Unconscious objectivity - aspects of a critique of the mathematical natural sciences (excerpts) - Claus Peter Ortlieb

Unconscious objectivity - aspects of a critique of the mathematical natural sciences (excerpts) - Claus Peter Ortlieb

A mathematician takes a sceptical look at the mathematical basis of modern natural science both from an immanent perspective—with regard to its epistemological contradictions (e.g., the divergence of the experimental method from the requirements of a strict empiricism)—as well as from a historical perspective that situates its rise and development in the context of the emergence of capitalist society in Western Europe, and proposes that it, too, like Ptolemaic astronomy, is a transient phenomenon that might be succeeded by another “Copernican revolution in thought”, one in accordance with a different kind of socio-economic system.

Unconscious Objectivity. Aspects of a Critique of the Mathematical Natural Sciences (Excerpts) – Claus Peter Ortlieb

It would be hard to find another subsystem of modern society that, both with regard to its self-image as well its public reputation, has proven to be as resistant to critique as the “hard sciences”, or “genuine science”, in the sense that Kant used the term, according to whom, “in any special doctrine of Nature there is only as much genuine science as there is mathematics”.1 It is not that critiques of the natural sciences do not exist, such as those that have derived above all, since the 1970s, from the feminist and alternative movements. For many scientists, the claim that the social use of scientific discoveries is more than just a sensitive issue is obviously true; and it is from the ranks of these scientists that the most rigorous and competent critiques of that aspect of the question of science derive. What aspects, however, of scientific knowledge itself, of the discovery of natural laws and irrefutable facts, can be subjected to critique? Thus, the question concerning the possibility of a different kind of science that was posed by the feminist critique, was neither taken seriously as a question, nor was it perceived as a problem, from the very start: it was instead refuted with sarcastic rejoinders that took the form of questions such as, will the law of gravity no longer be valid from now on, or will two and two will no longer make four; and this rendered any further discussion superfluous.

The empiricist image of a value-neutral science

Such a defensive attitude, immunized against all criticism, is nourished on the notion of the natural sciences as a neutral tool, or “value-neutral science”. We must note, to begin with, that this ideal constitutes a retreat, historically speaking. The contemporaries of Galileo, like Francis Bacon, Thomas Hobbes and Renee Descartes, had a much more ambitious concept of scientific thought, which they understood to be the road to the good life, to perpetual peace and, in short, to the solution of all the problems that are accessible to human knowledge. I will not devote any more time to these ideas here, since, in the era of nuclear technology and the threat of global catastrophe brought to us by the application of scientific discoveries, there is, after all, no one left who would defend them.

The modern concept of value-neutral science, on the other hand, is a much harder nut to crack. In its rather naïve version, which we can assume to be predominant among the non-specialist public, scientific knowledge simply appears to be a set of true propositions about nature, arrived at by way of exact observations and their precise mathematical characterization. This image has been propagated above all by positivism.

In view of the undeniable breaks that mark the history of the natural sciences, which obviously never would have taken place if the natural sciences are just a method that is restricted to verifying facts, scientists themselves, to the extent that they engage in reflection on this issue, see the question in a very nuanced way, supposing that human thought in its imperfection might never be capable of discovering the full truth. What the majority of these scientists have in common with the informed public, however, is the idea that there is a view of nature that is universally valid, for all human beings equally and regardless of the forms of society, and that scientific progress consists in an attempt to bring the state of knowledge increasingly closer to that view. This concept cannot be dissociated from the idea of a linear development, scientific progress, whose origins are projected into human prehistory or even deeper into the past, as Popper does, for example.2

One of the characteristic features of the natural sciences is the fact that historically, they only arose in one culture, bourgeois society. Furthermore, the Enlightenment had proclaimed the universality of this form of knowledge that it created, in consonance with its self-definition as the final and highest stage of human history. This objectivist concept of scientific knowledge cannot be refuted from an external standpoint, merely by probing its cultural and social context. I shall therefore examine scientific-mathematical activity, first of all, from an immanent perspective, taking Immanuel Kant as my starting point. Proceeding from Kant’s view on this question to Sohn-Rethel,3 Greiff,4 and Müller,5 I believe that the great philosopher of the Enlightenment had already developed the instruments that will allow us to dissolve Enlightenment thought from within, although he did not take this step himself.

The empiricist David Hume (concerning whom Kant had said that he had awakened him from his “dogmatic slumber”) had already proven that an empirical basis for objective knowledge is impossible, in view of the fact that no law of nature can be conclusively deduced from experience: “For all inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities. If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance.”6 The honorable empiricist must become a skeptic if he does not want to deceive himself: “It seems to me, that the only objects of the abstract science or of demonstration are quantity and number, and that all attempts to extend this more perfect species of knowledge beyond these bounds are mere sophistry and illusion.”7 Which does not prevent modern empiricism, however, from attempting to do so over and over again, insisting on an empirical foundation for all scientific knowledge of nature. However, the most recent, in historical terms, form of knowledge that refers exclusively to immediate experience (if such a thing ever really existed) seems to have been the Aristotelian theory of nature with its medieval adaptations. In contrast to these earlier forms of knowledge, the modern science of nature is constituted precisely by way of the dissociation of immediate empirical knowledge, and it is this “Copernican revolution in thought” (Kant) in which its peculiar success consists.8 I shall attempt to illustrate this point with some examples from the beginnings of modern science.

