For the sake of clarity and before really entering upon our general philosophical explanation, we shall bring the whole controversy to bear upon one precise example. We shall study one particular scientific concept possessed, in our estimation, of its full philosophical perspective, and hence interpretable from the standpoint of animism, realism, positivism, rationalism, complex rationalism and dialectical rationalism, by turns. We shall clearly explain the last two terms on the basis of the example selected. Moreover, complex rationalism and dialectical rationalism can be more briefly united under the designation of surrationalism, which we have already had occasion to outline briefly elsewhere. 
1 Cf. Article, Inquisitions, I, June, 1936.
We shall show that the philosophical evolution of a special piece of scientific knowledge is a movement through all these doctrines in the order indicated.
Obviously all scientific concepts have not arrived at the same stage of maturity; many remain involved with a more or less naïve realism; many are still defined with the arrogant humility of positivism; examined in its elements the philosophy of the scientific mind cannot, therefore, be a homogeneous philosophy. If philosophical discussions concerning science remain confused the reason is that a general answer is wanted just when we are beclouded by a particular piece of behavior. We say that the scientist is a realist, enumerating cases in which he is still a realist. We say that he is a positivist, choosing sciences in which he is still positivist. We say that the mathematician is a rationalist retaining thoughts whereby he is still Kantian.
The already’s are, of course, as unfaithful to philosophic truth as the still’s. Thus epistemologists say that the physicist is a rationalist, enumerating cases where he is already a rationalist—where he deduces certain experiments from prior laws; others say that the sociologist is a positivist, selecting the few examples where he is already a positivistwhere he puts values aside in order to confine himself to facts. Adventurous philosophers—an example will immediately occur to the readermust make the same admission: all they have to legitimatize their surrationalist doctrines are a very few cases where science in its most recent, and therefore least assured forms, is already dialectical. So the surrationalists themselves must realize that the greater part of scientific thought has remained in stages of its evolution which are philosophically primitive, and that they must expect to be the victims of a crushing controversy. Everything puts them in the wrong: everyday life, common sense, immediate cognition, technology; even whole sciences, incontestable sciences like biology into which rationalism cannot really sink its teethalthough certain themes of biological science could receive a rapid development as soon as formal causality, so misconstrued and lightly rejected by the realists, could be studied in a new philosophical spirit.
In the face of so many proofs adduced by the realists and the
positivists, the surrationalist is easily subdued. But, having made this gesture of humility, he can make an offensive comeback: the fact is that there does exist a multiplicity of philosophical explanations of science, notwithstanding the objection that a realistic science ought not to raise any metaphysical problems. The evolution of differing epistemologies is another established fact: the theory of energy entirely altered its character at the beginning of the present century. Regardless of what the particular problem is, the direction of epistemological evolution is clear and constant: the evolution of a particular piece of knowledge moves towards rational coherence. As soon as even two properties of an object arc known, they immediately get to be related. More advanced knowledge begets an exuberant growth of coordinated reasoning. However close you stay to realism, the merest move towards setting things in order introduces rational factors; once you go further than that into scientific thinking, you find that theories play a growing role. At the actual spearhead of science, it is theories alone which probe forward to discover the unknown characteristics of reality.
There is no end to the dispute about moral progress, social progress, poetic progress or the progress of happiness, but there is one form of progress which is beyond argument and that is scientific progress, as soon as it comes to be judged in the hierarchy of knowledge and in its specifically intellectual aspects. We are therefore going to take the direction of this progress as the axis of our philosophic study and if, on the abscissa of its development, philosophical systems place themselves regularly in an order constant for all notions, an order which moves from animism to surrationalism (via realism, positivism and simple rationalism) we shall be somewhat justified in speaking of a philosophical progress of scientific notions.
Let us dwell for a moment upon this notion of philosophic progress. It is a notion which has little meaning in pure philosophy. It would never occur to a philosopher to say that Leibnitz was an advance upon Descartes, or that Kant was an advance upon Plato. But the direction of the philosophical evolution of scientific notions is so clear that one must conclude that scientific knowledge orders thought, that science orders philosophy
itself. Scientific thought therefore furnishes a principal for the classification of philosophies and for the study of the progress of reason.
