"Anti-Dühring": discussion points

Submitted by martin on 2 December, 2009 - 7:21

Chapter one

1. In what way was the French Revolution a turning-point in world history such as no previous overturn or change had been?

2. Engels describes two early sorts of socialists: the "utopians" and those such as Babeuf. What separated the two sorts, and what did they have in common?

3. How did it come about that "a kind of eclectic, average socialism... has up to the present time [1877] dominated the minds of most of the socialist workers in France and England"?

4. What's the shortcoming of those early sorts of socialism, and the later "averaging-out" of them?

5. Engels follows Hegel in defining "dialectics" as the contrary of "metaphysics". What is the difference, as Engels describes it, between these two ways of trying to understand reality?

6. Engels is explicit that "dialectics" was not a discovery of Hegel's, but an approach which had been used by ancient Greek philosophers, by Descartes, Spinoza, Kant, Diderot, Rousseau, etc. What does he describe as special about Hegel's deployment of a "dialectical" approach?

7. Engels argues both that Hegel's philosophy was a "colossal miscarriage", and that it had "epoch-making merit". How?

Preliminary notes on chapters 2 to 14

In chapter 2 Engels reports that Dühring presented himself not just as a social and political analyst, but as "the man who claims to represent... philosophy in his age", the representative of "the natural system or the philosophy of reality".

Dühring claimed to have an entire system, "a clear theory going to the ultimate roots of things", which explained not only physics, chemistry, biology, etc., but, as part of the same "system", social and economic reality and an ideal socialist structure for the future.

The essence of chapters 3 to 14 is to debunk these claims, both by showing that Dühring's detailed claims were pompous charlatanism, and by explaining why any such system-building approach is untenable.

Unfortunately (in my view) this very instructive exposition is shot through with passages that appear - and sometimes very plausibly appear - to counter Dühring by proposing an alternative "philosophical" system which can build an account of the whole of natural science and of social science on a few basic "laws", namely the "laws of dialectics", "discovered" by Hegel.

Why? Here it is useful to review the background to Anti-Dühring being written.

Dühring had been a lawyer until 1859. He then turned to academic life, and got a job at the University of Berlin teaching economics and philosophy in 1864. At the same time he became interested in socialism.

From 1865 into the 1880s he published a stream of writings proposing a new version of socialism combined with anti-semitism and hostility to Marx.

Engels sums up Dühring 's politics as follows:

"The capitalist mode of production is quite good, and can remain in existence, but the capitalist mode of distribution is of evil, and must disappear... Herr Dühring's 'socialitarian system' is nothing more than the carrying through of this principle in fantasy.

"In fact... Herr Dühring has practically nothing to take exception to in the mode of production — as such — of capitalist society, that he wants to retain the old division of labour in all its essentials, and that he consequently has hardly a word to say in regard to production within his economic commune [i.e. the cooperative which in Dühring's scheme would be the basic economic unit]..."

Dühring was an admirer of Henry Carey (an American protectionist economist, and chief economic adviser to Abraham Lincoln when president) and of Friedrich List (a German protectionist economist); Engels accused Dühring of "a specifically Prussian socialism".

Politically, "there will also be army, police, gendarmerie. Herr Dühring has many times already shown that he is a good Prussian; here he proves himself a peer of that model Prussian who... 'carries his gendarme in his breast'..."

The gendarmerie will ban religion; retain bourgeois family institutions; enforce eugenic breeding.

Engels also hints that Dühring's gendarmerie will maintain women in subordination, but is less clear about this. I believe Dühring made a name for himself by supporting women's education. At the time - in the 1870s - at the University of Berlin, the great mathematician Sofia Kovalevskaya could get an education only by the professor, Karl Weierstrass, deciding to defy the authorities and give her private classes. (More on Weierstrass later).

Dühring's ready pen, his public profile (heightened by moves against him by the conservative university authorities, which eventually got him sacked in 1877), and the confused condition of the German socialist movement at the time, gave him influence.

Eduard Bernstein and Johann Most were enthusiasts for Dühring. (Since Bernstein was Jewish, that probably indicates that Dühring's anti-semitism was seen by contemporary socialists as a bizarre personal foible, rather than a political stance of some weight. They had no idea of the rise of modern anti-semitism that would follow in subsequent decades, and assumed that prejudice against Jews would gradually dissolve as part of the general bourgeois secularisation of society. That would explain why Engels makes surprisingly little of the anti-semitism in Anti-Dühring).

Even August Bebel wrote an article praising Dühring on the principle that the hard-pressed socialists should make the most of any support or publicity for any approximation of their views they could get from well-known public figures, and leave criticisms as secondary for the time being.

For a period in the mid 1870s, the German socialist press boosted Dühring as a "philosophical" authority for socialism, of status similar or greater than Marx's. (See David Riazanov's article on this. Remember also that few of Marx's writings would have been available in Germany then, whereas Dühring's writings were copious and well-publicised. According to Riazanov, Dühring's influence among socialists declined sharply from the early 1880s, partly because Anti-Dühring had convinced some prominent socialists like Bernstein, who then became important advocates for Marxism, but partly because Dühring himself, with his arrogance, undermined that influence).

Engels was persuaded to write Anti-Dühring in the mid 1870s not just to rebut Dühring's political conclusions, but in order to debunk him as a philosophical authority and to "make space" for a greater influence for Marx's writings.

Dühring had written a mildly sympathetic review of Capital in 1867. Dühring had also accused Marx of Hegelian mysticism, counterposing his, Dühring's, own version of dialectics, set out in a book entitled Natural Dialectic in 1865.

