University of Virginia Library

Chapter 3
Ultimate Scientific Ideas

§15. What are Space and Time? Two hypotheses are current respecting them: the one that they are objective, the other that they are subjective. Let us see what becomes of these hypotheses under analysis.

To say that Space and Time exist objectively, is to say that they are entities. The assertion that they are non-entities is self-destructive: non-entities are non-existences; and to allege that non-existences exist objectively is a contradiction in terms. Moreover, to deny that Space and Time are things, and so by implication to call them nothings, involves the absurdity that there are two kinds of nothing. Neither can they be regarded as attributes of some entity. Not only is it impossible to conceive any entity of which they are attributes, but we cannot think of them as disappearing, even if everything else disappeared; whereas attributes necessarily disappear along with the entities they belong to. Thus as Space and Time can be neither non-entities nor the attributes of entities, we are compelled to consider them as entities. But while, on the hypothesis of their objectivity, Space and Time must be classed as things, we find that to represent them in thought as things is impossible. To be conceived at all, a thing must be conceived as having attributes. We can distinguish something from nothing, only by the power which the something has to act on our consciousness. The effects it mediately or immediately produces on our consciousness we attribute to it, and call its attributes; and the absence of these attributes is the absence of the terms in which the something is conceived, and involves the absence of a conception. What, now, are the attributes of Space? The only one which it is possible to think of as belonging to it is that of extension, and to credit it with this is to identify object and attribute. For extension and Space are convertible terms: by extension, as we ascribe it to surrounding objects, we mean occupancy of Space; and thus to say that Space is extended, is to say that Space occupies Space. How we are similarly unable to assign any attribute to Time, scarcely needs pointing out. Nor are Time and Space unthinkable as entities only from the absence of attributes. There is another peculiarity, familiar to most people, which equally excludes them from the category. All entities actually known as such, are limited; and even if we suppose ourselves either to know or to be able to conceive some unlimited entity, we necessarily in so classing it separate it from the class of limited entities. But of Space and Time we cannot assert either limitation or the absence of limitation. We find ourselves unable to form any mental image of unbounded Space; and yet are unable to imagine bounds beyond which there is no Space. Similarly at the other extreme: it is impossible to think of a limit to the divisibility of Space; yet equally impossible to think of its infinite divisibility. And, without stating them, it will be seen that we labour under like impotences in respect to Time. Thus we cannot conceive Space and Time as entities, and are equally disabled from conceiving them as either the attributes of entities or as non-entities. We are compelled to think of them as existing, and yet cannot bring them within those conditions under which existences are represented in thought.

Shall we then take refuge in the Kantian doctrine? Shall we say that Space and Time are forms of the intellect, — á priori laws or conditions of the conscious mind?" To do this is to escape from great difficulties by rushing into greater. The proposition with which Kant's philosophy sets out, verbally intelligible though it is, cannot by any effort be rendered into thought — cannot be interpreted into an idea properly so called, but stands merely for a pseud-idea. In the first place, to assert that Space and Time are subjective conditions is, by implication, to assert that they are not objective realities: if the Space and Time present to our minds belong to the ego, then of necessity they do not belong to the non-ego. Now it is impossible to think this. The very fact on which Kant bases his hypothesis — namely that our consciousness of Space and Time cannot be suppressed — testifies as much; for that consciousness of Space and Time which we cannot rid ourselves of, is the consciousness of them as existing objectively. It is useless to reply that such an inability must inevitably result if they are subjective forms. The question here is — What does consciousness directly testify? And the direct testimony of consciousness is, that Time and Space are not within the mind but without the mind; and so absolutely independent that we cannot conceive them to become non-existent even supposing the mind to become non-existent. Besides being positively unthinkable in what it tacitly denies, the theory of Kant is equally unthinkable in what it openly affirms. It is not simply that we cannot combine the thought of Space with the thought of our own personality, and contemplate the one as a property of the other — though our inability to do this would prove the inconceivableness of the hypothesis — but it is that the hypothesis carries in itself the proof of its own inconceivableness. For if Space and Time are forms of intuition, they can never be intuited; since it is impossible for anything to be at once the form of intuition and the matter of intuition. That Space and Time are objects of consciousness, Kant emphatically asserts by saying that it is impossible to suppress the consciousness of them. How then, if they are objects of consciousness, can they at the same time be conditions of consciousness? If Space and Time are the conditions under which we think, then when we think of Space and Time themselves, our thoughts must be unconditioned; and if there can thus be unconditioned thoughts, what becomes of the theory?

