Marx has always been considered a pure materialist; there has never been any doubt about this point. However, in the first chapter of Das Kapital, ‘‘work’’ is a strange substance, different from the material nature of things, hidden in goods, called by Marx “ghost matter, gelatinious matter, almost no matter at all”. So, in goods there are, together, two kinds of substances: the matter of the objects, and the ghost matter, put there by the work that became itself a matter, and that remains even when you take off all the matter with which goods are made. The ontological monism of Marx -all things are matter-, stands postulating a very suspicious gelatinious matter. Why does Marx behave in this way? Mainly, to lay the foundations of the theoretical concept of “value”, essential to his economic theory. He makes a substantialistic foundation of “value”, thinking, with all the scientists of his time, that theoretical constructs have a substantial base. Even the image “gelatinous” is taken from physics: we might remember that the ether was equally gelatinous. This problem is solved by Diederich and Fulda´s formal reconstruction of value law, in which is no needed to say anything about the kind of substance value is. Let us see how they do it: (Value Law) z ★ v ★ p z is the time of work that is needed to make one product v is the value p is the price of that product ★ is a function that determines the value once the time is known, and then determines the price. The Value Law says that if one knows the time needed to make one product, there is a function that determines the value, and once that the value is determined, there is a function that determines the price. The substantial quality of value is eliminated. But, in this reconstruction, value itself is eliminable because it is possible to put a composit function ★★, and take off the formula the “value”, in this way: VL) z ★★ p And this is possible because in Diederich and Fulda´s reconstruction, even when “value” appears in the formula as a result of a function between “time” and “price”, there is no numerical value of “value”; there is only scales of “time” and “price”. If it is so, Marx´s theory is changed so deeply in this reconstruction, that Marx would not have accepted it. “Value” is a construct that can not be dismissed from the theory without eliminating the theory itself. Let us see first how Marx states the problem. Surprinsingly, he does not try to define “value”, but “equal value”, as it appears when two goods are exchanged in the market. The problem he tries to explain, is how is it possible that: 1 quarter of wheat = 1 quintal of iron Marx answers, followin Aristotle, that they must have something in common: a common substance, a substance created by human work, the value. Mach does the same when he defines first “equal mass” in his reconstruction of classic mechanics, and then defines “mass”, showing that the way Marx goes is legitimate, and that in this direction no common substance is needed. Some years later, Frege and Russell, trying to define “number”, stated that sets have “equal number” when it is possible to put their elements in biunivocal correspondance. “Number” is the set of all sets that have "equal number". In the same way, the symbol (=) (equal) that is put between two products when they are exchanged, needs no common substance. The only thing we need is to state a relationship of biunivocal correspondence between the elements of these two sets. From that point on, we can stand that there is a function in real numbers that goes from the set of time to the set of products, a different function for each kind of product and that this function determines the quantity of a certain product that is related to t hours of work; these functions change, as Marx said, with the development of the productive forces. The time socially necesary to produce an object is the measure of its value. In a formal way: M = fM (tM) N = fN (tN) M has the same value as N if and only if tM = tN. And the claim is that “value” is the set of all sets that have the same value, in a form that resembles the Frege-Russell solution to “number”. The set definition of “value” is possible, instead of defining it by means of an obscure metaphysical substance. Marx´s methodologic problem is solved.
Les besoins praxéologiques du professeurThe praxeological needs of the teacher