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, -- "a 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.*

<* To discuss Lord Kelvin's hvpothesis of vortex-atoms, from the scientific point of view, is beyond my ability. From the philosophical point of view, however I may say that since it postulates a homogeneous medium which is strictly continuous (non-molecular), which is incompressible, which is a perfect fluid in the sense of having no viscosity, and which has inertia, it sets out with what appears to me an inconceivability. A fluid which has inertia, implying mass, and which is yet absolutely frictionless. so that its parts move among one another without any loss of motion, cannot be truly represented in consciousness. Even were it otherwise, the hypothesis is held by Prof. Clerk Maxwell to be untenable (see art. "Atom," Ency. Brit.).>

§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.

Chapter 4   The Relativity of all Knowledge

§22. The same conclusion is thus arrived at from whichever point we set out. Ultimate religious ideas and ultimate scientific ideas, alike turn out to be merely symbols of the actual, not cognitions of it.

The conviction, so reached, that human intelligence is incapable of absolute knowledge, is one that has been slowly gaining ground. Each new ontological theory, propounded in lieu of previous ones shown to be untenable, has been followed by a new criticism leading to a new scepticism. All possible conceptions have been one by one tried and found wanting; and so the entire field of speculation has been gradually exhausted without positive result: the only result reached being the negative one above stated -- that the reality existing behind all appearances is, and must ever be, unknown. To this conclusion almost every thinker of note has subscribed. "With the exception," says Sir William Hamilton, "of a few late Absolutist theorizers in Germany, this is, perhaps, the truth of all others most harmoniously re-echoed by every philosopher of every school." And among these he names -- Protagoras, Aristotle, St. Augustin, Boethius, Averroes, Albertus Magnus, Gerson, Leo Hebraeus, Melancthon, Scaliger, Francis Piccolomini, Giordano Bruno, Campanella, Bacon, Spinoza, Newton, Kant.

It remains to point out how this belief may be established rationally, as well as empirically. Not only is it that, as in the earlier thinkers above named, a vague perception of the inscrutableness of things in themselves results from discovering the illusiveness of sense-impressions; and not only is it that, as shown in the foregoing chapters, experiments evolve alternative impossibilities of thought out of every fundamental conception; but it is that the relativity of our knowledge may be proved analytically. The induction drawn from general and special experiences, may be confirmed by a deduction from the nature of our intelligence. Two ways of reaching such a deduction exist. Proof that our cognitions are not, and never can be, absolute, is obtainable by analyzing either the product or thought, or the process of thought. Let us analyze each.

§23. If, when walking through the fields some day in September, you hear a rustle a few yards in advance, and on observing the ditch-side where it occurs, see the herbage agitated, you will probably turn towards the spot to learn by what this sound and motion are produced. As you approach there flutters into the ditch a partridge; on seeing which your curiosity is satisfied -- you have what you call an explanation of the appearances. The explanation, mark, amounts to this; that whereas throughout life you have had countless experiences of disturbance among small stationary bodies, accompanying the movement of other bodies among them, and have generalized the relation between such disturbances and such movements, you consider this particular disturbance explained, on finding it to present an instance of the like relation. Suppose you catch the partridge; and, wishing to ascertain why it did not escape, examine it, and find at one spot a trace of blood on its feathers. You now understand, as you say, what has disabled the partridge. It has been wounded by a sportsman -- adds another case to the cases already seen by you, of birds being killed or injured by the shot discharged at them from fowling-pieces. And in assimilating this case to other such cases, consists your understanding of it. But now, on consideration, a difficulty suggests itself. Only a single shot has struck the partridge, and that not in a vital place: the wings are uninjured, as are also those muscles which move them; and the creature proves by its struggles that it has abundant strength. Why then, you inquire of yourself, does it not fly? Occasion favouring, you put the question to an anatomist, who furnishes you with a solution. He points out that this solitary shot has passed close to the place at which the nerve supplying the wing-muscles of one side, diverges from the spine; and explains that a slight injury to this nerve, extending even to the rupture of a few fibres, may by preventing a perfect co-ordination in the actions of the two wings, destroy the power of flight. You are no longer puzzled. But what has happened? -- what has changed your state from one of perplexity to one of comprehension? Simply the disclosure of a class of previously known cases, along with which you can include this case. The connexion between lesions of the nervous system and paralysis of limbs has been already many times brought under your notice; and you here find a relation of cause and effect that is essentially similar.

