Projects per year
Abstract
Logicism presents one of the cornerstones of logical empiricism. At the same time, the views defended by Carnap, Hahn, and Hempel, among others, differ significantly from Frege’s original thesis. The present chapter will focus on several accounts of logicism developed in logical empiricism between 1920 and 1940. The aim here is twofold. The first aim is to survey how the classical logicist thesis was modified during the period in question. As we will show, this concerns not only a radically revised conception of the underlying logic but also a new focus on nonarithmetical mathematical theories to be reduced to logic. More specifically, philosophers such as Carnap aimed to formulate a generalized logicism valid for all branches of pure mathematics, including different theories of geometry, topology, and algebra. As will be shown, his and related accounts are best described as a form of conditional logicism based on an ifthenist reconstruction of mathematics. The second aim in this chapter is to clarify how these contributions are related to other developments in the foundations of logic and mathematics at the time. Specifically, the focus here will be on Carnap’s attempts to reconcile logicism with a structuralist account of mathematics.
Original language  English 

Title of host publication  Origins and Varieties of Logicism 
Subtitle of host publication  On the LogicoPhilosophical Foundations of Mathematics 
Place of Publication  New York 
Publisher  Routledge 
Number of pages  26 
ISBN (Electronic)  9780429277894 
DOIs  
Publication status  Published  30 Nov 2021 
Austrian Fields of Science 2012
 603113 Philosophy
Projects
 1 Finished

Structuralism: The Roots of Mathematical Structuralism
Schiemer, G. & Kolowrat, F.
1/03/17 → 28/02/22
Project: Research funding