The scientific concept upon which we wish to base our demonstration of the philosophic maturation of scientific thought is the concept of mass. We have already used this concept in our books La Valeur inductive de la Relativité and La Formation de 1'esprit scientifique to show active conceptualization contemporaneous with the change in definition of a concept. But we did not then have the opportunity to sketch the entire range of conceptualization. Because of the fact that the concept of mass, which has already been absorbed into the complex rationalism of relativity, has just been endued [sic] (by the mechanics of Dirac) with a precise and curious dialectic, it reveals itself to our eyes in complete philosophical perspective. The following are the five levels of the concept of mass, five levels upon which scientific philosophies are established which are different and quite evidently ordered and progressive.
In its earliest form, the notion of mass corresponds to a rough quantitative appreciationgreedy, as it were, for reality. Mass is appreciated with the eyes. For a greedy child the biggest fruit is the best, the one which speaks most clearly to his desire and which is the most substantial object of that desire. The notion of mass concretizes the very desire to eat.
The first contradiction then constitutes, as it always does, the first piece of knowledge. It is acquired through the contradiction between size and weight. An empty shell contradicts greed. From this disappointment evaluated knowledge comes into being, knowledge of the sort the fabulist takes to symbolize the experience of “old folks.” With a piece of wealth in the hollow of the hand, comes the understanding that the biggest piece is not necessarily the most valuable. A perspective of intensities suddenly comes to supplement the first prospects of quantity. At once the notion of mass interiorizes itself. It becomes synonymous with
profound wealth, intimate wealth, a concentration of goods. It then becomes the object of strange evaluations wherein animistic dreams of the greatest variety get free rein. At this stage the notion of mass is an obstacle-concept. The concept blocks knowledge instead of summarizing it.
It may be objected that we are starting our enquiry too low with a parody of scientific knowledge, thus postulating impediments which would hardly stop a reflective mind. We shall be glad to abandon this level of investigation, on the understanding, however, that no conviction be suffered to come and bask later on at this primitive hearth, and that no one permit himself to make any subsequent metaphorical use of the notion of mass in sciences where there is further danger of being seduced by this primitive allurement. Is it not striking, for example, that certain psychologists speak of mass or load of an activity as if this were a clear concept. No doubt they realize perfectly well what is confusing about this. They say themselves that it is a simple analogy. But this same psychological analogy has as its referent the animistic concept of mass. So it strengthens the obstacle-concept by a usage that has deceptive clarity. We can give immediate proof of this as follows: when a psychologist speaks of emotional overload he is always speaking of a more or less abundant mass. It would be absurd to speak of a little mass or a small stress of emotions. And, of course, one never does speak of it. Faced with an unconscious, inert, or indifferent patient, the psychiatrist says that this patient is suffering from reduced affectivity. Surreptitiously, as it is in the process of decreasing, the psychiatrist generally abandons his concept of affective mass or affective load. The only load is an overload. The concept is used more of bigness than of smallness. This is a strange way of measuring, in which increase alone counts.
From the dynamic point of view, the animistic concept of mass is as confused as it is from the static point of view. For homo faber mass is always a mace, and a mace is an instrument of the power of the will, which is as much as to say that its function is not easy to analyze. Correlatively, common sense neglects the mass of small things, of "insignificant" things. To sum up, mass is only a quantity if it is fairly big. Primitively, it is not, therefore, a concept of
general applicability, as a concept would be that was formed within a rationalist philosophy.
If we were to develop these ideas further in the direction of psychoanalysis of objective knowledge by systematically examining the early usages of the notion of mass, we would understand better how the pre-scientific mind came to postulate the concept of weightless bodies by renouncing too hastily the law of weight as a generalization. This would be an example of premature dialectic, working ill-advisedly upon things instead of working upon axioms. We consider this as an argument in favor of placing dialectical philosophy outside of rationalism, as a more supple form of rationalism. The use of a dialectic at the level of realism is always uncertain and provisional.
