by Sebastián Hdez. Solorza
Lee la versión en español: El debate entre Kliman y Romaniega. Marx vuelve a ganar
Editor’s note: The Spanish and English versions of Sebastián Hdez. Solorza’s commentary were published on the Tiempos Críticos website on July 16, 2026. We thank the author for allowing us to republish them here. His references to “Chapter 5” refer to “Contradictions in the General Formula of Capital,” which is Chapter 5 in the main English editions of Marx’s Capital. His commentary engages with various publications by Álvaro Romaniega as well as Andrew Kliman’s response to Romaniega and the discussion between them that took place in the comments section below Kliman’s article.
Introduction
In this text, I set out my position on the debate between Andrew Kliman and Álvaro Romaniega. I do so because, behind an apparently technical controversy, lies a fundamental scientific question: the difference between demonstrating the logical validity of an argument and establishing the empirical truth of a theory. Romaniega’s objection ultimately adopts an epistemologically untenable position because it demands a logical, mathematical, and abstract demonstration of the truth of an empirical theory before admitting the consequences that follow from it.
This shift may be related to the apriorist epistemological conception associated with part of the Austrian School, especially Mises’s praxeology. From that perspective, economics is conceived not primarily as an empirical science, but as a deductive science of human action, one that begins from certain axioms regarded as self-evident and derives its conclusions from them through logical reasoning. Yet turning that method into the universal criterion by which all economic theories must be assessed leads to a category mistake. Logic can determine whether a conclusion follows correctly from certain premises, but it cannot determine, by itself, whether those premises adequately represent reality. The truth of an empirical theory is not settled by an a priori deduction, but by its capacity to identify, explain, and coherently articulate real phenomena.
1. The Core of the Debate
In the first two versions of his critique, Romaniega presents gt · xt+1 as an additional hypothesis of the Temporal Single-System Interpretation (TSSI). From the third version onward, he formalises his objection in two steps. First, zero-sum exchange would imply that deviations from a certain reference price pᵒ cancel out: (p − pᵒ) · x = 0. Second, to transform that condition into the TSSI equality, g · x = (p − λ) · x = 0, it would be necessary to identify pᵒ = λ, where λ is the vector of Marxian values. His example deliberately assumes pᵒ ≠ λ in order to show that the first equality can hold while the second does not.
Kliman replies that Romaniega has introduced a reference price that does not belong to the original argument. In the TSSI, g does not mean a deviation from an independent and neutral standard; it is defined as the gain or loss of value in exchange, and therefore p = λ + g.
If circulation is zero-sum, one party’s gain in value is another party’s loss, so that g · x = 0. It follows directly that:
p · x = (λ + g) · x = λ · x
Total price equals total value, even though individual prices differ from their values. In other words, Marx wins again.
2. Romaniega’s Error: Substituting the Object of the Demonstration
Even at the risk of repetition, and for the sake of emphasis, let us review Romaniega’s error step by step. It consists in introducing a new magnitude, pᵒ, which forms no part of either Marx’s reasoning or the TSSI formulation, and then using it to refute a proposition that neither Marx nor the TSSI advances. Instead of analysing whether the gains and losses of value generated by exchange cancel one another out, he replaces the Marxian value λ with an alternative standard and shows that conservation measured against this new standard does not necessarily imply conservation measured against λ.
Romaniega begins with the condition:
(p − pᵒ) · x = 0,
and correctly notes that, in general, this does not imply:
(p − λ) · x = 0
when pᵒ ≠ λ. His counterexample is algebraically valid, but it does not affect Kliman’s argument. The reason is that Romaniega is comparing two different magnitudes:
Δp = p − pᵒ, g = p − λ
The first measures the deviation of prices from a standard introduced by Romaniega, whereas the second measures the gain or loss of value in the precise sense in which Marx and the TSSI employ that concept. Naturally, when pᵒ ≠ λ, there is no reason for the two deviations to coincide:
Δp ≠ g
This can also be seen from the identity:
p − λ = (p − pᵒ) + (pᵒ − λ)
Multiplying by x gives:
(p − λ) · x = (p − pᵒ) · x + (pᵒ − λ) · x
Therefore, even if Romaniega assumes that:
(p − pᵒ) · x = 0,
the following term remains:
(pᵒ − λ) · x
Yet this result shows only that his standard pᵒ may differ from the Marxian value λ. It does not show that the gains and losses of value defined by g = p − λ cease to cancel one another out in exchange. In other words, Romaniega proves that conservation with respect to a different magnitude is not equivalent to the conservation of value—something that Marx and the TSSI have never denied.