It results, therefore, that Space and Time are wholly incomprehensible. The immediate knowledge which we seem to have of them proves, when examined, to be total ignorance. While our belief in their objective reality is insurmountable, we are unable to give any rational account of it. And to posit the alternative belief (possible to state but impossible to realize) is merely to multiply irrationalities.

§16. Were it not for the necessities of the argument, it would be inexcusable to occupy the reader's attention with the threadbare, and yet unended, controversy respecting the divisibility of matter. Matter is either infinitely divisible or it is not: no third possibility can be named. Which of the alternatives shall we accept? If we say that Matter is infinitely divisible, we commit ourselves to a supposition not realizable in thought. We can bisect and re-bisect a body, and continually repeating the act until we reduce its parts to a size no longer physically divisible, may then mentally continue the process. To do this, however, is not really to conceive the infinite divisibility of matter, but to form a symbolic conception not admitting of expansion into a real one, and not admitting of other verification. Really to conceive the infinite divisibility of matter, is mentally to follow out the divisions to infinity. and to do this would require infinite time. On the other hand, to assert that matter is not infinitely divisible, is to assert that it is reducible to parts which no power can divide; and this verbal supposition can no more be represented in thought than the other. For each of such ultimate parts, did they exist, must have an under and an upper surface, a right and a left side, like any larger fragment. Now it is impossible to imagine its sides so near that no plane of section can be conceived between them; and however great be the assumed force of cohesion, it is impossible to shut out the idea of a greater force capable of overcoming it. So that to human intelligence the one hypothesis is no more acceptable than the other; and yet the conclusion that one or other must agree with the fact, seems to human intelligence unavoidable.

Again, let us ask whether substance has anything like that extended solidity which it presents to our consciousness. The portion of space occupied by a piece of metal, seems to eyes and fingers perfectly filled: we perceive a homogeneous, resisting mass, without any breach of continuity. Shall we then say that Matter is actually as solid as it appears? Shall we say that whether it consists of an infinitely divisible element or of units which cannot be further divided, its parts are everywhere in actual contact? To assert as much entangles us in insuperable difficulties. Were Matter thus absolutely solid it would be — what it is not — absolutely incompressible; since compressibility, implying the nearer approach of constituent parts, is not thinkable unless there is unoccupied space among the parts.

The supposition that Matter is absolutely solid being untenable, there presents itself the Newtonian supposition, that it consists of solid atoms not in contact but acting on one another by attractive and repulsive forces, varying with the distances. To assume this, however, merely shifts the difficulty. For granting that Matter as we perceive it, is made up of dense extended units attracting and repelling, the question still arises — What is the constitution of these units? We must regard each of them as a small piece of matter. Looked at through a mental microscope, each becomes a mass such as we have just been contemplating. Just the same inquiries may be made respecting the parts of which each atom consists; while just the same difficulties stand in the way of every answer. Even were the hypothetical atom assumed to consist of still minuter ones, the difficulty would reappear at the next step; and so on perpetually.

Boscovich's conception yet remains to us. Seeing that Matter could not, as Leibnitz suggested, be composed of unextended monads (since the juxtaposition of an infinity of points having no extension could not produce that extension which matter possesses), and perceiving objections to the view entertained by Newton, Boscovich proposed an intermediate theory. This theory is that the constituents of Matter are centres of force — points without dimensions — which attract and repel one another in such wise as to be kept at specific distances apart. And he argues, mathematically, that the forces possessed by such centres might so vary with the distances that, under given conditions, the centres would remain in stable equilibrium with definite interspaces; and yet, under other conditions, would maintain larger or smaller interspaces. This speculation, however, escapes all the inconceivabilities above indicated by merging them in the one inconceivability with which it sets cut. A centre of force absolutely without extension is unthinkable. The idea of resistance cannot be separated in thought from the idea of something which offers resistance, and this something must be thought of as occuppying space. To suppose that central forces can reside in points having positions only, with nothing to mark their positions — points in no respect distinguishable from surrounding points which are not centres of force — is beyond human power.

