So that as rational metaphysics teaches that man becomes all things by understanding them, this imaginative metaphysics shows that man becomes all things by not understanding them. For when he does not understand, he makes the things out of himself and becomes them by transforming himself into them. — Giambattista Vico, The New Science (Book II, §405)

Your nomination is spot-on: If Bergsonian mathematics exists, it must look something like Laws of Form - simultaneously rigorous and mystical, formal and generative, mathematical and philosophical, accepted and rejected.

a) The scientific intellect cannot measure time; what it measures are simultaneities in space.

b) When we “measure” time, we substitute spatial positions for temporal flow (durée).

c) The intellect, by nature, aims at fixities, “things-made,” rather than processes, or “things-in-the-making.”

d) Duration is the continuous, qualitative, and irreversible flow of becoming, necessarily excluded by the intellect.

e) Duration is not “psychological time.”

f) It is clock-time, that is artificial, conventional, and thus, psychological. It is a spatialized construct useful for science.

g) Science (analysis) is valid only in a universe that endures, and thus presupposes duration even while excluding it.

h) There is a difference in kind, not merely in degree, between space and time: the first cut.

i) Intuition makes the cut: it must become the method by which duration can be grasped directly.

j) To live is to endure: duration is the substance of existence itself, not an added dimension.

Original post

To David Johnson

To JFM

an unsent further response

For it is possible to sum up our conclusions as to pure perception by saying that there is in matter something more than, but not something different from, that which is actually given.

But between this perception of matter and matter itself there is but a difference of degree and not of kind, pure perception standing toward matter in the relation of the part to the whole.

This amounts to saying that matter cannot exercise powers of any kind other than those which we perceive. It has no mysterious virtue; it can conceal none.

The truth is that there is one, and only one, method of refuting materialism: it is to show that matter is precisely that which it appears to be. Thereby we eliminate all virtuality, all hidden power, from matter and establish the phenomena of spirit as an independent reality. But to do this we must leave to matter those qualities which materialists and spiritualists alike strip from it: the latter that they may make of them representations of the spirit, the former that they may regard them only as the accidental garb of space...This, indeed, is the attitude of common sense with regard matter, and for this reason common sense believes in spirit.

We must now add that, as pure perception gives us the whole or at least the essential part of matter (since the rest comes from memory and is super-added to matter), it follows that memory must be, in principle, a power absolutely independent of matter.

The first concerns the office of the brain in perception: we maintain that the brain is an instrument of action, and not of representation.

We become conscious of these mechanisms as they come into play; this consciousness of a whole past of efforts stored up in the present is indeed also a memory, but a memory profoundly different from the first, always bent upon action, seated in the present and looking only to the future. It has retained from the past only the intelligently coordinated movements which represent the accumulated efforts of the past; it recovers those past efforts, not in the memory-images which recall them, but in the definite order and systematic character with which the actual movements take place. In truth it no longer represents our past to us, it acts it; and if it still deserves the name of memory, it is not because it conserves bygone images, but because it prolongs their useful effect into the present moment.

Vital interiority. Life cannot be reduced to mechanical causation or the blind play of natural selection. Beneath the adaptive mechanisms that science studies, there is an interior, creative effort, an élan vital, which generates living forms and whose freedom and inventiveness mechanism presupposes but cannot explain. (JFM summary)

Forms of life. On Earth, the élan vital expresses itself in three divergent tendencies, modes of maintaining and channeling its act of self-creation ( autopoiesis):

Thus we must, consciously or unconsciously, have made use of the law of causality. Moreover, the more sharply the idea of efficient causality is defined in our mind, the more it takes the form of a mechanical causality. And this scheme, in its turn, is the more mathematical according as it expresses a more rigorous necessity. That is why we have only to follow the bent of our mind to become mathematicians. But, on the other hand, this natural mathematics is only the rigid unconscious skeleton beneath our conscious supple habit of linking the same causes to the same effects; and the usual object of this habit is to guide actions inspired by intentions, or, what comes to the same, to direct movements combined with a view to reproducing a pattern. We are born artisans as we are born geometricians, and indeed we are geometricians only because we are artisans. Thus the human intellect, inasmuch as it is fashioned for the needs of human action, is an intellect which proceeds at the same time by intention and by calculation, by adapting means to ends and by thinking out mechanisms of more and more geometrical form. Whether nature be conceived as an immense machine regulated by mathematical laws, or as the realization of a plan, these two ways of regarding it are only the consummation of two tendencies of mind which are complementary to each other, and which have their origin in the same vital necessities.

