The notion of money as a measure of value as an artifact of the value theory of the "older political economy". By this he means the "classical economics" of Adam Smith, David Ricardo, and John Stuart Mill. The classical economists by and large believed that the value of a good was an objective attribute of the good itself. Economic actors, according to classical theory, exchanged goods if the respective values of the goods were equal (a fallacy that goes back to Aristotle1). And how do economic actors determine if an objective attribute of one thing is equal to the same objective attribute of another thing? Well, how do you determine equality between other objective attributes (like length, weight, volume, temperature, etc)? You measure, of course! And assuming value is an objective quantitative attribute, it would seem that the best unit of its measurement would be the money unit.
However, the classical economists were entirely backwards in their value theory. Therefore, their conception of money as a measure of value (derived, as it was, from their value theory) was equally backwards. Classical value theory was finally supplanted by what Mises calls "modern value theory" in the late 19th century. By this, Mises means the subjective marginal utility theory of value. To understand Mises' monetary theory, it is necessary to understand subjective marginal utility. To come to do so, please read the following three comics.
According to modern value theory, then, value is derived from utility. Valuation is a matter of preferring one good over another according to the goods' respective marginal utilities. When you prefer one thing to another, you give the goods a sort of rank order. Therefore "ordinal numbers" (1st, 2nd, etc) can be applied to the valuation of goods. For example, you can say that, in order of your preference, a plum is 1st, an apple is 2nd, and an orange is 3rd. But preferring is not measuring. Therefore, "cardinal numbers" (1, 2, 3 1/3, 4.5 etc) cannot be applied to the valuation of goods.
While, after the advent of modern value theory, most economists accepted that valuation is not objective, and thus not cardinal, they just could not let go of cardinality altogether. Cardinality is necessary for the use of measurement and mathematics, and according to the prejudice of many thinkers, "science is measurement"2. Value could not be cardinal, because it is a subjective preference based on utility. But maybe utility itself could be thought of as cardinal!
Even one of the greatest pioneers of modern value theory (and Mises' teacher) Eugen von Bohm-Bawerk tried to bring cardinality back in in this manner. However, instead of formulating measurable utility, Bohm-Bawerk formulated measurable satisfaction. (The two notions are closely related; the "utility" of a good is the good's "causal relevance" for the satisfaction of desire.) Irving Fisher, on the other hand, did try to conceive of a way to measure utility itself. The following comic illustrates how how Mises, in this chapter, endeavors to correct Bohm-Bawerk and Fisher by showing that both attempts directly contravene the law of dimishing marginal utility (see the previous slideshow). Mises nicely summed up the core of why any idea of measuring utility is fallacious in Economic Calculation in the Socialist Commonwealth:
"Marginal utility does not posit any unit of value, since it is obvious that the value of two units of a given stock is necessarily greater than, but less than double, the value of a single unit."He never quite explicitly spells that argument out in Theory of Money and Credit. For the most part, he just states that the law of marginal utility precludes measuring utility, and assumes his target audience (other economists) should be able to see why that is so at once. However, that will leave most readers these days bewildered, so I hope the following comic helps in that regard.
Mises then goes on to counter Joseph Schumpeter's attempt to quantify satisfaction. He does so by pointing out that Schumpeter assumes that valuation must be preceded by some prior measuring process. But simple reflection demonstrates that, we are perfectly capable of looking at an apple and an orange and simply selecting one based on a direct comparison of the two choices. We do not need to infer any intermediary quantities, and then decide based on an arithmetic comparison of those two quantities.
In Section 2, Mises argues that since value cannot be quantified, neither can values be summed up to infer the "total value" of a collection of goods.
In Section 3, brings money back into the picture. Money is not a measure of value, because valuation is a process of prioritization, not of measurement. When a man buys a newspaper for a 25 cents, he is not really demonstrating that 25 cents is the measure of its value to him. He is demonstrating the he values the newspaper over 25 cents. Furthermore he values the newspaper over 24 cents, 23 cents, etc. And he may value the newspaper over 26 cents as well. And presumably, there is a certain number of cents above which he values the money over the newspaper. Strictly speaking, when a newspaper is purchased for 25 cents, 25 cents is the newspaper's price, not its value.
Money, however, does introduce arithmetic into economic affairs in an important way. While money does not measure value, money prices can quantitatively express value in a commensurable way. This makes economic calculation (which is the hallmark of the market economy) possible. However economic calculation, while closely related to it, is outside the theory of money and indirect exchange, and thus it must be covered in a future article.
1Murray N. Rothbard, It All Began, As Usual, with the Greeks (excerpted from An Austrian Perspective on the History of Economic Thought), Section 1.8
2This being the original motto of the Econometric Society. See Murray N. Rothbard; The Mantle of Science.