But though the conception of Matter as consisting of dense indivisible units is symbolic, and cannot by any effort be thought out, it may yet be supposed to find indirect verification in the truths of chemistry. These, it is argued, necessitate the belief that Matter consists of particles of specific weights, and therefore of specific sizes. The law of definite proportions seems impossible on any other condition than the existence of ultimate atoms; and though the combining weights of the respective elements are termed by chemists their "equivalents," for the purpose of avoiding a questionable assumption, we are unable to think of the combination of such definite weights, without supposing it to take place between definite molecules. Thus it would appear that the Newtonian view is at any rate preferable to that of Boscovich. A disciple of Boscovich, however, may reply that his master's theory is involved in that of Newton, and cannot indeed be escaped. "What holds together the parts of these ultimate atoms?" he may ask. "A cohesive force," his opponent must answer. "And what," he may continue, "holds together the parts of any fragments into which, by sufficient force, an ultimate atom might be broken?" Again the answer must be — a cohesive force. "And what," he may still ask, "if the ultimate atom were reduced to parts as small in proportion to it, as it is in proportion to a tangible mass of matter — what must give each part the ability to sustain itself?" Still there is no answer but — a cohesive force. Carry on the mental process and we can find no limit until we arrive at the symbolic conception of centres of force without any extension.

Matter then, in its ultimate nature, is as absolutely incomprehensible as Space and Time. Whatever supposition we frame leaves us nothing but a choice between opposite absurdities.*

§17. A body impelled by the hand is perceived to move, and to move in a definite direction; doubt about its motion seems impossible. Yet we not only may be, but usually are, quite wrong in both these judgments. Here, for instance, is a ship which we will suppose to be anchored at the equator with her head to the West. When the captain walks from stem to stern, in what direction does he move? East is the obvious answer — an answer which for the moment may pass without criticism. But now the anchor is heaved, and the vessel sails to the West with a velocity equal to that at which the captain walks. In what direction does he now move when he goes from stem to stern? You cannot say East, for the vessel is carrying him as fast towards the West as he walks to the East; and you cannot say West for the converse reason In respect to things outside the vessel he is stationary, though to all on board he seems to be moving. But now are we quite sure of this conclusion? — Is he really stationary? On taking into account the Earth's motion round its axis, we find that he is travelling at the rate of 1000 miles per hour to the East; so that neither the perception of one who looks at him, nor the inference of one who allows for the ship's motion, is anything like right. Nor indeed, on further consideration, do we find this revised conclusion to be much better. For we have not allowed for the Earth's motion in its orbit. This being some 68,000 miles per hour, it follows that, assuming the time to be midday, he is moving, not at the rate of 1000 miles per hour to the East, but at the rate of 67,000 miles per hour to the East. Nay not even now have we discovered the true rate and the true direction of his movement. With the Earth's progress in its orbit, we have to join that of the whole Solar system towards the constellation Hercules. When we do this, we perceive that he is moving neither East nor West, but in a line inclined to the plane of the Ecliptic, and at a velocity greater or less (according to the time of the year) than that above named. And were the constitution of our Sidereal System fully known, we should probably discover the direction and rate of his actual movement to differ considerably even from these. Thus we are taught that what we are conscious of is not the real motion of any object, either in its rate or direction, but merely its motion as measured from an assigned position — either our own or some other. Yet in this very process of concluding that the motions we perceive are not the real motions, we tacitly assume that there are real motions. We take for granted that there is an absolute course and an absolute velocity and we find it impossible to rid ourselves of this idea. Nevertheless, absolute motion cannot even be imagined, much less known. Apart from those marks in space which we habitually associate with it, motion is unthinkable. For motion is change of place; but in space without marks, change of place is inconceivable, because place itself is inconceivable. Place can be conceived only by reference to other places; and in the absence of objects dispersed through space, a place could be conceived only in relation to the limits of space; whence it follows that in unlimited space, place cannot be conceived — all places must be equidistant from boundaries which do not exist. Thus while obliged to think that there is an absolute motion, we find absolute motion cannot be represented in thought.