In correspondence at the time Marx explained Dühring's mildly sympathetic attitude to Capital as a product of "hatred for Roscher" (Wilhelm Roscher, the main German academic economist of the time, who argued that knowledge in economics could only be empirical and historical), and wrote on the question of dialectics:

"He knows full well that my method of exposition is not Hegelian, since I am a materialist, and Hegel an idealist. Hegel’s dialectic is the basic form of all dialectic, but only after being stripped of its mystical form, and it is precisely this which distinguishes my method".

Notice here that Marx credits Hegel with having expounded "the basic form of all dialectic" (i.e. not discovered some special new dialectical method of his own), but charges Hegel with having given dialectics a "mystical form", which must be stripped away to develop rational dialectics.

By 1868 Marx and Engels had scarcely mentioned Hegel in their writings, or in their correspondence with each other, for over twenty years, since Marx's Poverty of Philosophy, written in 1846-7. But by 1876 Engels, under pressure from Wilhelm Liebknecht, felt he had to blow Dühring out of the water, and quickly. Like it or not, he had to deal with Dühring across the whole range of subjects, not just rebut Dühring's political conclusions and leave the theoretical "high ground" to him.

Chapters 3 to 14 - the section on "philosophy" of Anti-Dühring - are very differently designed from the rest of the book. The sections on Political Economy and on socialism, especially the one on socialism, are mostly organised around positive exposition of the views of Engels and Marx, with criticisms of Dühring interlaced.

The section on "philosophy" is the opposite: it is organised around ideas taken from Dühring, with positive statements interlaced. The main drift of Engels' argument is that Dühring is not only wrong in his philosophy, but wrong to propound a "philosophy", a super-science standing above the sciences, at all. But there is an undercurrent of statements which seem to propose an alternative super-science of sorts.

In any case, the section on "philosophy" is so written that the reader feels much less than in the other sections that she or he is standing on the firm ground of an intellectual "commanding height", able to look down on and analyse Dühring's vagaries.

Maybe Engels felt more confident with the sections on political economy and socialism. Maybe as the writing wore on, Engels felt a more urgent need to cut to the chase, and reduce time spent on dissecting Dühring's vast writings. Maybe Engels was pushed towards a crisper approach by the hostile outcry which the first instalments of Anti-Dühring produced among German socialists (see Riazanov).

Maybe Engels was lured into expansiveness on Dühring's philosophical and scientific claims for "internal" reasons of Engels's own. Despite having had only three years of high school and no university education, Engels had an encyclopedic curiosity and great energy about pursuing it. In Manchester he had been friendly with Carl Schorlemmer, a communist and a professor of chemistry, and after Engels retired from business in 1870 he spent some time, as explains in his 1885 preface to Anti-Dühring, on reading up about natural science. This was in his mind when he set down to write Anti-Dühring, and he must have welcomed the chance to "try out" his new self-education.

The mood in German academia at that time was strongly empiricist, what would later be called "positivistic", and hostile to fancy philosophising. (Paradoxically, supposedly boneheadedly-empiricist British academia was more favourable to German idealism. James Hutchinson Stirling's The Secret of Hegel, published in 1865, sparked an interest which would make Hegelianism a major influence in some British universities in the later 19th century. George Eliot [Mary Ann Evans] had translated Strauss's young-Hegelian Life of Jesus (1860) and Feuerbach's Essence of Christianity (1854)).

Engels reacted against the mood in German academia. He describes his main concerns succinctly in notes for an unpublished work, Dialectics of Nature.

"One could let them alone and leave them to their not unpraiseworthy if narrow occupation of teaching atheism, etc., to the German philistine but for: 1, abuse directed against philosophy... which in spite of everything is the glory of Germany, and 2, the presumption of applying the theories about nature to society and of reforming socialism. Thus they compel us to take note of them".

He sees:

"Two philosophical tendencies, the metaphysical with fixed categories, the dialectical (Aristotle and especially Hegel) with fluid categories..."

The problems with Engels' reaction, in my view, are:

  • In some passages he "boxes himself in" to "applying theories about nature to society" as much as those he polemicises against, only with different theories. Although he has explained clearly enough that nothing happens because of dialectical "laws", and no definite conclusions can be derived from them, he still writes of "laws of dialectics" which are "the general laws of motions and development of nature, human society, and thought"; and he gives the impression, at least, that "laws", derived from patterns observed in water freezing or boiling, caterpillars developing into butterflies, and so on, could maybe be "laws" for social development too.
  • Perhaps in part because Engels lacked systematic training in philosophy of the sort that Marx had had, he let himself be boxed in to presenting Marx's method as pretty much the same as Hegel's, only somehow swivelled so that it would start from material reality rather than the Idea. That could not make sense: in Hegel's system, dialectics and idealism were two inseparable sides of the same coin.
  • Maybe through polemical over-reaction against contemporary empiricists, he gave too much credit to the "philosopy of nature" of Hegel and others. For example (footnote to the 1885 preface to Anti-Dühring), he gave credit to Hegel's idea that Newton's laws could be very easily derived from Kepler's empirical law of planetary orbits, that the period t of a planet's orbit was related to its semi-major axis s by an equation of form s^3 = constant. t^2. Hegel's derivation, in his Philosophy of Nature, is a mathematical botch.
  • Mathematics. Engels, unfortunately, takes most of what he says on mathematics straight from Hegel.

