Science and Marxism

Engels on materialism, the infinite and cosmology

With each epoch-making discovery even in the sphere of natural science [materialism] has to change its form… (Engels, Ludwig Feuerbach and the Outcome of Classical German Philosophy, Selected Works, p597)

Engels’ materialism

With each epoch-making discovery even in the sphere of natural science [materialism] has to change its form… (Engels, Ludwig Feuerbach and the Outcome of Classical German Philosophy, Selected Works, p597)

Since Einstein, quantum mechanics, and the Big Bang theory, materialism has to change its form. This means dialectical materialism too. We must remove old dogmas and begin again, starting from the recognition that the method of dialectical materialism at base is simply materialism represented dialectically.

Engels’ statement also applies in a general sense to our former concepts of space, time and the infinite universe. But by contrast, Woods criticises specific scientific theories of space and time for departing from the Newtonian concept of time and space as embraced by Engels.

If it appeared to materialists in the 19th Century, albeit without evidence, that the world must be infinite, the epoch-making discoveries we will shortly discuss have forced a change. These discoveries may not be the final word, but there is no going back to the old dogmas, to the Newtonian outlook.

Dialectical materialism takes from Hegel its “death blow to the finality of all products of human thought and action” as Engels puts it. It is simply wrong, purely from a dialectical standpoint, let alone the current scientific standpoint, to state as if it were an incontrovertible fact that, “Dialectical materialism conceives of the universe as infinite” as Woods does. (p189)

Infinite space and time

It may be argued that Engels’ works set into a kind of Marxist orthodoxy the Newtonian science of his time. In general, Engels was defending and exemplifying, quite correctly, a materialist approach to the world against those such as Eugen Dühring who were seeking to take the socialist movement back to an idealist, eclectic outlook. Engels necessarily proceeded on the basis of those current scientific ideas that appeared to be beyond question.

Woods, on the other hand, defends Engels’ point of view not for its inherent respect for scientific validity, its materialism, but as if Engels was guided by some higher principle (to which Woods elevates dialectical materialism), which in some way lifted the Marxist method above that of scientific investigation. He transforms Engels’ viewpoint into dogma. Woods says Reason in Revolt defends “the fundamental ideas of the movement” in his 2006 obituary of Ted Grant (cited as co-author of Reason in Revolt). In truth, Reason in Revolt defends Engels’ support for Newtonian physics somewhat as others defend the literal truth of The Bible, not as an expression of the Marxist method of historical materialism rooted in a particular epoch, a theoretical method that has to be continually re-evaluated as science advances our understanding of our world, but as a finished philosophical doctrine that literally serves for all time.

Engels’ assumptions of infinite space and time in Dialectics of Nature should be considered in the light of his more detailed, systematic and repeated embracing of the Kantian theory of the origin of all existing celestial bodies (for example in Anti-Dühring and Feuerbach), which Engels, at one point called, “the theory of the origin of the universe” (Dialectics of Nature, p273), and his endorsement of Hegel’s rejection of the spurious infinite. These indicate a method, while Engels’ assumption of infinite time and space merely represents the form, the science of the day. We should also keep in mind that most of Dialectics of Nature consists of unfinished and unrevised drafts and was abandoned unpublished in Engels lifetime, although the introduction appears complete, and the fragment of the chapter entitled Dialectics is invaluable in demystifying Hegel’s dialectics and making it accessible.

When Woods takes Engels as his authority for what he regards as dialectical materialism, it is doubly misleading, not just because it misrepresents Engels’ methodology, but also because Engels does not make the crude mistakes that Woods does in relation to the concept of an infinite universe. When Engels discusses infinity in space and time in Anti-Dühring, he talks about a “process” which is “unrolling” in the context of an infinity which is “composed of nothing but finites”.

