Abstract
In examining thevon Neumann-Morgenstern axioms for a cardinal utility measure, ProfessorGeorgescu-Roegen comes to the conclusion that it is not the Strong Independence Axiom which causes difficulties, as had been supposed by several authors, but an ordinalist assumption, namely, that there always exists an ordinal utility function. This assumption is called the ordinalist fallacy. By using a Mengerian hierarchy of wants, ProfessorGeorgescu-Roegen shows that there exists a realistic case for which the alternatives are not ordinally measurable. In this note it is pointed out that this situation can only occur if one insists that a utility function cannot be defined on anything less than the real number system. If one is satisfied with commodity combinations that are represented in terms of rational numbers, then there is no fallacy. It is suggested that the rational numbers are necessary and sufficient as a numerical domain for the foundation of economics as a quantitative science. If a utility function is defined on rational numbers, a cardinal measure can be postulated for hierarchies of wants.
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