Monadology and Sociology

Hypotheses fingo¹

I

The monads, children of Leibniz, have come a long way since their birth. By several independent paths, unremarked by scientists themselves, they slip into the heart of contemporary science. It is a remarkable fact that all the secondary hypotheses implicit in this great hypothesis, at least in its essentials if not in its strictly Lebnizian form, are now being proved scientifically. The hypothesis implies both the reduction of two entities, matter and mind, to a single one, such that they are merged in the latter, and at the same time a prodigious multiplication of purely mental agents in the world. In other words, it implies both the discontinuity of the elements and the homogeneity of their being. Moreover, it is only on these two conditions that the universe is wholly transparent to the gaze of the intellect. Now, on the one hand, as a result of having been sounded a thousand times and judged unfathomable, the abyss which separates movement and consciousness, object and subject, the mechanical and the logical, has at length been called once more into question, relegated to the status of an appearance, and finally denied altogether by the bravest souls, who have been echoed from every quarter. On the other hand, the progress of chemistry leads us to affirm the atom and to deny the material continuity which the continuous character of the physical and living manifestations of matter, extension, movement and growth seem superficially to reveal. There is nothing more profoundly surprising than the combination of chemical substances in definite proportions, to the exclusion of any intermediate proportion. Here there is no evolution and no transition: the dividing lines are clear and stark; and yet hence arises everything which is supple and harmoniously graduated in phenomena, almost as if the continuity of nuances were impossible without the discontinuity of colours. The path of chemistry is not the only one which seems to lead us in its progress to the monads; so too do physics, the natural sciences, history, and even mathematics. As Lange says: 'Of great importance, not only for this demonstration, but also especially for its far-reaching consequences, was Newton's assumption that the gravitation of a planet is only the sum of the gravitation of all its individual portions. From this immediately flowed the inference that the terrestrial bodies gravitate towards each other; and further, that even the smallest particles of these masses attract each other'.² With this viewpoint, which was much more original than it seems today, Newton broke, and indeed pulverized the individuality of the celestial body, which had until then been regarded as a superior unity whose internal relations bore no resemblance to its relations with other bodies. Great strength of mind was required to resolve this apparent unity into a multiplicity of distinct elements linked to each other in the same way as they are linked to the elements of other aggregates. The beginning of the progress of physics and astronomy can be dated to the day when this viewpoint replaced the contrary prejudice.

In this respect the founders of cellular theory have shown themselves to be Newton's true heirs. In the same way they have broken apart the unity of the living body, they have resolved it into a prodigious number of elementary organisms, isolated and egoistic, eager (avides) to develop themselves at the expense of the exterior, where the exterior includes their neighbouring brother cells as well as the inorganic particles of air, water, and all other substances. Schwann's³ position on this point has been no less fertile than Newton's. Thanks to his cellular theory, we know that 'there is no vital force, as a principle distinct from matter, either in the entirety of the organism, or in each cell. All phenomena of vegetable or animal life must be explained by the properties of atoms [let us say of the ultimate elements from which atoms are composed], whether these be the known forces of inert nature or forces hitherto unknown'.⁴ There is surely nothing more positivist or better conformed to a healthy and serious science than this radical negation of the vital principle, against which vulgar spiritualism likes to protest. However, it is clear where this tendency will lead us, if drawn to its logical conclusion: to the monads, which fulfil the most daring promises of Leibnizian spiritualism. Like the vital principle, illness, which was treated as a person by the ancient medical writers, has been pulverized into a great number of infinitesimal disorders of the histological elements. Moreover, thanks primarily to the discoveries of Pasteur, the parasitic theory of illness, which explains these disorders by means of the internal conflicts of miniscule organisms, finds more general application every day, and indeed excessively so, to the point where it should provoke some reaction. But parasites, too, have their parasites. And so on. The infinitesimal again!

The new theories in chemistry have been formed along analogous lines. As Wurtz says: 'This is the new and essential point. The properties of the radicals are referred to the elements themselves. Formerly they were considered as a whole. To the radical regarded as a whole was attributed the power of combining with or of being substituted for simple bodies. This was the fundamental point of view of Gerhardt's theory of types. We now go further. To discover and define the properties of radicals we go back to the atoms of which they are composed.'⁵ This eminent chemist's thought goes further than our remarks above. The examples which he cites demonstrate that, among the atoms of a radical, there is one in particular on whose atomicity and as yet unsatisfied avidity, outlasting the saturation of all the others, the combination which is produced ultimately depends.

