  Carnap’s conventionalism was the culmination of the logical positivists’ efforts to accommodate logic and mathematics within an empiricist setting. Rejecting the Kantian synthetic a priori, the positivists held that logic and mathematics were analytic. Kant had explained the  analytic-synthetic distinction  in terms of concept-containment, which struck the positivists as psychologistic and hence “unscientific.” The positivists instead treated analyticity as “truth by virtue of meaning.” Specifically, they treated it as the product of linguistic convention. For instance, we can adopt the stipulative convention that “bachelor” means “unmarried man.” “All bachelors are unmarried men” is true by virtue of this convention. The positivists sought to extend this analysis to far less trivial examples, most notably mathematical and logical truth. In this regard, they were heavily influenced by Gottlob Frege’s logicism and also by Ludwig Wittgenstein’s conception, developed in the Tractatus Logico-Philosophicus, of logical truths as tautologous and contentless (sinnloss). Alberto Coffa (1993), Michael Friedman (1999), and Warren Goldfarb (1997) offer detailed discussion of the role played by conventionalism in logical positivism.