Geocentrism and heliocentrism

The dawning of the bourgeois epoch began with a mathematical model. Nicolaus Copernicus (1473-1543), in his book, De Revolutionibus Orbium Coelestium, published shortly before his death, broke with the Ptolemaic or geocentric view of the world that was dominant during the Middle Ages. In a modified form, the Copernican view of the world is part of our common scientific heritage. No enlightened person would want to reject it in favor of the Ptolemaic system. But how do we know it is true? The men of the Middle Ages, after all, thought something else was true, and the evidence of our senses speaks in favor of their view. A response that is as banal as it is true is that such knowledge was communicated to us at an early age in school and in books.

It is obvious that there can be no astronomical observation that coincides with one of these two views of the world and not with the other, since as far as observation is concerned the latter are entirely identical. From the point of view of modern physics, this involves merely a shift of the system of reference.

Nor was the telescope, which Galileo used for the first time in his observation of the motions of the heavenly bodies, capable of proving one or the other view to be correct. What Galileo observed was the movement of the moons of Jupiter around the planet, but this does not prove the truth of the Copernican system, or at least it does not do so by way of observation but, in any event, only on the basis of a universal principle according to which the smallest celestial bodies revolve around the larger ones.

This concept of a universal principle, of the “laws of nature”, and the concomitant principle of parsimony, were imposed during the century and a half that separated Copernicus and Newton. Thus, Copernicus himself, in the preface to his book published in 1543, written in the form of a letter to Pope Paul III, does not so much insist on abiding by the data of observation, but, rather, on the categories of order and uniformity.

Abiding by the data of observation could not be relevant in choosing between the Copernican and the Ptolemaic systems, because, among other reasons, such conformance, as everyone knows, was impossible to arrive at on the basis of the circular movements postulated by both systems. Only with the discoveries of Johannes Kepler (1571-1630) were circular orbits replaced by elliptical orbits, and for the first time a unitary principle was capable of explaining a wide range of astronomical observations. Kepler took the conformance of prediction and observation very seriously: according to his own account, a discrepancy of only eight minutes caused him to discard a previous hypothesis and to reformulate astronomy in its entirety.

Nevertheless, the central concept of Kepler’s scientific system is that of harmony, in the sense that, “being is a cosmos, a purposively ordered whole, only in so far as its structure is characterized by strict mathematical laws”.9 This mode of thought can be illustrated by the following passage from the Mysterium Cosmographicum (1596), in which the planetary orbits are associated with the five Platonic solids: “The earth’s orbit is the measure of all things; circumscribed around it is a dodecahedron, and the circle containing this will be Mars; circumscribed around Mars a tetrahedron, and the circle containing this will be Jupiter; circumscribed around Jupiter a cube, and the circle containing this will be Saturn. Now, insert within the circle of the Earth, an icosahedron; this circle contains Venus. Within the circle of Venus insert an octahedron; this circle contains Mercury. You now have the reason for the number of the planets.” From our modern point of view, and in consideration of the fact that other planets have since been discovered, the argument is false; but it does testify to the role played in Kepler’s system by autonomous speculation, oriented by purely mathematical ideas, that is then compared with the empirical data.

The founding of the experimental method

Galileo Galilei (1564-1642), a contemporary of Kepler, is often considered to be a more sober person than Kepler and less prone to use speculative methods, although his own methods were not by any means based on immediate experience, either. Mulser ridicules the empiricist concept, for which observation must be the basis of all natural science, parodying the well-known legend about Galileo and the leaning tower as follows: “One fine day the young Galileo climbed the leaning tower of his native city of Pisa, bringing along with him various objects that, with visible pleasure, he dropped from the top of the tower, one after the other: a lead ball, an old telescope, his spectacles, a spoon, a sheet of paper, some feathers, some pollen and a bird. Then he ran down the stairs of the tower and verified that the ball, the spoon, the spectacles and the telescope were laying on the grass, while the sheet of paper was still falling before his very eyes; some feathers were still dancing in the air, the pollen was swept away by the wind and could no longer be detected, and the bird, yearning for the open horizon, disappeared in the sky. Galileo summarized the results of the experiment by proclaiming: ‘All bodies fall at the same rate’.”10

There is also, of course, a heroic version of this legend, a kind of founding myth of empiricism, according to which Galileo defied Aristotelian science by demonstrating that it was false before the assembled professors and students of the University of Pisa, by way of a few experiments carried out from the top of the Pisan bell tower. This story, written for the first time about sixty years after the alleged event and then passed on again and again by the historians of science, adorned with later embellishments, contradicts all the standard procedures of the universities of that time; Galileo himself, who was a champion when it came to the art of exhibiting his own merits, never mentioned it; and furthermore, the experiments, as they are depicted in the legend, would have failed.11