Like stars, like living things, like illnesses, like chemical radicals, nations are nothing more than entities which have long been taken for true beings in the ambitious and sterile theories of so-called philosophical historians. Has it not, for example, been sufficiently repeated that it is foolish to seek the cause of a political or social revolution in the influence of writers, of statesmen, or of any kind of instigator, and that it rather springs spontaneously from the genius of the race, from the bowels of the people, that anonymous and superhuman agent? But this convenient point of view, which consists in mistakenly seeing the creation of a new being in a phenomenon generated by the encounter of real beings (albeit a genuinely new and unforeseen phenomenon), can be upheld only provisionally. Having been rapidly exhausted by the literary abuses it has suffered, it is conducive to a serious return towards a clearer and more positive form of explanation, which accounts for a given historical event only by individual actions, and particularly by the action of inventive men who served as a model for others and reproduced thousands of copies of themselves, like mother-cells of the social body.

This is not all: these ultimate elements which form the final stage of every science, the social individual, the living cell, the chemical atom, are ultimate only from the point of view of their particular science. They themselves, as we know, are composite, not excepting the atom itself which, according to Thomson's hypothesis of the 'vortex atom',⁶ the most plausible or the least unacceptable of the conjectures which have been attempted on this subject, would be a whirling mass of simpler elements. Lockyer's⁷ studies of solar and stellar spectra have led him to suppose—and the conjecture seems probable—that certain weak lines observed by him are due to the elements of which are composed certain substances that on our planet are regarded as incomposite.

Scientists who live in daily contact with the so-called elements have no doubt of their complexity. While Wurtz shows himself to be favourable to Thomson's hypothesis, Berthelot says for his part: "The deeper study of the elementary masses which, on our current understanding, constitute the simple bodies leads every day more and more to an understanding of them not as indivisible atoms, homogenous and admitting of movement only as a whole,

but as highly complex constructions, furnished with a specific architecture and animated by highly varied internal movements'.⁸ Physiologists, for their part, do not maintain that the protoplasm is a homogenous substance, and judge only the solid part of the cell to be active and truly living. The soluble part, almost in its entirety, is nothing but a storehouse for fuel and nourishment (or a mass of excrement). Moreover, a better understanding of the solid part itself would doubtless lead us to eliminate almost everything from it. And, where will this process of elimination finish if not at a geometrical point, that is, at pure nothingness? Unless, as we will explain below, this point is a centre. And, in fact, in the true histological element (which is designated only improperly by the word 'cell') what it is essential to take into account is not its limit or envelope, but rather the central focus whence it seems to aspire to radiate indefinitely until the day when the cruel experience of external obstacles obliges it to close in on itself in order to preserve its being; but we are getting ahead of ourselves.

There is no way to call a halt to this descent to the infinitesimal, which, most unexpectedly, becomes the key to the entire universe. This may explain the growing importance of the infinitesimal calculus; and, for the same reason, the stunning and rapid success of the theory of evolution. In this theory, a specific form is, as a geometer would say, the integral of innumerable differentials called individual variations, which are themselves due to cellular variations, whose basis consists of a myriad of elementary changes. The source, reason, and ground of the finite and separate is in the infinitely small, in the imperceptible: this is the profound conviction which inspired Leibniz, and continues to inspire our transformists.

