‘In every epoch, and therefore also in ours, theoretical thought is a historical product, which at different times assumes very different forms and, therewith, very different contents. The science of thought is therefore, like every other, a historical science, the science of the historical development of human thought. And this is of importance also for the practical application of thought in empirical fields. Because in the first place the theory of the laws of thought is by no means an “eternal truth” established once and for all, as philistine reasoning imagines to be the case with the word “logic” (...) And dialectics has so far been fairly closely investigated by only two thinkers, Aristotle and Hegel. But it is precisely dialectics that constitutes the most important form of thinking for present-day natural science, for it alone offers the analogue for, and thereby the method of explaining, the evolutionary processes occurring in nature, inter-connections in general, and transitions from one field of investigation to another’ (Engels: Dialectics of Nature).

Already the Greeks understood the science of dialectics as capable not simply of ‘lining up’ facts, events differing in form and situation, but of interpreting them, i.e. to give them a unitary ‘vision’, to organise them ‘into a world’. Dialectical materialism does not, for fear of appearing to be a ‘philosophy’, renounce proposing its ‘worldview’, which is its own and exclusive, even when it recognises that it is the fruit of class struggle and is not due to a Tom or Dick.

Our science must be capable of foresight, and this is not to be understood ‘as a generic more or less sceptical waiting for events to unfold, whose unexpected novelties and changes of course indicate to the movement the new path it should take, but as a constant comparison of historical occurrences with previous “expectations” and “forecasts”; something the party, as a living organisation participating in historical events, is in a position to do (although it remains a constant challenge) by drawing on the theory which shaped its platform and its general character’ (from Economic and Social Structure of Russia Today, Foundations of Revolutionary Communism, I).

Communists are distinguished ‘[by the fact that,] [I]n the various stages of development which the struggle of the working class against the bourgeoisie has to pass through, they always and everywhere represent the interests of the movement as a whole (...) theoretically, they have over the great mass of the proletariat the advantage of clearly understanding the lines of march, the conditions, and the ultimate general results of the proletarian movement’ (Manifesto of the Communist Party).

This is why ‘the proletariat asserts its political autonomy by organising itself into a party’ (Lenin, What Is To Be Done?).

But the modern know-it-all, epistemologist and pragmatist, while not denying that science should allow for predictions, ends up arguing that all predictions belong to the sphere of the subjective, the conceptual in any case, and therefore cannot claim to be objective. He does not deny dialectics, but neglects to recognise the materialist foundations of dialectics, the only ones capable of attributing objective and necessary existence to things and their movement, outside of our will.

The aim of dialectical materialism is to grasp objective processes, independent of the perception and will of those who experience them, to know the development of things and learn their laws of motion.

The organisation of communists into a party is translated into the struggle

‘for the affirmation, in the activity of the party itself, of “compulsory” norms of action of the movement, which must not only bind the individual and the peripheral groups, but the party centre itself, to which total executive discipline is owed, insofar as it is strictly bound (without the right to improvise, to discover new situations, to open new courses of action) to the set of precise norms that the party has given itself for the guidance of action.
‘However, one must not misunderstand the universality of these norms, which are not immutable original norms, but derived norms. The established principles, from which the movement cannot free itself, because they arose – according to our thesis of the spur-of-the-moment formation of the revolutionary programme – at given and rare turning points in history, are not the tactical rules, but the laws of interpretation of history that form the baggage of our doctrine. These principles lead in their development to the recognition, in vast fields and in historical periods calculable over decades and decades, of the great course on which the party walks and from which it cannot deviate, for that would only accompany its collapse and historical liquidation. Tactical norms, which no one has the right to leave blank or to revise according to immediate conjunctures, are norms derived from that theorisation of great paths, of great developments, and they are practically firm but theoretically mobile norms, because they are norms derived from the laws of great courses, and with them, on the historical scale and not on that of manoeuvre and intrigue, avowedly transitory’ (Economic and Social Structure of Russia Today).