As regards dialectics: the virtue of dialectics, for Hegel, was precisely that it served idealism. "The proposition that the finite is ideal constitutes idealism. The idealism of philosophy consists in nothing else than in recognising that the finite has no veritable being. Every philosophy is essentially an idealism or at least has idealism for its principle, and the question then is only how far this principle is actually carried out".

What dialectics does, for Hegel, is dissolve the illusion that the finite does have veritable being: "Reason is negative and dialectical because it resolves the determinations of the understanding into nothing; it is positive because it generates the universal and comprehends the particular therein"

As regards mathematics: Hegel, in his main work, The Science of Logic, devotes much space to mathematics. Hegel had a reasonably good and up-to-date knowledge of mathematics for his time, but mathematics was to develop in and after his time, and, through excessive self-confidence maybe, there are also passages in Hegel on mathematics which are simply wrong, even in terms of the maths of his time.

Engels, of course, would have done very little maths at school; the evidence is that his self-education on the subject in the 1870s was very limited, much more limited than it was for example on chemistry, with Schorlemmer's guidance. He seems to have read only one textbook on calculus, and one that had been out of date even when Hegel was writing.

And Engels was unfortunate in the time of his writing. At the time he wrote, it looked as if mathematicians' inability to find rigorous proofs in calculus, an inability which had persisted for almost 200 years, was permanent. In fact, by the time Engels wrote Anti-Dühring, Richard Dedekind and Karl Weierstrass had solved that problem. Their work was not widely known. In the 1890s Bertrand Russell would study mathematics at Cambridge, yet not became aware of the work of Dedekind and Weierstrass (and be shaken by that awareness out of his youthful Hegelianism) until he visited Germany some years later.

Also, at the time Engels wrote, it looked as if the study of rigorous deductive reasoning, logic, had not advanced in over two thousand years, since Aristotle, and that because there was nothing to say about it. In fact, a huge explosion of new work in this field would begin within a year of Engels writing (Frege) and shows no sign of slowing down today.

Jean van Heijenoort's article on Engels and mathematics is spoiled by a rancid spite - it was written just after van Heijenoort had dropped out of socialist politics, and the accompanying emotion is all too visible - but seems to me solid in the gist of what it documents.

To be a great revolutionary, a major architect of socialist theory, and a person of huge intellectual capacity and energy, does not protect you from saying stupid things on subjects you know little about, let alone make you an infallible expert on everything. Engels's discussions on mathematics in Anti-Dühring, in my view, are entirely wide of the mark, and sometimes daft.

I think it is important when studying chapters 3 to 14 of Anti-Dühring to differentiate the very valuable main drift of the argument from the anachronisms and errors.

Chapter 2

Gist: Dühring claims to have found new and true philosophy, "final and ultimate truths", from which all natural and social science can be deduced. He has only contempt for other thinkers, from Kant through Hegel and the utopian socialists to Lassalle and Marx.

Part One. Chapter 3

Gist: Dühring claims to have found principles underlying all knowledge, just by thinking about them. This is simply a botched version of Hegel's procedure [which, of course, Dühring made a great noise about denouncing].

Dühring claims in particular that "he can produce... the whole of pure mathematics... a priori". In fact even pure mathematics draws material from the reality around us (numbers, shapes, and so on), although it abstracts from them.

[This is arguably true. Mathematics is not an empirical science, but the idea of deriving mathematics from "pure logic", or making it purely a matter of formal systems, was discredited by a number of mathematical discoveries in the 20th century. See here for a good short explanation.]

Engels goes on to say that "mathematical axioms are expressions of the scantiest thought-content, which mathematics is obliged to borrow from logic", and names two axioms. He asserts that to progress beyond those axioms "we are obliged to bring in real relations", suggesting (but not stating) empirical input.

[The bit about the axioms is taken straight from Hegel, and wrong. The systematic investigation of the axioms underlying mathematics got underway in the 20th century. The most commonly-used set of axioms contains nine propositions; one of them, the Axiom of Choice, is doubted by many mathematicians, and some mathematicians doubt others, too. No mathematician adds empirical input to get from axioms to theorems. There is - in the broad sense of the word "dialectical" - a "dialectical" relation between axioms and theorems].

Chapter 4

Gist: Dühring asserts that he will proceed "axiomatically" from the principle that "all-embracing being is one". Rubbish: a charlatan version of "one of the most absurd delirious fantasies of - a Hegel". The painstaking work of science cannot be short-cut by such phrases.

"The real unity of the world [i.e. that it hangs together, that it has patterns and regularities] consists in its materiality, and this is proved not by a few juggled phrases but by a long and wearisome development of philosophy and natural science".

  • Discussion points: what do you think Engels's main point in these three chapters is? Is he right?
  • "The real unity of the world... is proved..." [as above] - what do you think Engels means there? Is he right?
  • What do you think the status of the theorems of mathematics is? E.g. that there is no greatest prime number? How do you think we can decide mathematical propositions which mathematicians, so far, are unable to decide? Say, Goldbach's conjecture? Or the Continuum Hypothesis?

Chapter 5

Gist: Dühring, again by reasoning sucked out of his thumb, insists that the universe is limited in time and space.

However, Engels then reprises Hegel's ideas about infinity. In Hegel's day, mathematicians had convinced themselves that, for example, 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... (and so on to infinity) = 2, and knew how to calculate with much more complicated infinite series, but they were not yet clear about how to prove their results rigorously.

Hegel was concerned to affirm infinity - God, more or less, though Hegel, anxious about being accused of pantheism, would insist that the equation was not simple - as the true reality, more real than the changing and imperfect bustle of the finite. He wanted to distinguish this "good" infinity from the mathematicians' tricky and dubious infinity.

