Representation theorems and the semantics of decision-theoretic concepts

Contemporary decision theory places crucial emphasis on a family of mathematical results called representation theorems, which relate criteria for evaluating the available options (such as the expected utility criterion) to axioms pertaining to the decision-maker’s preferences (for example, the transitivity axiom). Various claims have been made concerning the reasons for the importance of these results. The goal of this article is to assess their semantic role: representation theorems are purported to provide definitions of the decision-theoretic concepts involved in the evaluation criteria (such as those of utility or subjective probability that feature in the subjective expected utility criterion). In particular, this claim shall be examined from the perspective of philosophical theories of the meaning of theoretical terms.