Whatever the value of this metaphysical digression may be, we have said enough to decry imprecise conceptual forms, such as the concept of mass in its primitive form. A mind which accepts a concept of this nature cannot arrive at scientific culture. Explicit declaration of its analogical character hardly suffices to counteract the danger of this usage. Animism quickly exceeds the bounds of definition and reintegrates special convictions in the mind. Moreover, there is a very curious symptom which one cannot reflect upon too much: that is the speed with which an animistic concept is grasped. A word or two is enough to teach what an emotional load is, and, in our opinion, this is a bad sign. As far as a theoretical knowledge of reality is concerned (a knowledge, that is to say, which exceeds the bounds of simple description, leaving arithmetic and geometry aside) everything which is easy to teach is inaccurate. We shall have occasion to return to this educational paradox. For the moment all we want to do is to show the total inaccuracy of the first notion about mass. In our opinion there is an error which needs to be corrected in connection with any scientific notion whatever. Before engaging in any objective knowledge at all, the mind must be psychoanalyzed not only in general but also at the level of all particular notions. As a scientific notion is very rarely psychoanalyzed in all its usages, and one must always be afraid of the contamination of one usage by another, we shall always and in all scientific concepts have to show the meanings which have not been psychoanalyzed. In a
subsequent chapter we shall come back to this plurality of meanings attached to one and the same concept and we shall find in it grounds for the dispersed scientific philosophy which we are defending in this work.
The second level at which the notion of mass can be studied correlates with prudent empirical usage and precise objective determination. The concept then comes to be associated with the use of scales. It derives immediate benefit from the objectivity of an instrument, even though a noteworthy lapse of time can be invoked in which the instrument precedes its own theory. In really active departments of science, nowadays, where the theory precedes the instrument, this is no longer true, and as a result the instrument of physics is a realized, concretized theory, rational in essence. As far as the old conceptualization of mass goes, scales were obviously used before the theory of the lever was known. So, directly, without thinking, as it were, the concept of mass presented itself as a substitute for a primary experience which was decisive and clear, simple and infallible. We may further remark that, even in cases where this concept functioned in a "composite" way, it was not thought out in a composite way: thus, in the case of the Roman scales where the comparison of weights was made by the intervention of an apparatus composed of a weight and of the arm of a lever, this composite operation was not one of which the operator was effectively aware: In other words scales behavior takes a form just as simple as basket behavior, as studied by Pierre Janet to characterize one of the first forms of human intelligence. This scales behavior runs through the ages, handed down in all its simplicity like a fundamental experience. It is nothing but a particular case of that simple use of a complicated machine of which, of course, countless more striking examples could be found in our own day, where the most complicated machine is simply run with a set of badly made, irrationally linked empirical concepts, which are assembled, however, in a manner which is pragmatically sound.
To any given, simple, positive concept; to any simple, positive usage of an instrument (even a theoretically complicated one)
there corresponds an empirical, sound, clear, positive, immovable thought. One is pleased to imagine that experience of this sort is a necessary and sufficient reference wherewith to legitimatize all theory. To weigh is to think. To think is to weigh. Philosophers are never tired of repeating the aphorism of Lord Kelvin who used to claim that he never went beyond the physics of the scales or the arithmetic of the shield. And in this way an empirical thought, bound up with such a peremptory simple experience, comes to be called realistic thinking.
Even in a very advanced science realistic behavior persists. Regression to realistic behavior appears even in a practice totally enlisted into the service of a theory. Such realistic ways of behaving reassert themselves because the rationalizing theorist needs to be understood by the simple experimenter, because he wants to talk faster, which in turn is why he reverts to the animist origins of language, being unafraid of the danger of simplifying thought, all because he is, in fact, a realist in ordinary, everyday life. The result is that rational values are late, ephemeral and rareor, as M. Duprée would say, precarious like all high values. In the realm of the mind too, bad money drives out good money, realism drives out rationalism. But an epistemologist who studies the ferments of scientific thought should always bring out the dynamic meaning of the discovery. We must therefore go on to emphasize the rational aspect which the concept of mass assumes.
