Bourgeois science in a sort of revival of the millennia-old paradox, or compromise, of Greek astronomy, applied to the class struggle, has the pretence of saving phenomena and at the same time principles; but when it realises the incompatibility of the two planes, it falls back on an epistemological move, dividing social physics into two parts, practical experience and hypotheses, the one being true and demonstrated, the other neither true nor probable, but simply useful.

Without claiming that the analogy is capable of perfectly rendering the impasse of the theoretical speculation of the various species and subspecies of petty-bourgeois determinism, we mean to say that all the big talk about an alleged paleo-Marxist geocentrism or Ptolemaism, in the name of modernism and the adaptation of culture to new social realities, ends up leading to a confusion of language that is there for all to see.

Since the premises of historical materialism are foreign to any form of philosophical apriorism, when one accuses it of wanting to save the principles at all costs (an alleged circularity and uniformity of the orbits of the class struggle), at the cost of disproving phenomena or disregarding facts, one does nothing but unwisely flirt with Galilean scientific language without getting anywhere.

The tragedy of the counter-revolution, more than in the physical destruction of proletarians and communists, lies in the falsification of revolutionary history. In so-called Marxism-Leninism, with a hyphen, in fact, began that abnormal dogmatics whereby the daily recitation of principles can justify any sort of practice, any tactical zig-zag. Orthodoxy ended up becoming an ecclesiastical matter, based on canons and inquisition, without any consideration of the actual dynamics of the class struggle.

Paraphrasing a famous proposition by the physicist Dirac: ‘the only purpose of theoretical physics is to calculate results that can be compared with experiment, and it is not at all necessary to provide a satisfactory description of the entire course of phenomena’, a solution that for reformist gradualism, today pure and simple opportunism, the theory of small steps, small adjustments, invisible gains is only a fascination dictated by the distortion of historical and dialectical materialism.

The nature of the Marxist theory of the class struggle can only by analogy evoke the models of interpretation of physical and social reality that bourgeois ideology has prepared in the course of its historical experience; in reality, its characteristic is to arise as a single block and not to be confused with the inevitable skirmish of polemics and coquetry with the philosophy and social science of the bourgeoisie.

The class struggle was not invented by Marx; he did nothing other than draw the consequences, not at all logical in themselves, but necessary on the basis of historical experience, which include the transition to the dictatorship of the proletariat and the exercise of proletarian power up to communism.

In our historical vision there are no ‘laboratories’ in the abstract where social experiments are carried out, because in the class struggle every abstract image of the world is reductive and ideological; just as the reference to the figure of the gymnasium, with regard to the economic struggle as a function of the political struggle, has nothing to do with fictions and moves to try out in the mirror. The nature of the materialist conception of revolution consists in the consciousness proper to the Party organ that every aspect of class struggle and social life is not fiction, but militancy, in the large social format of ionised and fighting molecules and in the invisible and non-‘accidental’ format of a few militants, who, without giving up, restore the revolutionary organ in the least favourable conditions.

Thus, the objections of the professors in their Byzantine theology do not in the slightest touch the substance of the historical tragedy of the counter-revolution and its effects.

We maintain that only the revolutionary theory of the proletariat has the capacity to satisfactorily pose the relationship between being and thought, and not by virtue of itself as thought, but insofar as it is the result of the necessity for the proletarian class, as the last class in history, to adapt its collective experience over time to external reality. This assertion has nothing wishful about it, since against all philosophies it does not claim to state a truth valid at all times and in all places, but to uphold the correct criterion, capable of establishing the correct relationship between theory and practice, without circumventing the age-old question of how to save principles and save phenomena.

‘We do not deny the existence of logic as an instrumental science and technique of the forms of thought; indeed, it is well known that in the Marxist conception its use is accompanied by that of dialectics, or the science of relations (...) But what must be made clear is that logic is constructed and justified by its application and correspondence to reality, and not codified a priori in our heads and only then applied to things. It is no longer the science of the principles of thought, which becomes the science of the principles of being, but is merely the science of the “forms” of thought, not absolute and fixed, but always ready to be modified by results and data from the outside world’.

The instrumentality of the theory (theory is a guide for action) of our view of reality does not entail a generic compromise, because we do not resist the modification of the ‘forms’ of thought whenever it is necessary.