‘Theory is a presentation of real processes and their correspondences that is intended to facilitate their general understanding in a certain field, moving only afterwards to prediction and modification. Law is the precise expression of a certain relation between two particular sets of material facts, which is constantly seen to occur, and as such enables the calculation of unknown relations (future, gentlemen philosophers, or present or past, does not mean: for example, a certain law, if well studied, may enable me to establish how much the sea level was at the temple of Serapis a thousand years ago) (...)
‘Theory is general, law is bounded and particular. Theory is generally qualitative and only establishes definitions of certain entities and quantities. Law is quantitative and seeks to achieve measurement.
‘A physical example: in the history of optics, two theories of light have alternated with varying success. That of emission says that light is the effect of the movement of minute corpuscular particles, that of undulation says that it is the effect of the oscillation of a fixed medium in which it is transmitted. Now, the easiest law of optics, that of reflection, says that the ray incident on the mirror makes the same angle with it as the ray emitted. Having verified this law a thousand times, the young gallant knows where to stand to see the beauty opposite intent on toileting: the fact is that the law accords with both theories, and it was other phenomena and other laws that determined the choice.
‘Now, according to the text, this is what would happen: the “law of exchange between equivalent values” accords as well with Stalin’s theory which says: there are mercantile forms in a socialist economy, as with our (modestly) theory which says: if there are mercantile forms and great production, it is capitalism. Check the law: easy, you go to Russia and see that you exchange in roubles at given prices as in any banal bazaar: the law of equivalent exchange applies. To see what the real theory is is a little more complicated: we deduce: we are in full, straightforward and authentic capitalism; Stalin fabricates a theory – precisely: theories are invented, laws are discovered – and says in defiance of Father Marx: given economic phenomena of socialism occur normally according to the law of exchange (called the law of value)’ (Dialogue with Stalin).

But the story is old:

‘This man (the Jesuit Scheiner) goes from hand to hand figuring things as they ought to be in order to serve his purpose, and he does not go from hand to hand accommodating his intentions step by step to things as they are’ (Galileo), or ‘He (Hegel) does not develop his thought out of what is objective, but what is objective in accordance with a ready-made thought which has its origin in the abstract sphere of logic’ (Marx).

We say: if there are mercantile forms and large-scale production, it is capitalism. We adhere in essence to the Galilean experimental method, the structure of which is articulated in observation, in the formulation of hypotheses, and in their verification or falsification on the experimental ground, which means real and objective, i.e. independent of will. The idealist, the pragmatist, the epistemologist, the more sophisticated the flatter, claims to adapt reality to his mental scheme precisely when he swears to reject any kind of apriorism in the name of facts, experience, readiness for the new, because everything is possible, everything is new. But the critique of the apriorism in dialectical materialism is of an entirely different kind, since it is not afraid to recognise the course of its historical-practical evolution.

The ideal dialectic tends to reproduce, to represent concrete reality according to what Marx specifies:

‘The concrete is concrete because it is the concentration of many determinations, hence unity of the diverse. It appears in the process of thinking, therefore, as a process of concentration, as a result, not as a point of departure, even though it is the point of departure in reality and hence also the point of departure for observation and conception. Along the first path the full conception was evaporated to yield an abstract determination; along the second, the abstract determinations lead towards a reproduction of the concrete by way of thought. In this way Hegel fell into the illusion of conceiving the real as the product of thought concentrating itself, probing its own depths, and unfolding itself out of itself, by itself, whereas the method of rising from the abstract to the concrete is only the way in which thought appropriates the concrete, reproduces it as the concrete in the mind (...)
‘This example of labour shows strikingly how even the most abstract categories, despite their validity – precisely because of their abstractness – for all epochs, are nevertheless, in the specific character of this abstraction, themselves likewise a product of historic relations, and possess their full validity only for and within these relations’.

