Marx’s Main Sophistry
by Lawrence Eubank (August 2025)
Reputation, Shakespeare has said, is a bubble, “oft got without merit.” And perhaps no reputation was ever gained with so little merit as that of Karl Marx. Anyone reading Das Kapital for the first time—as opposed to reading secondary sources—is likely to be struck by the contrast between Marx’s towering reputation in the public imagination and the convoluted muddle he actually puts on the page.
Let us attempt to examine the main thread of Marx’s argument in Das Kapital, paying special attention to the merits or otherwise of its reasoning.
The Analysis of a commodity
Marx’s work begins with “the analysis of a commodity,” a discussion of what determines a commodity’s value. He broaches the topic this way:
Let us take two commodities, e.g., corn and iron. The proportions in which they are exchangeable … can always be represented by an equation … e.g., 1 quarter corn = x cwt. iron. What does this equation tell us? It tells us that in two different things—in 1 quarter of corn and x cwt. of iron, there exists in equal quantities something common to both. —Karl Marx, Das Kapital, Part I, Chapter 1, Section 1
By that passage we are to understand that the value of a commodity is determined by the amount of some property or attribute contained within the commodity itself, as opposed to any external consideration such as market conditions or supply and demand. Marx asserts this point without giving any substantiation in facts or logic; he adopts it whole without any supporting evidence. It must therefore be considered an arbitrary assumption—and a rather naive one at that. It was considered and rejected as overly simplistic by Greek philosophers nearly 3 thousand years ago.
Identity of the “Common Something”
Marx asserts that the value of a commodity is determined by the amount of some property, attribute or “something common” within it. The question then is, what is the property which determines, and indeed constitutes, a commodity’s value? Marx tackles the question by process of elimination:
This common “something” cannot be either a geometrical, a chemical, or any other natural property of commodities. . .
[Commodities] have only one common property left, that of being products of labor. . .
We see then that that which determines the magnitude of the value of any article is the amount of labour socially necessary, or the labour time socially necessary for its production. . . As values, all commodities are only definite masses of congealed labor time. —Karl Marx, Das Kapital, Part I, Chapter 1, Section 1
Thus Marx by process of elimination identifies labor as the “common something” that constitutes value. His reasoning starts by considering the whole set of those properties which can be thought of as “in” or “common to” the commodity. Then he discards everything that, for whatever reason, he deems not to fit the criteria he has established for a possible answer.
That is, Marx has first begun by restricting the set of possible answers to things in, or common to, the commodity itself, with external social and economic considerations being ruled ineligible. Then he sorts through the remaining possibilities to identify his answer. The problem is that once he has reduced the investigation to his chosen boundaries, any hope of a sensible answer is lost. “Ask a foolish question, and you’ll get a foolish answer.”
“Formal Systems”
Marx’s argument in Das Kapital takes much the form of a “formal system.” A formal system is a framework for reasoning about a particular subject, developed using certain formalized rules and procedures.
We have all seen formal systems, though perhaps not under that name. Branches of mathematics are examples of formal systems. Each field—for instance, algebra—begins by identifying the objects it applies to, such as variables, constants, expressions, equations, etc. Next, axioms are adopted. These are statements which are assumed, not proved, and which help form the foundation of the formal system. Axioms in algebra include these:
Reflexive Axiom: A number is equal to itself. I.e., a = a.
Symmetric Axiom: If a = b then b = a.
Additive Axiom: If a=b, then a + c = b + c.
After the adoption of axioms, the formal system proceeds by the deriving of theorems. These are statements proved, i.e. logically deduced, from the axioms as well as the entire body of theorems that preceded the particular theorem.
The first theorems may be only a small departure or step up from the axioms. For instance, an early theorem in algebra is the distributive theorem: (b + c) a = ba + ca.
Then as we progress, we derive more complicated and less obvious theorems, such as the binomial theorem, the Fundamental Theorem of Algebra, and others, with each additional theorem being based on what has already been established. We end up with a powerful tool for solving equations, simplifying algebraic expressions, and solving problems of practical significance. The final result is a formal system — a logically consistent framework for reasoning, based on a chosen set of definitions and axioms with derived theorems.
The Formal System vs. the Real World
A formal system is not physics; that is, it is not a representation of the real, physical world. Rather, it is a logical construct telling us what conclusions can be drawn from chosen assumptions. It is not intended to be a description of physical reality. The distinction can be illustrated by the fact that in the geometry formal system, a line has only one dimension (length) and a point has no dimensions.
However, the formal system closely models the real world. The axioms of the system are chosen carefully so that, together with the theorems, they make a close parallel to the real world. As a result, when we solve a problem via the formal system—say, when we calculate the area of a triangle—we can confidently extend the theoretical result to the corresponding physical objects and their dimensions.
The deductions drawn from the theoretical system and those results in the real world are so similar that we rarely need to make a distinction between the two in our minds. The formal system is its own self-contained world, but it is a perfect mirror of the real world.
Das Kapital as a Formal system
Marx’s Das Kapital quite closely follows the structure of a formal system. His first axiom is, Value is determined by “something common to,” something “in,” commodities. His first theorem, which he proves by process of elimination, is that the “common something” which determines value is labor.
From the basis of those two starting points, Das Kapital continues as all formal systems do, adding deduced statement to deduced statement, with each new theorem being derived from all those that went before it.
Marx’s system does however differ from more traditional formal systems like algebra. Their usefulness comes from the care with which the axioms are chosen, in a conscientious effort to closely model the real world.