But why should such a transformation, which is incomprehensible if presented as a sum of definite and discrete differences, be readily understood if we consider it as a sum of infinitely small differences? We must show first of all that this is a real contrast. Suppose that, by some miracle, a body disappears and is annihilated from the place A where it was, then appears and comes back into being at the place Z a metre away from A, without having traversed the intermediate positions: such a displacement is beyond the power of our mind to grasp, while we would never be astonished to see this body move from A to Z along a line of juxtaposed positions. However, note that in the first case, we would have been no less amazed had we seen such an abrupt disappearance and reappearance take place over a distance of half a metre, or of 30, of 20, of 10, of 2 centimetres, or of any perceptible fraction of a millimetre. Our reason, if not our imagination, would be just as struck in the last case as in the original example. In the same way, if we are presented with two distinct living species, be they very distant or closely related, a fungus and a labiate herb, or two herbs of the same genus, in neither case will it be comprehensible that one could suddenly and with no transition turn into the other. But, if we were to be told that by hybridization the fertilized ovule of the one had undergone a deviation, extremely slight at first and then gradually increasing, from its habitual pathway, we would have no difficulty in accepting this. It will be argued that the inconceivability of the first hypothesis is due to a prejudice which has been formed in us by the association of ideas. Nothing could be truer, and precisely this proves that reality, the source of the experience which gave birth to this prejudice, conforms to the explanation of the finite by the infinitesimal. For pure reason, and still more reason alone, would never have guessed at this hypothesis; it would even, perhaps, be more inclined to see in the large the source of the small than in the small the source of the large, and it would gladly believe in divine forms which are complete ab initio, which could envelop a clod of earth all at once and penetrate it from the outside to the inside. It would even willingly agree with Agassiz⁹ that, from the outset, trees have been forests, bees hives, men nations. Science has been able to eliminate this point of view only by the rebellion of contrary facts. To mention only the most obvious, it is the case that an immense sphere of light spread through space is due to the unique vibration, multiplied by contagion, of one central atom of ether,¹⁰—that the entire population of a species originates from the prodigious multiplication of one unique first ovulatory cell, in a kind of generative radiation,—that the presence of the correct astronomical theory in millions of human brains is due to the multiplied repetition of an idea which appeared one day in a cerebral cell of Newton's brain. But, once more, what follows from this? If the infinitesimal differed from the finite only by degree, if at the basis of things as at their perceptible surface there existed only positions, distances, and displacements, why would a displacement which is inconceivable in the finite realm change its nature in becoming infinitesimal? The infinitesimal, therefore, is qualitatively different from the finite; movement has a cause distinct from itself; being is not exhausted by what appears in phenomena. Everything comes from the infinitesimal and everything returns to it; nothing in the sphere of the finite and complex—a surprising fact which nobody is surprised at—appears suddenly, nor dies away. What should we conclude from this, if not that the infinitely small, in other words the element, is the source and the goal, the substance and the reason of all things?—While the progress of physics leads physicists to quantify nature in order to understand it, it is remarkable that the progress of mathematics leads mathematicians, in order to understand quantity, to resolve it into elements which are not at all quantitative.¹¹

This growing importance which the growth of knowledge grants to the concept of the infinitesimal is all the more curious since the latter, in its ordinary form (leaving aside for a moment the monadic hypothesis), is nothing but a mass of contradictions. I will leave to Renouvier¹² the task of pointing them out. By what power could the absurd grant to the human mind the key to the world? Is it not because, through this purely negative concept, we aim at but do not reach, or look at but do not see, a much more positive concept which we do not own, but which should nonetheless be inscribed as a reminder in the inventory of our intellectual assets? This absurdity could very well be only the outer covering of a reality alien to everything we know, outside everything, space and time, matter and mind ... Outside mind? If so, the monadic hypothesis should be rejected ... but this must be examined further. However this question is resolved, these tiny beings which we call infinitesimal will be the real agents, and these tiny variations which we call infinitesimal will be the real actions.

Indeed, it seems to follow from the preceding that these agents are autonomous, and that these variations clash and obstruct one another as much as they compete. If everything comes from the infinitesimal, it is because an element, a unique element, initiates some change, movement, vital evolution, or mental or social transformation. If all these changes are gradual and apparently continuous, this shows that the initiative undertaken by the element, even if it receives some support, has also encountered some resistance. Let us imagine that all the citizens of a State, without exception, are fully in favour of a programme of political reorganization springing from the brain of one among their number, and more particularly from one point within this brain; the complete overhaul of the State according to this plan, rather than being progressive and fragmentary, will then be abrupt and total, however radical the project. The slowness of social modifications is explained only by the fact that the other plans for reform or ideals of the State which all other members of a nation knowingly or unknowingly entertain run contrary to this plan. In the same way, if matter were as inert and passive as is generally believed, I do not see why movement, in other words gradual displacement, should exist, nor why the formation of an organism should be subject to the progress of its embryonic phases, an obstacle opposed to the immediate realization of its adult stage which was nonetheless from the beginning the aim of the germ's impulse.

