A category mistake in the classical labour theory of value

No one likes being wrong. But being shown to be wrong, especially in science, is actually a gift to be welcomed, however hard that may be psychologically. Recognising and acknowledging error is a first and necessary step to a greater understanding of reality.

There is something wrong with the classical labour theory of value, including Marx’s version of it.

Some Marxists accept this proposition, others do not. But there is nothing to fear. Because identifying the wrongness immediately leads to a better labour theory of value.

So what is wrong with the classical labour theory of value?

The earliest critics of the classical labour theory of value were the classical author themselves. For example, both Ricardo and Marx theoretically struggled with different manifestations of the same underlying problem in their theories of value. Ricardo’s struggle became known as the problem of an invariable measure of value, and Marx’s struggle became known as the transformation problem. Sadly, most discussions of the transformation problem completely miss the indissoluble link with Ricardo’s problem, and therefore fail to fully encompass and express the entire problematic.

The problem of measuring economic value

Consider a tree A that is twice the height of a tree B. At a later date tree A is three times the height of tree B. Assume we only know the relative change in heights. Does this change indicate that tree A has increased in size, tree B has decreased in size, or some combination of these causes? To answer this question we need an absolute measure of height that is invariable over time.

The metre is such an invariable standard. We measure the absolute height of tree A and B in metres, both before and after the change. Then we can unambiguously determine the cause of the variation in relative heights.

The definition and adoption of the metre by the French state after the revolution in 1793 was accompanied by much theoretical debate and reflection. Ricardo, a contemporary of these events, recognised that an objective theory of economic value requires an analogous invariable standard of measurement.

Why? Because market prices—whether stated in terms of exchange ratios between commodities or in terms of a unit of account—cannot function as a standard because prices merely indicate relative values:

If for example a piece of cloth is now the value of 2 ounces of gold and was formerly the value of four I cannot positively say that the cloth is only half as valuable as before, because it is possible that the gold may be twice as valuable as before (Ricardo 2005, 289).

The cause of an altered exchange ratio might be due to an alteration in the absolute value of the standard itself. So picking a market price to measure absolute value is analogous to picking the height of a specific tree to function as an invariable standard of length. Between measurements the chosen tree might grow (or get cut down in size).

Perhaps we should not try to find a standard? This is not an option because, lacking an invariable standard, the theory of value collapses into subjectivity, leaving “every one to chuse his own measure of value” (Ricardo 2005, p.370). In consequence, public statements about objective value, such as ‘commodity A is now less valuable than one year ago’, would, strictly speaking, be nonsense.

Ricardo, therefore, wished to identify an Archimedean standpoint, outside the marketplace and system of relative prices, from which to measure the objective value of commodities. Although he knew of “no other criterion of a thing being dear or cheap but by the sacrifices of labour made to obtain it” (Ricardo 2005, p.397) his own arguments demonstrated that the profit component of natural prices appears to be unrelated to labour cost. He couldn’t link the price system to physical labour costs. So although “the great cause of the variation of [the value of] commodities is the greater or less quantity of labour that may be necessary to produce them” there is another “less powerful cause of their variation” (Ricardo, 2005, 404), which Ricardo suggested was “a just compensation for the time that profits were withheld” (Ricardo, [1817] 1996).

In consequence, natural prices (the measurand) vary independently of real costs of production defined in terms of labour costs (the candidate measure of value). A measure that fails to vary with its measurand is not fit for purpose.

Ricardo grappled with this problem, and wrote a remarkable unfinished essay on the topic in the last weeks of his life, which finally concluded that “it must then be confessed that there is no such thing in nature as a perfect measure of value” (Ricardo, 2005, 404). Ricardo retreated to proposing approximate, and therefore, imperfect measures of value, which minimise the discrepancies between the measure and measurand.

But a ruler that, on theoretical grounds alone, fails to invariably measure length is not merely an imperfect empirical tool – it implies that one’s theory of length is flawed.

Marx’s proposed solution

Marx, who inherited Ricardo’s problem, proposed a creative and novel resolution. He argued that natural prices are transformed, or distorted, labour costs due to capitalist property relations. Prices then appear to vary independently of labour costs because the transformation obscures the measurement relation. This explained Ricardo’s difficulties.