This third aspect takes on its full clarity at the end of the seventeenth century when rational mechanics comes into existence with Newton. It is the period of notional solidarity. A correlated use of notions follows the simple and absolute use of a notion. The notion of mass defines itself within a body of notions and not merely as a primitive element of direct and immediate experience. With Newton mass will be defined as force times acceleration. Force, acceleration, mass establish themselves correlatively in a relationship which is clearly rational since it is perfectly analyzed by the rational laws of arithmetic.
From the realist point of view, the three notions are as diverse as they can be. To join them in one and the same formula would
seem to be a more or less factitious procedure which cannot be qualified as realistic in all its proceedings. Indeed, why should we grant to the realist the right to a sort of eclecticism of the realistic function? Why shouldn't we oblige him to answer clearly the following question: "Of force, mass and acceleration which is real?" And if he answers as he is wont to do, "Everything is real," are we to accept a method of discussion which wipes out all philosophic differences, all precise questions, by one vague principle?
In our estimation, as soon as one has defined the three notions of force, mass and acceleration in correlation, one is suddenly a very long way from the fundamental principles of realism since any one of these notions can be evaluated by substitutions which introduce different realistic orders. Furthermore, by the very fact of correlation, one can deduce one of these notionsit doesn't matter whichfrom the two others.
In particular, the idea of mass, which is so clearly realist in its first form, is in some way refined by the passage, via Newton's mechanics, from its static to its dynamic aspect. Before Newton one studied mass in its being, as a quantity of matter. After Newton one studies it in a becoming of phenomena, as a coefficient of becoming. Moreover, we may note in passing how very curious it is that the need to understand becoming is what rationalizes the realism of being. In other words, rationalist values are really developing in the direction of philosophical complication. Even as first drafted, rationalism makes surrationalism predictable. Reason is in no way a faculty of simplification. It is a faculty which clarifies itself by enriching itself. It develops toward growing complexity, and we shall see this more clearly as we get to the following epistemological stages of the notion of mass.
In any case, to interpret in the realistic sense the correlation of the three notions of force, mass and acceleration, one must pass from the realism of things to the realism of laws. In other words, one must already acknowledge two orders of reality. Moreover, we shall not let the realist get away with so convenient a partition. He will have to answer our incessant objections by realizing more and more varied types of laws. Very soon the beautiful simplicity of realism will vanish, it will be scattered in all directions, in all its notions, without ever being able to describe
the hierarchy of levels by means of its own principles. So why not designate these levels of reality and their hierarchy in terms of the divisioning and hierarchizing principles, that is to say in terms of rational principles?
This methodological remark needs stressing. We must realize that, once the fundamental relationship of dynamics has been established, mechanics really comes to be rational from top to bottom. A special mathematics allies itself with experimentation and rationalizes it; rational mechanics rests upon apodictic values; it allows formal deductions; it opens onto an indefinite field of abstraction; it expresses itself in the most diverse symbolic equations. With Lagrange, with Poisson, with Hamilton "mechanical forms" of a more and more general character are introduced, in which mass is no more than an instant of the rational construct. Rational mechanics is to the mechanical phenomenon exactly what pure geometry is to phenomenal description. Rational mechanics swiftly conquers all the functions of a Kantian a priori. The rational mechanics of Newton is a scientific doctrine already provided with a Kantian philosophical character. The metaphysics of Kant was learned from the mechanics of Newton, and, reciprocally, one can explain Newtonian mechanics as rationalist information. It satisfies the mind independently of the verifications of experience. If experience should happen to contradict it, to elicit corrections, then a modification of mental principles would become necessary. An enlarged rationalism cannot be satisfied by a partial rectification. Everything which rectifies reason reorganizes it. Let us proceed to show, therefore, how the kaleidoscope of multiple philosophies has reorganized the system of "natural enlightenment".