Marx’s formal system, on the other hand, is not designed to model reality, but to allow him to reach a pre-conceived conclusion—namely, that the capitalist doesn’t make profit by any legitimate means, but by exploiting unpaid “surplus value” off the work of the laborers. That is the ultimate theorem which Marx derives as the peak of his theoretical formal system.
Another Important Theorem
Marx proceeds to another theorem, applying ad hoc logic of a sort, to declare that the capitalist does not buy labor. Rather, what the laborer sells, and what the capitalist buys, is not labor but something else:
On the surface of bourgeois society, the wage of the labourer appears as the price of labour, a certain quantity of money that is paid for a certain quantity of labour… —Karl Marx, Das Kapital, Part VI, Chapter 19
However, Marx informs us that the superficial impression is wrong. The capitalist can’t buy labor, because labor doesn’t exist:
In order to be sold as a commodity in the market, labour must at all events exist before it is sold. But, could the labourer give it an independent objective existence, he would sell a commodity and not labour… —Karl Marx, Das Kapital, Part VI, Chapter 19
Having established that the laborer can’t sell labor, Marx announces that what he really sells is his ability to labor:
What the [labourer] sells is his labour-power…
By labor-power or capacity for labor is to be understood the aggregate of those mental and physical capabilities existing in a human being, which he exercises whenever he produces a use-value of any description… —Karl Marx, Das Kapital, Part II, Chapter 6
The purchased commodity is then “consumed” by its purchaser:
The purchaser of labor-power consumes it by setting the seller of it to work. —Karl Marx, Das Kapital, Part III, Chapter 7, Section 1
—a new meaning for the word “consumption”!
It only remains to add that labor-power, like all other commodities, has a value. Marx will later show, by logic too convoluted to go into here, that the value of a day’s labor-power is half a day’s labor.
Denouement
These beginning theorems are followed by others, in the standard manner of formal systems. Marx develops theorems about the value of commodities, the purchasing of labor-power, and the value of labor-power. Those serve as stepping stones to his ultimate theorem, which states that the value of the finished commodity is exactly the same as the total values expended in producing the commodity.
Marx illustrates this apex theorem via a hypothetical example involving the production of ten pounds of yarn, by the spinning of ten pounds of cotton. In his example, the capitalist’s expenditures for production include 1) ten pounds of cotton (the raw material); 2) wear and tear on the capital equipment (the spindle); and 3) a day’s-worth of labor-power (not labor). To repeat, the value of a day’s labor-power is half a day’s labor, i.e., six hours of labor.
The total of those “labors” is 2 1/2 days of labor. That is the production cost, or what we may call the “value in.”
Next we can pick up Marx’s exposition of the “value out,” i.e., the value of the finished product:
Let us now consider the total value of the product, the 10 lbs. of yarn. Two and a half days’ labour has been embodied in it, of which two days were contained in the cotton and in the substance of the spindle worn away, and half a day was absorbed during the process of spinning… —Karl Marx, Das Kapital, Part III, Chapter 7, Section 2
I.e., two and a half days’ labor was expended and is therefore embodied or congealed in the commodity. That is the commodity’s value:
Our capitalist stares in astonishment. The value of the product is exactly equal to the value of the capital advanced. . . The price of the yarn is fifteen shillings, and fifteen shillings were spent in the open market upon the constituent elements of the product… —Karl Marx, Das Kapital, Part III, Chapter 7, Section 2
The implications of this point are major. If “value in” equals “value out,” if the cost of production equals the value of the finished product, then profit as normally conceived of is impossible. I.e., profit as an excess of selling price over production costs is impossible.
This impossibility means that the capitalist gains wealth not by profit as conventionally considered, but by some more devious and underhanded method. (Marx will show later that the underhanded method is one of robbing the laborer of unpaid labor or “surplus value.”)
“Stares in astonishment”
“I have a theory about television. . . I don’t believe it is possible!” —“The Return of Edwin Carp,” an episode of “The Dick Van Dyke Show”
Our hypothetical capitalist “stares in astonishment,” and well he might. Marx has demonstrated that profit, something the capitalist sees every day and indeed participates in, is impossible. There must be a flaw in that line of logic.
But this conundrum is easily explained. Marx is not writing about the real world and real markets. Rather, he is developing his formal system, expounding on theorems that have been logically derived from chosen premises.
In other words. Marx’s text sounds like a description of the real-world economy, because the terms he uses are the same — labor, capital, commodity, etc. But Marx’s book is something of a bait-and-switch. He is proving a point in an artificially-constructed logical system, or theoretical construct, which readers assume to be a point about the real world. But “here in the real world,” Marx’s conclusions are irrelevant.
An Alternative, Science-Fiction World
Formal systems can be an essential tool when the founding axioms are chosen intelligently and with an intuitive grasp of the subject matter. But if the founding axioms are not intelligently and honestly chosen, the resulting system is fraudulent, and any points derived from it are inevitably specious.
Marx’s theoretical system has no bearing or influence on real-world economies. Those economies continue to function in accordance with their own rules, ignoring any contrived, abstruse theories that purport to prescribe how they must work. “The dogs bark, but the caravan moves on.”
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Larry Eubank was a computer programmer and consultant for 25 years and is now a free-lance writer. He has written for Chronicles—A Magazine of American Culture and Quarterly Review. He is the author of Marx’s Sophistries.
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