Marx argued, however, that the transformation is conservative and therefore the measurement relation continues to hold between macroeconomic aggregates (e.g., total profits and total surplus labour etc). The conservation condition is essential to Marx’s solution since it restores an invariable measure, and therefore avoids the conclusion that, on theoretical grounds alone, the labour theory of value is flawed. According to Marx, therefore, the “form of value” (natural prices) only appears to contradict the “substance of value” (labour costs) in virtue of the institutional peculiarities of capitalist production.

Marx warned his readers, however, that his solution contained the “possibility of an error” (Marx, [1894] 1971, p. 165) if a particular assumption of his argument was relaxed (namely, his assumption that input costs are proportional to labour costs).

Marx’s critics promptly demonstrated that possibility and argued that, in general, Marx’s transformation cannot be conservative and hence fails to establish the desired measurement relation.

The quantitative incommensurability between labour-values and natural prices has knock-ons for other parts of Marx’s theory, such as his theory of exploitation, which claims that surplus-value, e.g. profits and interest income, is a money representation of the surplus-labour that workers supply to capitalists without payment. So, politically, there’s a lot at stake in this seemingly obscure debate in the theory of value.

Both Ricardo and Marx’s problems directly undermine the idea that labour costs can in principle explain economic value. And they are essentially the same problem manifesting in different guises.

Digging deeper: the cause of the problem

My paper, “A category mistake in the classical labour theory of value”, tackles Ricardo and Marx’s problematic in the context of a formal model of capitalist production. The formality is austere but has the advantage that it imparts precise semantics to some of the key concepts of the labour theory of value. This helps pinpoint a certain kind of logical error in the classical theory.

Philosophers, such as Gilbert Ryle (1984 [1949]) and Ludwig Wittgenstein (1953), argue that the underlying cause of a long-lived and insoluble problem is often a hidden conceptual confusion or mistake. The problem is insoluble because the conceptual framework in which the problem is stated is itself faulty. Empirical study, or experimental activity, cannot resolve such problems. Rather, the problem must be deflated or dissolved by applying conceptual analysis.

For instance, Ryle introduced the term “category-mistake” (Ryle 1984[1949], ch.1) to denote the conceptual error of expecting some concept or thing to possess properties it cannot have. For example, John Doe may be a relative, friend, enemy or stranger to Richard Roe; but he cannot be any of these things to the “Average Taxpayer”. So if “John Doe continues to think of the Average Taxpayer as a fellow-citizen, he will tend to think of him as an elusive an insubstantial man, a ghost who is everywhere yet nowhere” (Ryle 1984 [1949], p.18).

In the paper, I argue that the contradictions of the classical labour theory of value derive from a “theoretically interesting category-mistake” (Ryle 1984 [1949], p.19), specifically the mistake of supposing that classical labour-values, which measure strictly technical costs of production, are of the same logical type as natural prices, which measure social costs of production, and in consequence labour-values and prices, under appropriate equilibrium conditions, are mutually consistent. Since this supposition is mistaken, Ricardo’s search for an invariable measure of value and Marx’s search for a conservative transformation attempt to discover a commensurate relationship between concepts defined by incommensurate cost accounting conventions. They therefore seek an impossible “elusive and insubstantial man” or “ghost”.

Once the category mistake has been identified we can resolve the classical problems by “giving prominence to distinctions which our ordinary forms of language make us easily overlook” (Wittgenstein 1953, § 132). Such distinctions then solve, or more accurately, dissolve the problems.

Dissolving the problem

The key step is to notice that we can and should define a different measure of labour cost – total labour costs – that generalises the classical measure to include real costs induced by the institutional conditions of production. We then immediately possess a more general labour theory of value that includes both total and classical (i.e., technical) measures of labour cost. The general theory then applies the different measures in distinct, but complementary, theoretical roles, and in consequence separates issues normally conflated in the classical theories.

I note that classical labour costs, and total labour costs, happen to be identical in the special case of what Engels called “simple commodity production” (i.e., production in the absence of specifically capitalist property relations) and I note this also happens to be the case where the classical labour theory of value ‘works’. The reason the classical theory ‘works’, in this special case, is that total nominal costs (i.e., the natural price system) are compared with total labour costs: apples are compared with apples. The classical theory then breaks down, once we introduce capitalist property relations, because the classical definition of labour cost no longer satisfies the definition of a total labour cost. The classical theory, therefore, commits a category-mistake when it compares total nominal costs with partial labour costs – and then expects a commensurate relationship to obtain between them: apples are compared with oranges.

