Edited by John B. Davis, Alain Marciano and Jochen Runde
Peter Kesting and Arnis Vilks Historically, formalism in economics is closely related to the use of mathematics. Logically, however, the connection between formalism and mathematics is subtle. On the one hand, mathematics can be – and often has been – used in economic reasoning in a relatively informal manner. Even within mathematics itself, ideas and arguments have for centuries been often discussed in a rather loose and non-formal way. On the other hand, it will be argued below that formalism does not necessarily entail the use of mathematics, or at any rate, that it does not necessitate the particular kind of mathematization characteristic of present-day mathematical economics. Tentatively, and in a broad sense of the word, we take formalism to be an approach to theorizing that aims at making explicit the logical structure of any proposed theory. In this broad sense, formalism quite obviously does not require the use of mathematics, but it does require some notion of proof, deduction, or logical derivation. Of any assertion made in a theory, a formalist would indicate whether it is a derived one, and of any derived assertion he/she would indicate from where it can be derived. Two more speciﬁc notions of formalism will be deﬁned below – what we will call ‘basic formalism’, and the approach of present-day mathematical economics – which we will call ‘set-theoretic formalism’. Formalism in the broad sense has been followed in economic reasoning in varying degrees – more or less explicitly labeling underived statements as assumptions, postulates or axioms, and...
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