Let us suppose you are led to ask the anatomist questions about some organic actions which, remarkable though they are, you had not before cared to understand. How is respiration effected? You ask -- why does air periodically rush into the lungs? The answer is that influx of air is caused by an enlargement of the thoracic cavity, due, partly to depression of the diaphragm, partly to motion of the ribs. But how can these bony hoops move, and how does motion of them enlarge the cavity? In reply the anatomist explains that though attached by their ends the ribs can move a little round their points of attachment; he then shows you that the plane of each pair of ribs makes an acute angle with the spine; that this angle widens when the sternal ends of the ribs are raised; and he makes you realize the consequent dilatation of the cavity, by pointing out how the area of a parallelogram increases as its angles approach to right angles: you understand this special fact when you see it to be an instance of a general geometrical fact. There still arises, however, the question -- why does the air rush into this enlarged cavity? To which comes the answer that, when the thoracic cavity is enlarged, the contained air, partially relieved from pressure, expands, and so loses some of its resisting Power; that hence it opposes to the pressure of the external air a less pressure; and that as air, like every other fluid, presses equally in all directions, motion must result along any line in which the resistance is less than elsewhere; whence follows an inward current. And this interpretation you recognize as one, when a few facts of like kind, exhibited more plainly in a visible fluid such as water, are cited in illustration. Again, after being shown that the limbs are compound levers acting in essentially the same way as levers of iron, you would consider yourself as having obtained a partial rationale of animal movements. The contraction of a muscle, seeming before quite unaccountable, would seem less unaccountable were you shown how, by a galvanic current, a series of soft iron magnets could be made to shorten itself through the attraction of each magnet for its neighbours: -- an alleged analogy which especially answers the purpose of our argument, since, whether real or fancied, it equally illustrates the mental illumination that results on finding a class of cases within which a particular case may perhaps be included. Similarly when you learn that animal heat arises from chemical combination, and so may be classed with heat evolved in other chemical combinations -- when you learn that the absorption of nutrient liquids through the coats of the intestines is an instance of osmotic action -- when you learn that the changes undergone by food during digestion, are like changes artificially producible in the laboratory; you regard yourself as knowing something about the natures of these phenomena.

Observe now what we have been doing. We began with special and concrete facts. In explaining each, and afterwards explaining the general facts of which they are instances, we have got down to certain highly general facts: -- to a geometrical principle, to a simple law of mechanical action, to a law of fluid equilibrium -- to truths in physics, in chemistry, in thermology. The particular phenomena with which we set out have been merged in larger and larger groups of phenomena; and as they have been so merged, we have arrived at solutions we consider profound in proportion as this process has been carried far. Still deeper explanations are simply further steps in the same direction. When, for instance, it is asked why the law of action of the lever is what it is, or why fluid equilibrium and fluid motion exhibit the relations they do, the answer furnished by mathematicians consists in the disclosure of the principle of virtual velocities -- a principle holding true alike in fluids and solids -- a principle under which the others are comprehended.

Is this process limited or unlimited? Can we go on for ever explaining classes of facts by including them in larger classes; or must we eventually come to a largest class? The supposition that the process is unlimited, were any one absurd enough to espouse it, would still imply that an ultimate explanation could not be reached, since infinite time would be required to reach it. While the unavoidable conclusion that it is limited, equally implies that the deepest fact cannot be understood. For if the successively deeper interpretations of Nature which constitute advancing knowledge, are merely successive inclusions of special truths in general truths, and of general truths in truths still more general; it follows that the most general truth, not admitting of inclusion in any other, does not admit of interpretation. Of necessity, therefore, explanation must eventually bring us down to the inexplicable. Comprehension must become something other than comprehension, before the ultimate fact can be comprehended.

§24. The inference which is thus forced on us when we analyze the product of thought, as exhibited objectively in scientific generalizations, is equally forced on us by an analysis of the process of thought, as exhibited subjectively in consciousness. The demonstration of the relative character of our knowledge, as deduced from the nature of intelligence, has been brought to its most definite shape by Sir William Hamilton. I cannot here do better than extract from his essay on the "Philosophy of the Unconditioned," the passage containing the substance of his doctrine.

"The unconditionally unlimited, or the Infinite, the unconditionally limited, or the Absolute, cannot positively be construed to the mind; they can be conceived, only by a thinking away from, or abstraction of, those very conditions under which thought itself is realized; consequently, the notion of the Unconditioned is only negative, -- negative of the conceivable itself. For example, on the one hand we can positively conceive, neither an absolute whole, that is, a whole so great, that we cannot also conceive it as a relative part of a still greater whole; nor an absolute part, that is, a part so small, that we cannot also conceive it as a relative whole, divisible into smaller parts. On the other hand, we cannot positively represent, or realize, or construe to the mind (as here understanding and imagination coincide), an infinite whole, for this could only be done by the infinite synthesis in thought of finite wholes, which would itself require an infinite time for its accomplishment; nor, for the same reason, can we follow out in thought an infinite divisibility of parts. The result is the same, whether we apply the process to limitation in space, in time, or in degree. * * *

"As the conditionally limited (which we may briefly call the conditioned) is thus the only possible object of knowledge and of positive thought -- thought necessarily supposes conditions. To think is to condition; and conditional limitation is the fundamental law of the possibility of thought. For, as the greyhound cannot outstrip his shadow, nor (by a more appropriate simile) the eagle outsoar the atmosphere in which he floats, and by which alone he may be supported; so the mind cannot transcend that sphere of limitation, within and through which exclusively the possibility of thought is realized. * * * How, indeed, it could ever be doubted that thought is only of the conditioned, may well be deemed a matter of the profoundest admiration. Thought cannot transcend consciousness; consciousness is only possible under the antithesis of a subject and object of thought, known only in correlation, and mutually limiting each other; while, independently of this, all that we know either of subject or object, either of mind or matter, is only a knowledge in each of the particular, of the plural, of the different, of the modified, of the phaenomenal. We admit that the consequence of this doctrine is, -- that philosophy, if viewed as more than a science of the conditioned, is impossible. Departing from the particular, we admit, that we can never, in our highest generalizations, rise above the finite; that our knowledge, whether of mind or matter, can be nothing more than a knowledge of the relative manifestations of an existence, which in itself it is our highest wisdom to recognize aS beyond the reach of philosophy. * * *

