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There is nothing like this progress of opposites in Plato, who in the Symposium denies the possibility of reconciliation until the opposition has passed away. In his own words, there is an absurdity in supposing that 'harmony is discord; for in reality harmony consists of notes of a higher and lower pitch which disagreed once, but are now reconciled by the art of music' (Symp.). He does indeed describe objects of sense as regarded by us sometimes from one point of view and sometimes from another. As he says at the end of the Fifth Book of the Republic, 'There is nothing light which is not heavy, or great which is not small.' And he extends this relativity to the conceptions of just and good, as well as to great and small. In like manner he acknowledges that the same number may be more or less in relation to other numbers without any increase or diminution (Theat.). But the perplexity only arises out of the confusion of the human faculties; the art of measuring shows us what is truly great and truly small. Though the just and good in particular instances may vary, the IDEA of good is eternal and unchangeable. And the IDEA of good is the source of knowledge and also of Being, in which all the stages of sense and knowledge are gathered up and from being hypotheses become realities.

Leaving the comparison with Plato we may now consider the value of this invention of Hegel. There can be no question of the importance of showing that two contraries or contradictories may in certain cases be both true. The silliness of the so-called laws of thought ('All A = A,' or, in the negative form, 'Nothing can at the same time be both A, and not A') has been well exposed by Hegel himself (Wallace's Hegel), who remarks that 'the form of the maxim is virtually self-contradictory, for a proposition implies a distinction between subject and predicate, whereas the maxim of identity, as it is called, A = A, does not fulfil what its form requires. Nor does any mind ever think or form conceptions in accordance with this law, nor does any existence conform to it.' Wisdom of this sort is well parodied in Shakespeare (Twelfth Night, 'Clown: For as the old hermit of Prague, that never saw pen and ink, very wittily said to a niece of King Gorboduc, "That that is is"...for what is "that" but "that," and "is" but "is"?'). Unless we are willing to admit that two contradictories may be true, many questions which lie at the threshold of mathematics and of morals will be insoluble puzzles to us.

The influence of opposites is felt in practical life. The understanding sees one side of a question only—the common sense of mankind joins one of two parties in politics, in religion, in philosophy. Yet, as everybody knows, truth is not wholly the possession of either. But the characters of men are one-sided and accept this or that aspect of the truth. The understanding is strong in a single abstract principle and with this lever moves mankind. Few attain to a balance of principles or recognize truly how in all human things there is a thesis and antithesis, a law of action and of reaction. In politics we require order as well as liberty, and have to consider the proportions in which under given circumstances they may be safely combined. In religion there is a tendency to lose sight of morality, to separate goodness from the love of truth, to worship God without attempting to know him. In philosophy again there are two opposite principles, of immediate experience and of those general or a priori truths which are supposed to transcend experience. But the common sense or common opinion of mankind is incapable of apprehending these opposite sides or views—men are determined by their natural bent to one or other of them; they go straight on for a time in a single line, and may be many things by turns but not at once.

Hence the importance of familiarizing the mind with forms which will assist us in conceiving or expressing the complex or contrary aspects of life and nature. The danger is that they may be too much for us, and obscure our appreciation of facts. As the complexity of mechanics cannot be understood without mathematics, so neither can the many-sidedness of the mental and moral world be truly apprehended without the assistance of new forms of thought. One of these forms is the unity of opposites. Abstractions have a great power over us, but they are apt to be partial and one-sided, and only when modified by other abstractions do they make an approach to the truth. Many a man has become a fatalist because he has fallen under the dominion of a single idea. He says to himself, for example, that he must be either free or necessary—he cannot be both. Thus in the ancient world whole schools of philosophy passed away in the vain attempt to solve the problem of the continuity or divisibility of matter. And in comparatively modern times, though in the spirit of an ancient philosopher, Bishop Berkeley, feeling a similar perplexity, is inclined to deny the truth of infinitesimals in mathematics. Many difficulties arise in practical religion from the impossibility of conceiving body and mind at once and in adjusting their movements to one another. There is a border ground between them which seems to belong to both; and there is as much difficulty in conceiving the body without the soul as the soul without the body. To the 'either' and 'or' philosophy ('Everything is either A or not A') should at least be added the clause 'or neither,' 'or both.' The double form makes reflection easier and more conformable to experience, and also more comprehensive. But in order to avoid paradox and the danger of giving offence to the unmetaphysical part of mankind, we may speak of it as due to the imperfection of language or the limitation of human faculties. It is nevertheless a discovery which, in Platonic language, may be termed a 'most gracious aid to thought.'

The doctrine of opposite moments of thought or of progression by antagonism, further assists us in framing a scheme or system of the sciences. The negation of one gives birth to another of them. The double notions are the joints which hold them together. The simple is developed into the complex, the complex returns again into the simple. Beginning with the highest notion of mind or thought, we may descend by a series of negations to the first generalizations of sense. Or again we may begin with the simplest elements of sense and proceed upwards to the highest being or thought. Metaphysic is the negation or absorption of physiology—physiology of chemistry—chemistry of mechanical philosophy. Similarly in mechanics, when we can no further go we arrive at chemistry—when chemistry becomes organic we arrive at physiology: when we pass from the outward and animal to the inward nature of man we arrive at moral and metaphysical philosophy. These sciences have each of them their own methods and are pursued independently of one another. But to the mind of the thinker they are all one—latent in one another—developed out of one another.

This method of opposites has supplied new instruments of thought for the solution of metaphysical problems, and has thrown down many of the walls within which the human mind was confined. Formerly when philosophers arrived at the infinite and absolute, they seemed to be lost in a region beyond human comprehension. But Hegel has shown that the absolute and infinite are no more true than the relative and finite, and that they must alike be negatived before we arrive at a true absolute or a true infinite. The conceptions of the infinite and absolute as ordinarily understood are tiresome because they are unmeaning, but there is no peculiar sanctity or mystery in them. We might as well make an infinitesimal series of fractions or a perpetually recurring decimal the object of our worship. They are the widest and also the thinnest of human ideas, or, in the language of logicians, they have the greatest extension and the least comprehension. Of all words they may be truly said to be the most inflated with a false meaning. They have been handed down from one philosopher to another until they have acquired a religious character. They seem also to derive a sacredness from their association with the Divine Being. Yet they are the poorest of the predicates under which we describe him—signifying no more than this, that he is not finite, that he is not relative, and tending to obscure his higher attributes of wisdom, goodness, truth.