Another insuperable difficulty presents itself when we contemplate the transfer of Motion. Habit blinds us to the marvellousness of this phenomenon. Familiar with the fact from childhood, we see nothing remarkable in the ability of a moving thing to generate movement in a thing that is stationary. It is, however, impossible to understand it. In what respect does a body after impact differ from itself before impact? What is this added to it which does not sensibly affect any of its properties and yet enables it to traverse space? Here is an object at rest and here is the same object moving. In the one state it has no tendency to change its place, but in the other it is obliged at each instant to assume a new position. What is it which will for ever go on producing this effect without being exhausted? and how does it dwell in the object? The motion you say has been communicated. But how? — What has been communicated? The striking body has not transferred a thing to the body struck; and it is equally out of the question to say that it has transferred an attribute. What then has it transferred?

Once more there is the old puzzle concerning the connexion between Motion and Rest. A body travelling at a given velocity cannot be brought to a state of rest, or no velocity, without passing through all intermediate velocities. It is quite possible to think of its motion as diminishing insensibly until it becomes infinitesimal; and many will think equally possible to pass in thought from infinitesimal motion to no motion. But this is an error. Mentally follow out the decreasing velocity as long as you please, and there still remains some velocity; and the smallest movement is separated by an impassable gap from no movement. As something, however minute, is infinitely great in comparison with nothing; so is even the least conceivable motion infinite as compared with rest.

Thus neither when considered in connexion with Space, nor when considered in connexion with Matter, nor when considered in connexion with Rest, do we find that Motion is truly cognizable. All efforts to understand its essential nature do but bring us to alternative impossibilities of thought.

§18. On lifting a chair the force exerted we regard as equal to that antagonistic force called the weight of the chair, and we cannot think of these as equal without thinking of them as like in kind; since equality is conceivable only between things that are connatural. Yet, contrariwise, it is incredible that the force existing in the chair resembles the force present to our minds. It scarcely needs to point out that since the force as known to us is an affection of consciousness, we cannot conceive the force to exist in the chair under the same form without endowing the chair with consciousness. So that it is absurd to think of Force as in itself like our sensation of it, and yet necessary so to think of it if we represent it in consciousness at all.

How, again, can we understand the connexion between Force and Matter? Matter is known to us only through its manifestations of Force: abstract its resistance mediately or immediately offered and there remains nothing but empty extension. Yet, on the other hand, resistance is equally unthinkable apart from Matter — apart from something extended. Not only are centres of force devoid of extension unimaginable, but we cannot imagine either extended or unextended centres of force to attract and repel other such centres at a distance, without the intermediation of some kind of matter. The hypothesis of Newton, equally with that of Boscovich, is open to the charge that it supposes one thing to act on another through empty space — a supposition which cannot be represented in thought. This charge is indeed met by introducing a hypothetical fluid existing among the atoms or centres. But the problem is not thus solved: it is simply shifted, and reappears when the constitution of this fluid is inquired into. How impossible it is to elude the difficulty is best seen in the case of astronomical forces. The Sun gives us sensations of light and heat; and we have ascertained that between the cause as existing in the Sun, and the effect as experienced on the Earth, a lapse of eight minutes occurs: whence unavoidably result in us the conceptions of both a force and a motion. So that for assuming a luminiferous ether, there is the defence, not only that the exercise of force through 92,000,000 of miles of absolute vacuum is inconceivable, but also that it is impossible to conceive motion in the absence of something moved. Similarly in the case of gravitation. Newton described himself as unable to think that the attraction of one body for another at a distance, could be exerted in the absence of an intervening medium. But now let us ask how much the forwarder we are if an intervening medium be assumed. This ether whose undulations according to the received hypothesis constitute heat and light, and which is the vehicle of gravitation — how is it constituted? We must regard it in the way that physicists usually regard it, as composed of atoms or molecules which attract and repel one another: infinitesimal it may be in comparison with those of ordinary matter, but still atoms or molecules. And remembering that this ether is imponderable, we are obliged to conclude that the ratio between the interspaces of these atoms and the atoms themselves is immense. Hence we have to conceive these infinitesimal molecules acting on one another through relatively vast distances. How is this conception easier than the other? We still have mentally. to represent a body as acting where it is not, and in the absence of anything by which its action may be transferred; and what matters it whether this takes place on a large or a small scale? Thus we are obliged to conclude that matter, whether ponderable or imponderable, and whether aggregated or in its hypothetical units, acts on matter through absolutely vacant space; and yet this conclusion is unthinkable.

