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class="calibre5">a priori logical foundation. By imagining worlds in which these axioms are false, the mathematicians have used logic to loosen the prejudices of common sense, and to show the possibility of spaces differing—some more, some less—from that in which we live. And some of these spaces differ so little from Euclidean space, where distances such as we can measure are concerned, that it is impossible to discover by observation whether our actual space is strictly Euclidean or of one of these other kinds. Thus the position is completely reversed.

Formerly it appeared that experience left only one kind of space to logic, and logic showed this one kind to be impossible. Now, logic presents many kinds of space as possible apart from experience, and experience only partially decides between them. Thus, while our knowledge of what is has become less than it was formerly supposed to be, our knowledge of what may be is enormously increased. Instead of being shut in within narrow walls, of which every nook and cranny could be explored, we find ourselves in an open world of free possibilities, where much remains unknown because there is so much to know.

 

What has happened in the case of space and time has happened, to some extent, in other directions as well. The attempt to prescribe to the universe by means of a priori principles has broken down; logic, instead of being, as formerly, the bar to possibilities, has become the great liberator of the imagination, presenting innumerable alternatives which are closed to unreflective common sense, and leaving to experience the task of deciding, where decision is possible, between the many worlds which logic offers for our choice.

Thus knowledge as to what exists becomes limited to what we can learn from experience—not to what we can actually experience, for, as we have seen, there is much knowledge by description concerning things of which we have no direct experience. But in all cases of knowledge by description, we need some connexion of universals, enabling us, from such and such a datum, to infer an object of a certain sort as implied by our datum. Thus in regard to physical objects, for example, the principle that sense-data are signs of physical objects is itself a connexion of universals; and it is only in virtue of this principle that experience enables us to acquire knowledge concerning physical objects. The same applies to the law of causality, or, to descend to what is less general, to such principles as the law of gravitation.

 

Principles such as the law of gravitation are proved, or rather are rendered highly probable, by a combination of experience with some wholly a priori principle, such as the principle of induction. Thus our intuitive knowledge, which is the source of all our other knowledge of truths, is of two sorts: pure empirical knowledge, which tells us of the existence and some of the properties of particular things with which we are acquainted, and pure a priori knowledge, which gives us connexions between universals, and enables us to draw inferences from the particular facts given in empirical knowledge.

Our derivative knowledge always depends upon some pure a priori

knowledge and usually also depends upon some pure empirical knowledge.

 

Philosophical knowledge, if what has been said above is true, does not differ essentially from scientific knowledge; there is no special source of wisdom which is open to philosophy but not to science, and the results obtained by philosophy are not radically different from those obtained from science. The essential characteristic of philosophy, which makes it a study distinct from science, is criticism. It examines critically the principles employed in science and in daily life; it searches out any inconsistencies there may be in these principles, and it only accepts them when, as the result of a critical inquiry, no reason for rejecting them has appeared. If, as many philosophers have believed, the principles underlying the sciences were capable, when disengaged from irrelevant detail, of giving us knowledge concerning the universe as a whole, such knowledge would have the same claim on our belief as scientific knowledge has; but our inquiry has not revealed any such knowledge, and therefore, as regards the special doctrines of the bolder metaphysicians, has had a mainly negative result. But as regards what would be commonly accepted as knowledge, our result is in the main positive: we have seldom found reason to reject such knowledge as the result of our criticism, and we have seen no reason to suppose man incapable of the kind of knowledge which he is generally believed to possess.

 

When, however, we speak of philosophy as a criticism of knowledge, it is necessary to impose a certain limitation. If we adopt the attitude of the complete sceptic, placing ourselves wholly outside all knowledge, and asking, from this outside position, to be compelled to return within the circle of knowledge, we are demanding what is impossible, and our scepticism can never be refuted. For all refutation must begin with some piece of knowledge which the disputants share; from blank doubt, no argument can begin. Hence the criticism of knowledge which philosophy employs must not be of this destructive kind, if any result is to be achieved. Against this absolute scepticism, no logical argument can be advanced. But it is not difficult to see that scepticism of this kind is unreasonable.

