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'O Lord, how manifold are Thy works: in wisdom hast Thou made them all; the earth is full of Thy riches.'—Psalm civ. 24.

Those who believe that the creation and government of the world are the work of a Being Whom it is their duty to love with all their hearts, Who loves them with a love beyond all other love, to Whom they look for guidance now and unending happiness hereafter, have a double motive for studying the forms and operations of Nature; because over and above whatever they may gain of the purest and highest pleasure in the study, and whatever men may gain of material comfort in a thousand forms from the results of the study, they cannot but have always present to their minds the thought, that all these things are revelations of His character, and to know them is in a very real measure to know Him. The believer in God, if he have the faculty and the opportunity, cannot find a more proper employment of time and labour and thought than the study of the ways in which God works and the things which God has made. Among religious men we ought to expect to find the most patient, the most truth-seeking, the most courageous of men of science.

We know that it is not always so; and that on the contrary Science and Religion seem very often to be the most determined foes to each other that can be found. The scientific man often asserts that he cannot find God in Science; and the religious man often asserts that he cannot find Science in God. Each often believes himself to be in possession, if not of the whole truth, at any rate of all the truth that it is most important to possess. Science seems to despise religion; and religion to fear and condemn Science. Religion, which certainly ought to put truth at the highest, is charged with refusing to acknowledge truth that has been proved. And Science, which certainly ought to insist on demonstrating every assertion which it makes, is charged with giving the rein to the imagination and treating the merest speculations as well-established facts.

To propose to reconcile these opposites would be a task which hardly any sane man would undertake. It would imply a claim to be able to rise at once above both, and see the truth which included all that both could teach. But it is a very useful undertaking, and not beyond the reach of thoughtful inquiry by an ordinary man, to examine the relations between the two, and thus to help not a few to find a way for themselves out of the perplexity. And this inquiry may well begin by asking what is the origin and nature of scientific belief on the one hand and of religious belief on the other. In this Lecture I propose to deal with the former.

It is not necessary to include in the Science of which I am to speak either Mathematics or Metaphysics. In as far as I need touch on what belongs to either, it will be only for the purpose of answering objections or of excluding what is irrelevant. And the consequent restriction of our consideration to the Science which concerns itself with Nature greatly simplifies the task that I have undertaken. For it will be at once admitted in the present day by all but a very few that the source of all scientific knowledge of this kind is to be found in the observations of the senses, including under that word both the bodily senses which tell us all we know of things external, and that internal sense by which we know all or nearly all that takes place within the mind itself. And so also will it be admitted that the Supreme Postulate, without which scientific knowledge is impossible, is the Uniformity of Nature.

Science lays claim to no revelations. No voice of authority declares what substances there are in the world, what are the properties of those substances, what are the effects and operations of those properties. No traditions handed down from past ages can do anything more than transmit to us observations made in those times, which, so far as we can trust them, we may add to the observations made in our own times. The materials in short which Science has to handle are obtained by experience.

But on the other hand Science can deal with these materials only on the condition that they are reducible to invariable laws. If any observation made by the senses is not capable of being brought under the laws which are found to govern all other observations, it is not yet brought under the dominion of Science. It is not yet explained, nor understood. As far as Science is concerned, it may be called as yet non-existent. It is for this very reason possible that the examination of it may be of the very greatest importance. To explain what has hitherto received no explanation constitutes the very essence of scientific progress. The observation may be imperfect, and may at once become explicable as soon as it is made complete; or, what is of far more value, it may be an instance of the operation of a new law not previously known, modifying and perhaps absorbing the law up to that time accepted. When it was first noticed in Galileo's time that water would not ascend in the suction pipe of a pump to a greater height than 32 feet, the old law that nature abhors a vacuum was modified, and the reasons why and the conditions under which Nature abhors a vacuum were discovered. The suction of fluids was brought under the general law of mechanical pressure. The doctrine that Nature abhorred a vacuum had been a fair generalization and expression of the facts of this kind that up to that time had been observed. A new fact was observed which would not fall under the rule. The examination of this fact led to the old rule being superseded; and Science advanced a great step at once. So in our own day was the planet Neptune discovered by the observation of certain facts which could not be squared with the facts previously observed unless the Law of Gravitation was to be corrected. The result in this case was not the discovery of a new Law but of a new Planet; and consequently a great confirmation of the old Law. But in each case and in every similar case the investigation of the newly observed fact proceeds on the assumption that Nature will be found uniform, and on no other assumption can Science proceed at all.