Singularities, “Bad” infinity, and the beginning of the universe

Engels writes:

For that matter, Herr Dühring will never succeed in conceiving real infinity without contradiction. Infinity is a contradiction, and is full of contradictions. From the outset it is a contradiction that an infinity is composed of nothing but finites, and yet this is the case.

Engels reflects Hegel’s dialectic of the infinite – that the infinite is comprised of nothing but finites, for which concept Hegel himself credits Aristotle.

Woods misrepresents Engels, turning his position upside down, when discussing Hegel’s “bad” infinity. For those for whom this may be a matter of some contention, we will pause for a moments’ discussion. In the previous chapter, Hegel on the dialectics of infinity, we noted that the terms “bad infinity” (used by Engels), and “spurious infinity”, are references to the same Hegelian concept. Engels speaks of Hegel’s “bad” infinity in the Moscow translation of  Anti-Dühring whereas we find that the Miller edition of Hegel’s Science of Logic uses the term the “spurious” infinite to represent the same thing. We discussed what Hegel meant by the term.

In the course of his criticism of Herr Dühring, Engels says that:

Infinity – which Hegel calls bad infinity – is attributed to being, also in accordance with Hegel (Encyclopaedia, § 93), and then this infinity is investigated. (Anti-Dühring, p61)

What is perhaps self-evident to Engels and his contemporaries in the above statement, but less than evident to his modern reader, is that when Engels says that “bad” infinity is “attributed to being” in the above quote, he here refers in particular to Dühring’s concept of the primordial beginning of the universe, discussed in his section on ‘World Schematism’. This is a concept which Dühring had plagiarised from Hegel, and which both termed “Being”.

When Hegel appears to describe the world coming into being, at the very beginning of his Science of Logic, he begins with: “Being, pure being, without any further determination”. Hegel later defines this undifferentiated pure being from which the rest of the world appears to emerge as “infinite being” and appears to be a type of pantheistic godhead. (Science of Logic, p100, § 164)

The reader might wonder how Hegel’s beginning of the world in this “undifferentiated pure being” compares to the well known theory, based on the research done by Stephen Hawking and Roger Penrose in 1970, which suggests that the universe emerged from a “singularity”. But the concept of a singularity, although widely accepted for a time, is not, or at least no longer, part of the standard model of the Big Bang. One reason for this is that there is insufficient observational evidence, but another is that the theory of singularities is plagued with infinities, and scientists are usually averse to infinities which arise in theories, treating them as errors in the equations or an indication of a false theory. The standard Big Bang theory is based on well established evidence for a hot dense origin to the universe, by extrapolating the observed universe back in time, but it cannot extrapolate back as far as a singularity. Hawking himself went on to study the possibility that quantum mechanical effects would operate at very small sizes, so that no singularity would arise.

Strangely, Woods considers singularities “extremely unlikely”, despite the fact that if a singularity existed which had achieved infinite density it might be considered proof of the existence of something which was infinite.

Engels takes pleasure in showing that the anti-Marxist Dühring has plagiarised Hegel, including his concept of the world beginning with an undifferentiated essence. In the idealist Hegel’s system, this undifferentiated being is subject to a somewhat vague dialectical process, and develops into a more “determinate” being – that is, develops into the world as we know it. As an idealist, Hegel feels no compelling need for materialist causes to achieve this (and is, at any rate, working on many levels, least of all the physical.)

But Dühring takes at face value Hegel’s primordial “being” and then removes the dialectical concept from it. Dühring is scathingly critical of Hegel and castigates his dialectics. Dühring purports to embrace materialism, and has supposedly disproved the existence of God already – albeit, Engels points out ironically, using proofs like  those specious proofs that past philosophers used to prove the existence of God. But without any support from Hegel’s idealist dialectics, Dühring is deprived of any means to enable his second-hand unchanging undifferentiated being to change into the world as we know it, since he has said it is unchanging.

