Chapter 11

M. Bergson, if I am rightly informed, came into philosophy through the gateway of mathematics. The old antinomies of the infinite were, I imagine, the irritant that first woke his faculties from their dogmatic slumber. You all remember Zeno's famous paradox, or sophism, as many of our logic books still call it, of Achilles and the tortoise. Give that reptile ever so small an advance and the swift runner Achilles can never overtake him, much less get ahead of him; for if space and time are infinitely divisible (as our intellects tell us they must be), by the time Achilles reaches the tortoise's starting-point, the tortoise has already got ahead of _that_ starting-point, and so on _ad infinitum_, the interval between the pursuer and the pursued growing endlessly minuter, but never becoming wholly obliterated. The common way of showing up the sophism here is by pointing out the ambiguity of the expression 'never can overtake.' What the word 'never' falsely suggests, it is said, is an infinite duration of time; what it really means is the inexhaustible number of the steps of which the overtaking must consist. But if these steps are infinitely short, a finite time will suffice for them; and in point of fact they do rapidly converge, whatever be the original interval or the contrasted speeds, toward infinitesimal shortness. This proportionality of the shortness of the times to that of the spaces required frees us, it is claimed, from the sophism which the word 'never' suggests.

But this criticism misses Zeno's point entirely. Zeno would have been perfectly willing to grant that if the tortoise can be overtaken at all, he can be overtaken in (say) twenty seconds, but he would still have insisted that he can't be overtaken at all. Leave Achilles and the tortoise out of the account altogether, he would have said--they complicate the case unnecessarily. Take any single process of change whatever, take the twenty seconds themselves elapsing. If time be infinitely divisible, and it must be so on intellectualist principles, they simply cannot elapse, their end cannot be reached; for no matter how much of them has already elapsed, before the remainder, however minute, can have wholly elapsed, the earlier half of it must first have elapsed. And this ever re-arising need of making the earlier half elapse _first_ leaves time with always something to do _before_ the last thing is done, so that the last thing never gets done. Expressed in bare numbers, it is like the convergent series 1/2 plus 1/4 plus 1/8..., of which the limit is one. But this limit, simply because it is a limit, stands outside the series, the value of which approaches it indefinitely but never touches it. If in the natural world there were no other way of getting things save by such successive addition of their logically involved fractions, no complete units or whole things would ever come into being, for the fractions' sum would always leave a remainder. But in point of fact nature doesn't make eggs by making first half an egg, then a quarter, then an eighth, etc., and adding them together. She either makes a whole egg at once or none at all, and so of all her other units. It is only in the sphere of change, then, where one phase of a thing must needs come into being before another phase can come that Zeno's paradox gives trouble.

And it gives trouble then only if the succession of steps of change be infinitely divisible. If a bottle had to be emptied by an infinite number of successive decrements, it is mathematically impossible that the emptying should ever positively terminate. In point of fact, however, bottles and coffee-pots empty themselves by a finite number of decrements, each of definite amount. Either a whole drop emerges or nothing emerges from the spout. If all change went thus drop-wise, so to speak, if real time sprouted or grew by units of duration of determinate amount, just as our perceptions of it grow by pulses, there would be no zenonian paradoxes or kantian antinomies to trouble us. All our sensible experiences, as we get them immediately, do thus change by discrete pulses of perception, each of which keeps us saying 'more, more, more,' or 'less, less, less,' as the definite increments or diminutions make themselves felt. The discreteness is still more obvious when, instead of old things changing, they cease, or when altogether new things come. Fechner's term of the 'threshold,' which has played such a part in the psychology of perception, is only one way of naming the quantitative discreteness in the change of all our sensible experiences. They come to us in drops. Time itself comes in drops.

Our ideal decomposition of the drops which are all that we feel into still finer fractions is but an incident in that great transformation of the perceptual order into a conceptual order of which I spoke in my last lecture. It is made in the interest of our rationalizing intellect solely. The times directly _felt_ in the experiences of living subjects have originally no common measure. Let a lump of sugar melt in a glass, to use one of M. Bergson's instances. We feel the time to be long while waiting for the process to end, but who knows how long or how short it feels to the sugar? All _felt_ times coexist and overlap or compenetrate each other thus vaguely, but the artifice of plotting them on a common scale helps us to reduce their aboriginal confusion, and it helps us still more to plot, against the same scale, the successive possible steps into which nature's various changes may be resolved, either sensibly or conceivably. We thus straighten out the aboriginal privacy and vagueness, and can date things publicly, as it were, and by each other. The notion of one objective and 'evenly flowing' time, cut into numbered instants, applies itself as a common measure to all the steps and phases, no matter how many, into which we cut the processes of nature. They are now definitely contemporary, or later or earlier one than another, and we can handle them mathematically, as we say, and far better, practically as well as theoretically, for having thus correlated them one to one with each other on the common schematic or conceptual time-scale.