These fleeting intuitions, which light up their object only at distant intervals, philosophy ought to seize, first to sustain them, then to expand them and so unite them together. The more it advances in this work, the more will it perceive that intuition is mind itself, and, in a certain sense, life itself: the intellect has been cut out of it by a process resembling that which has generated matter. Thus is revealed the unity of the spiritual life. We recognize it only when we place ourselves in intuition in order to go from intuition to the intellect, for from the intellect we shall never pass to intuition...Philosophy introduces us thus into the spiritual life.

Life as a whole, from the initial impulsion that thrust it into the world, will appear as a wave that rises, and which is opposed by the descending movement of matter.

I was indeed very much struck to see how real time, which plays the leading part in any philosophy of evolution, eludes mathematical treatment. Its essence being to flow, not one of its parts is still there when another part comes along.

Things and events happen at certain moments; the judgment which determines the occurence of the thing or the event can only come after them; it therefore has its date. But this date at once fades away, in virtue of the principle deep-rooted in our intellect, that all truth is eternal. If the judgment is true now, it seems to us it must always have been so. (p22)

These conclusions on the subject of duration were,. seemed to me, decisive. Step by step they led me to raise intuition to the level of a philosophical method, “Intuition,” however, is a word whose use caused me some degree of hesitation. Of all the terms which designate a mode of knowing, it is still the most appropriate; and yet it leads to a certain confusion. Because a Schelling, a Schopenhauer and others have already called upon intuition, because they have more or less set up intuition in opposition to intelligence, one might think that I was using the same method. But of course, their intuition was an immediate search for the eternal! Whereas, on the contrary, for me it was a question, above all, of finding true duration. Numerous are the philosophers who have felt how powerless conceptual thought is to reach the core of the mind. Numerous, consequently, are those who have spoken of a supra-intellectual faculty of intuition. But as they believed that the intelligence worked within time, they have concluded that to go beyond the intelligence consisted in getting outside of time. They did not see that intellectualized time is space, that the intelligence works upon the phantom of duration, not on duration itself. that the elimination of time is the habitual, normal, commonplace act of our understanding...to pass from intellection to vision, from the relative to the absolute, is not a question of getting outside of time (we are already there); on the contrary, one must get back into duration and recapture reality in the very mobility which isits essence. -p30

For the concepts which the intelligence furnishes, the intuition simply substitutes one single concept which includes them all and which consequently is always the same, by whatever name it is called: Substance, Ego, Idea, Will....How much more instructive would be a truly intuitive metaphysics, which would follow the undulations of the real! True, it would not embrace in a single sweep the totality of things; but for each thing it would give an explanation which would fit it exactly, and it alone. It would not begin by defining or describing the systematic unity of the world: who knows if the world is actually one? -p31

It is true that philosophy then will demand a new effort for each new problem. No solution will be geometrically deduced from another. No important truth will be achieved by the prolongation of an already acquired truth. We shall have to give up crowding universal science potentially into one principle.

There is, however, a fundamental meaning: to think intuitively is to think in duration. Intelligence starts ordinarily from the immobile, and reconstructs movement as best it can with immobilities in juxtaposition. Intuition starts from movement, posits it, or rather perceives it as reality itself, and sees in immobility only an abstract moment, a snapshot taken by our mind, of a mobility.

no matter what name you give to the “thing itself,” whether you make of it the Substance of Spinoza, the Ego of Fichte, the Absolute of Schelling, the Idea of Hegel, or the Will of Schopenhauer, it will be useless for the word to present itself with its well-defined signification: it will lose it; it will be emptied of all meaning from the moment it is applied to the totality of things. Speaking only of the last of these great “syntheses,” isn’t it evident that a Will is only will on condition that it is set off against what does not will? How then is mind to be set off against matter, if matter is itself will? To place will everywhere is the same as leaving it nowhere, for it is to identify the essence of what I feel within myself—duration, outpouring, continuous creation—with the essence of what I perceive in things, where there is evidently repetition, previsibility, necessity. It makes little difference to me if one says “Everything is mechanism” or “Everything is will”: in either case everything is identical. In both cases, “mechanism” and “will” become synonyms of “being” and consequently synonyms of each other. Therein lies the initial vice of philosophical systems. They think they are telling us something about the absolute by giving it a name. But once again the word can have a definite meaning when it designates a thing; it loses that meaning as soon as you apply it to all things. -p48

Man is essentially a manufacturer. Nature, in denying him ready-made instruments like those the insects have, for example, has given him intelligence, that is to say, the power of inventing and constructing an indefinite number of tools.