Thus his coinage: "bad infinity". Engels reprises this directly. He also reprises directly a puzzling idea of Hegel's, that a mathematical infinite "must start from 1". But to show that:

.... + 1/16 + 1/8 + 1/4 + 1/2 + 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... = 3

is not at all trickier than showing:

1 + 1/2 + 1/4 + 1/8 + 1/16 + ... = 2

Another point to bear in mind here is that modern scientific investigations of the idea of the "Big Bang" show that Engels was a bit hasty to insist, on the basis of his own a priori argument, that the universe must be unbounded in time and space.

The moral of this story is, indeed, a "dialectical" one. Reasoning extrapolated from what seems obvious and common-sense from observation of the "middle-sized" phenomena and time scales which we are evolutionarily geared to observing can be utterly misleading when we try to conceptualise "very big" phenomena (the whole universe in time and space), as when we try to conceptualise the "very small" (sub-atomic physics).

Chapter 6

Gist: "Even Herr Dühring" cannot sweep aside Kant's theory about the formation of the planets from nebular dust.

Dühring demands details. But:

"To the question: why do toads not have tails? - up to now it has only been able to answer: because they have lost them. But should anyone get excited over that [gap in explanation]... such an application of morality to natural science does not take us one step further..."

This is an important point. Reasoning extrapolated from the "middle-sized" suggests to us a naïve idea that "everything happens for a reason". The suggestion is not all bad: it drives us to investigate. But it also drives us to quack theorising. And quantum physics now suggests to us that some phenomena cannot be accounted for in terms of a "reason for everything", that they have an irreducible element of uncertainty and unknowability. Mathematics tells us that some propositions are undecidable in terms of the axioms of mathematics.

Engels goes on to claim that "motion is the mode of existence of matter".

This claim also seems to be borrowed from old "philosophy of nature". It is not clear what it means. That all matter is in motion? Well, relative to some frame of reference, yes, of course. But that all grass is green does not signify that greenness is the mode of existence of grass.

Engels' point here is that Dühring's idea of a universe with a fixed start in time presupposes a transition from immobility to movement. How? "We always come back again to - the finger of God". (Engels is here trying to spook Dühring, who built much of his radical reputation on being anti-religious).

  • Discussion points: "why do toads not have tails?... only been able to answer: because they have lost them". Not much of an answer, is it? What is Engels getting at?
  • Do you think these chapters compel us to reject the "Big Bang" hypothesis as anti-Marxist?
  • "Motion is the mode of existence of matter". What do you make of that?

Chapter 7

Gist: Dühring, like Hegel, falls into postulating "inner purposes" - "nature" doing this or that for human-type reasons - when he tries to move from explaining astronomy and physics from his "basic principles" to explaining organic life. And he sentimentally denounces Darwin for "a piece of brutality directed against humanity". Engels defends Darwin.

[I think albumen here is an old term for what would later be described as proteins. "Chemism" is a term of Hegel's, more or less meaning "chemistry"].

[Engels quotes here frequently from Haeckel. Haeckel was the foremost German populariser of Darwin, and a well-known scientist in his own right. His books would be among the most read in the German Social Democratic Party's workers' libraries.

[Haeckel was also a "scientific racist", though he was generally considered to be "on the left" until he became a strong supporter of the German government in World War One. The "Monist League" which he had set up in 1906 included many Jewish members and many pacifists; after World War One it became pacifistic again, and was quickly banned by the Nazis in 1933].

Chapter 8

Gist: Dühring gives further grandiloquent and charlatanish definitions of "life".

Chapter 9

Gist: Engels now moves away from natural science to consider Dühring's "philosophy" on eternal truths, equality, freedom, necessity, etc.

Dühring tries to construct morals from eternal truths. Engels responds with a valuable explanation of the necessary piecewise progress of knowledge.

"The sovereignty of thought is realised in a series of extremely unsovereignly-thinking human beings; the knowledge which has an unconditional claim to truth is realised in a series of relative errors; neither the one nor the other can be fully realised except through an unending duration of human existence.

"Here once again we find the same contradiction as we found above, between the character of human thought, necessarily conceived as absolute, and its reality in individual human beings all of whom think only limitedly. This is a contradiction which can be resolved only in the course of infinite progress, in what is — at least practically for us — an endless succession of generations of mankind.

"In this sense human thought is just as much sovereign as not sovereign, and its capacity for knowledge just as much unlimited as limited. It is sovereign and unlimited in its disposition, its vocation, its possibilities and its historical ultimate goal; it is not sovereign and it is limited in its individual realisation and in reality at any particular moment".

The idea of thought progressing by an infinite series of successive approximations was strongly and explicitly rejected by Hegel.

[Engels's quip about the "counted uncountable" is, however, unfortunate. The natural numbers 1, 2, 3, etc.... are not countable in the sense that you can get to the end of counting them, but they are countable in the sense that you can count through them and be sure of getting to any particular number at a determined stage. Obviously... you get to the number one million, say, at the one-millionth stage. The even numbers, too, for example, are countable: you get to one million at the 500,000th stage. The rational numbers (fractions) are countable, though that is not so obvious. Are these trivial facts? Is every collection countable in that sense? Not at all. Just before Engels wrote, Georg Cantor had shown that the points on a line are not countable in that sense. In other words, the infinity of points on a line is bigger than the infinity of natural numbers. There is now a whole mathematics of "transfinite" (infinite) numbers.]

Pursuing the argument, Engels says: but surely there are some eternal truths? He answers: yes, but very few and sparse.