Motion, to take a good example, is originally a turbid sensation, of which the native shape is perhaps best preserved in the phenomenon of vertigo. In vertigo we feel that movement _is_, and is more or less violent or rapid, more or less in this direction or that, more or less alarming or sickening. But a man subject to vertigo may gradually learn to co-ordinate his felt motion with his real position and that of other things, and intellectualize it enough to succeed at last in walking without staggering. The mathematical mind similarly organizes motion in its way, putting it into a logical definition: motion is now conceived as 'the occupancy of serially successive points of space at serially successive instants of time.' With such a definition we escape wholly from the turbid privacy of sense. But do we not also escape from sense-reality altogether? Whatever motion really may be, it surely is not static; but the definition we have gained is of the absolutely static. It gives a set of one-to-one relations between space-points and time-points, which relations themselves are as fixed as the points are. It gives _positions_ assignable ad infinitum, but how the body gets from one position to another it omits to mention. The body gets there by moving, of course; but the conceived positions, however numerously multiplied, contain no element of movement, so Zeno, using nothing but them in his discussion, has no alternative but to say that our intellect repudiates motion as a non-reality. Intellectualism here does what I said it does--it makes experience less instead of more intelligible.

We of course need a stable scheme of concepts, stably related with one another, to lay hold of our experiences and to co-ordinate them withal. When an experience comes with sufficient saliency to stand out, we keep the thought of it for future use, and store it in our conceptual system. What does not of itself stand out, we learn to _cut_ out; so the system grows completer, and new reality, as it comes, gets named after and conceptually strung upon this or that element of it which we have already established. The immutability of such an abstract system is its great practical merit; the same identical terms and relations in it can always be recovered and referred to--change itself is just such an unalterable concept. But all these abstract concepts are but as flowers gathered, they are only moments dipped out from the stream of time, snap-shots taken, as by a kinetoscopic camera, at a life that in its original coming is continuous. Useful as they are as samples of the garden, or to re-enter the stream with, or to insert in our revolving lantern, they have no value but these practical values. You cannot explain by them what makes any single phenomenon be or go--you merely dot out the path of appearances which it traverses. For you cannot make continuous being out of discontinuities, and your concepts are discontinuous. The stages into which you analyze a change are _states_, the change itself goes on between them. It lies along their intervals, inhabits what your definition fails to gather up, and thus eludes conceptual explanation altogether.

'When the mathematician,' Bergson writes, 'calculates the state of a system at the end of a time _t_, nothing need prevent him from supposing that betweenwhiles the universe vanishes, in order suddenly to appear again at the due moment in the new configuration. It is only the _t_-th moment that counts--that which flows throughout the intervals, namely real time, plays no part in his calculation.... In short, the world on which the mathematician operates is a world which dies and is born anew at every instant, like the world which Descartes thought of when he spoke of a continued creation.' To know adequately what really _happens_ we ought, Bergson insists, to see into the intervals, but the mathematician sees only their extremities. He fixes only a few results, he dots a curve and then interpolates, he substitutes a tracing for a reality.

This being so undeniably the case, the history of the way in which philosophy has dealt with it is curious. The ruling tradition in philosophy has always been the platonic and aristotelian belief that fixity is a nobler and worthier thing than change. Reality must be one and unalterable. Concepts, being themselves fixities, agree best with this fixed nature of truth, so that for any knowledge of ours to be quite true it must be knowledge by universal concepts rather than by particular experiences, for these notoriously are mutable and corruptible. This is the tradition known as rationalism in philosophy, and what I have called intellectualism is only the extreme application of it. In spite of sceptics and empiricists, in spite of Protagoras, Hume, and James Mill, rationalism has never been seriously questioned, for its sharpest critics have always had a tender place in their hearts for it, and have obeyed some of its mandates. They have not been consistent; they have played fast and loose with the enemy; and Bergson alone has been radical.

