According to Carnap an account of the nature of mathematics, both pure and applied, must include the thesis that mathematical truths are devoid of factual content. He first formulated this thesis around 1930 and in its defence attempted to combine the reduction of mathematics to logic undertaken in the Principia with Wittgenstein’s insights into the nature of logic. In this paper I will show that this synthesis faces serious difficulties. Thus, it plays, with good reason, no longer a role in (...) Carnap’s mature philosophy of mathematics. (shrink)

Recent discussions of logical pluralism trace its origins to Rudolf Carnap’s principle of tolerance; indeed, the principle is seen as one of Carnap’s lasting philosophical contributions. In this paper, I will argue that Carnap’s reasons for adopting this principle are not purely logical, but are rather founded in the Vienna Circle’s manifesto—a programmatic document that brings the Circle’s philosophical work together with a program of social change. Building on work by Uebel, Romizi, and others, I argue that we must understand (...) the principle in light of Carnap’s role in writing the manifesto, and thus as integrated into the larger philosophical and political goals of the Circle. This history illuminates the often-ignored relationship between Carnap’s logical pluralism and his political views. Finally, I turn to the political situation of the post-World War 2 period in the United States. During this time, the Circle’s emigres in the USA transitioned their work from active efforts to reform society to the technical work that we recognize as the foundation of American analytic philosophy today. In this final section, I argue that the reasons that Carnap distanced himself from the political foundations of his view were due in large part to McCarthy-era persecution of left-wing academics. (shrink)

Im Rahmen dieses Beitrags beleuchten wir, wie Hans Hahn die Einflüsse Russells und Wittgensteins adaptiert, um seine individuelle Variante von Logizismus zu entwickeln. Von Bedeutung ist in diesem Zusammenhang Hahns unterschätzte Vorreiterrolle in der Entwicklung des logischen Toleranzprinzips und des logischen Pluralismus, also der Loslösung von der Vorstellung einer einzigen „korrekten“ Logik. Die detaillierten Arbeiten Uebels (2007, 2009) zur Entwicklung des logischen Pluralismus im Wiener Kreis verdienen zumindest zwei punktuelle Ergänzungen: Erstens untermauern die in diesem Kontext bisher unberücksichtigten Protokolle des (...) Wiener Kreises sowie Vorlesungsmitschriften Hermann Brochs die von Uebel im Gegensatz zu Goldfarb (1996) beschriebene Distanzierung Hahns von Wittgenstein. Zweitens relativieren Hahns und Mengers Arbeiten zu Occams Rasiermesser Uebels Einschätzung, Mengers Beitrag zum Toleranzprinzip sei „wenig philosophisch“. (shrink)

Although logicism played a significant role in Carnap's philosophical thinking, the relation of his philosophy of mathematics to the main tenets of the logicist tradition is complex and variable. is paper examines one aspect of this relation by discussing the following question: What elements of Carnap's Logical Syntax of Language, if any at all, indicate a real commitment to that tradition? It will be shown that although important aspects of Frege-Russell logicism are incorporated into the framework developed in that book, (...) it is nonetheless impossible to define a position within that framework which deserves to be called “typically logicist“. (shrink)