Another difficulty of conception, converse in nature but equally insurmountable, must be added. If, on the one hand, we cannot in thought see matter acting upon matter through vacant space; on the other hand, it is incomprehensible that the gravitation of one particle of matter towards another, and towards all others, should be the same whether the intervening space is filled with matter or not. I lift from the ground, and continue to hold, a pound weight. Now, into the vacancy between it and the ground, is introduced a mass of matter of any kind whatever, in any state whatever; and the gravitation of the weight is entirely unaffected. Each individual of the infinity of particles composing the Earth acts on the pound in absolutely the same way, whatever intervenes, or if nothing intervenes. Through eight thousand miles of the Earth's substance, each molecule at the antipodes affects each molecule of the weight, in utter indifference to the fullness or emptiness of the space between them. So that each portion of matter in its dealings with remote portions, treats all intervening portions as though they did not exist; and yet, at the same time, it recognizes their existence with scrupulous exactness in its direct dealings with them.

While then it is impossible to form any idea of Force in itself, it is equally impossible to comprehend its mode of exercise.

§19. Turning now from the outer to the inner world, let us contemplate, not the agencies to which we ascribe our subjective modifications, but the subjective modifications themselves. These constitute a series. Difficult as we find it distinctly to individualize them, it is nevertheless beyond question that our states of consciousness occur in succession.

Is this chain of states of consciousness infinite or finite? We cannot say infinite; not only because we have indirectly reached the conclusion that there was a period when it commenced, but also because all infinity is inconceivable — an infinite series included. If we say finite we say it inferentially; for we have no direct knowledge of either of its ends. Go back in memory as far as we may, we are wholly unable to identify our first states of consciousness. Similarly at the other extreme. We infer a termination to the series at a future time, but cannot directly know it; and we cannot really lay hold of that temporary termination reached at the present moment. For the state of consciousness recognized by us as our last, is not truly our last. That any mental affection may be known as one of the series, it must be remembered — represented in thought, not presented. The truly last state of consciousness is that which is passing in the very act of contemplating a state just past — that in which we are thinking of the one before as the last. So that the proximate end of the change eludes us, as well as the remote end.

"But," it may be said, "though we cannot directly know consciousness to be finite in duration, because neither of its limits can be actually reached, yet we can very well conceive it to be so." No: not even this is true. We cannot conceive the terminations of that consciousness which alone we really know — our own — any more than we can perceive its terminations. For in truth the two acts are here one. In either case such terminations must be, as above said, not presented in thought, but represented; and they must be represented as in the act of occurring. Now to represent the termination of consciousness as occurring in ourselves, is to think of ourselves as contemplating the cessation of the last state of consciousness; and this implies a supposed continuance of consciousness after its last state, which is absurd.

Hence, while we are unable to believe or to conceive that the duration of consciousness is infinite, we are equally unable either to know it as finite, or to conceive it as finite: we can only infer from indirect evidence that it is finite.

§20. Nor do we meet with any greater success when, instead of the extent of consciousness, we consider its substance. The question — What is this that thinks? admits of no better solution than the question to which we have just found none but inconceivable answers.

The existence of each individual as known to himself, has always been held the most incontrovertible of truths. To say — "I am as sure of it as I am sure that I exist," is, in common speech, the most emphatic expression of certainty. And this fact of personal existence, testified to by the universal consciousness of men, has been made the basis of more philosophies than one.