“Herr Dühring’s universe really starts with a being which lacks all inner differentiation, all motion and change” Engels says, and quotes Dühring: “…all periodical processes of nature must have had some beginning, and all differentiation, all the multifariousness of nature which appears in succession must have its roots in one self-equal state. This state may, without involving a contradiction, have existed from eternity… ” (Anti-Dühring, p58 and p62)

So here we have Dühring’s “bad” infinity – an actually existing infinity – an eternity of unchanging, undialectical existence of a “self-equal state” before the world came into being. Scientists today suppose there must be a substratum from which the Big Bang origin of the universe emerged, but current theories picture a very dynamic terrain. Dühring claims that the origin of the universe is an actual, eternally existing “self-equal state” or being. Hegel calls concepts such as the idea of infinity as an actually existing thing, the “spurious infinite”, which Engels translates as “bad” infinity. The one exception Hegel makes to the “spurious infinite” is the same exception that Aristotle makes, as we have explained – the divine. Hegel’s mysterious godhead is “infinite being”.

Engels gleefully points out the contradictions which Dühring has got himself into by plagiarising Hegel, and, as we have seen, gives a reference to Hegel’s Encyclopaedia: “Infinity – which Hegel calls bad infinity – is attributed to being, also in accordance with Hegel (Encyclopaedia, § 93), and then this infinity is investigated.” Dühring has painted himself into a tight spot. Engels refers the reader to paragraph 93 of Hegel’s Encyclopaedia (quoted below) and proceeds to show, with great delight, that Dühring’s investigation of the infinite is also plagiarised – this time from Kant.

Engels proceeds to remonstrate with Dühring’s notion that there can exist, “the counted infinite numerical series”. He challenges Dühring to do the “clever trick of counting it”. This again invokes Hegel’s spurious or bad infinity, because by a “counted” infinite series Dühring intends to indicate a finished, completed, existing infinity, a progress to infinity which is completed with the capturing, so to speak, of an actual, “counted” infinity. This is not the infinite process of counting, which is comprised only of finites. Engels can see how Dühring slips between acceptable notions of an infinite series and the bad or spurious infinity of an actually existing “self-equal state”.

The distinction, however, is subtle. Engels attacks the inconsistencies and vagaries in Dühring’s verbal gyrations around concepts of an infinite series, and these attacks could easily be mistaken for attacks on the concept of an infinite series as such, and this is what Woods does. Nevertheless, two paragraphs later, Engels plainly states that infinity is a contradiction and is “composed of nothing but finites”.

It is in these paragraphs – to add further confusion – that Engels makes a clear assertion of infinite space and time. He does so because that was the overwhelmingly accepted scientific conception of the period, and he keeps his dialectical insights in check where physical evidence is lacking. But Engels does not hesitate to call attention to the passage in Hegel’s Encyclopaedia where he calls infinite space a “barren declamation”, and modern science would tend to agree.

In his Encyclopaedia, paragraph § 93, Hegel briefly refers to the false concept of a progression towards infinity, as opposed to a process which can be infinitely repeated but which gets no nearer to infinity. He then says:

When time and space, for example, are spoken of as infinite, it is in the first place the infinite progression on which our thoughts fasten. We say, Now, This time, and then we keep continually going forwards and backwards beyond this limit. The case is the same with space, the infinity of which has formed the theme of barren declamation to astronomers with a talent for edification.

In the attempt to contemplate such an infinite, our thought, we are commonly informed, must sink exhausted. It is true indeed that we must abandon the unending contemplation, not however because the occupation is too sublime, but because it is too tedious. It is tedious to expatiate in the contemplation of this infinite progression, because the same thing is constantly recurring. We lay down a limit: then we pass it: next we have a limit once more, and so on for ever. All this is but superficial alternation, which never leaves the region of the finite behind.

To suppose that by stepping out and away into that infinity we release ourselves from the finite, is in truth but to seek the release which comes by flight. But the man who flees is not yet free: in fleeing he is still conditioned by that from which he flees.

