Logical & philosophical foundations for arithmetical logic
pp. 331-342
in: Irvine (ed), Physicalism in mathematics, Berlin, Springer, 1990Abstract
Arithmetical Logic is the title of a constructivist programme which aims to provide a logic of mathematics, rather than a mathematical logic. Specifically, it aims to provide a logic of arithmetic in which arithmetic is taken as the foundation of all mathematics. Such a logic of arithmetic is, in a sense, an arithmetization of logic, since the constructivist wishes to overturn the Fregean logicist perspective and make way for an internal logic of mathematical discourse. Here, formal logic does not have any special status; it is a theory of inference coupled with an arithmetical, rather than an algebraic or set-theoretic, representation theory.