And as for eternal good and evil - scarcely! "The conceptions of good and evil have varied... much from nation to nation and from age to age..." And, argues Engels, in the Europe of his day were to be found "Christian-feudal morality", "modern-bourgeois morality", and "the proletarian morality of the future".

[Actually Engels's examples of admitted "eternal truths" are unfortunate, and strengthen his point. In "clock arithmetic" on a clock with numbers 0, 1, 2 (instead of the usual 1 to 12), twice two is one, not four. The three angles of a triangle add up to more than two right angles if the triangle is on a spherical surface (for example, the Earth). There is a Paris in Texas. People who cannot eat food, because for example they are in a coma, can be supplied with nutrients by direct injection...]

[Engels's contention that "with the introduction of variable magnitudes and the extension of their variability to the infinitely small and the infinitely large, mathematics... fell from grace", is wrong. Firstly, the introduction of variables brings no particular problem for mathematical rigour. Hegel, for reasons I don't understand, argues that linear relations like y = 3 x + 2 are not really algebra at all, but even quadratics, cubics, etc. bring no special problem. On "the infinitely small and the infinitely large", see chapter 12].

  • Discussion points: why isn't morality a matter of eternal truths? How do we distinguish that from saying that whatever "works" for us is moral?
  • Actual truth is only a "series of relative errors"? What do you make of that?
  • Calculus makes maths dialectical? What do you make of that?

Chapter 10

Gist: In devising his ideas about future society, Dühring relies on an axiomatic, true-for-all-time principle of equality.

This, writes Engels, is "the old favourite ideological method, also known as the a priori method, which consists in ascertaining the properties of an object, by logical deduction from the concept of the object, instead of from the object itself. First the concept of the object is fabricated from the object; then the spit is turned round, and the object is measured by its reflexion, the concept. The object is then to conform to the concept, not the concept to the object.

"With Herr Dühring the simplest elements, the ultimate abstractions he can reach, do service for the concept, which does not alter matters; these simplest elements are at best of a purely conceptual nature. The philosophy of reality, therefore, proves here again to be pure ideology, the deduction of reality not from itself but from a concept..."

How does Dühring get his axiom? By the Robinson Crusoe method of deducing truths for all society from a hypothetical society of two people.

[Engels could have used this example as a happier choice for illustrating the point he makes later about quantitative change eventually spilling over into qualitative change. A large-scale society cannot be understood as a scaled-up copy of a society of two people...]

Dühring says that the two people are axiomatically equal. So, says Engels, they are not man and woman? We know that women's equality is not an axiom of primitive humanity. They two are "heads of households"? So women don't even get counted in Dühring's axiomatic society, except as part of households?

And, retorts Engels, what if one person is stronger and more forceful than the other, and makes the other his slave? Does that prove that slavery is an eternal truth?

Further, Dühring himself soon starts making qualifications. Force may have to be used against children, madmen... and whole populations considered guilty of "perversity".

Engels: this "call[s] into being a morality by which all the infamous deeds of civilised robber states against backward peoples... can be justified".

Equality, argues Engels, is in fact an idea generated by the "economic conditions of modern bourgeois society".

  • Discussion points: why is it that bourgeois society, and not other societies, gives the idea of equality "the fixity of a popular prejudice" (as Marx puts it in Capital?
  • Why are "Robinson Crusoe" arguments not good ways of understanding society?

Chapter 11

Gist: Dühring insists that the proper basis of criminal law is... revenge.

Dühring is ignorant of law, assuming that Prussian law is a model for all.

Dühring is muddled on freedom. First he denounces "silly delusions of inner freedom", and says we must talk instead of the resultant of rational judgement and "instinctive impulses" to get a "practical regulation of life".

Then he identifies freedom with "susceptibility to conscious motives".

This, says Engels, is a "vulgarisation" of Hegel's idea that "freedom is the appreciation of necessity".

[Engels endorses Hegel here. But this seems to me to miss two points. Firstly, Hegel's ideas on freedom were inextricably intertwined with the character of Hegel's dialectics as dialectics of reconciliation.

[Hegel: "Law, morality, the State, and they alone, are the positive reality and satisfaction of freedom... In so far as the state, our country, constitutes a community of existence, and as the subjective will of man subjects itself to the laws, the antithesis of freedom and necessity disappears..."

[Second, the really valuable idea of Hegel on freedom was that freedom was not something original and primitive, lost because of the exigencies of social life, but that freedom had to be won by and in social life. "Freedom... does not exist as original and natural. Rather must it be first sought out and won; and that by an incalculable medial discipline of the intellectual and moral powers..."]

Engels continues: real freedom also depends on technical progress. It cannot be defined in abstraction from that.

  • Discussion points: why should freedom depend on technical progress?
  • "Freedom... does not exist as original and natural..." Do you think that was really a valuable idea of Hegel's?
  • "Freedom is the recognition of necessity"? What do you make of that?

Chapter 12

Gist: Dühring says that contradiction is absurdity, and Hegel's ideas on contradiction show that Hegel was absurd. Engels disputes this.

Dühring says that Marx's argument in Capital depends on using absurd Hegelian wordplay about contradictions. Engels disputes that.

First: Dühring on Marx on contradiction

Dühring quotes Marx from chapter 11 of Capital on the argument that money becomes capital, but not every sum of money can become capital: it requires a certain minimum size.

At the end of the argument, Marx comments: " Here, as in natural science, is shown the correctness of the law discovered by Hegel (in his Logic), that merely quantitative differences beyond a certain point pass into qualitative changes". In a footnote, Marx explains the reference to natural science as being to the way that quantitative changes in the composition of carbon-oxygen-hydrogen compounds produce qualitative changes in their properties. The basic idea here is direct from Hegel, though Hegel used the example of different oxides of nitrogen.