Moreover, Galileo himself has in his voluminous works described, in great detail, the methods that he employed and the experiments that he had himself carried out; and, not surprisingly, they are very different from the way they are depicted in the legend. His typical procedure is illustrated, in the Third Day of the Discorsi of 1638, by the example of objects in free fall. It does not begin with observation, but with a mathematical definition: “By steady or uniform motion, I mean one in which the distances traversed by the moving particle during any equal intervals of time, are themselves equal.”12 A mathematical proposition follows: “If a moving particle traverses two distances in equal intervals of time, these distances will bear to each other the same ratio as the speeds. And conversely if the distances are as the speeds then the times are equal”;13 a proposition that is first proven mathematically. Only later does the empirical demonstration begin, but not in the form of observations that can be made with the naked eye, but in the mode of instructions for the creation of experimental conditions that could approach as closely as possible to the ideal of uniformly accelerated motion.14

To summarize: what Galileo did in this case was to deliberately create a situation that approximated as possible to the ideal conditions that his mathematical constructs assumed. Experiment obviously can never be the origin of such an investigation; it can only be its endpoint, since the experimental conditions must be created in accordance with a goal, and this can only be done knowing the conclusion in advance and, therefore, under the direction of the theory.

The difference between observation and experiment can never be emphasized enough. Overlooking this difference has led many astray, such as, for example, Emil Strauss, who, in the introduction to his 1890 German translation of Galileo’s Dialogue, adduces, as proof of the superiority of modern science over medieval and other modes of thought, “the false, and even stupid, Aristotelian claim … that the velocity of a falling body is proportional to its weight and inversely proportional to the density of the medium through which it is falling”. This statement offers a fine example of the typical Enlightenment thinking that believes that its own form of knowledge is the only possible form and that the members of other cultures, who obtain different results, must simply be idiots or otherwise impaired. The fact is that Aristotle was not so far off the mark, as long as we are talking about everyday observations. In other words: Galileo, had he proceeded in accordance with the legend of the leaning tower, would have obtained a similar result. The result that was entirely different from the one obtained by Galileo, formulated as the law of gravity, is due to a very different method that consists precisely, among other things, in abstracting from the “density of the medium”. Its experimental confirmation presupposes that experimental conditions can be created that would allow us to treat the density of the medium as a nugatory factor.

As everyone knows, experiments can fail. In a letter to Carcaville written in 1637, Galileo emphasizes that this does not render his theoretical reflections worthless: “If experience shows us that the properties we have deduced are confirmed by the free fall of natural bodies, we may affirm without risk of being mistaken that the movement of every solid body is identical to the movement that we have defined and presupposed; if it is not, our demonstrations do not, however, lose anything of their force and consistency, given that they only had to be valid under the assumption that we have established.”15 In modern, 20th century terminology, now that mathematics has become an independent discipline, this means that the correction of the mathematical demonstrations does not depend on any kind of empirical proof: a principle that we now consider to be self-evident; all that was necessary, however, was for someone to consider approaching the knowledge of nature in this way.

In fact, even abstract representations of completely unreal motions which are not observed anywhere can have a meaning; this is precisely the stuff upon which physics depends for its existence (and with it, all the mathematical sciences of nature), at least since Isaac Newton (1642-1727).

In his 1687 Principia, Newton created a mathematical-deductive and unifying foundation for the motions of the heavenly bodies and sub-lunar physics. In order to do this, he had to derive from the Galilean concept of motion (which is not an empirical concept but a mathematical one) the extreme consequence, that of “explaining the real by the impossible”.16 We shall illustrate this by examining some of his axioms: “Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.”17 This is, so to speak, a natural law in the subjunctive form: no such “right” line motion has ever been observed, and Newton knew that such movement was impossible, since according to his own law of gravity there is no space in which no force at all is active. Which does not prevent him, however, from placing at the beginning of his Principia a law that is not susceptible of any kind of directly empirical confirmation: “The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.”18 Once again, all direct empirical experience contradicts Newton and is, once again, in favor of Aristotle, who asserted that a force is necessary to maintain movement, while alteration (reduction of velocity) is produced on its own.

The concept of force, too, which is a central part of Newton’s theory, is not of an empirically verifiable nature: forces cannot be measured or observed directly; the only things that can be measured are the effects that theory attributes to them.

Since we are modern people, we are accustomed to view the world in the light of the basic concepts and principles of modern science; and we even believe we have derived them from experience and observation. “We do not realize the boldness of Galileo’s assertion that ‘the book of nature is written in the language of mathematics’, nor are we aware of the paradoxical character of his decision to treat mechanics as a branch of mathematics, that is, to replace the real world of everyday experience with a hypostatized, mathematical world”;19 the boldness of deducing propositions concerning nature, in defiance of all empirical plausibility, from mathematical concepts such as time, space and motion. The conception of nature derived from this view, which seems obvious to us, had been judged to be erroneous and even absurd in Greek antiquity and in the Middle Ages.20

The Copernican revolution in thought

It is above all the precise descriptions that Galileo offers us regarding his procedures that makes it possible to systematically determine the method that took shape between the time of Copernicus and the time of Newton, and which is still fundamental for the mathematical natural sciences. A critical examination reveals that this method is based on a series of fundamental assumptions that mutually support one another, but which are not for their part susceptible to any kind of empirical grounding, but which, to the contrary, precede all scientific knowledge.

