In a previous entry, I asserted that Voigt's Zahl und Mass in der Ökonomik
contain[s] more error than insight. Here, I'll discuss one of the more egregious errors. In section V, Voigt writes
An die Spitze der Erörterung dieses vielberufenen Begriffes sollte gestellt werden, dass es Einheiten des Wertes giebt, dass man also untersuchen kann, wievielmal so gross ein Wert als ein anderer ist und Güter gleichen Wertes durch einander ersetzen kann, dass also der Wert ein eigentliches in einer Kardinalzahl ausdrückbares Mass hat.
which may be translated as
At the forefront of discussion of this much used concept should be placed that there are units of value that one thus can investigate how many time as large a value is as another and can replace goods of the same value with each other, that thus the value has a real measure expressible in a cardinal number.
I'll deal first with the point that it seems that one can investigate how many times as large a value is as another.
Numbers are used in many ways. Depending upon the use, what is revealed by arithmetic may be a great deal or very little. Sometimes numbers are ascribed with so little meaning that we may as well consider them strings of numerals, the characters that we use for numbers, and not numbers at all. Sometimes numbers do nothing but provide an arbitrary order, good for something such as a look-up table but nothing else. Sometimes they provide a meaningful order, but one in which the results of most arithmetic operations are meaningless, as when items produced at irregular intervals are given sequential serial numbers. (The difference between any two such numbers tells one which was produced before the other, but little else.) Sometimes the differences between the differences are meaningful, as when items are produce at regular intervals and given sequential serial numbers. And so forth.
Monetary prices are quantities, but they are more specifically quantities of money; that does not make them quantities of value nor proxies of quantities of value. One would have to show that the results of every arithmetic operation on such a quantity of money said something about value for it to be shown that value were itself a quantity.
The second part of Voigt's claim is that one
Güter gleichen Wertes durch einander ersetzen kann [
can replace goods of the same value with each other]. But an equivalence between things corresponding to the same numbers doesn't make results of the application of arithmetic to those numbers meaningful. (Consider lots of items produced at irregular intervals, with each item in the lot given the same serial number, unique to the lot but otherwise random.) And we should ask ourselves under just what circumstances we can and cannot ersetzen one set of commodities of a given price with another of the same price.
Nor does somehow combining the use of quantities of money for prices with a property of equivalence imply that value is a quantity.
Voigt is unusual not in making this unwarranted inference, but in so clearly expressing himself as he does. From the observation that prices are usually quantities of something, which quantities increase as value increases, most people, and even most economists blithely infer that value itself behaves as a quantity.