Now it is this assumption which must be first examined. What is its source? What is its justification? What, if any, are its limits?

It is not an assumption that belongs to Science only. It is in some form or other at the bottom of all our daily life. We eat our food on the assumption that it will nourish us to-day as it nourished us yesterday. We deal with our neighbours in the belief that we may safely trust those now whom we have trusted and safely trusted heretofore. We never take a journey without assuming that wood and iron will hold a carriage together, that wheels will roll upon axles, that steam will expand and drive the piston of an engine, that porters and stokers and engine-drivers will do their accustomed duties. Our crops are sown in the belief that the earth will work its usual chemistry, that heat and light and rain will come in their turn and have their usual effects, and the harvest will be ready for our gathering in the autumn. Look on while a man is tried for his life before a jury. Every tittle of the evidence is valued both by the judge and jury according to its agreement or disagreement with what we believe to be the laws of Nature, and if a witness asserts that something happened which, as far as we know, never happened at any other time since the world began, we set his evidence aside as incredible. And the prisoner is condemned if the facts before us, interpreted on the assumption that the ordinary laws of Nature have held their course, appear to prove his guilt.

What right have we to make such an assumption as this?

The question was first clearly put by Hume, and was handled by him with singular lucidity; but his answer, though very near the truth, was not so expressed as to set the question at rest.

The main relation in which the uniformity of Nature is observed is that of cause and effect. Hume examines this and maintains that there is absolutely nothing contained in it but the notion of invariable sequence. Two phenomena are invariably found connected together; the prior is spoken of as the cause, the posterior as the effect. But there is absolutely nothing in the former to define its relation to the latter, except that when the former is observed the latter, as far as we know, invariably follows. A ball hits another ball of equal size, both being free to move. There is nothing by which prior to experience we can determine what will happen next. It is just as conceivable that the moving ball should come back or should come to rest, as that the ball hitherto at rest should begin to move. A magnet fastened to a piece of wood is floating on water. Another magnet held in the hand is brought very near one of its poles or ends. If two north poles are thus brought together the floating magnet is repelled; if a north and a south pole are brought together the floating magnet is attracted. The motion of the floating magnet is in each case called the effect; the approach of the magnet held in the hand is called the cause. And this cause is, as far as we know, invariably followed by this effect. But to say that one is cause and the other effect is merely to say that one is always followed by the other; and no other meaning, according to Hume, can be attached to the words cause and effect.

Having established this interpretation of these words, Hume goes on to ask: What can be the ground in reason for the principle universally adopted, that the law of cause and effect rules phenomena, and that a cause which has been followed by an effect once will be followed by the same effect always? And he concludes that no rational ground can be found at all, that it is the mere result of custom without anything rational behind it. We are accustomed to see it so, and what we have been so perpetually accustomed to see we believe that we shall continue to see. But why what has always been hitherto should always be hereafter, no reason whatever can be given. The logical conclusion obviously is to discredit all human faculties and to land us in universal scepticism.

It was at this point that Kant took up the question, avowedly in consequence of Hume's reasoning. He considered that Hume had been misled by turning his attention to Physics, and that his own good sense would have saved him from his conclusion had he thought rather of Mathematics. Kant's solution of the problem, based mainly on the reality of Mathematics, and especially of Geometry, is the direct opposite of Hume's.