"We are thus taught the salutary lesson, that the capacity of thought is not to be constituted into the measure of existence; and are warned from recognizing the domain of our knowledge as necessarily co-extensive with the horizon of our faith. And by a wonderful revelation, we are thus, in the very consciousness of our inability to conceive aught above the relative and finite, inspired with a belief in the existence of something unconditioned beyond the sphere of all comprehensible reality."

Clear and conclusive as this statement of the case appears when carefully studied, it is expressed in so abstract a manner as to be not very intelligible to the general reader. A more popular presentation of it. with illustrative applications, as given by Mr. Mansel in his Limits of Religious Thought, will make it more fully understood. The following extracts, which I take the liberty of making from his pages, will suffice.

"The very conception of consciousness in whatever mode it may be manifested, necessarily implies distinction between one object and another. To be conscious, we must be conscious of something; and that something can only be known, as that which it is, by being distinguished from that which it is not. But distinction is necessarily imitation; for, if one object is to be distinguished from another, it must possess some form of existence which the other has not, or it must not possess some form which the other has. * * * If all thought is limitation; -- if whatever we conceive is, by the very act of conception, regarded as finite, -- the infinite, from a human point of view, is merely a name for the absence of those conditions under which thought is possible. To speak of a Conception of the Infinite is, therefore, at once to affirm those conditions and to deny them. The contradiction, which we discover in such a conception, is only that which we have ourselves placed there, by tacitly assuming the conceivability of the inconceivable. The condition of consciousness is distinction; and condition of distinction is limitation. We can have no consciousness of Being in general which is not some Being in particular: a thing, in consciousness, is one thing out of many. In assuming the possibility of an infinite object of consciousness, I assume, therefore, that it is at the same time limited and unlimited; -- actually something, without which it could not be an object of consciousness, and actually nothing, without which it could not be infinite. * * *

"A second characteristic of Consciousness is, that it is only possible in the form of a relation. There must be a Subject, or person conscious, and an Object, or thing of which he is conscious. There can be no consciousness without the union of these two factors; and, in that union, each exists only as it is related to the other. The subject is a subject, only in so far as it is conscious of an object; the object is an object, only in so far as it is apprehended by a subject: and the destruction of either is the destruction of consciousness itself. It is thus manifest that a consciousness of the Absolute is equally self-contradictory with that of the Infinite. To be conscious of the Absolute as such, we must know that an object, which is given in relation to our consciousness, is identical with one which exists in its own nature, out of all relation to consciousness. But to know this identity, we must be able to compare the two together; and such a comparison is itself a contradiction. We are in fact required to compare that of which we are conscious with that of which we are not conscious; the comparison itself being an act of consciousness, and only possible through the consciousness of both its objects. It is thus manifest that, even if we could be conscious of the absolute we could not possibly know that it is the absolute: and, as we can be conscious of an object as such, only by knowing it to be what it is, this is equivalent to an admission that we cannot be conscious of the absolute at all. As an object of COnsciousness, every thing is necessarily relative; and what a thing may be out of consciousness no mode of consciousness can tell us. * * *

"This contradiction, again, admits of the same explanation as the former, * * * Existence, as we conceive it, is but a name for the several ways in which objects are presented to our consciousness, -- a general term, embracing a variety of relations. The Absolute, on the other hand, is a term expressing no object of thought, but only a denial of the relation by which thought is constituted."