Of course, the great and much-vexed question consists, not just today, in deciding who has the authority to modify and adapt phenomena to principles, practice to theory, and vice versa. For us, even when the clash between antithetical worldviews, from philosophy to physics, has taken shape and been embodied in people, from Galileo to Darwin, it has never been people, even eminent ones, who decided, nor the institutions in their economic and legal apparatuses: we have said, and we have no need to return to the issue, that the truth of science is not settled on the basis of Central Committee circulars or Holy Office decrees.

Historical antagonism is antagonism between classes, and all the nomenclatures that claim to replace or exclusively embody this contradiction invent themselves in order to secure a place on the stage of history.

Thus, historical materialism does not shy away from the science of relations, from the effort to define the boundaries between being and thought, and feels elevated in its method and essence even when, indeed especially when, seemingly insoluble questions are addressed and correctly resolved, even at the level of the science of logic and the instrumental technique of the forms of thought.

On the contrary, we do not share the diplomatic attitude of the bourgeois and opportunist culture of our times, when, in the name of the autonomy of individual languages or scientific statutes, each one ‘independent and free’, it refuses to consider the nature of the relationship between the different languages, denying the very science of relations!

Yet certain solutions, or hypotheses of solutions proposed in certain particular historical epochs, even when they do not satisfy us, are an answer that historical materialism is able to consider in their scope and value; when it is revealed to us that insoluble problems and the object of diatribe with no possibility of agreement have obtained a new approach, we are able to recognise the reason for such a question.

The concept of infinity is an example of this. What was not possible to philosophy, was possible to mathematics, and for us it is a confirmation of our method. The first sketches of a rigorous mathematical theory of infinity encountered a series of paradoxes, such as the one whereby the infinite number of points contained in a line segment would be the same as the infinite number of points contained in a segment twice as long. Or consider two concentric circumferences, one twice as long as the other, if the radii are drawn, each point of the larger circumference can be made to correspond to one of the smaller circumference; that is, the infinite number of points of the larger circumference must be the same as the infinite number of points of the smaller circumference, even though the latter is half as long as the other.

Medieval philosophers such as Thomas Aquinas deduced from such arguments that numerical infinity was intrinsically contradictory. For Thomas, only God is infinite. Later, other thinkers, such as Galileo, advanced the hypothesis that there could be numerous infinities, but that these numbers nevertheless followed laws that were very different from those governing finite numbers. It would take until the late 1800s for a comprehensive theory of mathematical infinities to be worked out.

Cantor, in an 1885 essay, among other things replied: ‘the actual infinite presents itself in three different contexts; 1) when it is found realised in its most complete form in a completely independent, otherworldly being, Deo, in which case I call it the Absolute Infinite, or simply the absolute; 2) when it is realised in the contingent, created world; 3) when the intellect grasps it in the abstract as a mathematical quantity, number, or type of order’. For Cantor there were, in short, three types of infinity. The first, that of the theologians, the second, that of the physicists, as when we say ‘an infinite number of stars’, the third that which interests mathematicians, which indicates, simply, a number greater than any other ordinary finite number, and is designated by the last letter of the Greek alphabet lowercase omega, ω.

Cantor’s operation reminds us of Engels’ remark regarding the questions posed by the distinguished astronomer Father Secchi ‘God is nowhere treated worse than by the natural scientists who believe in him’. So Father Secchi ‘begged God to accommodate himself outside the solar system’. Cantor places God outside the operations of the mathematics of infinity.

Marxist materialism can be seen to be confirmed when it witnesses these operations, but it grasps their limit, within the context of the division of labour that also prevails, in one form or another, in intellectual and philosophical work: Cantor seems to repeat the classic ‘let me work’, clearing the ground of the intrusions of others and declaring his incompetence to resolve difficulties that do not concern him; but it is in the borderlands that the hardest battles are fought and the greatest conflicts are resolved.

Our thesis is that ‘old, overly narrow absolutes must be broken in order to construct new and more valid true absolutes. But no longer absolutes from which one starts as from a condemnation imposed prior to any achievement, absolutes that are earned, reached, passed into.

The famous continuum hypothesis of 1875 clearly postulates the existence of different degrees of infinity. The idea was so astonishing that some refused to believe it. But thanks to the simple diagonal procedure of a square, it is proved beyond doubt that the set of real numbers is larger than the set of natural numbers.