If it be also said that the infinite is unattainable, the statement is true, but only because to the idea of infinity has been attached the circumstance of being simply and solely negative. With such empty and other-world stuff philosophy has nothing to do. What philosophy has to do with is always something concrete and in the highest sense present. (Encyclopaedia, para 94)

Hegel returns us to the concrete from false notions of an infinite progression through space and time. Hegel applies the term “spurious” or “bad” infinity not only to a notion that an infinity of space actually exists, but also to the supposedly “sublime” descriptions of a “progress” to infinity through a tedious repetition, for instance of galaxies beyond galaxies stretching to infinity. His point is that there is no such thing as an independently existing infinity and one does not make any progress towards it.

It is remarkable that Woods missed this since Engels specifically refers to it at the beginning of the chapter from which Woods quotes. In fact, Woods twice uses the same large quote from Engels to back up his assertions about his notion of infinity. (p218 and p358) But he twice stops short of the paragraph which immediately follows and casts an entirely new light on what preceded it:

For that matter, Herr Dühring will never succeed in conceiving real infinity without contradiction. Infinity is a contradiction, and is full of contradictions. From the outset it is a contradiction that an infinity is composed of nothing but finites, and yet this is the case.

The limitedness of the material world leads no less to contradictions than its unlimitedness, and every attempt to get over these contradictions leads, as we have seen, to new and worse contradictions. It is just because infinity is a contradiction that it is an infinite process, unrolling endlessly in time and in space. The removal of the contradiction would be the end of infinity. Hegel saw this quite correctly, and for that reason treated with well-merited contempt the gentlemen who subtilised over this contradiction. (Anti-Dühring, Part V, p66)

Here Engels refines his support for infinite space and time with Hegel’s concept of the infinite (as being comprised of nothing but finites) clearly in mind. This passage bears some, slightly forced, comparison with modern science, which currently calculates that the universe will expand indefinitely – an infinite process, unrolling endlessly.


For Engels, the “Kantian theory of the origin of all existing celestial bodies”, which we discussed in the chapter, Kant’s cosmology and Engels’ commentary, means not just that the galaxies of our universe have a history in time, coming into being at some definite time in the past, but also that they will pass away.

“Nature,” Engels emphasises, “does not just exist, but comes into being and passes away.” And he discusses exactly this passing away, basing himself on some scientific speculation of the period.

Nevertheless, ‘all that comes into being deserves to perish’… instead of the bright, warm solar system with its harmonious arrangement of members, only a cold, dead sphere will still pursue its lonely path through universal space. And what will happen to our solar system will happen sooner or later to all the other systems of our island universe; it will happen to all the other innumerable island universes, even to those the light of which will never reach the earth while there is a living human eye to receive it.

And when such a solar system has completed its life history and succumbs to the fate of all that is finite, death, what then?

Later, Engels adds:

The view is being arrived at that heavenly bodies are ultimately destined to fall into one another… so that all motion in general will have ceased. (Dialectics of Nature, p38, p50-2)

Surely, all this demonstrates that Engels would have expressed little surprise if told that our universe was discovered to have a history in time – a birth perhaps ten to twenty billion years ago? Surely he would say that Kant predicted it centuries ago?

In fact, in note form, he did: “Kant – the theory of the origin of the universe before Laplace”. (Dialectics of Nature, p273) Engels emphasises “before” because the work of Laplace provided a proof of Kant’s insight, at least in relation to the development of solar systems, now typically termed the Kant-Laplace nebular hypothesis. This note appears in the fragment headed “Büchner”, which is thought to be the first fragment or set of notes which Engels made for the composition of Dialectics of Nature, written in 1873.