Dühring charges Marx with using "the confused, hazy Hegelian notion that quantity changes into quality" to deduce that "therefore an advance, when it reaches a certain size, becomes capital by this quantitative increase alone".

Engels's retort, essentially, and I think he is right on this, is that there is no "therefore" about it. Marx demonstrated his argument about a necessary minimum size for a stash of money to become capital strictly from the economic relations, with no reference to Hegel. Then, after concluding the argument, he referred to Hegel.

So - and this is very important - by Engels's own clear argument, the supposed "Hegelian" law of the transformation of quantity into quality has no "therefore" about it, no power to direct us to draw conclusions. Marx would have been wrong if he had tried to derive his idea about the minimum stash from the "law" of the transformation of quantity into quality.

In other words, the word "law" is being used loosely here, and not in the sense of "scientific law" as we would understand it today; for the whole point about a scientific law is that there is a great deal of "therefore" about it, that in appropriate situations it indicates very definite conclusions. Bridge-builders build bridges so as not to fall down by designing them according to the laws of statics. (This also, of course, means that these laws can be tested; if the indicated conclusions are empirically false, then we have to re-examine the laws).

Another question should be asked here: what, then, was the point of Marx's remark, if he had already established his point, and Hegel's "law" could not have established it anyway?

Conceivably, it could be that the "law" didn't have a "therefore" about it in the sense of mandating specific conclusion in the specific case, but did have a "therefore" about it in the sense of laying down certain general conditions which a conclusion would have to fulfill - in the same way as, say, when investigating routes between two points in a city divided by a river, one on the north side and one on the south side, a general "law" could have the "therefore" that the route must cross the river an odd number of times, but couldn't give us an exact itinerary.

In this case? I don't see it.

It could be something looser, a sort of "rule of thumb", on the lines of "look out for points where quantitative change tips over into qualitative change". There's some sense to that, though the credit probably goes as much to ancient Greek philosophers (like Eubulides, with his paradox about when a process of adding one grain to another become a heap) as to Hegel.

Actually, I would argue that the truth is simpler. Marx's reference is a quip, an in-joke, a garrulous digression. It is of similar character to the more obviously jokey reference to Hegel in chapter 7.

There, Marx defines what an instrument of labour is: the worker "makes use of the mechanical, physical, and chemical properties of some substances in order to make other substances subservient to his aims", and can't resist a footnote: "Reason is just as cunning as she is powerful. Her cunning consists principally in her mediating activity, which, by causing objects to act and re-act on each other in accordance with their own nature, in this way, without any direct interference in the process, carries out reason’s intentions."

Has Marx "gone Hegelian" in middle age? Has he forgotten all the ideas of his youth? Has he suddenly gone over to Hegel's idea of an abstruse Reason shaping history, which he criticised in the 1840s?

No, comrades. He is making a joke. It is an in-joke, almost a private joke for himself. He is saying to himself: Remember all those phrases from Hegel which were our intellectual stock-in-trade, back then in the 1840s? Striking, vivid phrases: Hegel, despite the obscurity of many of his texts, had great literary skill, and left behind more colourful phrases, more quotable quotes, than any other philosopher ever has.

Remember how Hegel himself, and other Hegelians, used to try to deduce them by speculative wordplay from general concepts like "being", "essence", etc.? Well, some of the patterns they talked about really exist. But if you want to find them, you have to do real scientific analysis, not speculative philosophy. "Reason" doesn't use lathes and steam-engines. Workers do.

Neither Marx, nor even Engels, can be blamed for the fact that, decades later, over-solemn and over-pompous Marxists would read Capital and, where they saw a reference to Hegel, think: "Wow! Hegel! This must be serious. Never mind all the economic stuff. This is the deep stuff, the philosophy".

The gist of Engels's reply to Dühring here is absolutely right. But the way he does it, and the fact that Engels goes on to expand Marx's footnote at some length, risks giving the reader the impression that Engels is saying not only that Marx is right about money and capital, but also that there is a "deep" law here, "discovered" by Hegel.

Marx's sentence, by the way, appears in the English edition of Capital as "... the law discovered by Hegel..." This is slightly misleading. The German word translated as "discovered" is "entdeckten". Entdecken can be translated as discover, but there are other German words also translatable as discover, and among them entdecken leans towards discover in the sense of detect, register, notice. The French edition of Capital, which Marx worked on intensely and credited with "an independent scientific value", has constaté, which is roughly equivalent to ascertained, registered, noticed.

In other words, Marx could just as well have written "the pattern noted by Hegel" as the more portentous "the law discovered by Hegel". But then the quip, the jibe at Hegelian pomposity, would not have been so sweet.

The more general argument about "contradiction which is objectively present in things"

Engels could have argued that social structures, unlike stones or numbers, do have "contradictions" - irresoluble conflicts - "objectively present" in them.

However, here Engels straightaway bases his disputation on a fallacious argument.

When mathematicians calculate the slope of a curve at a point, he says, they do it by assuming that a small enough segment of curve following that point can be equated to a straight line. (Or, he could say, when we calculate the speed of a falling object at an instant, we do it by assuming that the object falls at constant speed for a very short time after that instant). Those are contradictory procedures, yet lead to correct results.

Engels will make the same argument in chapter 13, dealing with differential calculus. We calculate dy/dx by assuming simultaneously that dy and dx are very small but not zero, and that they are both zero. Contradiction!