Here let me point out how the same general inference may be evolved from another fundamental condition to thought, omitted by Sir W. Hamilton and not supplied by Mr. Mansel; -- a condition which, under its obverse aspect, we have already contemplated in the last section. Every complete act of consciousness, besides distinction and relation, also implies likeness. Before it can constitute a piece of knowledge, or even become an idea, a mental state must be known not only as separate in kind or quality from certain foregoing states to which it is known as related by succession, but it must further be known as of the same kind or quality with certain other foregoing states. That organization of changes which constitutes thinking, involves continuous integration as well as continuous differentiation. Were each new affection of the mind perceived simply as an affection in some way contested with preceding ones -- were there but a chain of impressions, each of which as it arose was merely distinguished from its predecessors; consciousness would be a chaos. To produce that orderly consciousness which we call intelligence, there requires the assimilation of each impression to others that occurred earlier in the series. Both the successive mental states, and the successive relations which they bear to one another, must be classified; and classification involves not only a parting of the unlike, but also a binding together of the like. In brief, a true cognition is possible only through an accompanying recognition. Should it be objected that if so there cannot be a first cognition, and hence there can be no cognition, the reply is that cognition proper arises gradually -- that during the first stage of incipient intelligence, before the feelings produced by intercourse with the outer world have been put into order, there are no cognitions; and that, as every infant shows us, these slowly emerge out of the confusion of unfolding consciousness as fast as the experiences are arranged into groups -- as fast as the most frequently repeated sensations, and their relations to one another, become familiar enough to admit of their recognition as such or such, whenever they recur. Should it be further objected that if cognition presupposes recognition, there can be no cognition, even by an adult, of an object never before seen; there is still the sufficient answer that in so far as it is not assimilated to previously-seen objects it is not known, and that it is known only in so far as it is assimilated to them. Of this paradox the interpretation is, that an object is classifiable in various ways with various degress of completeness. An animal hitherto unknown (mark the word), though not referable to any established species or genus, is yet recognized as belonging to one of the larger divisions-mammals, birds, reptiles, or fishes; or should it be so anomalous that its alliance with any of these is not determinable, it may yet be classed as vertebrate or invertebrate; or if it be one of those organisms in which it is doubtful whether the animal or vegetal traits predominate, it is still known as a living body. Even should it be questioned whether it is organic, it remains beyond question that it is a material object, and it is cognized by being recognized as such. Whence it is clear that a thing is perfectly known only when it is in all respects like certain things previously observed. that in proportion to the number of respects in which it is unlike them, is the extent to which it is unknown; and that hence when it has absolutely no attribute in common with anything else, it must be absolutely beyond the bound of knowledge.

Observe the corollary which here concerns us. A cognition of the Real, as distinguished from the Phenomenal, must, if it exists, conform to this law of cognition in general. The First Cause, the Infinite, the Absolute, to be known at all, must be classed. To be positively thought of, it must be thought of as such or such -- as of this or that kind. Can it be like in kind to anything of which we have experience? Obviously not. Between the creating and the created, there must be a distinction transcending any of the distinctions between different divisions of the created. That which is UnCauSed cannot be assimilated to that which is caused: the two being, in the very naming, antithetically opposed. The Infinite cannot be grouped along with something finite; since, in being so grouped, it must be regarded as not infinite. It is impossible to put the Absolute in the same category with anything relative, so long as the Absolute is defined as that of which no necessary relation can be predicated. Is it then that the Actual, though unthinkable by classification with the Apparent, is thinkable by classification with itself? This supposition is equally absurd with the other. It implies the plurality of the First Cause, the Infinite, the Absolute; and this implication is self-contradictory. There cannot be more than one First Cause; seeing that the existence of more than one would involve the existence of something necessitating more than one, which something would be the true First Cause. How self-destructive is the assumption of two or more Infinites, is manifest on remembering that such Infinites, by limiting each other, would become finite. And similarly, an Absolute which existed not alone but along with other Absolutes, would no longer be an absolute but a relative. The Unconditioned therefore, as classable neither with any form of the conditioned nor with any other Unconditioned, cannot be classed at all. And to admit that it cannot be known as of such or such kind, is to admit that it is unknowable.

Thus, from the very nature of thought, the relativity of our knowledge is inferable in three ways. As we find by analyzing it, and as we see it objectively displayed in every proposition, a thought involves relation, difference, likeness. Whatever does not present each of these does not admit of cognition. And hence we may say that the Unconditioned, as presenting none of them, is trebly unthinkable.

§25. From yet another point of view we may discern the same great truth. If, instead of examining our intellectual powers directly as displayed in the act of thought, or indirectly as displayed in thought when expressed by words, we look at the connexion between the mind and the world, a like conclusion is forced on us. The very definition of Life, phenomenally considered, when reduced to its most abstract shape, discloses this ultimate implication.

All vital actions, considered not separately but in their ensemble, have for their final purpose the balancing of certain outer processes by certain inner processes. There are external forces having a tendency to bring the matter of which living bodies consist, into that stable equilibrium shown by inorganic bodies; there are internal forces by which this tendency is constantly antagonized; and the unceasing changes which constitute Life, may be regarded as incidental to the maintenance of the antagonism. For instance, to preserve the erect posture certain weights have to be neutralized by certain strains: each limb or other organ, gravitating to the Earth and pulling down the parts to which it is attached, has to be preserved in position by the tension of sundry muscles; or, in other words, the forces which would if allowed bring the body to the ground, have to be counterbalanced by other forces. Again, to keep up the temperature at a particular point, the external process of radiation and absorption of heat by the surrounding medium, must be met by a corresponding internal process of chemical combination, whereby more heat may be evolved; to which add that if from atmospheric changes the loss becomes greater or less, the production must become greater or less. Similarly throughout the organic actions at large.