It will be most easy to give a clear account of Kant's solution by using a very familiar illustration. There is a well-known common toy called a Kaleidoscope, in which bits of coloured glass placed at one end are seen through a small round hole at the other. The bits of glass are not arranged in any order whatever, and by shaking the instrument may be rearranged again and again indefinitely and still without any order whatever. But however they may be arranged in themselves they always form, as seen from the other end, a symmetrical pattern. The pattern indeed varies with every shake of the instrument and consequent re-arrangement of the bits of glass, but it is invariably symmetrical. Now the symmetry in this case is not in the bits of glass; the colours are there no doubt, but the symmetrical arrangement of them is not. The symmetry is entirely due to the instrument. And if a competent enquirer looks into the instrument and examines its construction, he will be able to lay down with absolute certainty the laws of that symmetry which every pattern as seen through the instrument must obey.

Just such an instrument, according to Kant, is the human mind. Space and Time and the Perceptive Faculties are the parts of the instrument. Everything that reaches the senses must submit to the laws of Space and Time, that is, to the Laws of Mathematics, because Space and Time are forms of the mind itself, and, like the kaleidoscope, arrange all things on their way to the senses according to a pattern of their own. This pattern is as it were super-added to the manifestations that come from the things themselves; and if there be any manifestations of such a nature that they could not submit to this addition, or, in other words, could not submit to Mathematical Laws, these manifestations could not affect our senses at all. So too our Understanding has a pattern of its own which it imposes on all things that reach its power of perception. What cannot be accommodated to this pattern cannot be understood at all. Whatever things may be in themselves, their manifestations are not within the range of our intelligence, except by passing through the arranging process which our own mind executes upon them.

It is clear that this wonderfully ingenious speculation rests its claims for acceptance purely on the assertion that it and it alone explains the facts. It cannot be proved from any principle of reason. It assumes that there is a demonstrative science of Mathematics quite independent of experience, and that there are necessary principles of Physics equally independent of experience. And it accounts for the existence of these.

With Mathematics we are not now concerned, and I will pass them by with only one remark. The ground on which Kant's theory stands is not sufficient, for this simple reason. It accounts for one fact; it does not account for another fact. It accounts for the fact that we attach and cannot help attaching a conviction of necessity to all mathematical reasoning. We not only know that two straight lines cannot enclose a space, but we know that this is so and must be so in all places and at all times, and we know it without any proof whatever. This fact Kant accounts for. Space is according to him a part of our kaleidoscope; you can always look into it and see for yourself what are the laws of it. But there is another fact. This space of which we are speaking is unquestionably to our minds not a thing inside of us but outside of us. We are in it. We cannot get rid of a sense that it is independent of ourselves. We can imagine ourselves non-existing, minds and all. We cannot imagine space non-existing. If it be a part of our minds, how is it that we can picture to ourselves the non-existence of the mind which is the whole, but not the non-existence of space which, according to the hypothesis, is the part? For this fact, which we commonly call the objectivity of space, Kant's theory does not account. In fact Kant appears to have no escape from assigning this objectivity of space to delusion. But a theory which requires us to call an ineradicable conviction of consciousness a delusion cannot be said to explain all the facts. John Stuart Mill maintains that the other fact, namely, the conviction of the necessity of mathematical truth, is a delusion. And his account also must be pronounced for that reason to fail in accounting for all the facts.