Belief in the reality of self cannot, indeed, be escaped while normal consciousness continues. What shall we say of these successive impressions and ideas which constitute consciousness? Are they affections of something called mind, which, as being the subject of them, is the real ego? If we say this we imply that the ego is an entity. Shall we assert that these impressions and ideas are not the mere superficial changes wrought on some thinking substance, but are themselves the very body of this substance — are severally the modified forms which it from moment to moment assumes? This hypothesis, equally with the foregoing, implies that the conscious self exists as a permanent continuous being; since modifications necessarily involve something modified. Shall we then betake ourselves to the sceptic's position, and argue that our impressions and ideas themselves are to us the only existences, and that the personality said to underlie them is a fiction? We do not even thus escape; since this proposition, verbally intelligible but really unthinkable, itself makes the assumption which it professes to repudiate. For how can consciousness be wholly resolved into impressions and ideas, when an impression of necessity imples something impressed? Or again, how can the sceptic who has decomposed his consciousness into impressions and ideas, explain the fact that he considers them as his impressions and ideas? Or once more, if, as he must, he admits that he has an impression of his personal existence, what warrant can he show for rejecting this impression as unreal while he accepts all his other impressions as real?

But now, unavoidable as is this belief, it is yet a belief admitting of no justification by reason: nay, indeed, it is a belief which reason, when pressed for a distinct answer, rejects. One of the most recent writers who has touched on this question — Mr. Mansel — does, indeed, contend that in the consciousness of self we have a piece of real knowledge. His position is that "let system makers say what they will, the unsophisticated sense of mankind refuses to acknowledge that mind is but a bundle of states of consciousness, as matter is (possibly) a bundle of sensible qualities." But this position does not seem a consistent one for a Kantist, who pays but small respect to "the unsophisticated sense of mankind" when it testifies to the objectivity of space. Moreover, it may readily be shown that a cognition of self, properly so called, is negatived by those laws of thought which he emphasizes. The fundamental condition to all consciousness, insisted upon by Mr. Mansel in common with Sir William Hamilton and others, is the antithesis of subject and object. On this "primitive dualism of consciousness," "from which the explanations of philosophy must take their start," Mr. Mansel founds his refutation of the German absolutists. But now what is the corollary, as bearing on the consciousness of self? The mental act in which self is known implies, like every other mental act, a perceiving subject and a perceived object. If, then, the object perceived is self, what is the subject that perceives? or if it is the true self which thinks, what other self can it be that is thought of? Clearly, a true cognition of self implies a state in which the knowing and the known are one — in which subject and object are identified; and this Mr. Mansel rightly holds to be the annihilation of both.

So that the personality of which each is conscious, and the existence of which is to each a fact beyond all others the most certain, is yet a thing which cannot be known at all, in the strict sense of the word.

§21. Ultimate Scientific Ideas, then, are all representative of realities that cannot be comprehended. After no matter how great a progress in the colligation of facts and the establishment of generalizations ever wider and wider, the fundamental truth remains as much beyond reach as ever. The explanation of that which is explicable, does but bring into greater clearness the inexplicableness of that which remains behind. Alike in the external and the internal worlds, the man of science sees himself in the midst of perpetual changes of which he can discover neither the beginning nor the end. If he allows himself to entertain the hypothesis that the Universe originally existed in a diffused form, he finds it impossible to conceive how this came to be so; and equally, if he speculates on the future, he can assign no limit to the grand succession of phenomena ever unfolding themselves before him. In like manner if he looks inward he perceives that both ends of the thread of consciousness are beyond his grasp. Neither end can be represented in thought. When, again, he turns from the succession of phenomena, external or internal, to their intrinsic nature, he is just as much at fault. Supposing him in every case able to resolve the appearances, properties, and movements of things, into manifestations of Force in Space and Time; he still finds that Force, Space, and Time pass all understanding. Similarly, though analysis of mental actions may finally bring him down to sensations, as the original materials out of which all thought is woven, yet he is little forwarder; for he can give no account either of sensations themselves or of that which is conscious of sensations. Objective and subjective things he thus ascertains to be alike inscrutable in their substance and genesis. In all directions his investigations eventually bring him face to face with an insoluble enigma; and be ever more clearly perceives it to be an insoluble enigma. He learns at once the greatness and the littleness of the human intellect — its power in dealing with all that comes within the range of experience, its impotence in dealing with all that transcends experience. He, more than any other, truly knows that in its ultimate nature nothing can be known.

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