The idea of the straight line, let it be noted, is not the exclusive property of geometry. There is a biological rectilinearity and a logical rectilinearity. In the same way that, in passing from one point to another, the abbreviation or diminution of the number of intervening points cannot continue indefinitely and must stop at the limit which we call the straight line, just so, in the passage from one specific form to another, from an individual state to another, there is a minimal, irreducible intervening series of forms or states which must be traversed, which alone may perhaps explain the abbreviated repetition by the embryo of some of the successive forms of its ancestors; and similarly, in expounding a body of knowledge, is there not a way to go straight from one thesis to the next, and does it not consist in linking them by a chain of logical positions or positings which necessarily come in between the two? A truly surprising necessity. This rational, rectilinear order of exposition, much favoured by introductory books which summarize in a few pages the labour of centuries (and the limit of the ambition of such volumes), coincides frequently but not invariably, and in many points but not in all, with the historical order of appearance of the successive discoveries which are synthesized in the science. Perhaps this is the case with the famous recapitulation of phylogeny by ontogeny,¹³ which would then be the rectification and not only the prodigious acceleration of the more or less winding path along which the ancestral forms, the accumulated biological inventions which are bequeathed all together to the ovule, followed one another in previous eras.¹⁴

The real support which the theory of evolution gives to the monadological hypotheses will be still more evident if we imagine this great system in the new forms which it will soon take on, and whose outline can already be seen. For evolutionary theory itself evolves. It evolves not by a series or a competition of blind groupings, or of fortuitous and involuntary adaptations to the observed facts, in conformity with the procedures of transformation which it wrongly attributes to living nature, but by the accumulated efforts of perfectly aware scientists and theoreticians, knowingly and voluntarily occupied in modifying the fundamental theory to fit it as closely as possible to the scientific data known to them, and also to the preconceived ideas they hold dear. This theory is for them a generic form which they are working to specify, each in his own way. But, among these various products of the unprecedented fermentation created by Darwin, there are only two which add to or substitute for the master's own idea something truly new and fertile. I refer firstly to the evolution by association of elementary organisms into more complex organisms formulated by Edmond Perrier,¹⁵ and secondly by the evolution by leaps or crises,¹⁶ which, suggested and predicted some years ago by Cornet's prescient writings,¹⁷

has spontaneously sprouted anew¹⁸ here and there in the minds of several contemporary scientists. The specific transformation of a pre-existing form in view of a new adaptation, according to one of these theorists, must have come about at a given moment in a quasi-immediate manner (that is, I think, very short relative to the prodigious duration of species once they are formed, but perhaps very long with respect to our brief existence) and, he adds, by a regular process and not by groping its way forward. Similarly, for another transformist, the species, from its relatively rapid formation up to its equally rapid decomposition, actually remains fixed within certain limits, because it is essentially in a state of stable organic equilibrium. Deeply troubled in its own constitution by any excessive change in its environment (or by any internal revolution due to the contagious rebellion of an element) the organism goes beyond its species only, as it were, to roll onto the slope of another species, itself in stable equilibrium, and there remains for some period of time which for us would be an eternity.

Of course, I need not here discuss these conjectures. It is sufficient to note that they are growing, or rather advancing through the undergrowth, still lowly but pervasive, while natural selection loses ground every day, showing itself better at purifying forms than perfecting them, and better at perfecting them than fundamentally modifying them. I would add that, by the one or the other of the two ways mentioned above, we are necessarily led to populate and fill living bodies with spiritual or quasi-spiritual atoms. To what may we ascribe the need for society which Perrier sees as the soul of the organic world, if not to tiny persons? And what could this transformation be, this direct, regular, and rapid process imagined by other thinkers, if not the accomplishment of hidden workers who collaborate in realizing some specific plan for reorganization previously conceived and willed by one among their number?