The mathematical natural sciences are based on the assumption that there are universally valid laws of nature, that is, laws that are independent of time and place. This assumption cannot be demonstrated by simple observation; instead, reality seems rather disorderly and irregular. Aristotelian science maintains that the heavenly spheres obey laws that are entirely different from the laws that rule the sub-lunar world, insofar as it spoke of “laws” in our sense of the word, since the idea of universal laws of nature presupposed an objective concept of time that is linear and divisible at will, as well as a homogeneous concept of space (and therefore not, for example, a space that is divided into spheres).

The next assumption of the mathematical natural sciences states that the laws of nature can be described in mathematical terms, an assumption that constitutes the basis for measurement, which is central for the natural sciences; otherwise the idea of looking for laws of nature by way of measurements would not make any sense.

The disordered and motley reality cannot be measured; therefore, one proceeds in another manner, as is demonstrated, for example, by all the writings of Galileo and Newton. One starts with a thought experiment, that is, the formulation of certain ideal conditions (this will take place if …), from which one can deduce certain conclusions by way of mathematical procedures. Both the ideal conditions as well as the mathematical conclusions then enter into the experimental proof, the former as preconditions that must be observed precisely, the latter as indices of what it is that must be measured.

Only on the basis of such considerations can the experiment take place. A good experimenter must be capable of inventing some experimental devices that approach as closely as possible to the ideal postulated conditions and at the same time render the desired measurements possible, without which the process of measurement (the physical intervention of the experimenter) would distort the ideal outcome; which constitutes, as everyone knows, a whole separate branch of science that, especially in the physics of the 20th century, requires an immense technical apparatus. The criterion of the success of an experiment is considered to be its repeatability: every time that identical conditions are created, the same effect must be produced, and the measurements must produce the identical result.

It is not considered to be an argument against the validity of the experimental method that real experiments, when repeated, never lead to exactly identical results, not even within the precise framework that is now attributed to measurements; for the experimental method is based on the assumption that the phenomena that are observed are composed, on the one hand, of laws of nature, which can be formulated in mathematical terms, and, on the other hand, by so-called confounding factors, which are, so to speak, the laws of nature that we do not yet control. An experiment is an action, an active intervention in nature, devoted to the artificial creation of certain situations in which the confounding factors have been eliminated.21

A natural event seems, on the face of it, to be rather disorderly; viewed through the lens of the scientific-mathematical method, it is presented as the effect of a set of natural laws. In order to understand one of these laws, it is necessary to eliminate the others, that is, to assure that its effects are kept constant. It is in this analytic procedure, in the decomposition of the event into isolated factors, that the connection between the natural sciences and technology resides: to the extent that the experimenter is successful in isolating individual factors, it is possible to recombine them at will and synthesize them into technical systems.

Immanuel Kant, who had devoted ten years of his life to scientific activity, summarizes the scientific-mathematical method in the Preface to the Second Edition of The Critique of Pure Reason (1787) as follows: “Reason must approach nature with the view, indeed, of receiving information from it, not, however, in the character of a pupil, who listens to all that his master chooses to tell him, but in that of a judge, who compels the witnesses to reply to those questions which he himself thinks fit to propose. To this single idea must the revolution be ascribed, by which, after groping in the dark for so many centuries, natural science was at length conducted into the path of certain progress.”22

The passage reveals, on the one hand, the important role that Kant attributed to the “principles of reason” that cannot be deduced from empirical knowledge (the Kantian a priori). Thus, the problem that caused Hume to become a skeptic is resolved, a problem that still haunts the minds of modern empiricists: the problem of knowing how objective knowledge is possible.

On the other hand, Kant’s language clearly reveals its origins in Enlightenment thought, which considers “reason” to be a universal property or capacity of the human species but nonetheless claims that it is exclusively a property of Enlightenment thought itself, denying it to foreign or previous cultures. Disregarding this prejudice for now, we must nonetheless point out that the scientific-mathematical method had to be effectively imposed against medieval ways of thinking, so that the formula of the “Copernican revolution in thought” was indeed accurate; it is just that this revolution paved the way for a kind of reason that is specific to the bourgeois era, against the reason of the Middle Ages, which was very different: as different as it was, however, it was not therefore absolute irrationality.23

The concept of “objective knowledge” thus acquires a different meaning from the one it has in our usual linguistic usage, which is that of an ahistorical knowledge, independent of the forms of society and valid equally for all human beings. It would be impossible to convince a member of a different or previous culture, which did not recognize the basic assumptions of the scientific-mathematical method, that is, the principles of bourgeois reason, of the truth of the scientific knowledge of nature. The only part of this science that might plausibly convince him is the experiment: when action A is carried out, defined down to the last detail (which would have to seem to him to be half ritual and half grotesque), effect B is regularly produced. But this gets us nowhere, as long as our interlocutor does not share my basic assumption that certain universal laws of nature are expressed in the experiment, but rather believes, to the contrary, that natural events are arbitrary and without rules.

