Paul Rusnock

Russell, in his History of Western Philosophy, wrote that modern analytical philosophy had its origins in the construction of modern functional analysis by Weierstrass and others. As it turns out, Bolzano, in the first four decades of the nineteenth century, had already made important contributions'to the creation of "Weierstrassian" analysis, some of which were well known to Weierstrass and his circle. In addition, his mathematical research was guided by a methodology which articulated many of the central principles of modern philosophical analysis. That Russell was able to discover philosophical content within mathematical analysis was thus not surprising, for it had been carefully put there in the first place. Bolzano can and should, accordingly, be viewed as a founder of modern analytical philosophy, and not necessarily as an uninfluential one. This paper considers his work in mathematical and philosophical analysis against some of the relevant historical background.

This essay presents a new interpretation of Bolzano's account of necessary truth as set out in ?182 of the Theory of Science. According to this interpretation, Bolzano's conception is closely related to that of Leibniz, with some important differences. In the first place, Bolzano's conception of necessary truth embraces not only what Leibniz called metaphysical or brute necessities but also moral necessities (truths grounded in God's choice of the best among all metaphysical possibilities). Second, in marked contrast to Leibniz, Bolzano maintains that there is still plenty of room for contingency even on this broader conception of necessity