which alone is real, is spherical. Nothing can be spherical unless it has a boundary, and it cannot have a boundary unless’there is something (at least empty space) outside of it. Therefore to suppose the Universe as a whole to be spherical is self-contradictory.
First we say: “Reality is an uncle.’ This is the Thesis. But the existence of an uncle implies that of a nephew. Since nothing really exists except the Absolute, and we are now committed to the existence of a nephew, we must conclude: “The Absolute is a nephew.” This is the Antithesis. But there is the same objection to this as to the view that the Absolute is an uncle; therefore we are driven to the view that the Absolute is the whole composed of uncle and nephew. This is the Synthesis. But this synthesis is still unsatisfactory, because a man can be an uncle only if he has a brother or sister who is a parent of the nephew. Hence we are driven to enlarge our universe to include the brother or sister, with his wife or her husband. In this sort of way, so it is contended, we can be driven on, by the mere force of logic, from any suggested predicate of the Absolute to the final conclusion of the dialectic, which is called the “Absolute Idea.” Throughout the whole process, there is an underlying assumption that nothing can be really true unless it is about Reality as a whole.
Knowledge as a whole has its triadic movement. It begins with senseperception, in which there is only awareness of the object. Then, through sceptical criticism of the senses, it becomes purely subjective. At last, it reaches the stage of self-knowledge, in which subject and object are no longer distinct. Thus self-consciousness is the highest form of knowledge. This, of course, must be the case in Hegel’s system, for the highest kind of knowledge must be that possessed by the Absolute, and as the Absolute is the Whole there is nothing outside itself for it to know.
the best thinking, according to Hegel, thoughts become fluent and interfuse. Truth and falsehood are not sharply defined opposites, as is commonly supposed; nothing is wholly false, and nothing that we can know is wholly true.
“Reason,” Hegel says, “is the conscious certainty of being all reality.” This does not mean that a separate person is all reality; in his separateness he is not quite real, but what is real in him is his participation in Reality as a whole. In proportion as we become more rational, this participation is increased.
I come now to a singular feature of Hegel’s philosophy, which distinguishes it from the philosophy of Plato or Plotinus or Spinoza. Although ultimate reality is timeless, and time is merely an illusion generated by our inability to see the Whole, yet the time-process has an intimate relation to the purely logical process of the dialectic.
“That this ‘Idea’ or ‘Reason’ is the True, the Eternal, the absolutely powerful essence; that it reveals itself in the world, and that in that world nothing else is revealed but this and its honour and glory—is the thesis which, as we have said, has been proved in philosophy,
Spirit, and the course of its development, is the substantial object of the philosophy of history. The nature of Spirit may be understood by contrasting it with its opposite, namely Matter. The essence of matter is gravity; the essence of Spirit is Freedom. Matter is outside itself, whereas Spirit has its centre in itself. “Spirit is self-contained existence.”
“But what is Spirit? It is the one immutably homogeneous Infinite —pure Identity—which in its second phase separates itself from itself and makes this second aspect its own polar opposite, namely as existence for and in Self as contrasted with the Universal.”
“The history of the world is the discipline of the uncontrolled natural will, bringing it into obedience to a universal principle and conferring subjective freedom. The East knew, and to the present day knows, only that One is free; the Greek and Roman world, that some are free; the German world knows that All are free.”
“The German spirit is the spirit of the new world. Its aim is the realization of absolute Truth as the unlimited self-determination of freedom—that freedom which has its own absolute from itself as its purport.”
But from the point of view of the Absolute the distinction between monarch and subjects, like all other distinctions, is illusory, and when the monarch imprisons a liberal-minded subject, that is still Spirit freely determining itself.
German history is divided by Hegel into three periods: the first, up to Charlemagne; the second, from Charlemagne to the Reformation; the third, from the Reformation onwards. These three periods are distinguished as the Kingdoms of the Father, the Son, and the Holy Ghost, respectively. It seems a little odd that the Kingdom of the Holy Ghost should have begun with the bloody and utterly abominable atrocities committed in suppressing the Peasants’ War, but Hegel, naturally, does not mention so trivial an incident.
In Italy and France, while there has been a romantic admiration of the Germans on the part of a few men such as Tacitus and Machiavelli, they have been viewed, in general, as the authors of the “barbarian” invasion, and as enemies of the Church, first under the great Emperors, and later as the leaders of the Reformation. Until the nineteenth century the Latin nations looked upon the Germans as their inferiors in civilization. Protestants in Germany naturally took a different view. They regarded the late Romans as effete, and considered the German conquest of the Western Empire an essential step towards revivification. In relation to the conflict of Empire and Papacy in the Middle Ages, they took a Ghibelline view: to this day, German schoolboys are taught a boundless admiration of Charlemagne and Barbarossa.
Nations, in Hegel, play the part that classes play in Marx. The principle of historical development, he says, is national genius. In every age, there is some one nation which is charged with the mission of carrying the world through the stage of the dialectic that it has reached. In our age, of course, this nation is Germany. But in addition to nations, we must also take account of world-historical individuals; these are men in whose aims are embodied the dialectical transitions that are due to take place in their time. These men are heroes, and may justifiably contravene ordinary moral rules. Alexander, Caesar, and Napoleon are given as examples. I doubt whether, in Hegel’s opinion, a man could be a “hero” without being a military conqueror.
For truth is the unity of the universal and subjective Will, and the universal is to be found in the State, in its laws, its universal and rational arrangements. The State is the Divine Idea as its exists on earth.” Again: “The State is the embodiment of rational freedom, realizing and recognizing itself in an objective form. . . . The State is the Idea of Spirit in the external manifestation of human Will and its Freedom.”