The palpable successes of the scientific-mathematical method are undeniable. They are visible, for example, in the form of technological systems, that is, certain systems in which conditions similar to those that characterize experiments are artificially created, eliminating confounding factors as far as possible. But the success of certain activities does not necessarily imply the “truth” of their underlying beliefs (and much less a truth that would be above all forms of society). The Chinese art of acupuncture is also successful, to which many people whom Western medicine could not help can testify. To infer from this success, however, that the beliefs upon which that art is based must be true, would at the very least contradict the accepted scientific beliefs concerning the human body.

An even less plausible argument in favor of the often-proclaimed superiority of the scientific-mathematical way of thinking as opposed to others is the fact that scientific thought has successfully been imposed on a world scale, together with commodity society. When all is said and done, the methods to which the primitive accumulation of the commodity system owes its rise in Europe are well known: the extermination and colonization of other peoples,24 as well as the exploitation—imposed by the logic of the commodity and, therefore, ruthless—of trade advantages and advances related to modernization. In view of these facts, the argument that European thought successfully “converted” the members of other cultures because it offered them more profound knowledge is hardly convincing. Just as scientific thought was at first repressed by the power of the Church that forced Galileo’s retraction, so, too, was it finally imposed thanks to the power of the society of the commodity.

Objective knowledge and the bourgeois subject

Since the outwardly apparent connection between bourgeois society and mathematical natural science is so obvious,25 we must inquire as to the nature of their internal or causal connection. A crudely “materialist” approach that attempts to reduce all social phenomena to economic development (which has always also presupposed that the economy is a separate sphere) necessarily fails to answer this question, even if only because the natural sciences did not begin to play a role as productive forces until the era of industrial capitalism, some three centuries after their appearance. And even if there were already in the beginnings of the modern era certain problems pertaining to the economy to whose solution science may have been capable of making a contribution, this does not explain the radical transformation with regard to method in the transition from medieval science to modern science.

Alfred Sohn-Rethel has elaborated, with his theory of a “secret identity of commodity form and thought form”,26 an ambitious theory that relates the rise of Western abstract thought with the first coining of money and commodity exchange. It must be objected, first, that simple commodity exchange, which Marx analyzes as the incipient logic of developed capitalist society, has never existed as a historically independent social formation (as Sohn-Rethel appears to assume), and, second, that the antecedents of industrial capital, including merchants and usurers capital, have also existed in other societies (in China and in India, for example), without their way of thinking having taken the same course as that of the West and, furthermore, without giving rise to an independent capitalist development.27

I do not want to continue to pursue this discussion here, since what I am interested in is not Western abstract thought in general, but only the particular form that it assumes in the objective knowledge of the mathematical natural sciences. Furthermore, I do not seek to construct a causal explanation of historical development, for which I lack the means, but shall instead restrict my efforts to examining the structural relations between the scientific-mathematical method, described as an “ideal type”, and the logic of commodity society in its current, highly developed form. Thus qualified, Sohn-Rethel’s theory seems viable to me, although in what follows I can only offer a few illustrative notes.

The link that connects commodity society with the objective form of knowledge is the bourgeois subject, that is, the specific constitution of the consciousness that, on the one hand, must survive in the society of the commodity and of money, and that, on the other hand, requires the subject to be capable of objective knowledge.

The commodity-form, that is, the social determination of things as commodities, has in modern bourgeois society become the universal form due to the fact that capitalism has transformed labor power into a commodity over which its bearers have free disposal: that is, they are free from ties of personal dependence, free from all coercion, except the compulsion to earn money. But this impersonal coercion is universal, so that money has become the exclusive goal of labor and the sale of each person’s own labor power has become the predominant form of reproduction. In commodity society, the satisfaction of any concrete need depends on money. The need to have the maximum possible amount of money thus becomes the primary “self-interest”, equal for all members of society, although they all have to engage in competition with one another as economic monads. The subjects of commodity exchange, free and equal in this abstract sense, imagine themselves to be autonomous individuals who honorably earn their livelihoods by their labor.

The apparent autonomy of the individual corresponds to the apparent neutrality of the economic process, which is presented to the economic monads as a process that is ruled by laws, and which can only be described with the concepts of systems theory that have been borrowed from the natural sciences. The bourgeois subject is unconscious with regard to his own social condition in two senses: under no other obligation than to assure his own survival (which, however, he cannot successfully fulfill on an individual basis), he feeds with his abstract labor the megamachine of the valorization of capital, concerning whose functioning, however, he assumes no responsibility whatsoever, since he experiences it as ruled by natural laws that are inaccessible to his own action.