In the lower kinds of life the adjustments thus maintained are direct and simple; as in a plant, the vitality of which mainly consists in osmotic and chemical actions responding to the co-existence of light, heat, water, and carbon-dioxide around it. But in animals, and especially in the higher orders of them, the adjustments become extremely complex. Materials for growth and repair not being, like those which plants require, everywhere present, but being widely dispersed and under special forms, have to be found, to be secured, and to be reduced to a fit state for assimilation. Hence the need for locomotion; hence the need for the senses; hence the need for prehensile and destructive appliances; hence the need for an elaborate digestive apparatus. Observe, however, that these complications are nothing but aids to the maintenance of the organic balance, in opposition to those physical, chemical, and other agencies which tend to overturn it. And observe, further, that while these complications aid this fundamental adaptation of inner to outer actions, they are themselves nothing but additional adaptations of inner to outer actions. For what are those movements by which a predatory creature pursues its prey, or by which its prey seeks to escape, but certain changes in the organism fitted to meet certain changes in its environment? What is that operation which constitutes the perception of a piece of food, but a particular correlation of nervous modifications, answering to a particular correlation of physical properties? What is that process by which food when swallowed is made fit for assimilation, but a set of mechanical and chemical actions responding to the mechanical and chemical characters of the food? Hence, while Life in its simplest form is the correspondence of certain inner physico-chemical actions with certain outer physico-chemical actions, each advance to a higher form of Life consists in a better preservation of this primary correspondence by the establishment of other correspondences.

So that, passing over its noumenal nature of which we know nothing, Life is definable as the continuous adjustment of internal relations to external relations. And when we so define it, we discover that the physical and the psychical life are equally comprehended by the definition. This which we call Intelligence, arises when the external relations to which the internal ones are adjusted become numerous, complex, and remote in time or space. Every advance in Intelligence essentially consists in the establishment of more varied, more complete, or more involved adjustments. And even the highest generalizations of science consist of mental relations of co-existence and sequence, so co-ordinated as exactly to tally with certain relations of co-existence and sequence that occur externally. A caterpillar, finding its way on to a plant having a certain odour, begins to eat -- has inside of it an organic relation between a particular impression and a particular set of actions, answering to the relation outside of it between scent and nutriment. The sparrow, guided by the more complex correlation of impressions which the colour form, and movements of the caterpillar gave it, and guided by other correlations which measure the position and distance of the caterpillar, adjusts certain correlated muscular movements so as to seize the caterpillar. through a much greater distance is the hawk, hovering above, affected by the relations of shape and motion which the sparrow presents; and the much more complicated and prolonged series of related nervous and muscular changes, gone through in correspondence with the sparrow's changing relations of position, finally succeed when they are precisely adjusted to these changing relations. In the fowler, experience has established a relation between the appearance and flight of a hawk and the destruction of other birds, including game. There is also in him an established relation between those visual impressions answering to a certain distance in space, and the range of his gun. And he has learned, too, what relations of position the sights must bear to a point somewhat in advance of the flying bird, before he can fire with success. Similarly if we go back to the manufacture of the gun. By relations of co-existence between colour, density, and place in the earth, a particular mineral is known as one which yields iron; and the obtainment of iron from it, results when certain correlated acts of ours are adjusted to certain correlated affinities displayed by ironstone, coal, and lime, at a high temperature. If we descend yet a step further, and ask a chemist to explain the explosion of gunpowder, or apply to a mathematician for a theory of projectiles, we still find that special or general relations of co-existence and sequence among properties, motions, spaces, etc., are all they can teach us. And lastly, let it be noted that what we call truth guiding us to successful action and consequent maintenance of life, is simply the accurate correspondence of subjective to objective relations; while error, leading to failure and therefore towards death, is the absence of such accurate correspondence.

If, then, Life, as knowable by us, inclusive of Intelligence in its highest forms, consists in the continuous adjustment of internal relations to external relations, the relative character of our knowledge is necessarily implied. The simplest cognition being the establishment of some connexion between subjective states, answering to some connexion between objective agencies; and each successively more complex cognition being the establishment of some more involved connexion of such states, answering to some more involved connexion of such agencies; it is clear that the process, no matter how far it be carried, can never bring within the reach of Intelligence, either the states themselves or the agencies themselves. Ascertaining which things occur along with which, and what things follow what, supposing it to be pursued exhaustively must still leave us with co-existences and sequences only. If every act of knowing is the formation of a relation in consciousness answering to a relation in the environment, then the relativity of knowledge is self-evident -- becomes indeed a truism. Thinking being relationing, no thought can ever express more than relations.

And here let us note how that to which our intelligence is confined, is that with which alone our intelligence is concerned. The knowledge within our reach is the only knowledge that can be of service to us. This maintenance of a correspondence between internal actions and external act ions, merely requires that the agencies acting upon us shall be known in their co-existences and sequences, and not that they shall be known in themselves. If x and y are two uniformly connected properties in some outer object, while a and b are the effects they produce in our consciousness, then the sole need is that a and b and the relation between them, shall always answer to x and y and the relation between them. It matters nothing to us if a and b are like x and y or not. Could they be identical with them, we should not be one whit the better off; and their total dissimilarity is no disadvantage.

Deep down then in the very nature of Life, the relativity of our knowledge is discernible. The analysis of vital actions in general, leads not only to the conclusion that things in themselves cannot be known to us, but also to the conclusion that knowledge of them, were it possible, would be useless.

§26. There remains the final question -- What must we say concerning that which transcends knowledge? Are we to rest wholly in the consciousness of phenomena? Is the result of inquiry to exclude utterly from our minds everything but the relative? or must we also believe in something beyond the relative?