Newtonian rationalism directs all mathematical physics in the nineteenth century. The elements which it has selected as fundamental: absolute space, absolute time and absolute mass remain, in all constructions, simple, separate elements always recognizable as such. They become basic systems of measurement which serve to measure everything like the centimeter-gram-second system. These elements correspond to what one might call notional atoms;
to pose an analytical question about them would make no sense. They are the a priori of metric philosophy. Everything which can be measured must and can rest upon these metric bases.
But now, with the era of relativity, there comes an epoch in which rationalism, essentially closed within Newtonian and Kantian concepts, is about to open. Let us observe how this opening takes place with respect to the notion of mass now under consideration.
The opening is made, so to speak, onto the interior of the notion. It becomes apparent that the notion of mass has an internal functional structure, whereas previously all functions of the notion of mass were somehow external, since they were only to be found in composition with other simple notions. The notion of mass which we were just characterizing as a notional atom, becomes susceptible of analysis. For the first time a notional atom can be decomposed, so that we arrive at the metaphysical paradox that an element can be complex. The corollary is that the notion of mass is simple only as a first approximation. Relativity discovers that the mass which has been posited up to now as being by definition independent from speed, as being an absolute in time and space, as being a just basis for a system of absolute unities, is, as a matter of fact, a complicated function of speed. The mass of an object is therefore relative to the displacement of the object. It is useless to expect to be able to define a mass in the state of rest which would properly pertain to this object. Absolute rest has no meaning, nor has the notion of absolute mass. It is as impossible to escape from relativity with respect to mass as it is to escape from it with respect to space-time.
This internal complication of the notion of mass is accompanied by noticeable complications in what may be called the external usage: mass does not behave in the same way with respect to tangential acceleration as it does with respect to normal acceleration. It is therefore impossible to define it as simply as Newtonian dynamics did. There is a further notional complication: in relativist physics mass is no longer different in kind from energy.
In short the simple notion makes way for a complex notion without, moreover, abrogating its role as an element. Mass re-
mains a basic notion and this basic notion is complex. In certain cases only can the complex notion be simplified. It simplifies itself in practical application by abandoning certain delicate refinements, by subduing certain subtle variations. But outside of the problem of practical application and hence at the level of rational, a priori, constructions, the number of internal functions of the notion increases. This is as much as to say that upon a particular notion, upon an elementary notion, rationalism multiplies itself, fragments itself, pluralizes itself. According to the degree of accuracy, the element upon which reason works gets to be more or less complex. Traditional rationalism is profoundly convulsed by this multiple usage of elementary notions. Bodies of approximation, bodies of explanation, and bodies of rationalization come into being—the three expressions being cognates. It is to be understood that these bodies are taken in the same sense as that of the corpus which fixes the organization of a private law. Rationalism as it multiplies becomes conditional. It is touched by relativity: an organization is rational relative to a body of notions. There is no absolute reason. Rationalism is functional. It is multifarious and living.
Let us then resume our battle with the realist. Will he admit defeat? He always has the option to extend his definition of reality. Just a moment ago we had him admitting, under the stress of argument, that there was a realism of laws above the realism of things and of facts. He is now in the process of arranging this realism of laws in series: he will distinguish between a reality of the general, simple law and the reality of a more complicated law; he will confine himself to a realism of degrees of approximation, to a realism of orders of greatness. But as, by degrees, this hierarchy extends itself, one can see that it derogates from the essential philosophic function of realism for which data are data without special distinction. indeed the most evident function of data is precisely the fact that they reject all special distinction.