The habit of speaking of “the State,” as if there were only one, is misleading so long as there is no world State. Duty being, for Hegel, solely a relation of the individual to his State, no principle is left by which to moralize the relations between States. This Hegel recognizes. In external relations, he says, the State is an individual, and each State is independent as against the others. “Since in this independence the being-for-self of real spirit has its existence, it is the first freedom and highest honour of a people.” He goes on to argue against any sort of League of Nations by which the independence of separate States might be limited. The duty of a citizen is entirely confined (so far as the external relations of his State are concerned) to upholding the substantial individuality and independence and sovereignty of his own State. It follows that war is not wholly an evil, or something that we should seek to abolish. The purpose of the State is not merely to uphold the life and property of the citizens, and this fact provides the moral justification of war, which is not to be regarded as an absolute evil or as accidental, or as having its cause in something that ought not to be.
He is opposed to the creation of institutions—such as a world government —which would prevent such situations from arising, because he thinks it a good thing that there should be wars from time to time. War, he says, is the condition in which we take seriously the vanity of temporal goods and things. (This view is to be contrasted with the opposite theory, that all wars have economic causes.) War has a positive moral value: “War has the higher significance that through it the moral health of peoples is preserved in their indifference towards the stabilizing of finite determinations.” Peace is ossification; the Holy Alliance, and Kant’s League for Peace, are mistaken, because a family of States needs an enemy. Conflicts of States can only be decided by war; States being towards each other in a state of nature, their relations are not legal or moral. Their rights have their reality in their particular wills, and the interest of each State is its own highest law.
Such is Hegel’s doctrine of the State—a doctrine which, if accepted, justifies every internal tyranny and every external aggression that can possibly be imagined. The strength of his bias appears in the fact that his theory is largely inconsistent with his own metaphysic, and that the inconsistencies are all such as tend to the justification of cruelty and international brigandage. A man may be pardoned if logic compels him regretfully to reach conclusions which he deplores, but not for departing from logic in order to be free to advocate crimes. Hegel’s logic led him to believe that there is more reality or excellence (the two for him are synonyms) in wholes than in their parts, and that a whole increases in reality and excellence as it becomes…
The question of reality is metaphysical, the question of value is ethical. They are commonly treated as if they were scarcely distinguishable, but to my mind it is important to keep them apart.
Hegel conceives the ethical relation of the citizen to the State as analogous to that of the eye to the body: in his place the citizen is part of a valuable whole, but isolated he is as useless as an isolated eye. The analogy, however, is open to question; from the ethical importance of some wholes, that of all wholes does not follow.
An eye in a living body is useful, that is to say, it has value as a means; but it has no more intrinsic value than when detached from the body. A thing has intrinsic value when it is prized for its own sake, not as a means to something else. We value the eye as a means to seeing. Seeing may be a means or an end; it is a means when it shows us food or enemies, it is an end when it shows us something that we find beautiful. The State is obviously valuable as a means: it protects us against thieves and murderers, it provides roads and schools, and so on. It may, of course, also be bad as a means, for example by waging an unjust war. The real question we have to ask in connection with Hegel is not this, but whether the State is good per se, as an end: do the citizens exist for the sake of the State, or the State for the sake of the citizens? Hegel holds the former view; the liberal philosophy that comes from Locke holds the latter. It is clear that we shall only attribute intrinsic value to the State if we think of it as having a life of its own, as being in some sense a person. At this point, Hegel’s metaphysic becomes relevant to the question of value. A person is a complex whole, having a single life; can there be a super-person, composed of persons as the body is composed of organs, and having a single life which is not the sum of the lives of the component persons? If there can be such a super-person, as Hegel thinks, then the State may be such a being, and it may be as superior to ourselves as the whole body is to the eye. But if we think this super-person a mere metaphysical monstrosity, then we shall say that the intrinsic value of a community is derived from that of its members, and that the State is a means, not an end. We are thus brought back from the ethical to the metaphysical question.
Suppose I say “John is the father of James.” Hegel, and all who believe in what Marshal Smuts calls “holism,” will say: “Before you can understand this statement, you must know who John and James are. Now to know who John is, is to know all his characteristics, for apart from them he would not be distinguishable from any one else. But all his characteristics involve other people or things. He is characterized by his relations to his parents, his wife, and his children, by whether he is a good or a bad citizen, and by the country to which he belongs. All these things you must know before you can be said to know whom the word ‘John’ refers to. Step by step, in your endeavour to say what you mean by the word ‘John,’ you will be led to take account of the whole universe, and your original statement will turn out to be telling you something about the universe, not about two separate people, John and James.” Now this is all very well, but it is open to an initial objection. If the above argument were sound, how could knowledge ever begin? I know numbers of propositions of the form “A is the father of B,” but I do not know the whole universe. If all knowledge were knowledge of the universe as a whole, there would be no knowledge. This is enough to make us suspect a mistake somewhere. The fact is that, in order to use the word “John” correctly and intelligently, I do not need to know all about John, but only enough to recognize him. No doubt he has relations, near or remote, to everything in the universe, but he can be spoken of truly without taking them into account, except such as are the direct subject-matter of what is being said. He may be the father of Jemima as well as of James, but it is not necessary for me to know this in order to know that he is the father of James. If Hegel were right, we could not state fully what is meant by “John is the father of James” without mentioning Jemima: we ought to say “John, the father of Jemima, is the father of James.” This would still be inadequate; we should have to go on to mention his parents and…
Hegel thought that, if enough was known about a thing to distinguish it from all other things, then all its properties could be inferred by logic. This was a mistake, and from this mistake arose the whole imposing edifice of his system. This illustrates an important truth, namely, that the worse your logic, the more interesting the consequences to which it gives rise.