‘[M]odern materialism is essentially dialectic, and no longer needs any philosophy standing above the other sciences. As soon as each special science is bound to make clear its position in the great totality of things and of our knowledge of things, a special science dealing with this totality is superfluous. That which still survives, independently, of all earlier philosophy is the science of thought and its laws – formal logic and dialectics. Everything else is subsumed in the positive science of nature and history’. (Introduction to Anti-Dühring)

But to the ‘realists’, empiricists, pragmatists, and epistemologists, it appears that too much has been conceded to theory on the part of dialectical materialism, which claims to have a ‘worldview’; and they croak incoherently: ‘Is this not perhaps a philosophy of history, is this not dogmatism?’

In the final warning of the second edition of Capital (24 January 1873) Marx wrote:

‘Of course the method of presentation must differ in form from that of inquiry. The latter has to appropriate the material in detail, to analyse its different forms of development, to trace out their inner connexion. Only after this work is done, can the actual movement be adequately described. If this is done successfully, if the life of the subject-matter is ideally reflected as in a mirror, then it may appear as if we had before us a mere a priori construction’. Here is revealed the secret of our dogmatism which terrifies the easy discoverers of ever new, ever free theories.

‘In fact, the materialistic denial that a theoretical system that has arisen at a given moment (and even worse if in the mind and ordered work of a given man, thinker or historical leader or both together) can contain the entire course of the historical future and its rules and principles irrevocably, is not to be understood in the sense that there are no systems of principles that are stable over a very long historical period. On the contrary, their stability and resistance to being undermined and even to being improved upon is a major element of strength of the social class to which they belong and whose historical task and interests they reflect.
‘The succession of such systems of doctrine and praxis is linked, no longer to the advent of men, but to the succession of modes of production, i.e. the types of material organisation of the life of human collectivities. This is the nature of communist dogmatism: not to believe, indeed to rule out, that great scientific theories in the field of natural and historical dialectics can arise at every street corner and can be easily interchangeable, or tweaked at will’ (Milano meeting, 1952, The Historical Invariance of Marxism).

It is precisely for this reason that

‘Marxism poses the question of philosophy in an original way and in this sense refuses to let itself be lumped in with the various philosophies historically listable, or even worse, systematically. We will therefore not say that there is a Marxist philosophy, but neither will we say that Marxism is not a philosophy or that Marxism has no philosophy. This would give rise to an equivocation and to a very serious danger: that of believing that Marxism stands on “foreign” ground to that which philosophers have for millennia hypothesised. And from this one could with serious deviation deduce that the Marxist militant remains free, having accepted certain directives of political and social action, and “confessed” certain economic and historical theories, to declare himself for one of the many philosophies: realism or idealism, materialism or spiritualism, monism or dualism, or whatever’ (Communism and Human Knowledge)

Not only that, but for the Marxist,

‘whose system is based on the direct derivation of ideologies from the same material world in which the facts and relations of interests take place and become real forces (...) there is no convenient safe in which to store, while it trades in fact with its opponents in the practical field, an intact doctrine of its own’.

Thus, while bourgeois and opportunist ideology can trade in principles, in the name of their ‘conquered’ secularism, the communists, precisely because they have long been enemies of every unjustified apriorism, defend their principles and their class theory.

Without needing to refer to our tradition of fidelity to the historical experience of the proletariat, we can draw heavily on the more general history of human social life that precedes the modern class struggle, to obtain confirmation that our caution in judging the validity of ‘resistant’ theories and the nature of ‘consciousness’ is well founded. We are indeed convinced that, against the idealist and superficially empiricist tendencies that are in vogue, the steps of human ‘thought’, which we deny as autonomous and existing in itself, with its own universal history and independent from material life, are not only very slow, but in a certain sense imperceptible to those who do not have a serious notion of actual social dialectics.

Not only that, but today we have proof that in the hands of the ‘philosophers’, human thought would not have progressed; today it is the mathematicians who claim credit for progress; we, much less specialised and slower, attribute it to the dialectic of social classes; to the necessities of material and spiritual life as it has been confirmed in the clash between the antagonistic interests of modern historical formations.