The answer of pure logic is held to be that by the limits of our intelligence we are rigorously confined within the relative, and that anything transcending the relative can be thought of as a pure negation, or as a non-existence. "The absolute is conceived merely by a negation of conceivability" writes Sir William Hamilton. "The Absolute and the Infinite," says Mr. Mansel, "are thus, like the Inconceivable and the Imperceptible, names indicating, not an object of thought or of consciousness at all, but the mere absence of the conditions under which consciousness is possible." So that since reason cannot warrant us in affirming the positive existence of that which is cognizable only as a negation, we cannot rationally affirm the positive existence of anything beyond phenomena.

Unavoidable as this conclusion seems, it involves, I think, a grave error. If the premiss be granted the inference must be admitted; but the premiss, in the form presented by Sir William Hamilton and Mr. Mansel, is not strictly true. Though, in the foregoing pages, the arguments used by these writers to show that the Absolute is unknowable, have been approvingly quoted; and though these arguments have been enforced by others equally thoroughgoing; yet there remains to be stated a qualification which saves us from the scepticism otherwise necessitated. It is not to be denied that so long as we confine ourselves to the purely logical aspect of the question, the propositions quoted above must be accepted in their entirety; but when we contemplate its more general, or psychological, aspect, we find that these propositions are imperfect statements of the truth: omitting, or rather excluding, as they do, an all-important fact. To speak specifically: -- Besides that definite consciousness of which Logic formulates the laws, there is also an indefinite consciousness which cannot be formulated. Besides complete thoughts, and besides the thoughts which though incomplete admit of completion, there are thoughts which it is impossible to complete; and yet which are still real, in the sense that they are normal affections of the intellect.

Observe, in the first place, that every one of the arguments by which the relativity of our knowledge is demonstrated, distinctly postulates the positive existence of something beyond the relative. To say that we cannot know the Absolute, is, by implication, to affirm that there is an Absolute. In the very denial of our power to learn what the Absolute is, there lies hidden the assumption that it is; and the making of this assumption proves that the Absolute has been present to the mind, not as a nothing but as a something. Similarly with every step in the reasoning by which this doctrine is upheld. The Noumenon, everywhere named as the antithesis to the Phenomenon, is necessarily thought of as an actuality. It is impossible to conceive that our knowledge is a knowledge of Appearances only without at the same time assuming a Reality of which they are appearances; for appearance without reality is unthinkable. Strike out from the argument the terms Unconditioned, Infinite, Absolute, and in place of them write, "negation of conceivability," or "absence of the conditions under which consciousness is possible," and the argument becomes nonsense. To realize in thought any one of the propositions of which the argument consists, the Unconditioned must be represented as positive and not negative. How then can it be a legitimate conclusion from the argument, that our consciousness of it is negative? An argument the very construction of which assigns to a certain term a certain meaning, but which ends in showing that this term has no such meaning, is simply an elaborate suicide. Clearly, then, the very demonstration that a definite consciousness of the Absolute is impossible to us, unavoidably presupposes an indefinite consciousness of it.

Perhaps the best way of showing that we are obliged to form a positive though Vague consciousness of this which transcends distinct consciousness, is to analyze our conception of the antithesis between Relative and Absolute. It is a doctrine called in question by none, that such antinomies of thought as Whole and Part, Equal and Unequal, Singular and Plural, are necessarily conceived as correlatives: the conception of a part is impossible without the conception of a whole; there can be no idea of equality without one of inequality. And it is undeniable that in the same manner, the Relative is itself conceivable as such, only by opposition to the Irrelative or Absolute. Sir William Hamilton, however, in his trenchant (and in most parts unanswerable) criticism on Cousin, contends, in conformity with his position above stated, that one of these correlatives is nothing more than the negation of the other. "Correlatives,' he says, "certainly suggest each other, but correlatives may, or may not, be equally real and positive. In thought contradictories necessarily imply each other, for the knowledge of contradictories is one. But the reality of one contradictory, so far from guaranteeing the reality of the other, is nothing else than its negation. Thus every positive notion (the concept of a thing by what it is) suggests a negative notion (the concept of a thing by what it is not); and the highest positive notion, the notion of the conceivable, is not without its corresponding negative in the notion of the inconceivable. But though these mutually suggest each other, the positive alone is real; the negative is only an abstraction of the other, and in the highest generality, even an abstraction of thought itself." Now the assertion that of such contradictories "the negative is only an abstraction of the other" -- "is nothing else than its negation," -- is not true. In such correlatives as Equal and Unequal, it is obvious enough that the negative concept contains something besides the negation of the positive one; for the things of which equality is denied are not abolished from consciousness by the denial. And the fact overlooked by Sir William Hamilton is, that the like holds even with those correlatives of which the negative is inconceivable, in the strict sense of the word. Take for example the Limited and the Unlimited. Our notion of the Limited is composed, firstly of a consciousness of some kind of being, and secondly of a consciousness of the limits under which it is known. In the antithetical notion of the Unlimited, the consciousness of limits is abolished, but not the consciousness of some kind of being. It is quite true that in the absence of conceived limits, this consciousness ceases to be a concept properly so called; but it is none the less true that it remains as a mode of consciousness. If, in such cases, the negative contradictory were, as alleged, "nothing else" than the negation of the other, and therefore a mere non-entity then it would follow that negative contradictories could be used interchangeably: the Unlimited might be thought of as antithetical to the Divisible; and the Indivisible as antithetical to the Limited. While the fact that they cannot be so used, proves that in consciousness the Unlimited and the Indivisible are qualitatively distinct, and therefore positive or real; since distinction cannot exist between nothings. The error, (naturally fallen into by philosophers intent on demonstrating the limits and conditions of consciousness,) consists in assuming that consciousness contains nothing but limits and conditions; to the entire neglect of that which is limited and conditioned. It is forgotten that there is something which alike forms the raw material of definite thought and remains after the definiteness which thinking gave it has been destroyed. Now all this applies by change of terms to the last and highest of these antinomies -- that between the Relative and the Non-relative. We are conscious of the Relative as existence under conditions and limits. It is impossible that these conditions and limits can be thought of apart from something to which they give the form. The abstraction of these conditions and limits is, by the hypothesis, the abstraction of them only. Consequently there must be a residuary consciousness of something which filled up their outlines. And this indefinite something constitutes our consciousness of the Non-relative or Absolute. Impossible though it is to give to this consciousness any qualitative or quantitative expression whatever, it is not the less certain that it remains with us as a positive and indestructible element of thought.