But the realist who makes a hierarchy of reality in this way actually is making a reality of his own defeat, because it was certainly not under the inspiration of realism that science brought to light the internal structure of its basic notions. There is only
one way to bring about the advance of science, and that is to give the lie to science as already constituted, to change its constitution, in other words. The realist is not in a good position to do this because, apparently, realism is a philosophy whose adherents are always right. It is a philosophy which assimilates everything or at least which absorbs everything. It does not constitute itself because it believes itself to be already constituted, a fortiori it never changes its constitution. Realism is a philosophy which never becomes involved, whereas rationalism always becomes involved and stakes its entire being on every experiment. But, there again, success is on the side of the greatest risk. Certainly the whole hierarchy which we see establishing itself among notions is the work of the theoretical, reorganizational effort undertaken by scientific thought. The hierarchy of notions represents a progressive extension of the domain of rationality, or rather the ordered constitution of different domains of rationality, each of them specified by subtle associated functions. Nor is any one of these extensions the result of a realistic study of phenomena. They are all noumenal in character. Initially they all represent noumena in search of their phenomenon. Reason, therefore, is certainly an autonomous activity which tends to fulfil itself.
But contemporary rationalism does not only enrich itself by covert self-multiplication, by complication of basic notions, it is also animated by a dialectic which is, to a certain degree, external, a dialectic which realism is powerless to describe, and, naturally, even more powerless to invent. Here, too, the concept of mass provides us with a lucid example. We shall go on to show the new philosophical light in which mass presents itself in Dirac's mechanics. We shall thus have one exact example of what we propose to call an element of dialectical surrationalism which constitutes the fifth level of dispersed philosophy.
The mechanics of Dirac arose, as everyone knows, out of a concept of the phenomenon of propagation which was about as general and as total as it could be. The immediate question: "Propagation of what?" simply gives into naive, urgent realism which must ever be setting the object ahead of its phenomena. But in
fact in mathematical organization, you have to prepare the domain of definition before you can define, just as in laboratory practice the phenomenon must be prepared in order to be produced. As a result, contemporary scientific thought begins by an epoché, a placing of reality between parentheses. And in a somewhat paradoxical, but in our opinion, suggestive, form, one can say that the mechanics of Dirac begins by examining the propagation of "parentheses" from the outset, in a spatial configuration. It is the manner in which propagation takes place which finally defines what is propagated. The mechanics of Dirac is, therefore, from the outset, derealized. We shall see later how it will pursue its realization or rather its realizations, when it reaches its full development.
Dirac begins by pluralizing the equations of propagation. As soon as one ceases to suppose that it is an object which is being moved (an object, faithful to the naive intuitions of realism, carrying all the characteristic of an object around with it) one is led to posit as many functions of propagation as there are phenomena propagating themselves. Pauli had already understood that, since the electron was apparently capable of two spins, there had to be at least two functions whereby to study the propagation of these two phenomenon-producing characteristics. Dirac pushed the pluralism of propagation even further. He was at great pains to lose nothing of the functionality of mechanical elements, to protect the different variables from all degeneration. From then on calculation does the job. The matrices solidarize the propagated phenomena dialectically by giving to each its due and by establishing their relative phase with accuracy. Instead of the mathematical melodic line which used heretofore to accompany the work of the physicist there is now a whole harmony which embellishes propagation mathematically. In the mechanics of Dirac there is, in quite an exact sense, a quartet which the mathematician has to conduct in order to regulate the four functions associated with all propagation.
But since, in a philosophical work, we can only give a vague idea of the "idealism" of the mechanics of Dirac, let us turn forthwith to the results and take into consideration the notion of mass alone.
Calculation yields up this notion to us along with the others, the magnetic and electric moments, the spins, respecting to the very end the fundamental syncretism which is so characteristic of complete rationalism. But now comes the surprise, now comes the discovery. At the end of the calculation, the notion of mass is delivered up to us strangely dialectized. One mass was all we needed. Calculation gives us two—two masses for a single object.  One of these masses sums up perfectly everything that was known about mass in the four antecedent philosophies: naïve realism, clear empiricism, Newtonian rationalism, full Einsteinian rationalism. But the other mass, the dialectic of the first, is a negative mass. That is a concept which cannot be assimilated at all in the four antecedent philosophies. As a result, one half of the mechanics of Dirac rejoins and continues classical mechanics and relativist mechanics; the other half branches off at a fundamental notion; it gives us something else; it yields an external dialectic, a dialectic which could never have been discovered by meditating upon the essence of the concept of mass, or by delving more deeply into the Newtonian and relativist notion of mass.