The nexus between the possibility of an objective knowledge and the consciousness of one’s own identity was emphasized by Hume and Kant, each in his own particular way. For the empiricist skeptic Hume, not only is the representation of an identical object a metaphysical illusion, so, too, is the consciousness of personal identity, since neither can be derived from experience. Kant’s argument is complementary to Hume’s: since objective knowledge is a fact and, therefore possible, whereas its conditions of possibility cannot be deduced from experience, as Hume had demonstrated, these conditions must be given a priori, prior to all experience. Objective knowledge presupposes a subject who is capable of constituting the objects of experience as identical objects, which itself presupposes the consciousness of an Ego that is identical to itself.28

Consciousness of identity cannot be deduced from experience; it is prior to all empirical knowledge. Nor is it, moreover, something that is innate to human beings as such, but rather something that is socially constituted. In order to specify the nature of the constitution of a subject that is capable of objective knowledge, we must examine the demands imposed by the application of the scientific-mathematical method. Analyzing the current precepts, formulated in the imperative mode, which the manuals of experimental physics offer for conducting experiments (elimination of the “subjective factor”, while simultaneously preserving the condition of the observer), Greiff has shown that these precepts apply to a subject whose intelligence does not depend on his feelings: it is only the latter that must be eliminated. The intervention in nature presupposed by the experiment is, above all, an intervention of the experimenter on himself: the elimination of his corporeality and his feelings. Thus, the illusion is produced that the subject has nothing to do with the process of knowledge: “Because apparently the subject, once eliminated, does not return to intervene in the cognitive act; he seems to be an annoyance, when not even superfluous, for the objectivity of knowledge. The fact that the observer, in the cognitive act, has to conceive of himself as a confounding factor and an obstacle that must be eliminated, produces the conviction that the truth resides in nature rather than in the knowledge of nature; the conviction that regularity obeys natural causes and any deviations from regularity are due to human causes. It produces the illusion of laws that are proper to nature itself and that would be manifested in all their splendor if there were no subject at all. But this is a mere illusion; for the elimination of the subject also constitutes a subjective action, an operation that the subject himself must perform…. [Conformance with laws] is something that the scientist himself produces by obeying certain explicit and determined laws. If the prescribed actions are omitted, he will not get to know nature as a system that is subject to laws; that is, rather than knowledge that is objective and in conformance with laws, there would only be perceptions that vary from one observer to another.”29

All measuring is a reciprocal relation, measured by the mathematical-scientific method, between the inquiring subject and the nature that is the object of his inquiry; thus, one can never refer to “nature in itself” but only to this specific form of interaction.30 The subject-object relation produced by the experiment and expressed in the form of a law cannot be simply reduced to one of its two poles: not even that of the subject, as a strict culturalism might seem to suggest. The laws of nature are neither the products of a discourse that can be fabricated at will, disregarding the objective side, nor are they mere properties of nature that have nothing to do with the subjective bearers of knowledge.

The illusion that causes the regularity produced by the experiment to seem as if it were a property of nature, is the same illusion by which the blind social process of commodity society presents itself to people as a process that is ruled by laws, external to people themselves, when in fact it is they who constitute it by way of their actions as bourgeois subjects.

The subject as “conscious actor who has no consciousness of his own form”31 conceives himself as separated from nature and from the other subjects, whom he experiences as mere “external world”; with which the total social framework, specific to bourgeois society, the only one that produces such a form of consciousness, is unconsciously presupposed.32 The systemic nexus of the commodity-form, thus objectivized, also constitutes the equality of the subjects that is presupposed by the objective form of knowledge: equality as commodity-selling and money-earning monads, responsible adult citizens, all enjoying equal rights and subject to identical rules and laws.

This equality, however, must have been produced in advance by way of an action of the subject with regard to himself: an action that trains body and mind, and objectivizes his own capacities and spiritual states, by eliminating individual peculiarities. This is, by the way, the proposal, not at all a secret, of the Humboldtian concept of “scientific education”, adopted by the German universities, with the practical exploitation of the “secret identity of commodity form and thought form”, long before Sohn-Rethel had provided it with a theoretical formulation. Even Schopenhauer, who hated mathematics, had to grant that it did have a salutary effect with respect to self-discipline.

In and of themselves, of course, there is not much reason to object to self-discipline and orderly thought. The dissolution of all thought into “feeling” does no harm to the commodity-form (since it is the commodity-form itself that produces the separation between “body” and “mind”, and between “feeling” and “thought”); it is not even a revolt but rather a surrender to the objectivized process, a mere festive compensation for the everyday dull routine. What must be criticized is the unconsciousness with which the discipline of objective thought is inculcated, observable in any mathematics class in which mathematics in its current form is taught to first year students, without a word about its historical genesis or its social implications. This is the regimentation, the production of consciousness that is unconscious of its form: in learning formal rules and calculations without the least meaningful context, until its own logic is developed in the mind and the question about its meaning is no longer posed.