To show what I mean by this, let me contrast his procedure with that of some of the transcendentalist philosophers whom I have lately mentioned. Coming after Kant, these pique themselves on being 'critical,' on building in fact upon Kant's 'critique' of pure reason. What that critique professed to establish was this, that concepts do not apprehend reality, but only such appearances as our senses feed out to them. They give immutable intellectual forms to these appearances, it is true, but the reality _an sich_ from which in ultimate resort the sense-appearances have to come remains forever unintelligible to our intellect. Take motion, for example. Sensibly, motion comes in drops, waves, or pulses; either some actual amount of it, or none, being apprehended. This amount is the datum or _gabe_ which reality feeds out to our intellectual faculty; but our intellect makes of it a task or _aufgabe_--this pun is one of the most memorable of Kant's formulas--and insists that in every pulse of it an infinite number of successive minor pulses shall be ascertainable. These minor pulses _we_ can indeed _go on_ to ascertain or to compute indefinitely if we have patience; but it would contradict the definition of an infinite number to suppose the endless series of them to have actually counted _themselves_ out piecemeal. Zeno made this manifest; so the infinity which our intellect requires of the sense-datum is thus a future and potential rather than a past and actual infinity of structure. The datum after it has made itself must be decompos_able_ ad infinitum by our conception, but of the steps by which that structure actually got composed we know nothing. Our intellect casts, in short, no ray of light on the processes by which experiences _get made_.

Kant's monistic successors have in general found the data of immediate experience even more self-contradictory, when intellectually treated, than Kant did. Not only the character of infinity involved in the relation of various empirical data to their 'conditions,' but the very notion that empirical things should be related to one another at all, has seemed to them, when the intellectualistic fit was upon them, full of paradox and contradiction. We saw in a former lecture numerous instances of this from Hegel, Bradley, Royce, and others. We saw also where the solution of such an intolerable state of things was sought for by these authors. Whereas Kant had placed it outside of and _before_ our experience, in the _dinge an sich_ which are the causes of the latter, his monistic successors all look for it either _after_ experience, as its absolute completion, or else consider it to be even now implicit within experience as its ideal signification. Kant and his successors look, in short, in diametrically opposite directions. Do not be misled by Kant's admission of theism into his system. His God is the ordinary dualistic God of Christianity, to whom his philosophy simply opens the door; he has nothing whatsoever in common with the 'absolute spirit' set up by his successors. So far as this absolute spirit is logically derived from Kant, it is not from his God, but from entirely different elements of his philosophy. First from his notion that an unconditioned totality of the conditions of any experience must be assignable; and then from his other notion that the presence of some witness, or ego of apperception, is the most universal of all the conditions in question. The post-kantians make of the witness-condition what is called a concrete universal, an individualized all-witness or world-self, which shall imply in its rational constitution each and all of the other conditions put together, and therefore necessitate each and all of the conditioned experiences.

Abridgments like this of other men's opinions are very unsatisfactory, they always work injustice; but in this case those of you who are familiar with the literature will see immediately what I have in mind; and to the others, if there be any here, it will suffice to say that what I am trying so pedantically to point out is only the fact that monistic idealists after Kant have invariably sought relief from the supposed contradictions of our world of sense by looking forward toward an _ens rationis_ conceived as its integration or logical completion, while he looked backward toward non-rational _dinge an sich_ conceived as its cause. Pluralistic empiricists, on the other hand, have remained in the world of sense, either naïvely and because they overlooked the intellectualistic contradictions, or because, not able to ignore them, they thought they could refute them by a superior use of the same intellectualistic logic. Thus it is that John Mill pretends to refute the Achilles-tortoise fallacy.

The important point to notice here is the intellectualist logic. Both sides treat it as authoritative, but they do so capriciously: the absolutists smashing the world of sense by its means, the empiricists smashing the absolute--for the absolute, they say, is the quintessence of all logical contradictions. Neither side attains consistency. The Hegelians have to invoke a higher logic to supersede the purely destructive efforts of their first logic. The empiricists use their logic against the absolute, but refuse to use it against finite experience. Each party uses it or drops it to suit the vision it has faith in, but neither impugns in principle its general theoretic authority.

Bergson alone challenges its theoretic authority in principle. He alone denies that mere conceptual logic can tell us what is impossible or possible in the world of being or fact; and he does so for reasons which at the same time that they rule logic out from lordship over the whole of life, establish a vast and definite sphere of influence where its sovereignty is indisputable. Bergson's own text, felicitous as it is, is too intricate for quotation, so I must use my own inferior words in explaining what I mean by saying this.