What attitude will the new scientific mind take toward such a concept? But first of all, what would have been the attitude of a scientist of the preceding era, at the level of nineteenth century physics?
There seems to be no doubt whatever about what the latter would be. For the scientist of the nineteenth century the concept of a negative mass would have been a monstrosity. It would have branded any theory which produced it as with a fundamental error. It was no real help that there was supposedly complete freedom of expression within a philosophy of as if. There were limits after all to liberty and the philosophy of as if could never have succeeded in interpreting a negative quantity as if it were a mass.
At this point the dialectical philosophy of "why not?" makes its entry, a philosophy which is characteristic of the new scientific mind. Why can't mass be negative? What essential theoretical modification could legitimatize a negative mass? What experimental prospect was there of discovering a negative mass? What characteristic is it which, in its propagation, would reveal itself
1 Cf. Louis de Broglie, L'Electron magnétique, p. 207.
as a negative mass? In short, theory stands its ground, it does not hesitate to seek the realization of an entirely new concept having no roots in common reality, at the cost of some basic modifications.
Thus realization takes precedence over reality. By so doing it demotes reality. A physicist only really knows reality when he has made it come real, when he is thus master of the eternal rebeginning of things and when he constitutes within himself an eternal return to reason. The ideal of realization is, moreover, very demanding: any theory which realizes partially must realize totally. It cannot be right in a fragmentary manner. Theory is mathematical truth which has not yet found its complete realization. The scientist must seek out this complete realization. He must force nature to go as far as our mind goes.
As we draw towards the end of our effort to reveal an example of dispersed philosophy, working within just one concept, we are about to meet with an objection. This we could have avoided if we had allowed ourselves the fairly legitimate right of using different concepts to illustrate the different states of dispersed philosophy. But let us examine the objection as it comes to the reader's mind. It will be urged that the concept of negative mass has not yet found its experimental interpretation and that, in consequence, our example of dialectical rationalization is left hanging; the most it does is to raise a question. But it is already very striking that such a question can be asked at all. The possibility underscores the interrogatory value of mathematical physics. Furthermore, we must emphasize the very special character such a question possesses: the question is a theoretically precise one touching a phenomenon which is totally unknown. This precise unknown thing is just the opposite of the irrational vague thing to which realism too often attributes a weight, or a function, or a reality. A question of this kind is inconceivable in a realist philosophy, or an empirical philosophy, or a positivist philosophy. [????] can only be interpreted by an open rationalism. When it is [????] with all its antecedent mathematical construction, it is definitely an opening.
Our thesis would, of course, lose much of its force if there were no other examples to fall back upon in which a dialectically interpreted fundamental notion is in fact made to come real. But this is the case for negative energy. The concept of negative energy presented itself in Dirac's mechanics in exactly the same manner as the concept of negative mass. With respect to it we could repeat point for point all the preceding criticisms; we could affirm that such a concept would have appeared monstrous to science of the nineteenth century and that its manifestation in any theory would have seemed the sign of a capital error entirely vitiating the theoretical construction. Yet Dirac did not make of it an objection to his system. On the contrary, since his equations of propagation led to the concept of negative energy, Dirac made it his task to find a phenomenal interpretation of this concept. His ingenious interpretation might have seemed to be a pure construction of the mind, but the experimental discovery of the positive electron by Blackett and Occhialini very soon came to give an unexpected confirmation to the views of Dirac. To be exact, it was not the concept of negative energy which brought about the search for the positive electron. There was, as there often is, an accidental synthesis of the theoretical discovery and of the experimental discovery; but the bed was made, and made to measure, for the new phenomenon to come and he on. There was a theoretical prediction which awaited the fact. In a certain sense, one can therefore say that, by following the construct of Dirac, the dialectic of the notion of energy found its double realization.