The excision of individual peculiarities to which the scientific subject must submit in order not to spoil the experiment, is the same excision to which the objects of his contemplation are subjected, in the mathematical abstraction of the thought experiment: by abstracting from their qualities, and even from everything concrete. Recall the Galilean definition of uniformly accelerated motion or the famous “point masses” of Newtonian mechanics.

An essential criterion of mathematical deduction is that it should remain separate from concrete reality. The history of mathematics since Galileo is characterized by a growing isolation from that excised part of human thought, which again and again sneaks in through some back door, threatening to “obscure” mathematical thought. If in the 19th century the self-image of mathematics was still marked by its role as the language in which, as Galileo said, the book of nature is written, thus preserving a certain link with the concrete, in 1900 mathematics constituted, with David Hilbert’s formalist theory, a science in its own right, which consisted in the application of certain fixed rules for the transformation of chains of signs, to which a meaningful content was no longer attributed. It was not by chance that this development took place during the same period during which the commodity-form was finally imposed universally as the principle of socialization, and personal relations of domination and dependence, inherited from feudalism, were for the most part replaced by formal rules that applied to everyone equally and no longer served any individual purpose.

In the 20th century, mathematics as the abstract core of the (mathematical) natural sciences was erected into a “royal discipline” (Hilbert) that no other science could do without. The disappearance of the models of classical physics, which were certainly abstract but were nonetheless derived from experience, which in the physics of elementary particles, for example, have been replaced by purely mathematical models, disconnected from any mechanical analogy, is also part of this development; so that now one may read in the popular science magazines that space is “in reality” curved and has eleven dimensions: which, however, already constitutes a visualization that is strictly unjustified.


A question for the future concerns the role and the form that the natural sciences, as activities and as institutions, can and must have in a post-capitalist society. To the extent that the natural sciences extend the possibilities of human action, they constitute a useful tool that must not be repudiated. But the “natural science as the religion of our times” (Pietschmann), which promotes the regularity produced by the objective form of knowledge to a property of nature itself and erects a nature ruled by laws into a worldview, determining what we see and what we do not see, this science will not survive our modern epoch. The image of “nature” has always been a socially constituted image; and I do not see why a society liberated from every abstract-universal and unconscious form would still need a unitary image of nature that is equally and at all times obligatory for all.33

A positive determination of a way of life, thought and knowledge beyond the commodity-form is not something that can be asked of a scientist and a bourgeois subject, such as the author of this text. If this text at least serves as the stimulus for debate, then it will have achieved a great deal. For, when all is said and done, why should the “Copernican revolution in thought” announced by Kant, who founded modern science, have to be the last revolution of its kind?

Claus Peter Ortlieb

Translated in November 2014 from the Spanish translation published in the journal, Mania, no. 7, pp. 39-53, Barcelona, July 2000.

The Spanish translation referred to above is a translation of excerpts from an article originally published in Krisis, no. 21-22, Nuremberg, 1998, under the title, “Bewusstlose Objektivität. Aspekte einer Kritik der mathematischen Naturwissenschaft.”

Source of the Spanish translation: http://planeta.clix.pt/obeco/

German original: http://www.exit-online.org/textanz1.php?tabelle=autoren&index=3&posnr=20&backtext1=text1.php

