Elements for a Logic Reconstruction of Marx's Work-Value Theory

Abstract

In this article, Sneed’s structural metatheory is applied to the analysis of Marx’s work-value theory. As a result, we obtain a primitive base and a partial reconstruction of this theory.

The primitive base consists of six terms: use-value (U), work process (T), product (π), duration (of work processes) (δ), homogeneity (of use-values) (G) and value (v). U is a non-empty, finite set; T is a ternary relation included in P (U)×P (U)×P (U); π is a function from T to U; δ is a real-valued function with T as its domain; G is an equivalence relation included in U×U; and v is a function with positive real values and with U as its domain.

The fundamental laws of the theory are the following: (1) the Law of Decomposition of Value, which affirms that the value of any product is equal to the sum of the values of its prime materials, plus the sum of the portions of value that the work means transfer to the product, plus the amount of work that the work force adds to the prime material; (2) the Law of Homogeneity, which affirms that two products of the same gender are made of homogeneous materials; and, (3) a law which affirms that the number of work processes required for the production of any use-value is finite, and at the same time affirms that no work process produces the prime materials of processes that properly precede it. It is pointed out that the so-called Law of Value is derivable if two more terms are added to this primitive base: (1) human individual (H) and (2) property (PR).

Nine theorems are presented. For example, it is demonstrated that the set made up of a work process together with all those that precede it constitutes a sup semilattice. It is also demonstrated that from certain instances of the Law of Decomposition of Value it is possible to obtain a system of linear equations, which is appropriate for simultaneously determining the values of all the genders of products.

A few difficulties are pointed out which a logical reconstruction of the work-value theory has to face, and the WVT-theoreticity of the G and v concepts is argued in favor of. We conclude by pointing out that the fetishism of merchandise is a theme that seems to overflow the framework of political economy in a strict sense and which seems to fall under the theory of ideologies and/or an epistemology.

[A.G. de la S.]