Descartes’ ‘methodical doubt’, with which modern philosophy began, is not of this kind, but is rather the kind of criticism which we are asserting to be the essence of philosophy. His ‘methodical doubt’

consisted in doubting whatever seemed doubtful; in pausing, with each apparent piece of knowledge, to ask himself whether, on reflection, he could feel certain that he really knew it. This is the kind of criticism which constitutes philosophy. Some knowledge, such as knowledge of the existence of our sense-data, appears quite indubitable, however calmly and thoroughly we reflect upon it. In regard to such knowledge, philosophical criticism does not require that we should abstain from belief. But there are beliefs—such, for example, as the belief that physical objects exactly resemble our sense-data—which are entertained until we begin to reflect, but are found to melt away when subjected to a close inquiry. Such beliefs philosophy will bid us reject, unless some new line of argument is found to support them. But to reject the beliefs which do not appear open to any objections, however closely we examine them, is not reasonable, and is not what philosophy advocates.

 

The criticism aimed at, in a word, is not that which, without reason, determines to reject, but that which considers each piece of apparent knowledge on its merits, and retains whatever still appears to be knowledge when this consideration is completed. That some risk of error remains must be admitted, since human beings are fallible.

Philosophy may claim justly that it diminishes the risk of error, and that in some cases it renders the risk so small as to be practically negligible. To do more than this is not possible in a world where mistakes must occur; and more than this no prudent advocate of philosophy would claim to have performed.

CHAPTER XV THE VALUE OF PHILOSOPHY

Having now come to the end of our brief and very incomplete review of the problems of philosophy, it will be well to consider, in conclusion, what is the value of philosophy and why it ought to be studied. It is the more necessary to consider this question, in view of the fact that many men, under the influence of science or of practical affairs, are inclined to doubt whether philosophy is anything better than innocent but useless trifling, hair-splitting distinctions, and controversies on matters concerning which knowledge is impossible.

 

This view of philosophy appears to result, partly from a wrong conception of the ends of life, partly from a wrong conception of the kind of goods which philosophy strives to achieve. Physical science, through the medium of inventions, is useful to innumerable people who are wholly ignorant of it; thus the study of physical science is to be recommended, not only, or primarily, because of the effect on the student, but rather because of the effect on mankind in general. Thus utility does not belong to philosophy. If the study of philosophy has any value at all for others than students of philosophy, it must be only indirectly, through its effects upon the lives of those who study it. It is in these effects, therefore, if anywhere, that the value of philosophy must be primarily sought.

 

But further, if we are not to fail in our endeavour to determine the value of philosophy, we must first free our minds from the prejudices of what are wrongly called ‘practical’ men. The ‘practical’ man, as this word is often used, is one who recognizes only material needs, who realizes that men must have food for the body, but is oblivious of the necessity of providing food for the mind. If all men were well off, if poverty and disease had been reduced to their lowest possible point, there would still remain much to be done to produce a valuable society; and even in the existing world the goods of the mind are at least as important as the goods of the body. It is exclusively among the goods of the mind that the value of philosophy is to be found; and only those who are not indifferent to these goods can be persuaded that the study of philosophy is not a waste of time.

 

Philosophy, like all other studies, aims primarily at knowledge. The knowledge it aims at is the kind of knowledge which gives unity and system to the body of the sciences, and the kind which results from a critical examination of the grounds of our convictions, prejudices, and beliefs. But it cannot be maintained that philosophy has had any very great measure of success in its attempts to provide definite answers to its questions. If you ask a mathematician, a mineralogist, a historian, or any other man of learning, what definite body of truths has been ascertained by his science, his answer will last as long as you are willing to listen. But if you put the same question to a philosopher, he will, if he is candid, have to confess that his study has not achieved positive results such as have been achieved by other sciences. It is true that this is partly accounted for by the fact that, as soon as definite knowledge concerning any subject becomes possible, this subject ceases to be called philosophy, and becomes a separate science. The whole study of the heavens, which now belongs to astronomy, was once included in philosophy; Newton’s great work was called ‘the mathematical principles of natural philosophy’.

Similarly, the study of the human mind, which was a part of philosophy, has now been separated from philosophy and has become the science of psychology. Thus, to a great extent, the uncertainty of philosophy is more apparent than real: those questions which are already capable of definite answers are placed in the sciences, while those only to which, at present, no definite answer can be given, remain to form the residue which is called philosophy.

 

This is, however, only a part of the truth concerning the uncertainty of philosophy. There are many questions—and among them those that are of the profoundest interest to our spiritual life—which, so far as we can see, must remain insoluble to the human intellect unless its powers become of quite a different order from what they are now. Has the universe any unity of plan or purpose, or is it a fortuitous concourse of atoms? Is consciousness a permanent part of the universe, giving hope of indefinite growth in wisdom, or is it a transitory accident on a small planet on

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