And the essential object of society is to insert a certain fixity into universal mobility. Societies are just so many islands consolidated here and there in the ocean of becoming. -p82

As far as I am concerned, I value scientific knowledge and technical competence as much as intuitive vision. I believe that it is of man’s essence to create materially and morally, to fabricate things and to fabricate himself. Homo faber is the definition I propose. Homo sapiens, born of the reflection Homo faber makes on the subject of his fabrication, seems to me to be just as worthy of esteem as long as he resolves by pure intelligence those problems whicqh depend upon it alone. -p84

My initiation into the true philosophical method began the moment I threw overboard verbal solutions, having found in the inner life and important field of experiment. -p89

Some fifty years ago I was very much attached to the philosophy of Spencer. I perceived one fine day that, in it, time served no purpose, did nothing. Nevertheless, I said to myself, time is something. Therefore it acts, What can it be doing? Plain common sense answered: time is what hinders everything from being given at once. It retards, or rather it is retardation. It must therefore, be elaboration. -p93 (emph added)

Introduction to Metaphysics

IV. The difficulties inherent in metaphysics, the antinomies it raises, the contradictions into which it falls, the division into opposing schools and the irreducible oppositions between systems, are due in large part to the fact that we apply to the disinterested knowledge of the real the procedures we use currently with practical utility as the aim.

V. It was bound to fail. This is the impotence, and this alone, pointed out by the skeptical, idealistic and critical doctrines, all those doctrines, in fact, which question our mind’s ability to attain the absolute. But it does not follow from the fact that we fail to reconstitute living reality with concepts that are rigid and ready-made, that we could not grasp it in any other manner.

VI. But the truth is that our mind is able to follow the reverse procedure. It can be installed in the mobile reality, adopt its ceaselessly changing direction, in short, grasp it intuitively. But to do that, it must do itself violence, reverse the direction of the operation by which it ordinarily thinks, continually upsetting its categories, or rather, recasting them. In so doing it will arrive at fluid concepts, capable of following reality in all its windings and of adopting the very movement of the inner life of things.

VII. This reversal has never been practised in a methodical manner; but a careful study of the history of human thought would show that to it we owe the greatest accomplishments in the sciences, as well as whatever living quality there is in metaphysics. The most powerful method of investigation known to the mind, infinitesimal calculus, was born of that very reversal. Modern mathematics is precisely an effort to substitute for the ready-made what is in process of becoming, to follow the growth of magnitudes, to seize movement no longer from outside and in its manifest result, but from within and in its tendency towards change, in short, to adopt the mobile continuity of the pattern of things.

Generally speaking, industry has not troubled enough about the greater or lesser importance of needs to be satisfied. It simply complied with public taste, and manufactured with no other thought than that of selling. Here as elsewhere, we should like to see a central, organizing intelligence, which would co-ordinate industry and agriculture and allot to the machine its proper place, I mean the place where it can best serve humanity.

Man will only rise above earthly things if a powerful equipment supplies him with the requisite fulcrum. He must use matter as a support if he wants to get away from matter. In other words, the mystical summons up the mechanical. This has not been sufficiently realized, because machinery, through a mistake at the points, has been switched off on to a track at the end of which lies exaggerated comfort and luxury for the few, rather than liberation for all. We are struck by the accidental result, we do not see mechanization as it should be, as what it is in essence.

If our organs are natural instruments, our instruments must then be artificial organs. The workman's tool is the continuation of his arm, the tool equipment of humanity is therefore a continuation of its body. Nature, in endowing us with an essentially tool-making intelligence, prepared for us in this way a certain expansion...Hence the tremendous social, political and international problems which are just so many definitions of this gap, and which provoke so many chaotic and ineffectual efforts to fill it. What we need are new reserves of potential energy–moral energy this time. So let us not merely say, as we did above, that the mystical summons up the mechanical. We must add that the body, now larger, calls for a bigger soul, and that mechanism should mean mysticism. .... Machinery will find its true vocation again, it will render services in proportion to its power, only if mankind, which it has bowed still lower to the earth, can succeed, through it, in standing erect and looking heavenwards.