  • 1. Kant, Metaphysical Foundations of Natural Science (1786), Preface.
  • 2. Karl R. Popper, Objective Knowledge. An Evolutionary Approach, Revised Edition, Oxford University Press, New York, 1979.
  • 3. Alfred Sohn-Rethel, Geistige und körperliche Arbeit, Frankfurt, 1970; Das Geld, die bare Münze des Apriori, Berlin, 1990. In English: Intellectual and Manual Labour: A Critique of Epistemology, Humanities Press, Atlantic Highlands, N.J., 1977.
  • 4. Bodo von Greiff, Gesellschaftsform und Erkenntnisform. Zum Zusammenhang von wissenschaftlicher Erfahrung und gesellschaftlicher Entwicklung, Frankfurt, 1976.
  • 5. Rudolf-Wolfgang Müller, Geld und Geist. Zur Entstehungsgeschichte von Identitätsbewusstsein und Rationlität seit der Antike, Frankfurt, 1977.
  • 6. David Hume, An Enquiry Concerning Human Understanding, 1748.
  • 7. Ibid.
  • 8. Thus, we are not advocating Feyerabend’s “anything goes” “gnoseological anarchism” (see Paul K. Feyerabend, Against Method, Fourth Edition, Verso Books, New York, 2010). Feyerabend, who is himself part of the empiricist tradition, shows that modern science does not abide by the criteria of empiricism; but this does not prove that methods have to be arbitrarily chosen, but rather that the criteria in question are erroneous.
  • 9. Ernst Cassirer, Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit, Vol. I, 1910, p. 330.
  • 10. Peter Mulser, “Über Voraussetzungen einer quantitativen Naturbeschreibung”, in Valentino Braitenberg and Inga Hosp (eds.), Die Natur ist unser Modell von ihr, Reinbek, 1996, p. 157.
  • 11. See Alexandre Koyré, Estudios de historia del pensamiento cientifico, Siglo XXI, Madrid, 1990, pp. 196-205.
  • 12. Galileo Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze (1638).
  • 13. Galileo Galilei, op. cit., Third Day, Theorem II, Proposition II.
  • 14. The effective implementation of his experiments in Galileo’s time encountered enormous difficulties, since the technical conditions were extremely primitive compared, for example, with those that are available in any physics lab at any college. The experiments conducted by Galileo to determine the uniform acceleration of objects in free fall were totally worthless; Galileo himself therefore avoided, wherever possible, giving concrete numerical values, and when he did so he was wrong from beginning to end: his values were more or less half of what the true values are recognized to be today. This fact once again shows that the replacement of the qualitative physics of Aristotle with the quantitative physics of Galileo, who worked with mathematical precision and rigor, was not due to experience (see Koyré, op. cit., pp. 274-305). We can thus understand why Galileo sometimes used the trick of presenting merely imaginary experiments as if they had really been carried out (Koyré, p. 202).
  • 15. Quoted by Cassirer, op. cit., p. 386.
  • 16. Koyré, op. cit., p. 183.
  • 17. Isaac Newton, Principia Mathematica.
  • 18. Ibid.
  • 19. Koyré, op. cit., p. 183.
  • 20. Ibid., pp. 180-195.
  • 21. The ubiquity of confounding factors, admitted by the natural sciences themselves, renders the theory of modern empiricism, according to which a theory can be tested by “the falsification of its scientific hypotheses by way of experimentation” (Popper), more than questionable. The law of gravity, for example, cannot be falsified. An experiment whose measurements contradict that law is either not taken seriously, or else incites the search for unknown confounding factors.
  • 22. Immanuel Kant, Critique of Pure Reason, Preface to the Second Edition (1787).
  • 23. It all depends on the criteria that are used: thus, for example, the “Dark” Middle Ages did not experience excesses of violence like those of the bourgeois era; those which are often attributed to it (pogroms, witch-hunts) took place in the early years of the Modern Era. Karl-Georg Zinn (Kanonen und Pest. Über die Ursprünge der Neuzeit im 14. Und 15. Jahrhundert, Opladen, 1989) shows that the nutritional status of the vast majority of the population steadily declined between 1450 and 1850 and that only since 1850 has it once again begun to improve, even if only in the industrialized countries, thanks to the industrial production of food, with all the well-known defects that this kind of production entails. If one adopts as a criterion the gap between social reality and the possibilities opened up by the corresponding state of the productive forces, modern society is the most irrational society that has ever existed.
  • 24. Even the superiority of European weapons technology in the early Middle Ages was not due to any advances in technological development, but to the impulse, which was eventually imposed on the entire society, to employ all existing technical knowledge, as well as enormous economic resources, preferentially for the development and production of firearms. The “military-industrial complex”, that obvious characteristic of bourgeois society, dates from that era (see Zinn, op. cit.).
  • 25. Modern science arose in the centers of the urban bourgeoisie; the relocation of the latter’s main centers of development from Northern Italy and Germany to England and Holland provoked a corresponding, somewhat later, relocation of the centers of scientific research to those same regions. Wolfgang Lefevre, in Naturtheorie und Produktionsweise (Darmstadt, 1978), maintains that the natural sciences were initially above all an ideological instrument of the bourgeoisie in its struggle against the privileges of the nobility: if nature obeys universal laws, then the “natural” order of society is the one whose members abide by those same laws.
  • 26. Sohn-Rethel, op. cit.
  • 27. Zinn, op. cit., maintains that bourgeois society arose from a kind of “historical accident”, due to the plague of the 14th century and the resulting destruction of feudal structures, combined with the contemporaneous introduction of firearms, whose mass production reinforced the formation of central State powers and the monetary economy (substitution of taxes for tribute in kind): which would at least explain why it was only in Europe that the embryonic forms of commodity society managed to shatter feudal structures.
  • 28. Kant, Critique of Pure Reason, B 132/134.
  • 29. Greiff, op. cit., p. 93.
  • 30. This fact is familiar to quantum physics, in which observations cannot be made without seriously influencing the “natural” course of things; although in general this is often swept under the rug by way of the entirely unfounded assumption that behind the regularity produced by the interaction of the subject and the microstructure the “real” laws of nature, independent of the subject, lie concealed.
  • 31. Robert Kurz, “Subjektlose Herrschaft”, Krisis, no. 13 (1993), p. 68. An English translation of this text is available online (as of November 2014) at: https://libcom.org/library/domination-without-subject-part-two-robert-kurz.
  • 32. Ibid., p. 69.
  • 33. I repeat, because I have already had some experiences with misunderstandings with regard to this question, that this does not mean “anything goes” in the sense of Feyerabend, but rather the attribution of the meaning that corresponds to a method; which obviously is not the same as placing it on the same level as a voodoo curse.