Let us now return to negative mass. What is the phenomenon which would correspond to the concept of negative mass prepared by the mechanics of Dirac? Since we do not know how to answer the question as a mathematician would, let us assemble the vague, philosophical questions which occur to us.
Is negative mass the characteristic which should be found in the dematerialization process whereas positive mass should be linked with matter resulting from materialization? In other words do the processes of material creation and destructionsomething so new for the scientific mind!—have a relationship with the pro-
found dialectics of basic concepts like positive and negative masses and positive and negative energies? Is there a connection between negative energy and negative mass?
We have an objective when we ask such vague, evasive questions—questions which are not anticipated by any of our previous works. In point of fact, we should like to give the impression that it is in this area of dialectical surrationalism that the scientific mind dreams. It is here and nowhere else that anagogical dreaming comes into being, dreaming which ventures into thought, dreaming which thinks while it ventures, dreaming which seeks an illumination of thought by thought, which finds a sudden intuition beyond the veils of informed thought. Ordinary dreaming works at the other extreme, in the area of depth psychology, following the seductions of the libido, the temptations of the intimate, the vital certainties of realism, the joy of possession. The psychology of the scientific mind can only be properly understood when one keeps these two sorts of dreaming separate. Jules Romains understood the reality of this distinction; he has a brief page in which he writes: "I am even, in certain respects, a surrationalist."  In our opinion, there is more delay about referring to reality than Jules Romains imagines, dreaming by educated thought in terms of its own education lingers on. But its role is indispensable and a dispersed philosophy, to be complete, must study the area of anagogical dreaming.
In our estimation, anagogical dreaming under its present scientific impulse, is essentially mathematical. It aspires to more mathematics and to more numerous, more complex, mathematical functions. When one follows the efforts of contemporary thought to understand the atom, one comes close to believing that the fundamental role of the atom is to oblige men to do mathematics. De la mathématique avant toute chose . . . Et pour cela préfère l'impair . . . In short, the ars poetica of physics is done with numbers, with groups, with spins, to the exclusion of monotonous distributions, repetitive quanta, and without obstacle to the working out of any process whatever. What poet will arise to sing of this panpythagorism, this synthetic arithmetic which begins by giving
1 Jules Romains, Essai de réponse à la plus vaste question. N.R.F. August 1, 1939, p. 185.
its four quanta, its four figure number to every existent thing as if the simplest, the poorest, the most abstract of electrons already had, of necessity, more than a thousand facets. It matters little that there are only a few electrons in an atom of helium or lithium, each gets its serial number in four figures; a squad of electrons is as complicated as a regiment of infantrymen.
But enough of these outpourings. It was a poet that we needed and, alas! all that we can conjure up is the figure of a colonel counting the soldiers of his regiment. The hierarchy of things is more complex than the hierarchy of men. The atom is a mathematical society which has not yet told us its secret; one does not command this society with the arithmetic of a soldier.
SOURCE: Bachelard, Gaston. The Philosophy of No: A Philosophy of the New Scientific Mind, translated from the French by G. C. Waterston (New York: Orion Press, 1968), Chapter 1, The Various Metaphysical Explanations of a Scientific Concept, pp. 15-33. Original French publication, 1940.
Translator’s Preface vii PREFACE: Philosophic Thought and the Scientific Mind 3 ONE The Various Metaphysical Explanations of a Scientific Concept 15 TWO The Notion of an Epistemological Profile 34 THREE Non-substantialism, the Preliminaries of a Non-Lavoisian Chemistry 44 FOUR The Elementary Spatial Connections of Non-analytics 80 F IVE Non-Aristotelian Logic 90 SIX The Synthetic Value of the “Philosophy of No” 115
The Synthetic Value of the Philosophy of No by Gaston Bachelard
Excursus on Bachelard’s The Philosophy of No (Excerpt) by Maire Jaanus Kurrik
Gaston Bachelard on Surrationalism & a Revolution of Reason
Surrationally Yours by R. Dumain
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