have formerly been verified, and are therefore taken as true, and if our inferences are intuited as thoroughly consistent with these truths, we see that they also must be true.

We are incessantly translating our sensations into inferences, our perceptions into conceptions, and retranslating our conceptions into images of perceptions; in this play of Feeling and Thought, this interblending of the real and ideal, there is ample room for Error to slip in unobserved. Our safeguard is Reflection, which discerns the values of our symbols, the inferences connected with our sensations. When Reflection discloses Equivalence, it transforms Conviction into Certitude, subjective Opinion into objective Truth.

66. The Principle of Equivalence, as I prefer to name this test of Truth, in order to get rid of the objections raised against identical propositions, will be found to clear up many obscure questions; and we shall presently apply it to the difficulty which has often puzzled philosophers who have clearly seen that no conclusion can be more than a specification of what is contained in its premises, and who fail to see how this is reconcilable with the fact that new truths are said to be discovered deductively. Other applications must, however, first engage our attention.

*See PROBLEM III., Chap. VI.

CHAPTER IV.

THE CERTAINTY OF TRUTHS.

67. Ir may seem frivolous to ask whether, having ascertained a truth, we are warranted in proclaiming its absolute certainty. Yet according to most philosophers it is a vital question whether the certainty attainable by man is not purely relative; in other words, whether any truth can be proclaimed absolutely true. The dispute is kept up simply because the disputants shift their positions. Once fix the import of the terms, and a final agreement is possible.

All knowledge is relative to the knowing mind. This is indisputable. In this sense, therefore, all knowledge. must be relative. Absolute knowledge, or absolute truth, is a contradiction in terms, unless we mean by it irreversible certainty. That is absolutely true which cannot be otherwise. The only rational statement of the question, then, is this: Granting that our knowledge of Things never can transcend sensible relations, never can include the modes of Existence which lie outside these relations, are we not to accept the known relations as certainly true and irreversible, because of unknown relations excluded from our expressions? Obviously our truth has reference only to the relations formulated; and no doubt is thrown upon an intuition or a demonstration, because it is an intuition or demonstration of one item in the great Whole, not of the great Whole itself. If we can resolve an equation of the first or second

degree, this absolute certainty is not disturbed because there are equations of a sixth degree which surpass our powers.

68. It is clearly open to us to attain absolute certainty of relative knowledge; and every identical proposition is an irreversible truth within the limits of the formulated terms. History tells plainly enough that the theories with which men have explained the facts observed have been continuously changing, the confidence of yesterday being displaced by the doubt of to-day; and impressed vividly by this spectacle of change, some have given a willing ear to the sceptical conclusion that nothing can be certainly known, one opinion being as true or as false as another. They might with equal justice conclude that the Universe has no reality, because its forms are unceasingly changing. Things are not more stable than theories. Such stability as belongs to either is but that of a moment in the flux of Evolution: Távra pet. The acorn is an acorn, although it will (under requisite conditions) become an oak. The insect is what it is at each stage of its metamorphosis. To deny its reality at any one stage, because of the changes which will occur under changed conditions, is absurd. Equally, though less obviously, absurd is the denial of the truth of a proposition because an enlarged experience may show, or has shown, many facts which that proposition does not include, and which were not expressed in its terms. No truth can be overturned. It can only be restricted to a narrower range, when more facts, or more factors of the facts, appear in the field of vision, and thus a larger import is given to the terms.

69. There is a development of Knowledge, as there is a development of the Cosmos. The reader may accept or reject the view of the Cosmos as existing only so far as it is incorporated in Mind; but he must admit that the

development of the known Cosmos is simply that of our knowledge of it. The confused excitation of sensibility gradually assumes shapes; and objects exist as objects of Consciousness when the Chaos passes into a Cosmos: as more and more facts of Feeling are grouped in symbols and in series, the Cosmos becomes intelligible. Thus, the dominant theories of successive epochs in the development of man express the successive stages in the development of our Cosmos. In this sense the early theories were true; they were true as the ideal representations of the real order, at least in so far as they exactly formulated all that had been observed; and false in so far as they excluded facts that were observed, or included facts contradictory of what had been observed.

What men observed of the movements of the heavenly bodies (it was not much) was rightly interpreted by them on the theory of the heavens revolving round the earth at rest. This formula of the facts failed, indeed, to include what afterwards became known; but although it was displaced by the Copernican hypothesis, which allowed the sun to be at rest, and sent the earth and the planets whirling round the sun, this displacement was no more than the displacement of a provisional organ by a new organ (like the branchiæ of the tadpole giving place to the lungs of the frog). It was not an exhibition of the untruth of the old theory; on the contrary, that formula so far expressed real observations that, even now, in spite of Copernicus, Galileo, Newton, and Laplace, we habitually regard the earth as at rest, and only adopt the enlarged theory for astronomical purposes, when dealing with phenomena which were hardly suspected when the old theory was framed. Nay, even the Copernican hypothesis of the sun being at rest no longer adequately expresses the observed facts, which disclose that the sun is no more at rest than the earth is, but moves with its

whole system in the direction of the constellation of Hercules. Nor have we any grounds for supposing even this interpretation to be final: it embodies present knowledge, that is all. To-morrow a new observation, or a new method of analysis, may displace all our astronomical theories.

This advance of knowledge, and restriction of the theories which express our knowledge, is improperly invoked as a justification of Scepticism. Instead of exclaiming, "See how men differ and err! there can be no fixed Truth!" we should note how knowledge widens, and how truths. successively express the widening Experience; just as the organism develops, and is at each stage adapted to its conditions of existence. The transformation of theories, like the metamorphoses of organisms, takes place by an incorporation of the new material with the old.

70. Are then all theories true? By no means. Nor are all judgments correct. Errors abound. But the test is final. A false judgment is an inference which sensation irresistibly disproves. A false theory is a formula which the facts contradict. When a man errs in supposing that the moon is larger at the horizon than at the zenith, or that a certain tower is round, which, seen at a lesser distance, appears square, the error of judgment is that of generalizing the terms without at the same time generalizing their import, and assuming that a change in the conditions will not bring with it a correlative change in the expressions. If he simply confined himself to the facts, and said, The moon appears larger at the horizon, and, The tower appears round at this distance, he would express identical propositions; and the truths would not be disturbed by the other truths expressing other conditions, when the moon would appear smaller and the tower square. It may be said that these identical propositions are of little use, and that they need the enlightenment of Science to explain on psychological and optical principles how