The counterexample therefore changes the object that was to be analysed. The original question was whether, given commodities with values λ, exchange at prices p can create an additional quantity of value or merely redistribute the value already existing. To answer this question, the relevant magnitude is:
g = p − λ,
not the deviation from an external standard pᵒ. If one party’s gain in value is the other party’s loss, then:
g · x = 0,
and it follows immediately that:
p · x = (λ + g) · x = λ · x
Romaniega identifies neither an internal contradiction nor a mathematical error in this derivation. He proves a different proposition concerning a magnitude that he himself has introduced, and then attributes that result to the argument he intended to refute. His counterexample is correct with respect to his own construction, but irrelevant to Marx and the TSSI.
3. Why Kliman is Right in the Debate
Within Marx’s theory and the interpretative purpose of the TSSI, the value λ is the magnitude that exists prior to exchange and whose redistribution is being studied. Introducing another vector pᵒ, described as what commodities “really are worth”, amounts to replacing the Marxian theory of value with another theory of value. That may constitute an external critique—why accept λ as the correct value?—but it does not demonstrate an internal inconsistency in Marx or the TSSI.
The example of the merchant makes this clear. If a merchant buys for 95 a commodity whose value is 100, the merchant gains 5, but the producer loses exactly the same 5. An individual gain has been created through circulation, but no new total social value has been created. At this point, Romaniega and Rallo confuse the appropriation of value with the production of value.
Kliman’s question concerns internal validity:
Given Marx’s premises, do the aggregate equalities follow?
The answer is yes. Romaniega shifts the discussion towards the soundness or truth of the premises:
Is the Marxian theory that determines λ actually correct?
These are different questions. Refuting Marx’s theory of value might render the conclusion false as a description of reality, but it would not show that the conclusion fails to follow from its premises.
This is why Kliman’s response is forceful:
Romaniega has come close to demanding a logico-mathematical proof that Marx’s value theory is correct. But the theory is an empirical theory, and no empirical theory is proven “correct” by logical, mathematical, or other a priori means. The grounds for acceptance (non-rejection) of an empirical theory are a posteriori: it predicts and/or plausibly explains the relevant phenomena. As Marx himself noted long ago, “[t]he chatter about the need to prove the concept of value arises only from complete ignorance both of the subject under discussion and of the method of science.”
4. The Scientific and Epistemological Question
The meaning of Marx’s statement, quoted by Kliman, must be specified. Marx is not claiming that the concept of value should be accepted dogmatically, that it requires no scientific justification, or that it is immune to criticism and evidence. What he rejects is the demand to “prove” the concept of value as though it were a mathematical theorem that could be deduced a priori from more elementary axioms. A scientific concept that expresses a real social relation is not demonstrated in the same manner as an algebraic identity; it is developed through the analysis of reality and justified by its capacity to explain coherently the phenomena that constitute its object.
Value does not appear in Marx as an arbitrary definition or as a premise selected for convenience. It is a theoretical determination constructed through the analysis of the commodity, the social division of labour, exchange, money, and capitalist relations of production. Its validity must be assessed through the explanatory capacity of the theory as a whole—that is, whether it enables us to understand the commodity-form, money, profit, surplus-value, competition, accumulation, crises, and so forth. To demand a logical-mathematical proof of the concept of value, independently of any investigation of those phenomena, therefore reveals a confusion about the nature of scientific concepts and the method by which a social reality is known.
This criterion is not peculiar to economics. In the empirical sciences, theories are not “proved” like mathematical theorems; they are provisionally accepted because they organise evidence, explain phenomena, and generate testable predictions. Newtonian gravitation, for example, was not deduced from indubitable axioms. It was justified because it explained and made it possible to calculate the motion of terrestrial and celestial bodies. General relativity subsequently showed that Newton’s theory had a limited domain of validity, without implying that it had lacked a scientific basis.
Likewise, the germ theory of disease was not established by an abstract logical deduction, but through microscopic observations, experiments, epidemiological regularities, and the effectiveness of interventions based upon it. The theory of evolution by natural selection is supported by the convergence of fossil, genetic, anatomical, and biogeographical evidence, not because the existence of natural selection can be derived exclusively from logical principles. Plate tectonics was not established by proving the concept of a “plate” a priori, but because that concept made it possible to integrate and explain the distribution of earthquakes and volcanoes, continental drift, palaeomagnetism, and the spreading of the ocean floor.
Something similar applies to theoretical entities that are not immediately observable. No one demands that the electron, the gravitational field, the gene, or a tectonic plate be “proved” through pure logic before being employed scientifically. Their existence and properties are justified indirectly by the observable effects they explain, by the coherence of the theories in which they are integrated, and by the success of the research they guide. This does not mean that such concepts are beyond question: they can be revised, redefined, or abandoned if another theory explains the evidence better. It means only that their assessment belongs to the domain of empirical investigation, not to that of absolute mathematical demonstration.
