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

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

A. W. Carus
Cambridge University
Steve Awodey
Carnegie Mellon University
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
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Reprint years 2004
DOI 10.1023/A:1005622201768
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