In order to reach the depths of the infinite degrees of infinity, one can only turn to the heavens, to the absolute infinite. Set theorists use for the latter the Greek letter Ω, capital omega. But once again mathematics runs into an obstacle: what would happen to Ω after adding something to it, Ω + 1? The same paradox occurs in theology if one considers these two statements: 1) whenever one completely knows a thing, say D, one can know something greater, such as, for example, a pair of replicas of D; 2) God is that than which nothing greater can exist. Theologians therefore deduce from this that God is not something that can be fully known. St. Gregory, for example, declared: ‘No matter how far our mind may have progressed in the contemplation of God, it does not attain to what He is, but to what is beneath Him’. Set theory adopts a very similar attitude with regard to the absolute infinite.

In our Philosophical Notes it is said ‘especially the faculty of abstracting and generalising is acquired by a long exercise of the collective and personal faculty of thinking, and the exercise consists in the repetition of infinite particular applications all satisfying experimental conditions’. The purported absolutes of thought are nothing but successive generalisations, more often than not destined to give way to others, therefore lacking definitive value; in any case, they are the opposite of primitive, unmodifiable principles functioning as starting points.

That in the course of human history they have taken the name of God or of I does not disturb us much. The particular historical, ethnographic, etc. facts that prove this are innumerable. The savage cannot think of a number greater than 3 or 5, the ordinary man already makes an effort to see clear in his thought a demonstration of elementary mathematics, and refuses to admit that calculating on the infinitesimal parts of finite quantities makes any sense. The modern mathematician, on the other hand, does such calculations as a matter of course, but may feel a sense of unease at the proposal of further abstractions such as differential forms with more than three dimensions, Cantorian numbers (two infinite numbers, better called transfinites, can be greater than each other), etc., etc.

But what ‘bourgeois science’ itself admits within the closed little garden of specialisations, it then takes care to destroy in ordinary life with repeated appeals to realism and common sense. Since higher infinities have little practical application, why break one’s head over speculations that call into question the more general ideological scaffolding and trappings, when, with the most elementary and suggestive recourse to the Infinite, to Being, to God, or even worse to Man with a capital M, one thinks one can get away with it.

Until 20 years ago, many scientists believed that the universe contained an infinite number of stars. But recent developments, in particular the discovery by Penzias and Wilson of the cosmic background radiation, a remnant of the ‘big bang’, the original conflagration of the universe, seem to assign the universe a number of 1 followed by 24 zeros of stars. Even if the universe is not infinite, it is still possible that it will last forever. What about a universe whose lifespan was ω + ω years? Some cosmologists argue that if one could enter a rotating black hole, one could exit ω years into the future. It may be that infinity can be found in the real world on the side of the infinitely small. Cantor himself proposed, in his time, the curious theory according to which there would exist two types of substances, matter and ether, the latter being somehow associated with energy transfers. Material objects would be infinitely divisible into ω levels of massive particles, whereas ‘ether’ objects an even greater infinity of ether particles.

The conclusion that Cantor’s infinities are not a single absolute infinity, but many transfinites, all relative, all augmentable, indicates that the proponents of the a-priori have nothing left but to take refuge in acts of faith, which in the not-so-distant past have produced inquisitions and burnings, certainly serious and indicative of brutal historical contradictions, which however do not withstand comparison with the tragedies of the modern class struggle, with the diktats of the Politburos which, in the name of socialism, have claimed to establish theoretical truth in the field of science.

We true communists know, and historically bear its mark in our living flesh, that the new absolutes, upheld in the name of general theoretical relativism, certainly do more harm than the transcendent and invisible Absolute. That is why, while opportunism and the bourgeoisie have now delegated high theoretical and scientific speculation to the specialists, within the cloisters of the Academies of Science and to university barons, we consider it as belonging to the Party organ, in its sublime moments and in its most depressed and depressing historical lows, the task of not abandoning knowledge and the sculpting of theory, whatever the contingent result may be, however modest our contribution may be; if our task is that of obscure artisans assigned to wield the chisel and incapable of shaping hard material, we are rewarded by the awareness that the organic work recognises and treasures our irreplaceability.

In the more proper field of language, the same observations can be made both on the value of words and their relations. The verb to be, which represents the abstraction of abstractions and is the pillar on which the proponents of a-priori wish to rest the absolute laws of thought, goes back to an Indo-European root meaning to breathe, i.e. a very concrete way of being, belonging only to living organisms.

What then to say when supposed materialists identify being with thought? Yesterday and today, this kind of mysticism justifies fixed and irreplaceable universal laws in physical, organic, historical, and economic reality, up to a sacred respect for the unsurpassable archetypes of humanity for all time, the feminine and the masculine, the servant and the master, the ruler and the ruled.