The analogy does not, by itself, demonstrate that the Marxian theory of value is true. It does show, however, that demanding an a priori logical-mathematical proof of its fundamental concept is an epistemologically inappropriate criterion for evaluating an empirical theory. The scientifically relevant question is not whether value can be deduced from incontestable axioms, but whether the category of value can coherently explain the forms and regularities of capitalist production and whether its consequences are compatible with historical and economic evidence. This is the meaning of Marx’s observation: whoever demands a “proof of the concept of value” confuses the formal proof of a theorem with the empirical and theoretical justification of a scientific category.
In other words, Marx’s statement allows us to distinguish between two different operations. One thing is to demonstrate formally a consequence from certain premises; another is to justify scientifically the categories through which reality is interpreted. The concept of value belongs to the second level. The proposition in Chapter 5 belongs to the first: once a magnitude of value existing prior to exchange has been established, Marx demonstrates that pure circulation can alter its distribution among agents, but not its total magnitude.
Romaniega’s demand does not deepen the discussion; it changes its object, as explained above. The question was whether the demonstration in Chapter 5 contains the logical error he claimed to have identified. Having failed to show such an error, Romaniega shifts the burden of proof and demands that Kliman first demonstrate the truth of Marx’s entire theory of value. But a particular investigation does not have to re-establish every concept it presupposes in order to examine a delimited question. Chapter 5 is not intended to reconstruct the concept of value from scratch, but to investigate whether exchange can increase an already existing quantity of value. Kliman expressly draws this distinction: values are the data of the transformation, whereas the question in dispute is whether the aggregate equalities follow from them and from Marx’s demonstration.
Otherwise, an infinite regress would arise. Before accepting the demonstration in Chapter 5, one would have to prove the theory of value; before accepting that proof, one would have to prove the categories used in it; and before those, one would have to prove the premises on which they rest. No science could begin under such a requirement. Science formulates concepts through the investigation of its object, derives logical consequences from them, and evaluates their explanatory capacity against reality. It does not require every concept to be proved a priori before it can be used.
5. Conclusion: Marx Wins Again
Conservation measured against an arbitrary standard pᵒ does not, by itself, guarantee conservation measured against λ, as Romaniega argues. But this algebraic result does not affect the TSSI and, consequently, does not refute Marx’s demonstration. In the TSSI, g does not represent a deviation from any standard that might be introduced retrospectively; it represents the gain or loss of value produced by exchange. By definition:
g = p − λ
If the gain obtained by one party to the exchange is exactly the loss suffered by the other, then:
g · x = 0
And therefore:
p · x = (λ + g) · x = λ · x
The result does not depend on every commodity being sold individually at its value. Prices may stand above or below values and generate particular gains and losses. What they cannot do, through pure exchange, is produce a net gain for the participants as a whole. Circulation changes who appropriates the existing value, but it does not create an additional quantity of social value.
Within the theory Romaniega seeks to refute, λ is the magnitude of value whose redistribution is being analysed. Anyone wishing to deny that this magnitude represents a real relation must develop an external critique of the Marxian theory of value and confront it with the evidence. What one cannot do is replace λ with another standard pᵒ, demonstrate that the two magnitudes do not coincide, and present that difference as an internal inconsistency in Marx. That is not a refutation; it is a change in the object being measured.
Introducing pᵒ as what commodities “really are worth” solves nothing either. It merely displaces the problem: what determines pᵒ, what social relation does it express, and what evidence allows it to be regarded as more real than λ? Without an independent theory answering those questions, pᵒ does not constitute a scientific alternative to the Marxian concept of value, but an ad hoc standard introduced to produce the desired result. The reasoning becomes circular: first, a standard different from λ is defined as true; then, it is concluded that λ is not the true standard.
The objection thus culminates in a self-referential scepticism and an epistemic regress, because it denies the possibility of analysing the consequences of a theory until the absolute truth of its concepts has been demonstrated a priori. Yet no empirical science can satisfy that standard and, if applied consistently, it would make all scientific inquiry impossible.
Marx wins again because the demonstration in Chapter 5 accomplishes exactly what it sets out to do. It does not seek to demonstrate the entire theory of value anew, but to answer a delimited question: can exchange, by itself, increase the total quantity of value in existence? The answer is quite simply no. If one party obtains more value through exchange than it gives, another must receive less value than it gives. One party’s gain is the other’s loss; individual appropriation changes, but total value does not.
Romaniega demonstrates only that a deviation from his standard pᵒ is not necessarily equal to a deviation from λ. That is algebraically correct, but irrelevant to the issue under debate. He identifies no logical error in Marx, does not refute the zero-sum condition, and does not demonstrate that circulation creates value. His counterexample replaces the Marxian magnitude that was to be examined with a different one and then presents the difference between the two as though it were a contradiction in the original theory.
The outcome of the debate can therefore be stated precisely:
- Kliman demonstrates that Romaniega’s objection does not affect the demonstration in Chapter 5;
- Romaniega does not refute the proposition that exchange merely redistributes existing value; and
- Marx wins again because the distinction between the production and appropriation of value remains intact.
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