It is true that slope and speed at a point are puzzling. Slope is rise divided by run; but if we are at a point, then both rise and run are zero, so "slope" is zero divided by zero, or indeterminate. Speed is distance divided by time, but if we want speed at a precise moment, then both distance and time are zero, so we have not speed but zero divided by zero.

Engels also refers to the classical Greek paradoxes of Zeno about motion. If an object is moving, when does it move? At each instant, it is just where it is at that instant, and not anywhere else. The paradox here is essentially the same as the mathematicians' problem.

Mathematicians had wrestled with the calculus problem for almost two hundred years (and philosophers with Zeno's paradoxes, for 2300 years) before Engels wrote Anti-Dühring, and with limited success. However, in the years shortly before Engels wrote the book, unknown to him, Karl Weierstrass and Richard Dedekind had devised solutions. They had also shown that some of the dodgy arguments used when mathematicians didn't know how to make reasoning about calculus rigorous were wrong. Other rigorous accounts of calculus have been developed since the 1960s, by Abraham Robinson [non-standard analysis] and Errett Bishop [constructive analysis]. Engels's argument thus falls down with a crash.

What Engels could have argued instead, without the folly of trying to derive ponderous philosophical laws from scraps of science which many of his readers would not have understood at all, is the point he made in his notes for Dialectics of Nature: "Two philosophical tendencies, the metaphysical with fixed categories, the dialectical (Aristotle and especially Hegel) with fluid categories..."

If we approach any complex subject with rigid categories, then either we will end up stumped, or we will end up cramming reality into our categories any old how. A more rational approach is to develop and modify our categories as our investigation shows their inadequacies (or, if you like, "contradictions").

This method of successive approximations has to avoid lurching to the opposite pole of indefinitely redefining concepts so that they become so shapeless as to accommodate anything. At a certain point, when concepts come to lack coherence and grip, they must be discarded outright and replaced by new ones.

The calculus, and the ancient Greek paradoxes of Zeno, really were difficulties requiring much thought (difficulties, however, to be solved by theoretical effort, not just rejoiced in as impressive examples of how contradictory nature is!). But Engels then gives three examples of "contradictions" from mathematics which are not even paradoxes in any real way.

"It is a contradiction that a root of A should be a power of A, and yet A^(1/2) = square root of A". But powers of A are initially defined only for whole-number powers: A^2 is A times A, A^3 is A times A times A, and so on. At that stage, A^(1/2) means nothing. Then we extend our thinking to fractional powers. We define A^(/2) as the square root of A, A^(1/3) as the cube root, etc. Then we can show that this extended definition of powers fits seamlessly with our original, more limited, idea.

What Engels might more reasonably have said is this: at first we think of powers and roots as opposite things. Then when we develop the theory more we see that all roots can be reckoned to be just special sorts of powers. That happens often when we develop theory: a development of our concepts shows that two things previously counterposed can be subsumed into a wider concept.

If Engels had done that, he would not have made the mistake of saying that the square root of minus one is "a contradiction... a real absurdity". It would indeed be absurd to say that a real number is the square root of minus one. Absurd? Just plain wrong.

To be able to work with the square root of minus one we have to extend our concept of numbers. It is only a further stage in a series of extensions of that concept.

At first we have only the numbers we can actually perceive as multiples: one, two, three, up to maybe seven. We can't see any number bigger than about seven (unless because of a pattern and already knowing something about arithmetic, as when we can learn to see a pattern of three times three as nine). Some human languages have no number-words beyond one, two, three, four, many.

Then we develop the idea of counting without end. We can't directly see 1729, and probably could not even count 1729 objects with any assurance, but we can develop an abstract concept of 1729 as a continuation of a process of counting.

Then we extend our concept to include zero as a number (remember, zero wasn't a number in the Roman numeral system).

Then we extend to include negative numbers. Then, to include fractions. Then, to include numbers which can denote lengths, for example, but are not fractions, like the square root of two, and π.

"Imaginary" numbers, like the square root of minus one, are a further extension. There are many other extensions. Mathematicians generally reckon that "imaginary" numbers are no more imaginary than, say, negative numbers. They "contradict" naïve notions of number, what Hegel called "pictorial thinking", but then science often contradicts first impressions.

Engels also claims that the very use of variables - algebra - involves contradictions. Not so.

Chapter 13

Gist: Dühring again accuses Marx of using Hegelian waffle as a "crutch", by citing "the Hegelian negation of the negation" as his argument for saying that socialism will emerge out of capitalism.

Engels responds:

1. Marx does not propose as the socialist future some fanciful "higher unity" of "property which is at once both individual and social". He proposes social ownership of the means of production and individual ownership of consumer goods.

2. As with the argument about the minimum size needed for stashes of money to become capital, Marx establishes his case here with strictly factual arguments from the reality of capitalism. Engels summarises those arguments.

"And now I ask the reader: where are the dialectical frills and mazes and conceptual arabesques?"

Only after establishing his case does Marx comment that it resembles the Hegelian "negation of the negation".

In any case, Engels comments, dialectics is not a "proof-producing instrument". Dialectics can't "prove" anything.

What can it do then? The obvious conclusion is that dialectics are a heuristic method (as Merriam-Webster defines it: "involving or serving as an aid to learning, discovery, or problem-solving", from Greek heuriskein, to discover). Be on guard against fixed categories: dissect, analyse, criticise your categories continually. Be on guard against extrapolating too far, where the larger-scale may be qualitatively different from the smaller-scale. Work through successive approximations. Understand that social formations are in constant flux, that they are riven by irreconcilable conflicts, that they have to be understood as they are in their movement and not just in a "snapshot".