But our present concern is not with Mathematics but with Physics. And here Kant fails altogether to convince; for, taking Time and the Perceptive Powers of the Understanding as parts of the human mind, he shows, what indeed is clearer and clearer every day, that the principles (so called) of Physics are indispensable Postulates, not indeed of observing with the senses, but of comprehending with the understanding, whatever happens. In order to give anything that can be called an explanation of any event we must show that it falls under the general rules which constitute the uniformity of Nature. We have no other meaning for the words understanding or explaining an event. Thinking, when analysed, is found to consist in bringing all that happens under universal laws, and no phenomenon can be said to be explained in thought except by being so related to all other phenomena. But it does not by any means follow that events cannot happen or cannot affect our senses without being susceptible of such explanation. To say that an event cannot be understood, and to say either that it cannot happen or that it cannot be observed by the senses, are two very different things. The fact is that Mathematics and Physics do not, as Kant assumes, present the same problem for solution, and do not therefore admit of one solution applicable to both. It is not the case that there is a science of abstract Physics corresponding to the science of Mathematics and sharing in the same character of necessity. In Mathematics we have truths which we cannot but accept, and accept as universal and necessary: in Physics we have no such truths, nor has Kant even endeavoured to prove that we have. The very question therefore that we are asked to solve in regard to Mathematics does not present itself in Physics. I am constrained to believe that two and two are four and not five; I am not constrained to believe that if one event is followed by another a great many times it will be so followed always. And the question is, why, without any constraint, I nevertheless so far believe it that I require special evidence in any given case to convince me to the contrary. And Kant's answer is irrelevant. He says that we cannot think the sequence of events unless they fall under the postulates of thinking, that is, the postulates of science; but this is no answer to the question. Why do we believe that, unless the contrary be proved, everything that is observed by the senses is capable of being reduced under these postulates of thinking? The sequence of things cannot otherwise be explained; but why should the sequence of all things that happen be capable of being explained? The question therefore still remains unanswered. What right have we to assume this Uniformity in Nature? or, in other words, what right have we to assume that all phenomena in Nature, observed by our senses, are capable of being brought within the domain of Science? And to answer this question we must approach it from a different side.

And there is the more reason for this because it is undeniable that both the definition and the universality of the relation of cause and effect, as they were accepted by Hume and his followers, are not accepted by men in general. In ordinary language something more is meant by cause and effect than invariable sequence, and the common assumption is not that all Nature obeys this rule with absolutely no variation, but that the rule is sufficiently general for all practical purposes.

If then we begin by asking what is the process of Science in dealing with all questions of causation, we find that this process when reduced to its simplest elements always consists in referring every event as an effect to some cause which we know or believe to have produced some other and similar event. Newton is struck by a falling apple. His first thought is, 'how hard the blow.' His second is wonder, 'how far the earth's attraction, which has caused this hard blow, extends.' His third, 'why not as far as the moon?' And he proceeds to assign the motion of the moon to the same cause as that which produced the motion of the apple. Taking this as a working hypothesis, he examines what would be the motions of all the planets if this were true. And the examination ends with establishing the high probability of the Law of Gravitation.

Now this being the invariable process of Science, it follows that our conception of cause must come originally from that cause which we have within ourselves and with which we cannot but begin, the action of the human will. It is from this action that is obtained that conception which underlies the ordinary conception of cause, namely, that of force or power.

This conception of force or power is derived from the consciousness of our own power to move our limbs, and perhaps too of passions, temptations, sentiments to move or oppose our wills. This power is most distinctly felt when it is resisted. The effort which is necessary when we choose to do what we have barely strength to do, impresses on us more clearly the sense of a force residing in ourselves capable of overcoming resistance. Having the power to move our limbs, and that too against some resistance, we explain, and in no other way can we explain, other motions by the supposition of a similar power. In so doing we are following strictly the scientific instinct and the scientific process. We are putting into the same class the motions that we observe in other things and the motions that we observe in ourselves; the latter are due to acts of our own wills, the former are assigned to similar acts of other wills. Hence in infancy, and in the infancy of mankind, the whole world is peopled with persons because everything that we observe to move is personified. A secret will moves the wind, the sun, the moon, the stars, and each is independent of the others.

Soon a distinction grows up between the things that seem to have a spontaneous motion and those that have not, and spontaneous motion is taken as the sign of life. And all inanimate things, of whatever kind, are held to be moved, if they move at all, by a force outside themselves. Their own force is limited to that of resisting, and does not include that of originating motion. But though they cannot originate motion they are observed to be capable of transmitting it. And the notion of force is expanded by the recognition that it can be communicated from one thing to another and yet to another, and that we may have to go back many steps before we arrive at the will from which it originated. We began with the notion of a power the action of which was or appeared to be self-originated: we come to the notion of a power the action of which is nothing more than the continuance of preceding action. And the special characteristic of the action of this force as thus conceived, which we may call the derivative force, is seen to be its regularity, just as the special characteristic of the self-originating action was its spontaneity.