More manifest still will this truth become when it is observed that our conception of the Relative itself disappears' if our consciousness of the Absolute is a pure negation. It is admitted, or rather it is contended, by the writers I have quoted above, that contradictories can be known only in relation to each other -- that equality, for instance, is unthinkable apart from Inequality; and that thus the Relative can itself be conceived only by opposition to the Non-relative. It is also admitted, or rather contended, that the consciousness of a relation implies a consciousness of both the related terms. If we are required to conceive the relation between the Relative and Non-relative without being conscious of both, "we are in fact" (to quote the words of Mr. Mansel differently applied) "required to compare that of which we are conscious with that of which we are not conscious; the comparison itself being an act of consciousness, and only possible through the consciousness of both its objects." What then becomes of the assertion that "the Absolute is conceived merely by a negation of conceivability," or as "the mere absence of the conditions under which consciousness is possible?" If the Non-relative or Absolute, is present in thought only as a mere negation, then the relation between it and the Relative becomes unthinkable, because one of the terms of the relation is absent from consciousness. And if this relation is unthinkable, then is the Relative itself unthinkable, for want of its antithesis: whence results the disappearance of all thought whatever.

Both Sir William Hamilton and Mr. Mansel do, in other places, distinctly imply that our consciousness of the Absolute, indefinite though it is, is positive. The very passage in which Sir William Hamilton asserts that "the absolute is conceived merely by a negation of conceivability," itself ends with the remark that, "by a wonderful revelation we are thus, in the very consciousness of our inability to conceive aught above the relative and finite, inspired with a belief in the existence of something unconditioned beyond the sphere of all comprehensible reality." The last of these assertions practically admits that which the first denies. By the laws of thought as Sir William Hamilton interprets them, he finds himself forced to the conclusion that our consciousness of the Absolute is a pure negation. He nevertheless finds that there does exist in consciousness an irresistible conviction of the real "existence of something unconditioned." And he gets over the inconsistency by speaking of this conviction as "a wonderful revelation," "a belief" with which we are "inspired:" thus apparently hinting that it is supernaturally at variance with the laws of thought. Mr. Mansel is betrayed into a like inconsistency. When he says that "we are compelled, by the constitution of our minds, to believe in the existence of an Absolute and Infinite Being, -- a belief which appears forced upon us, as the complement of our consciousness of the relative and the finite;" he clearly says by implication that this consciousness is positive, and not negative. He tacitly admits that we are obliged to regard the Absolute as something more than a negation -- that our consciousness of it is not "the mere absence of the conditions under which consciousness is possible."

The supreme importance of this question must be my apology for taxing the reader's attention a little further, in the hope of clearing up the remaining difficulties. The necessarily positive character of our consciousness of the Unconditioned, which, as we have seen, follows from an ultimate law of thought, will be better understood on contemplating the process of thought.

One of the arguments used to prove the relativity of our knowledge, is, that we cannot conceive Space or Time as either limited or unlimited. It is pointed out that when we imagine a limit, there simultaneously arises the consciousness of a space or time beyond the limit. This remoter space or time, though not contemplated as definite, is yet contemplated as real. Though we do not form of it a conception proper, since we do not bring it within bounds, there is yet in our minds the unshaped material of a conception. Similarly with our consciousness of Cause. We are no more able to form a circumscribed idea of Cause, than of Space or Time; and we are consequently obliged to think of the Cause which transcends the limits of our thought as positive though indefinite. As on conceiving any bounded space, there arises a nascent consciousness of space outside the bounds; so, when we think of any definite cause, there arises a nascent consciousness of a cause behind it; and in the one case as in the other, this nascent consciousness is in substance like that which suggests it, though without form. The momentum of thought carries us beyond conditioned existence to unconditioned existence; and this ever persists in us as the body of a thought to which we can give no shape.