The intellectual history and development of the classical labour theory of value is best understood in terms of an unidentified and recurring category-mistake in the sense of Ryle. Category-mistakes are precisely the kind of hidden conceptual errors that cause longstanding and insoluble theoretical difficulties, which explains why the problems of the classical theory have persisted for so long without resolution, despite a voluminous and longstanding literature on the issues.

The classical authors attempt to explain the structure of total costs of production – which include both technical costs due to the material conditions of production (e.g., the cost of physical capital and labour inputs) and additional social costs due to the institutional conditions of production (e.g., the cost of money-capital, state imposed taxes, etc.) – in terms of the structure of technical costs of production alone, which explicitly ignore institutional conditions. This conceptual error is the underlying cause of the almost two hundred year history of the “value controversy”.

In the paper I explain why the more general theory has both an invariable measure of value and lacks a transformation problem. The main technical result is the theorem that natural prices are proportional to physical real costs of production measured in labour time. Hence, prices and labour costs, in appropriate equilibrium conditions, are “two sides of the same coin”. The measurement relation, missing from the classical theory, is therefore established, which implies that labour costs can in principle explain economic value. The more general theory therefore removes the primary theoretical obstacle that has hindered the development of the classical theory of value since its inception.


Marx, K., [1894] 1971. Capital. Vol. 3. Progress Publishers, Moscow.

Ricardo, D., [1817] 1996. Principles of Political Economy and Taxation. Prometheus Books, New York.

Ricardo, D., 2005. Absolute value and exchangeable value. In: Sraffa, P., Dobb, M. H. (Eds.), David Ricardo, the Works and Correspondence, Vol. 4 (Pamphlets and Papers 1815–1823). Liberty Fund, Indianapolis.

Ryle, G., [1949] 1984. The Concept of Mind. University of Chicago Press, Chicago.

Wittgenstein, L., 1953. Philosophical Investigations. Blackwell, Oxford.

In case a reader might think that citing ordinary language philosophers may be evidence of bourgeois deviation I suggest to chillax! 😉

 

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10 comments

  1. This is an interesting take on the issues, not least because it’s an example of what it alleges about classical value theory, namely a theoretically-interesting mistake.

    My reading of Marx is that his theory includes a kind of category mistake not as a shortcoming of reasoning but of the reality that Marx is theorising, namely the defects of value as a representation of labour: “It is as if alongside and external to lions, tigers, rabbits, and all other actual animals, which form when grouped together the various kinds, species, subspecies, families etc. of the animal kingdom, there existed also in addition the animal, the individual incarnation of the entire animal kingdom.”

    From the translation by Albert Dragstedt of the first chapter of the first German edition of Capital. In Value: Studies By Karl Marx, New Park Publications, London, 1976, pp. 7-40.

    https://www.marxists.org/archive/marx/works/1867-c1/commodity.htm

    For the Hegelian background to this, see Chris Arthur, ‘The concept of money’ in Karl Marx and Contemporary Philosophy ed. A. Chitty and M. McIvor, Springer, 2009, pp 159–173

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  2. Hi Julian

    Thanks for commenting!

    I agree that Marx, as a follower of Hegel, is committed to an ontology that admits dialectical contradictions. Marx therefore expects “irrational” kinds to exist in reality. And Marx emphasises that capitalism is a contradictory social reality, and points out that capitalist property relations distort the form of value away from classical labour values (which they do).

    But the question at hand is whether Marx’s transformation is free from logical contradiction. In other words, does Marx’s transformation procedure express a real contradiction, inherent in social reality, or alternatively a logical contradiction in Marx’s cognition it? That’s a substantive question that cannot be addressed by immediate recourse to Hegel.

    A logical contradiction denotes an impossibility (e.g., a square circle); in contrast, a real, or dialectical, contradiction denotes the struggle of parts of a system to control a property of the system in incompatible ways (e.g., two teams in a game of tug-of-war that attempt to pull the rope in opposite directions). Real contradictions are the cause of change and motion. Hence, a system with real contradictions is logically possible (since free of logical contradiction) but may ultimately be unstable and therefore transient on some time-scale.