Let us take the classical and typically philosophical-mathematical problem of infinity as an example. Infinity, Aristotle notes, must exist. After all, if it did not exist, it would have to be invented because everyone needs it, from philosophers to mathematicians to physicists. Just think that without infinity, time would have a beginning, the number series an end, and magnitudes would not be divisible into other magnitudes. But infinity is either in potential or in act. Potentiality is a quantity that can never be exhausted: for example, the increasing series of whole natural numbers (1, 2, 3, 4, 5...); in act, a quantity that lies beyond any finite quantity, for example, the set of all natural numbers. To avoid certain logical and physical paradoxes, Aristotle only accepted potential infinity and denied actual infinity.

However, old and new paradoxes will remain, both in the one and the other type of infinity. Take the potential one: the credit for having first noticed its paradoxicality belongs to Zeno of Elea, a follower of Parmenides, conspirator and enemy of tyrants to the point of biting off his tongue and spitting it in the face of Nearchus, (by the way, it would be time to see who is more ‘progressive’, as our current opportunists would say, the theorists of being, Zeno and Parmenides, or the obscure Heraclitus, the theorist of becoming) who invented the paradox of Achilles and the tortoise.

Suppose Achilles runs at ten times the speed of the tortoise. He is confident of winning and therefore gives the animal a hundred metre head start. Now it happens that when Achilles arrives where the tortoise started it has run 10 metres. In order to try to reach it, Achilles covers these 10 metres as well, but in the meantime the tortoise has moved 1 metre. If Achilles covers this metre as well, the tortoise is still 10 centimetres ahead. Conclusion: no matter how fast the swift-footed one runs, he never catches up with the tortoise. In the hands of philosophers, Zeno’s paradox did not make substantial progress.

Bertrand Russell (late nineteenth century – early twentieth century) castigated their stupidity for not having understood its true meaning. The fact remains that after two thousand years, having passed into the hands of mathematicians, real progress was finally made. Note that in the space of two thousand years there were three distinct modes of production, the slave, the feudal, and the capitalist mode, practically speaking. In short, the mathematicians’ solution – which only came to full awareness with Weierstrass and Bolzano – consists in proving that the series of distances covered by Achilles (100 metres, and then 10 metres, 1 metre, and so on) is a convergent series that has a limit, that is, a finite sum (in our case, 111.1 metres recurring). With this, the paradox disappears because it is shown that by summing finite quantities infinitely one obtains a finite quantity.

But is it really true that the paradox arises from a linguistic trap, in this case set by the adverb ‘never’? This adverb basically means two things: ‘at no time’, as, for example, in the phrase ‘I will never read it’, and ‘without end’, for example as in the phrase ‘this sequence never ends’. When one meaning is substituted for the other, Zeno’s paradox emerges. Modern philosophers of language, such as Wittgenstein, have since extended this by circumstance saying that all philosophical problems dissolve precisely by revealing the traps of language, and that there are no philosophical problems, but rather linguistic perplexities.

Without professing linguistic philosophy, the Marxist tradition of the Left has tackled this fundamental problem head on, without falling into the formalistic exaggerations of the adherents of this speciality of thought. For us, the issue falls within the broader problem of the so-called ‘a priori givens of the intellect’:

‘Undoubtedly we express, record, communicate our knowledge by means of thought, and, in a more concrete sense, by means of spoken and written language. On the data thus accumulated we then make operations or reasonings from which we draw new results in the form of suppositions or predictions that are in turn confirmed in general by events in the real world.
‘The argument seems very strong that this whole system: notion, reasoning, foresight, cannot subsist without the subject man, and moreover thinking man, and that its relations and connections are not the property of an external extra-human world, but of a world that is such insofar as it is known and thought of by us. In truth, the serious difficulty of this problem consists more in the imperfections of the language into which we try to translate it. If we claim to solve it by thinking, we have already placed ourselves on the ground of those who want to convince us that every result is conditioned by intrinsic laws of thought. The correct procedure, however, is the opposite: the mechanism inherent in the instrument of thought, i.e. language, needs to be perfected and corrected in order for the question to be eliminated. Correcting and modifying the mechanism of language means appropriately modifying the value of the terms that represent real things and facts and of the logical-mathematical relations that can be increasingly adapted to their purposes.
‘It is a fact that the mechanism of language changes from epoch to epoch and from people to people (although the fundamental laws can and should be considered common to the various idioms), but also from school to school, from author to author, from researcher to researcher. The value of linguistic terms and relationships is constantly changing and evolving; it is precisely the experience of the outside world that ultimately decides the validity of changes. It is only that the slowness of these makes one believe that they are unimportant and thus limited by the absolute content of thought. This will become clearer from the discussion of the alleged a priori validity of logical schemes and mathematical principles’ (Philosophical Notes).

We have now given proof of this with the question of mathematical infinity and the convergent series of numbers. Likewise, the theories of demonstration and proof change according to human needs, and according to the inexhaustible need that the ordo rerum and the ordo idearum agree, to the point that the different schools, expressions of opposing historical and, in modern terms, class reasons, not only do not understand each other as is claimed, but cannot understand each other, up to the fortunate formula of the incommensurability of theories. In truth, it should not be believed, to take a classic, and for us, fundamental example, that Galileo or Bellarmine did not understand each other, but rather that their logic, whether they were aware of it or not, was not their personal logic, but the expression of two antagonistic ways of understanding the physical world and the operability within it.

And this is all the more interesting if we consider that modern ‘epistemologists’, et pour cause, no longer feel able to side with Galileo in accordance with the progressive spirit, but can snobbishly indulge themselves in considering the reliability of geocentrism, if only as a suggestive hypothesis today extremely tantalising. Bellarmine in fact, like Urban VIII, demanded that Galileo treat the heliocentric theory only ex supposition, as a mere calculating tool, but not until its negation had been proven contradictory.

Now, Bellarmine said,

‘I will not believe that there is such a demonstration until it is shown to me, nor is it the same thing to demonstrate that, supposing the sun to be in the centre and the earth in the heavens, the appearances are saved and to demonstrate that in truth the sun is in the centre and the earth in the heavens’.

The quibble driven by his distrust in reason is clearly visible, both because the demonstration is logically impossible and because he too attaches no weight to empirical evidence. In fact, according to his criterion, any theory will always remain a supposition, no matter what support it has. Galileo clearly saw all this and had no difficulty in replying to Bellarmine that when a theory is, like the Ptolemaic one, refuted by experience, then it is ‘indubitably false’, whereas when, as in the Copernican one, it is well confirmed, then ‘it may be true’ since ‘no greater truth can and should be sought in a position than that of responding to all particular appearances’.

This is what we claim when we say that

‘The great conquests of knowledge (...) do not consist in establishing new eternal and irrevocable truths by means of revealing discoveries, since the road always remains open to further developments and to richer scientific and mathematical representations of the phenomena of a given field. Instead, they consist essentially in definitively breaking down the premises of ancient errors, including the blinding force of tradition which prevented our knowledge from reaching a representation of the real relationships of things’ (Force, Violence, Dictatorship in the Class Struggle).

The purported absolutes of thought are nothing but successive generalisations, most often destined to give way to others, thus lacking definitive value. In any case, they are the opposite of unchangeable primitive principles functioning as starting points. Nor do we share the pure and simple explanation of logical contradictions as linguistic perplexities, which mathematics may think it can resolve against the vagueness and primitiveness of philosophies: we maintain that contradictions are in reality, and that both thought and language merely reflect at a certain level of representation. On the other hand, mathematics is nothing other than the logico-linguistic attempt to deal with coherent and consequential definitions against general and merely approximate principles.