Hence our firm belief in objective reality. When we are taught that a piece of matter, regarded by us as existing externally, cannot be really known, but that we can know only certain impressions produced on us, we are yet, by the relativity of thought, compelled to think of these in relation to a cause -- the notion of a real existence which generated these impressions becomes nascent. If it be proved that every notion of a real existence which we can frame, is inconsistent with itself -- that matter, however conceived by us, cannot be matter as it actually is, our conception, though transfigured, is not destroyed: there remains the sense of reality, dissociated as far as possible from those special forms under which it was before represented in thought. Though Philosophy condemns successively each attempted conception of the Absolute -- though in obedience to it we negative, one after another; each idea as it arises; yet, as we cannot expel the entire contents of consciousness, there ever remains behind an element which passes into new shapes. The continual negation of each particular form and limit, simply results in the more or less complete abstraction of all forms and limits; and so ends in an indefinite consciousness of the unformed and unlimited.

And here we come face to face with the ultimate difficulty -- How can there be constituted a consciousness of the unformed and unlimited, when, by its very nature, consciousness is possible only under forms and limits? Though not directly withdrawn by the withdrawal of its conditions, must not the raw material of consciousness be withdrawn by implication? Must it not vanish when the conditions of its existence vanish? That there must be a solution of this difficulty is manifest; since even those who would put it do, as already shown, admit that we have some such consciousness; and the solution appears to be that above shadowed forth. Such consciousness is not, and cannot be, constituted by any single act, but is the product of many mental acts. In each concept there is an element which persists. It is impossible for this element to be absent from consciousness, or for it to be present in consciousness alone. Either alternative involves unconsciousness -- the one from want of the substance; the other from want of the form. But the persistence of this element under successive conditions, necessitates a sense of it as distinguished from the conditions, and independent of them. The sense of a something that is conditioned in every thought cannot be got rid of, because the something cannot be got rid of. How then must the sense of this something be constituted? Evidently by combining successive concepts deprived of their limits and conditions. We form this indefinite thought, as we form many of our definite thoughts, by the coalescence of a series of thoughts. Let me illustrate this. A large complex object, having attributes too numerous to be represented at once, is yet tolerably well conceived by the union of several representations, each standing for part of its attributes. On thinking of a piano, there first rises in imagination its outer appearance, to which are instantly added (though by separate mental acts) the ideas of its remote side and of its solid substance. A complete conception, however, involves the strings, the hammers, the dampers, the pedals; and while successively adding these, the attributes first thought of lapse partially or wholly out of consciousness. Nevertheless, the whole group constitutes a representation of the piano. Now as in this case we form a definite concept of a special existence, by imposing limits and conditions in successive acts; so, in the converse case, by taking away limits and conditions in successive acts, we form an indefinite notion of general existence. By fusing a series of states of consciousness, from each of which, as it arises, the limitations and conditions are abolished, there is produced a consciousness of something unconditioned. To speak more rigorously: -- this consciousness is not the abstract of any one group of thoughts, ideas, or conceptions; but it is the abstract of all thoughts, ideas, or conceptions. That which is common to them all we predicate by the word existence. Dissociated as this becomes from each of its modes by the perpetual change of those modes, it remains as an indefinite consciousness of something constant under all modes -- of being apart from its appearances. The distinction we feel between specialized existences and general existence, is the distinction between that which is changeable in us and that which is unchangeable. The contrast between the Absolute and the Relative in our minds, is really the contrast between that mental element which exists absolutely, and those which exist relatively.

So that this ultimate mental element is at once necessarily indefinite and necessarily indestructible. Our consciousness of the unconditioned being literally the unconditioned consciousness, or raw material of thought to which in thinking we give definite forms, it follows that an ever-present sense of real existence is the basis of our intelligence. As we can in successive mental acts get rid of all particular conditions and replace them by others, but cannot get rid of that undifferentiated substance of consciousness which is conditioned anew in every thought, there ever remains with us a sense of that which exists persistently and independently of conditions. While by the laws of thought we are prevented from forming a conception of absolute existence; we are by the laws of thought prevented from excluding the consciousness of absolute existence: this consciousness being, as we here see, the obverse of self-consciousness. And since the measure of relative validity among our beliefs, is the degree of their persistence in opposition to the efforts made to change them, it follows that this which persists at all times, under all circumstances, has the highest validity of any.

The points in this somewhat too elaborate argument are these: In the very assertion that all knowledge, properly so called, is Relative, there is involved the assertion that there exists a Non-relative. In each step of the argument by which this doctrine is established, the same assumption is made. From the necessity of thinking in relations, it follows that the Relative is itself inconceivable, except as related to a real Non-relative. Unless a real Non-relative or Absolute be postulated, the Relative itself becomes absolute, and so brings the argument to a contradiction. And on watching our thoughts we have seen how impossible it is to get rid of the consciousness of an Actuality lying behind Appearances; and how from this impossibility, results our indestructible belief in that Actuality.