Unfortunately, Engels then discusses, not capitalist society, but the life-cycles of barley grains, butterflies, and rock formations.

Do these show "negation of the negation" patterns? Or, rather, since, as Engels has already noted, our scientific knowledge of such things is always limited, do our current best theories about them show "negation of the negation" patterns?

The short answer is, yes, if you define "negation of the negation" or "transformation of quantity into quality" loosely enough, then pretty nearly any halfway-developed and plausible scientific theory - whether likely to stand for a long time, or about to be radically refuted and replaced by a new theory - is likely to show such patterns. Nature is "dialectical", in that sense, but the comment adds nothing to our knowledge.

Engels, unfortunately, immediately confirms this dismissive view of "the dialectics of nature" by producing a very contrived example of "negation of the negation" from mathematics.

If we negate a, we get minus a, he says. If we negate the negation by squaring minus a, then we get a-squared, so we're back to a again - negation of the negation! But Engels offers not a word to explain why squaring should be counted as "negation", and why a-squared should be considered a "higher unity" of some sort (which is the significance of "negation of the negation" in Hegel).

Despite having said that dialectics is not "a proof-producing instrument", Engels calls "negation of the negation" a "law"; and writes that "dialectics... is the science of the general laws of motion and development of nature, human society and thought".

Now in ordinary usage a scientific law is "a proof-producing instrument". The reason why airplanes are designed according to Newtonian "laws of motion" is to get "proof" from those laws, before the airplanes are built, that they will fly. So the term "law" is unfortunate here.

It is not, by the way, from Hegel. For Hegel, "transition from quantity to quality" or "negation of the negation" are not laws. His conception of logic is that the logic of development of every entity is the logic of its Concept, and is generated by the "self-movement" of the concept rather than by an externally-stated series of "laws". If there are universal patterns, it is only inasmuch as Concept is a "moment" of the Absolute Concept.

"Law" is only "essential Appearance" for Hegel. It stands no higher than "the procedure of physics, which reduces the world of phenomena to general laws and reflective determinations... based on spirit merely in its phenomenal aspect...".

In his doctoral dissertation, Marx commented on Hegel's finesse on the old "cosmological proof" for the existence of God - since contingent things exist, and must have some cause, there must be a first cause, an "absolutely necessary being" - and its demolition by Kant. For Hegel, dialectics serve to invert the argument. Marx summarises Hegel: "since contingency does not exist" - since dialectics can show finitude to be inherently contradictory and perishable and thus not true - "God exists".

Marx further inverted Hegel: "all proofs for the existence of God are proofs for his non-existence: they are refutations of all conceptions of a god. Valid proofs would have to state, on the contrary: 'Since nature is imperfect, God exists'; 'Since a non-rational world exists, God exists'; 'Since there is no rationale in things, God exists'... God exists for the man to whom the world is non-rational and who is therefore non-rational himself...

"If someone had taken a Wendish god to the ancient Greeks, he would have found proof for the non-existence of this god, because this god did not exist for the Greek. What a certain country is for foreign gods, the country of reason is for God altogether - namely, a place where God no longer exists".

But Engels in this chapter is suggesting, or laying himself open to be interpreted as proposing - I would put it no stronger than that - a different inversion of Hegel. Hegel takes dialectics as proving that finitude is inherently contradictory and perishable and thus not true; that the only truth is the Absolute Concept. Engels suggests taking contradictions and perishability in the world, on the contrary, to be the sign, the general law, of true reality; things are not truly real unless they are contradictory and perishable.

In the same chapter Engels says that in "modern materialism" there is "no longer a philosophy at all", no "science of sciences standing apart"; i.e. that although there are theories of economic life and of socialist politics to counterpose to Dühring's - and Engels will counterpose them in the following chapters - what we have to counterpose to Dühring's philosophy is not another philosophy but the work of "positive sciences".

A set of "general laws of motion and development of nature, human society and thought", in some places (though, as we have seen, not others) said to have been "discovered" by Hegel, does however look very much like a science standing above the sciences, a "philosophy", a doctrine of the same general character as Dühring's world schematism only, supposedly, better.

Hegel: because the finite is contradictory and perishable, it has no veritable being, and truth resides in infinity.

Engels (as some passages point to reading him, despite his admonitions pointing in a different direction): because contradictoriness and perishable exist in finite things, the deep truth, the veritable being, "the general laws of motion" of everything, reside in the principle of contradictoriness and perishability.

I do not think many Marxists came to read "dialectics" that way until Stalinism. But then, for a whole long epoch, the "laws of dialectics" also became law for communists who feared being branded and persecuted as renegades. We are still in the shadow of that epoch.

Stalin declared that "dialectical materialism is the world outlook of the Marxist-Leninist party", and enunciated four "principal features" as a catechism for the loyal:

  • Nature Connected and Determined
  • Nature is a State of Continuous Motion and Change
  • Natural Quantitative Change Leads to Qualitative Change
  • Contradictions Inherent in Nature

Chapter 14

Engels's conclusion: Dühring is a charlatan, whose method is "an infinitely vulgarised duplicate of Hegelian logic [which] shares the superstition that...'basic forms' or logical categories have led a mysterious existence somewhere before and outside of the world..."

  • Discussion points: what is Engels's main point in these chapters? Do you think he is right?
  • "Laws of dialectics"? What do you think?
  • Marx's references to Hegel in Capital are quips? What do you think of that?

Click here for notes on parts 2 and 3 of Anti-Dühring.

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