1. The Gradation of the Means

Acting man transfers the valuation of ends he aims at to the means.

Other things being equal, he assigns to the total amount of the various means the same value he attaches to the end which they are fit to bring about. For the moment we may disregard the time needed for production of the end and its influence upon the relation between the value of the ends and that of the means.

The gradation of the means is like that of the ends a process of preferring a to b. It is preferring and setting aside. It is manifestation of a judgment that a is more intensely desired than is b. It opens a field for application of ordinal numbers, but it is not open to application of cardinal numbers and arithmetical operations based on them. If somebody gives me the choice among three tickets entitling one to attend to operas Aida, Falstaff, and Traviata and I take, if I can only take one of them, Aida, and if I can take one more, Falstaff also, I have made a choice. That means: under given conditions I prefer Aida and Falstaff to Traviata; if I could only choose one of them, I would prefer Aida and renounce Falstaff. If I call the admission to Aida a, that to Falstaff b and that to Traviata c, I can say: I prefer a to b and b to c.

The immediate goal of acting is frequently the acquisition of countable and measurable supplies of tangible things. Then acting man has to choose between countable quantities; he prefers, for example, 15r to 7p; but if he had to choose between 15r and 8p, he might prefer 8p. We can express this state of affairs by declaring that he values 15r less than 8p, but higher than 7p. This is tantamount to the statement that he prefers a to b and b to c. The substitution of 8p for a, of 15r for b and of 7p for c changes neither the meaning of the statement nor the fact that it describes. It certainly does not render reckoning with cardinal numbers possible. It does not open a field for economic calculation and the mental operations based upon such calculation. [p. 201]