    But dialectical methodology doesn’t imply that we may ignore logical contradiction. Hegel, for example, writes:

    “Intelligent reflection, to mention this here, consists, on the contrary, in grasping and asserting contradiction. Even though it does not express the Notion of things and their relationships and has for its material and content only the determinations of ordinary thinking, it does bring these into a relation that contains their contradiction and allows their Notion to show or shine through the contradiction. Thinking reason, however, sharpens, so to say, the blunt difference of diverse terms, the mere manifoldness of pictorial thinking, into essential difference, into opposition. Only when the manifold terms have been driven to the point of contradiction do they become active and lively towards one another, receiving in contradiction the negativity which is the indwelling pulsation of self-movement and spontaneous activity” (Hegel, Science of Logic, p. 442).

    The language is opaque but Hegel’s methodological remarks here are highly sophisticated. Often, to make theoretical progress, we need to compress and reduce the “manifold terms” of a complex theory into an essential logical contradiction at the level of “ordinary thinking” (non-dialectical). The logical contradiction may then reveal an underlying process of change that the theory fails to adequately reflect.

    My reading of Marx is that his transformation indeed contains a logical contradiction, and by sharpening it we gain a better understanding of Marx’s theory and social reality.

    Best wishes,

    -Ian.

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  3. Hi Dave,

    Thanks for commenting. The expression for C* in (1) is quite unwieldy. The main point, however, is that C* is identical to C, as explained in the paragraph beginning “We now show that C* is equivalent to C …”. So the interpretation of the coefficients are identical: each element c_{i,j} of matrix C* is the quantity of commodity i, consumed by capitalists, per unit output of commodity j.

    The motivation for Proposition 2 is to demonstrate that matrix C (or C*) is independent of the price system, and a function of the technique and the real distribution of income (in the natural price equilibrium). The numerical example in the appendix gives a concrete example.

    Hope this helps.

    Best wishes,
    Ian.

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  4. Hi Toure

    Thanks for commenting!

    There’s really a lot to say here, but I’ll try to be brief. I have enormous respect for Anwar Shaikh’s contributions to Marxist economics.

    Shaikh, in his 1984 paper, “The Transformation from Marx to Sraffa”, sets out to explain why Marx’s aggregate equalities (between classical labour values and natural prices) necessarily fail to hold. Earlier authors, such as Bortkiewicz, demonstrated this algebraically, but Shaikh digs deeper and gives us the economic reasons.

    Shaikh explains, in some detail, that classical labour values and natural prices must diverge because of the transfer of labour value out of the “circuit of capital” and into capitalists’ “circuit of revenue” (in the form of the labour value of capitalists’ consumption goods). Shaikh has made many important and seminal contributions to Marxist economics. And this identification is one of them.

    Shaikh’s identification of the underlying problem is entirely consistent with my own work in this area. Shaikh basically shows that natural prices include the money cost of capitalist consumption goods but classical labour values exclude the labour cost of producing those goods (since, according to classical labour value accounting, their value is not reproduced in the “circuit of capital” but consumed in the “circuit of revenue”). So Shaikh and I entirely agree on the cause of the divergence.

    From this point onwards we differ, however.

    I point out that classical labour values do not measure the labour supplied to produce commodities in the institutional circumstances of capitalist production. On this point, see:

    https://ianwrightsite.wordpress.com/2017/05/19/just-what-is-a-labour-value-anyway/

    And I point out that we can naturally generalise the classical concept of labour value to actually measure this magnitude. This leads directly to a more general labour theory of value that dissolves the transformation problem.

    Shaikh, in contrast, works solely with classical labour values. He therefore has no recourse other than to follow Ricardo in viewing the relationship between price and labour time as necessarily approximate, even in theory. In consequence, he initiates an important empirical research programme to measure the size of the deviations between input-output prices and labour values. His empirical studies (corroborated by many other subsequent authors) reveal that the size of the deviations are “quite moderate” in practice.

    Notwithstanding the importance and interest of these empirical results the existence of high statistical correlation between classical labour values and aggregate prices does not address the theoretical problems of the classical labour theory of value. The existence of a strong empirical correlation between input-output prices and classical labour values is consistent with there being another “less powerful cause” (Ricardo), other than labour time, of the variation in natural prices. Ricardo, for example, predicted the divergence would be empirically small, yet nonetheless knew that even small divergences invalidate a labour theory of value.

    Sraffa, for example, distinguishes between two kinds of measurement error:

    “…one should emphasize the distinction between two types of measurement. First…the one in which the statisticians are mainly interested. Second… measurement in theory. The statisticians’ measures were only approximated and provided a suitable field for work in solving index number problems. The theoretical measures required absolute precision. Any imperfections in those theoretical measures were not merely upsetting, but knocked down the whole theoretical basis” (quoted in Lutz and Hague (1961, pp. 305–306)).