Notes

1. [Trans. Note: The epigraph references Newton's famous tag 'hypotheses non fingo' (I make no hypotheses), in the General Scholium to the Principia Mathematica.]↩
2. [Trans. Note: Ludwig Lange (1863-1936), History of Materialism: And Criticism of its Present Importance, vol. I, trans. E. C. Thomas, London, Kegan Paul, Trench, Trübner, 1925, p. 311.]↩
3. [Trans. Note: Theodor Schwann (1810-1882) was one of the key early proponents of the theory that all living organisms are made up of cells.]↩
4. [Trans. Note: These two sentences are marked as a citation in the text, but appear to be not a verbatim quote but a summary paraphrase of the final section ('Theory of the Cells') of T. Schwann, Microscopical researches into the accordance in the structure and growth of animals and plants, trans. H. Smith, London, Sydenham Society, 1847.]↩
5. [Trans. Note: A. Wurtz, The Atomic Theory, trans. E. Cleminshaw, London, Kegan Paul, 1880, pp. 265-266 (Tarde's emphasis).]↩
6. [Trans. Note: J. J. Thomson's 'nebular' or 'vortex atom' theory, prior to the discovery of the electron, posited that the atom consisted of nebular 'vortices' in the ether. As of the writing of Monadology and Sociology, little was known of the internal structure of the atom.]↩
7. [Trans. Note: Norman Lockyer (1836-1920), astronomer and pioneer of astronomical spectroscopy.]↩
8. [Trans. Note: Marcellin Berthelot (1827-1907), chemist. The citation has not been traced.]↩
9. [Trans. Note: Louis Agassiz (1807-1873), palaeontologist. Tarde's reference is to Agassiz' defence of special creation—the position that animal species and human 'races' were separately created by God—and of the fixity and unchangeability of the species thus created.]↩
10. [Trans. Note: The ether, in the physics of Tarde's time, is the all-pervading substance which serves as the medium through which light propagates.]↩
11. [Trans. Note: Tarde may be thinking here of the work of Georg Cantor and Richard Dedekind in the 1870s and 1880s on the set-theoretical foundations of natural number.]↩
12. [Trans. Note: Charles Renouvier (1815-1903), philosopher. Renouvier strongly criticized the concepts of infinite and infinitesimal magnitude as logically contradictory.]↩
13. [Trans. Note: Reading ontogenèse with the 1893 text; the 1895 text has autogenèse (autogeny).]↩
14. [Trans. Note: The theory of ontogenetic recapitulation, most famously formulated by Ernst Haeckel (1834-1919) as 'ontogeny recapitulates phylogeny', holds that the developing embryo 'recapitulates' in miniature the evolution of the species.]↩
15. [Trans. Note: Edmond Perrier (1844-1921), zoologist. As described by Tarde, Perrier propounded the theory that higher organisms evolved from colonies or associations of smaller organisms. See E. Perrier, Les Colonies animales et la formation des organismes, Paris, Masson, 1881. The 1893 text cites Perrier's courses at the Museum (the National Museum of Natural History in Paris) and adds the following footnote: 'This biological theory has the advantage that it agrees in every point with the linguistic theory of the formation of languages by the aggregation of several words into one'.]↩
16. [Trans. Note: The 1893 text adds the English phrase 'saltatory evolution'.]↩
17. [Trans. Note: Antoine Augustin Cournot (1801-1877), mathematician, economist and philosopher. See his Traité de l'enchaînement des idées fondamentales, section III.8, Œuvres complètes, Vol. III, N. Bruyère (ed.), Paris, Vrin, 1982, pp. 267-277.]↩
18. [Trans. Note: The 1893 text adds: '… sprouted anew at once in the mind of two contemporary scientist, both avowed transformists. By one of those coincidences which often occur in the history of science, and which invariably denote the full maturity of an idea whose hour has come and which imperiously demands attention, the latter of the above-mentioned hypotheses, published in 1877 by the American naturalist Dall, was presented in 1879 at the scientific section of the Academy of Brussels by the Belgian scientist de Sélys Longchamps as his own discovery'. The idea in the next sentence is credited to de Sélys Longchamps (Michel-Edmond de Sélys Longchamps (1813-1900), naturalist) and in the sentence following ('another transformist') to Dall (William Healey Dall (1845-1927), naturalist). See W. H. Dall (1877) On a provisional hypothesis of saltatory evolution. American Naturalist, vol. 11, no. 3, pp. 135-137.]↩