As experience increases the regularity of the action of the derivative force is more and more observable, and then arises the notion of a law or rule regulating the action of every such force. And a perpetually increasing number of phenomena are brought under this head, and are shown to be, not the immediate results of self-originating action, but the more or less remote results of derivative action governed by laws. And even a large number of those phenomena, which specially belong to life and living creatures, in whom alone, if anywhere, the self-originating action is to be found, are observed to be subject to law and therefore to be the issue not of self-originating but of derivative action. And this observed regularity it is found possible to trace much more widely than it is possible to trace any clear evidence of what we understand by force. And so, at last, we frequently use the word force as it were by anticipation, not to express the cause of the phenomena, which indeed we do not yet know, but as a convenient abbreviation for a large number of facts classed under one head. And this it is which enables Hume to maintain that we mean no more by a cause than an event which is invariably followed by another event. We discover invariability much faster than we can discover causation; and having discovered invariability in any given case, we presume causation even when we cannot yet show it, and use language in accordance with that presumption. Thus, for instance, we speak of the force of gravitation, although we cannot yet prove that there is any such force, and all that we know is that material particles move as if such a force were acting on them.

As Science advances it is seen that the regularity of phenomena is far more important to us than their causes. And the attention of all students of Nature is fixed on that rather than on causation. And this regularity is seen to be more and more widely pervading all phenomena of every class, until the mind is forced to conceive the possibility that it may be absolutely universal, and that even will itself may come within its supreme dominion.

But to the very last the idea of causation retains the traces of its origin. For in the first place every step in this building up of science assumes a permanence underlying all phenomena. We cannot believe that the future will be like the past except because we believe that there is something permanent which was in the past and will be in the future. And this assumption of something permanent in things around us comes from the consciousness of something permanent within us. We know our own permanence. Whatever else we know or do not know about ourselves, we are sure of our own personal identity through successive periods of life. And as our explanation of things outside begins by classing them with things inside we still continue to ascribe permanence to whatever underlies phenomena even when we have long ceased to ascribe individual wills to any except beings like ourselves. And without this assumption of permanence our whole science would come to the ground.

And in the second place let it be remembered that we began with the will causing the motions of the limbs. Now there is, as far as we know, no other power in us to affect external nature than by setting something in motion. We can move our limbs, and by so doing move other things, and by so doing avail ourselves of the laws of Nature to produce remoter effects. But, except by originating motion, we cannot act at all. And, accordingly, throughout all science the attempt is made to reduce all phenomena to motions. Sounds, colours, heat, chemical action, electricity, we are perpetually endeavouring to reduce to vibrations or undulations, that is, to motion of some sort or other. The mind seems to find a satisfaction when a change of whatever kind is shown to be, or possibly to be, the result of movement. And so too all laws of Nature are then felt to be satisfactorily explained when they can be traced to some force exhibited in the movement of material particles. The law of Gravitation has an enormous evidence in support of it considered simply as a fact. And yet how many attempts have been made to represent it as the result of vortices or of particles streaming in all directions and pressing any two bodies together that lie in their path! The facts which establish it are enough. Why then these attempts? What is felt to be yet wanting? What is felt to be wanting is something to show that it is the result of some sort of general or universal motion, and that it thus falls under the same head as other motions, either those which originate in ourselves and are propagated from our bodies to external objects, or those which, springing from an unknown beginning, are for ever continuing as before.

This then is the answer to the question, Why do we believe in the uniformity of Nature? We believe in it because we find it so. Millions on millions of observations concur in exhibiting this uniformity. And the longer our observation of Nature goes on, the greater do we find the extent of it. Things that once seemed irregular are now known to be regular. Things that seemed inexplicable on this hypothesis are now explained. Every day seems to add not merely to the instances but to the wide-ranging classes of phenomena that come under the rule. We had reason long ago to hold that the quantity of matter was invariable. We now have reason to think that the quantity of force acting on matter is invariable. And to this is to be added the evidence of scientific prediction, the range of which is perpetually increasing, and which would be obviously impossible if Nature were not uniform. And yet again to this is to be added that this uniformity does not consist in a vast number of separate and independent laws, but that these laws already form a system with one another, and that that system is daily becoming more complete. We believe in the uniformity of Nature because, as far as we can observe it, that is the character of Nature.

