Carnap, completeness, and categoricity:The gabelbarkeitssatz OF 1928 [Book Review]

Erkenntnis 54 (2):145-172 (2001)

Authors
A. W. Carus
Cambridge University
Steve Awodey
Carnegie Mellon University
Abstract
In 1929 Carnap gave a paper in Prague on Investigations in General Axiomatics; a briefsummary was published soon after. Its subject lookssomething like early model theory, and the mainresult, called the Gabelbarkeitssatz, appears toclaim that a consistent set of axioms is complete justif it is categorical. This of course casts doubt onthe entire project. Though there is no furthermention of this theorem in Carnap''s publishedwritings, his Nachlass includes a largetypescript on the subject, Investigations inGeneral Axiomatics. We examine this work here,showing that it provides important insights intoCarnap''s development during this critical period, thetransition from Aufbau to Syntax,especially regarding the nature and motivation ofCarnap''s logicism. Moreover, we show how theAxiomatics influenced Carnap''s student Gödel inreaching the fundamental logical results that soonafterwards undermined Carnap''s project.
Keywords Philosophy   Philosophy   Epistemology   Ethics   Logic   Ontology
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1005622201768
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 41,507
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Carnap's Early Semantics.Georg Schiemer - 2013 - Erkenntnis 78 (3):487-522.
Carnap’s Defense of Impredicative Definitions.Vera Flocke - 2019 - Review of Symbolic Logic 12 (2):372-404.

View all 20 citations / Add more citations

Similar books and articles

Carnap, Semantics and Ontology.Gregory Lavers - 2004 - Erkenntnis 60 (3):295-316.
A Reserved Reading of Carnap's Aufbau.Christopher Pincock - 2005 - Pacific Philosophical Quarterly 86 (4):518–543.
The Justification of Concepts in Carnap's Aufbau.Jonathan Y. Tsou - 2003 - Philosophy of Science 70 (4):671-689.
Completeness and Categoricity: Frege, Gödel and Model Theory.Stephen Read - 1997 - History and Philosophy of Logic 18 (2):79-93.
Was Carnap a Complete Verificationist in the Aufbau?Richard Creath - 1982 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1982:384 - 393.

Analytics

Added to PP index
2009-01-28

Total views
68 ( #114,480 of 2,248,762 )

Recent downloads (6 months)
6 ( #311,032 of 2,248,762 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature