In R. Creath (ed.), Vienna Circle Institute Yearbook. Springer Verlag. pp. 13--36 (2012)

Georg Schiemer
University of Vienna
This paper discusses Carnap’s attempts in the late 1920s to provide a formal reconstruction of modern axiomatics.1 One interpretive theme addressed in recent scholarly literature concerns Carnap’s underlying logicism in his philosophy of mathematics from that time, more specifically, his attempt to “reconcile” the logicist approach of reducing mathematics to logic with the formal axiomatic method. For instance, Awodey & Carus characterize Carnap’s manuscript Untersuchungen zur allgemeinen Axiomatik from 1928 as a “large-scale project to reconcile axiomatic definitions with logicism, and transform implicit into explicit definitions.” It is argued that Carnap’s central idea was to balance a Fregean foundational stance with the modern model-theoretic viewpoint introduced in Hilbert’s Grundlagen der Geometrie ). It was also shown in recent literature that Carnap’s attempt to provide a logicist reconstruction of axiomatics is limited in several ways.2 No closer attention, however, has so far been dedicated to some of the details of his proposed reconciliation
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DOI 10.1007/978-94-007-3929-1_2
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References found in this work BETA

The Problem of Logical Constants.Mario Gómez-Torrente - 2002 - Bulletin of Symbolic Logic 8 (1):1-37.

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Logic in the 1930s: Type Theory and Model Theory.Georg Schiemer & Erich H. Reck - 2013 - Bulletin of Symbolic Logic 19 (4):433-472.
Hilbert's Axiomatic Method and Carnap's General Axiomatics.Michael Stöltzner - 2015 - Studies in History and Philosophy of Science Part A 53:12-22.
Pasch's Empiricism as Methodological Structuralism.Dirk Schlimm - 2020 - In Erich Reck & Georg Schiemer (eds.), The Pre-History of Mathematical Structuralism. New York: Oxford University Press. pp. 80-105.

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