In the first place, logic, giving primarily the relations between concepts as such, and the relations between natural facts only secondarily or so far as the facts have been already identified with concepts and defined by them, must of course stand or fall with the conceptual method. But the conceptual method is a transformation which the flux of life undergoes at our hands in the interests of practice essentially and only subordinately in the interests of theory. We live forward, we understand backward, said a danish writer; and to understand life by concepts is to arrest its movement, cutting it up into bits as if with scissors, and immobilizing these in our logical herbarium where, comparing them as dried specimens, we can ascertain which of them statically includes or excludes which other. This treatment supposes life to have already accomplished itself, for the concepts, being so many views taken after the fact, are retrospective and post mortem. Nevertheless we can draw conclusions from them and project them into the future. We cannot learn from them how life made itself go, or how it will make itself go; but, on the supposition that its ways of making itself go are unchanging, we can calculate what positions of imagined arrest it will exhibit hereafter under given conditions. We can compute, for instance, at what point Achilles will be, and where the tortoise will be, at the end of the twentieth minute. Achilles may then be at a point far ahead; but the full detail of how he will have managed practically to get there our logic never gives us--we have seen, indeed, that it finds that its results contradict the facts of nature. The computations which the other sciences make differ in no respect from those of mathematics. The concepts used are all of them dots through which, by interpolation or extrapolation, curves are drawn, while along the curves other dots are found as consequences. The latest refinements of logic dispense with the curves altogether, and deal solely with the dots and their correspondences each to each in various series. The authors of these recent improvements tell us expressly that their aim is to abolish the last vestiges of intuition, _videlicet_ of concrete reality, from the field of reasoning, which then will operate literally on mental dots or bare abstract units of discourse, and on the ways in which they may be strung in naked series.

This is all very esoteric, and my own understanding of it is most likely misunderstanding. So I speak here only by way of brief reminder to those who know. For the rest of us it is enough to recognize this fact, that altho by means of concepts cut out from the sensible flux of the past, we can re-descend upon the future flux and, making another cut, say what particular thing is likely to be found there; and that altho in this sense concepts give us knowledge, and may be said to have some theoretic value (especially when the particular thing foretold is one in which we take no present practical interest); yet in the deeper sense of giving _insight_ they have no theoretic value, for they quite fail to connect us with the inner life of the flux, or with the causes that govern its direction. Instead of being interpreters of reality, concepts negate the inwardness of reality altogether. They make the whole notion of a causal influence between finite things incomprehensible. No real activities and indeed no real connexions of any kind can obtain if we follow the conceptual logic; for to be distinguishable, according to what I call intellectualism, is to be incapable of connexion. The work begun by Zeno, and continued by Hume, Kant, Herbart, Hegel, and Bradley, does not stop till sensible reality lies entirely disintegrated at the feet of 'reason.'

Of the 'absolute' reality which reason proposes to substitute for sensible reality I shall have more to say presently. Meanwhile you see what Professor Bergson means by insisting that the function of the intellect is practical rather than theoretical. Sensible reality is too concrete to be entirely manageable--look at the narrow range of it which is all that any animal, living in it exclusively as he does, is able to compass. To get from one point in it to another we have to plough or wade through the whole intolerable interval. No detail is spared us; it is as bad as the barbed-wire complications at Port Arthur, and we grow old and die in the process. But with our faculty of abstracting and fixing concepts we are there in a second, almost as if we controlled a fourth dimension, skipping the intermediaries as by a divine winged power, and getting at the exact point we require without entanglement with any context. What we do in fact is to _harness up_ reality in our conceptual systems in order to drive it the better. This process is practical because all the termini to which we drive are _particular_ termini, even when they are facts of the mental order. But the sciences in which the conceptual method chiefly celebrates its triumphs are those of space and matter, where the transformations of external things are dealt with. To deal with moral facts conceptually, we have first to transform them, substitute brain-diagrams or physical metaphors, treat ideas as atoms, interests as mechanical forces, our conscious 'selves' as 'streams,' and the like. Paradoxical effect! as Bergson well remarks, if our intellectual life were not practical but destined to reveal the inner natures. One would then suppose that it would find itself most at home in the domain of its own intellectual realities. But it is precisely there that it finds itself at the end of its tether. We know the inner movements of our spirit only perceptually. We feel them live in us, but can give no distinct account of their elements, nor definitely predict their future; while things that lie along the world of space, things of the sort that we literally _handle_, are what our intellects cope with most successfully. Does not this confirm us in the view that the original and still surviving function of our intellectual life is to guide us in the practical adaptation of our expectancies and activities?