And I use the word character on purpose, because it indicates better than any other word that I could find at once the nature and limitation of our belief.

For, if the origin of this belief be what I have described, it is perfectly clear that, however vast may be the evidence to prove this uniformity, the conclusion can never go beyond the limits of this evidence, and generality can never be confounded with universality. The certainty that Nature is uniform is not at all, and never can be, a certainty of the same kind as the certainty that four times five are twenty.

We can assert that the general character of Nature is uniformity, but we cannot go beyond this. Every separate law of nature is established by induction from the facts, and so too is the general uniformity. Every separate law of Nature is a working hypothesis. So too is the uniformity of Nature a working hypothesis, and it never can be more. It is true that there is far more evidence for the uniformity of Nature as a whole than for any one law of Nature; because a law of Nature is established by the uniformity of sequences in those phenomena to which it applies; whereas every uniformity of sequence, of whatever kind, is an evidence of the general uniformity. The evidence for the uniformity of nature is the accumulated evidence for all the separate uniformities. But, however much greater the quantity of evidence, the kind ever remains the same. There is no means by which we can demonstrate this uniformity. We can only make it probable. We can say that in almost every case all the evidence is one way; but whenever there is evidence to the contrary we cannot refuse to examine it.

If a miracle were worked science could not prove that it was a miracle, nor of course prove that it was not a miracle. To prove it to be a miracle would require not a vast range of knowledge, but absolutely universal knowledge, which it is entirely beyond our faculties to attain. To say that any event was a miracle would be to say that we knew that there was no higher law that could explain it, and this we could not say unless we knew all laws: to say that it was not a miracle would be ex hypothesi to assert what was false. In fact, to assert the occurrence of a miracle is simply to go back to the beginning of science, and to say: Here is an event which we cannot assign to that derivative action to which we have been led to assign the great body of events; we cannot explain it except by referring it to direct and spontaneous action, to a will like our own will. Science has shown that the vast majority of events are due to derivative action regulated by laws. Here is an event which cannot be so explained, any more than the action of our own free will can be so explained. Science may fairly claim to have shown that miracles, if they happen at all, are exceedingly rare. To demonstrate that they never happen at all is impossible, from the very nature of the evidence on which Science rests. But for the same reason Science can never in its character of Science admit that a miracle has happened. Science can only admit that, so far as the evidence goes, an event has happened which lies outside its province.

To believers the progress of Science is a perpetual instruction in the character which God has impressed on His works. That He has put Order in the very first place may be a surprise to us; but it can only be a surprise. In the great machinery of the Universe it constantly happens to us to find that that which is made indispensable, is nevertheless not the highest. The chosen people were not the highest in all moral or even in all spiritual characteristics; if we refuse the explanation given by Goethe that they were chosen for their toughness, yet we have no better to give. The eternal moral law is of all we know the highest and holiest. Yet the religious instinct seems to have been more indispensable for the development of humanity according to the Divine purpose than the observance of that moral law in all its fulness. It would never have occurred to us beforehand to permit in Divine legislation any concession to the hardness of men's hearts; yet we know that it was done. Science now tells us that Order takes a rank in God's work far above where we should have placed it. It is not the highest; it is far from the highest: but it appears to be in some strange way the most indispensable. God is teaching us that Order is far more universal, far more penetrating than we should have supposed. But, nevertheless, it is not itself God; nor the highest revelation of God. It is the stamp which, for reasons higher than itself, He appears to have put on His works. What is the limit to its application we do not know. There may be instances where this Order is apparently broken, but really maintained, because one physical law is absorbed in a higher; there may be instances where the physical law is superseded by a moral law. But we shall neither refuse to recognise that God has stamped this character on His works, nor let it on the other hand come between us and Him. For we know still that He is greater than all that He hath made, and He speaks to us by another voice besides the voice of Science.