    We know, on theoretical grounds alone, that the existence of capitalist profit introduces an additional degree-of-freedom that deforms natural prices away from classical labour-values. In consequence, classical labour-values cannot be their measure, and the value-theoretic claims of the classical labour theory of value are left hanging, a point the classical economists understood very well. The fact that their theoretical measures lack absolute precision indicates a logical, not an empirical, problem.

    E.g., the correctness of the labour theory of value cannot depend on the empirical “strength” of aggregate correlations. For example, at what level of correlation should we decide to reject the classical labour theory? Below 95%, 90% – or is 85% ok? Also, the correlations vary over time. Should we therefore consider that the classical labour theory was more correct in 2011 compared to 2014? Perhaps the residual lack of correlation, however “small”, is precisely a reward to capitalists for their patience, which is entirely unrelated to labour time?

    So Shaikh accepts that there can only be an approximate relationship between natural prices and classical labour values. In a sense, he adopts a Ricardian 93% labour theory of value. In contrast, I think Marx was right to stipulate that — in theory — there must be a one-to-one relationship between labour time and natural prices (in appropriate theoretical conditions). But to discover that one-to-one relationship requires generalising Marx’s theory.

    I hope these preliminary comments go some way to answering your question. I haven’t mentioned Shaikh’s iterative interpretation of Marx’s transformation problem. This is also interesting and important work. But it doesn’t really alter the conclusions above.

    Best wishes,
    -Ian.

    (1961) The Theory of Capital, Proceedings of a Conference held by the International Economic Association
    Lutz, F A, Hague, Douglas (Eds.) Palgrave.

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    • I will have to wrap my head in all of this, i’m reading your papers and Shaik’s new book. But the precision of aggregate equalities is an important question. A good theory must be abble to account for them and not only in statistical terms but in theoretical/logical ones ( like in quantum mesurement problems). Thanks you for the reply.

      Yours.

      Sounkou.

      Liked by 1 person

  5. What do you think of Harry Cleaver’s interpretation of Marx’s labor theory of value in his new book ‘Rupturing the Dialectic: The Struggle against Work, Money, and Financialization’:

    You can find a PDF on his academia.edu: https://www.academia.edu/32888580/Rupturing-the-Dialectic-final.pdf

    His older book ‘Reading Capital Politically’ also engages with this: https://libcom.org/files/cleaver-reading_capital_politically.pdf

    For an in-depth philosophical study of Marx’s theory of value, I also recommend Moishe Postone’s book ‘Time, Labor and Social Domination’:

    http://gen.lib.rus.ec/book/index.php?md5=AD3DB7D2575DF41FE7F3BF216653F3C7

    The anarchist David Graeber also deal with Marx’s theory when he compares it to Marcel Mauss’ theories in his book ‘Toward An Anthropological Theory of Value: The False Coin of Our Own Dreams’:

    https://monoskop.org/images/3/36/Graeber_David_Toward_an_Anthropological_Theory_of_Value.pdf

    Here too: http://www.commoner.org.uk/10graeber.pdf

    Like

  6. Hi John

    Thanks for commenting!

    I’ve not read Harry Cleaver’s works so cannot comment. Is there anything specific that you think is worth raising?

    I have read Moishe Postone’s book. I cannot recommend it at all, either as economics or philosophy. However, I’d be interested to know why you think it has value.

    David Graeber’s “Toward an Anthropological Theory of Value” is an excellent work. I think the wider, anthropological perspective is very helpful and illuminating, although I do not agree with all of Graeber’s formulations with respect to value theory. I should re-read it, and blog a short commentary, which would certainly be helpful to me, and perhaps others.

    Best wishes,
    -Ian.

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  7. Harry Cleaver’s take on Marx is quite unique.

    His approach is more “political” than any other one I’ve read.

    He treats the various other interpretations of Marx in his the first book ‘Reading
    Capital Politically’.

    In ‘Rupturing the Dialectic: The Struggle against Work, Money, and Financialization’ he focuses on the labor theory of value (its history and his own interpretation).

    If you’re a fan of “people’s historians” like E.P Thompson and Peter Linebaugh, you’re going to like Cleaver’s stuff.

    Liked by 1 person

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