But Engels has more to say on the matter. One must allow for some naturally out-dated science and scientific terminology, such as the use of the term “motion”, which was the very latest terminology at the time but was shortly to be superseded by the term “energy”. We also remember the fact that Engels predates Einstein and Hubble, both of whom gave a much more definite material meaning to time and space, matter and energy, so that they can only arise together. Making this reasonable allowance, Engels would not encounter many objections from modern scientists in seeking a substratum from which our universe emerged:

This much is certain: there was a time when the matter of our island universe had transformed a quantity of motion [i.e. energy] – of what kind we do not yet know – into heat, such that there could be developed from it the solar systems appertaining to (according to Mädler) at least twenty million stars, the gradual extinction of which is likewise certain.

How did this transformation take place? We know just as little as [the astro-physicist] Father Secchi knows whether the future caput mortuum [worthless remains] of our solar system will once again be converted into the raw material of a new solar system.

But here either we must have recourse to a creator, or we are forced to the conclusion that the incandescent raw material for the solar systems of our universe was produced in a natural way by transformations of motion which are by nature inherent in moving matter, and the conditions of which therefore also must be reproduced by matter, even if only after millions and millions of years and more or less by chance but with the necessity that is also inherent in chance. (Dialectics of Nature, p51)

Leaving aside the exact terminology of ‘matter’ and ‘motion’, most scientists would not deny the main thrust behind such speculation, which is that whatever substratum gave rise to our universe, the processes are natural and are likely to reoccur. The difference is that scientists today do not take for granted that any newly emerging universe needs to have the same physical constants, so that it may not be comprised of energy, matter, space and time in the way that our universe is.

Does not Engels’ approach show that Woods’ scheme has no history in time? That in Reason in Revolt’s cosmological speculations we find just an endless repetition: “only galaxies and more galaxies stretching out to infinity”?

And does not Engels also see that there are processes going on inside these stars? That they and the galaxies they inhabit are consuming and changing their elemental constituent atoms, so that they must have a history in time? This history is written in the current make-up of the elements (for instance hydrogen, helium, oxygen, carbon, nitrogen, silicon, calcium, and iron) found in stars, which can be detected in their light. It tells us whether they are first generation stars, or stars that are consuming in part the remnants of a previous generation of stars. Observation can in practice tell how old galaxies are. How could an infinite universe be a never-ending replication of our current state – galaxies stretching to infinity? Would this not be a rather static viewpoint?

Woods poses a challenge, which might as well be directed at Engels: “The problem is: how to get from nothing to something? If one is religiously minded, there is no problem; God created the universe from nothing.” (p210)

In his notes, Engels quotes Angelo Secchi without comment:

Secchi (p 810) himself asks: When the sun and the whole system are extinct, “are there forces in nature which can reconvert the dead system into its original state of glowing nebula and reawaken it to new life? We do not know.” (Dialectics of Nature, p367, quoting from Secchi’s book Die Sonne)

Engels’ reply in general terms is the same reply that modern science and materialist scientists generally give: “we do not know”, although there are many interesting possibilities. (Undoubtedly, there are some scientists who, despite investigating materialist reality, hold religious beliefs and in some cases support ‘creationist’ theories.) But Woods forgets that coming in to being and passing away is one of the fundamental laws of dialectics. From what substratum, we do not know, but “Nature,” says Engels, “does not just exist, but comes into being and passes away.” (Dialectics of Nature, p38) From a purely dialectical point of view, this presents no problems.

Engels shows that dialectical materialism refuses to “conceive of the universe as infinite”, except perhaps as an infinite process which is composed of the finite and, perhaps, is comprised of universes which come into being and will have an end.

But as for a cyclical universe, such as the theory that Woods endorsed in 2002, the infinite repetition of Big Bangs, Engels refutes it in advance – its authors, Steinhardt and Turok, now recognise their mistake here – when he says that:

… in the last resort, Nature works dialectically and not metaphysically; that she does not move in the eternal oneness of a perpetually recurring circle, but goes through a real historical evolution. (Socialism, Utopian and Scientific, Selected Works, p407)

Next: The infinite in mathematics