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- S. Awodey & A. W. Carus (2001). Carnap, Completeness, and Categoricity:The Gabelbarkeitssatz OF 1928. Erkenntnis 54 (2):145-172.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.
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This paper will deal with three questions regarding Carnap's transition from the position he held at the time of writing Syntax to the doctrines he held during his semantic phase: (1) What was Carnap's attitude towards truth at the time of writing Syntax? (2) What was Carnap's position regarding questions of reference and ontology at the time of writing Syntax? (3) Was Carnap's acceptance of Tarski's analysis of truth and reference detrimental to his philosophical project? Section 1 of this paper will deal with the first of these questions. Special attention will be paid to identifying what it was that prevented Carnap from defining a truth predicate for descriptive languages in Syntax. Section 2 of this paper will deal with the question of Carnap's attitude towards reference and ontology in Syntax. It will be shown that the attempt in Syntax to address ontological questions is seriously defective. Section 3 of this paper addresses the last of the questions posed above. It is argued that in the light of what is established in Sections 1 and 2, Carnap could not have retained the position of Syntax with respect to truth and reference.
It is argued that Carnap was not a complete verificationist in the Aufbau despite the widespread view that he was. That doctrine would be intrinsic to constructionalism only if either of two additional assumptions are made, and there is no reason to believe that Carnap made these assumptions. Further, in the Aufbau Carnap did not demand verifiability independently of constructionalism, and his clear rejection of verifiability in Pseudoproblems counts heavily against his ever having accepted it in the Aufbau.
No categories
Rudolf Carnap’s Der logische Aufbau der Welt ( The Logical Structure of the World ) is generally conceived of as being the failed manifesto of logical positivism. In this paper we will consider the following question: How much of the Aufbau can actually be saved? We will argue that there is an adaptation of the old system which satisfies many of the demands of the original programme. In order to defend this thesis, we have to show how a new ‘ Aufbau -like’ programme may solve or circumvent the problems that affected the original Aufbau project. In particular, we are going to focus on how a new system may address the well-known difficulties in Carnap’s Aufbau concerning abstraction, dimensionality, and theoretical terms.
Frege?s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such as arithmetic and set theory. As such, it was seen to fail by Gödel?s incompleteness theorem of 1931. It is argued, however, that this is to impose a later interpretation on the word ?complete? it is clear from Dedekind?s writings that at least as good as interpretation of completeness is categoricity. Whereas few interesting first-order mathematical theories are categorical or complete, there are logical extensions of these theories into second-order and by the addition of generalized quantifiers which are categorical. Frege?s project really found success through Gödel?s completeness theorem of 1930 and the subsequent development of first- and higher-order model theory.
In Carnap’s autobiography, he tells the story how one night in January 1931, “the whole theory of language structure” in all its ramifications “came to [him] like a vision”. The shorthand manuscript he produced immediately thereafter, he says, “was the first version” of Logical Syntax of Language. This document, which has never been examined since Carnap’s death, turns out not to resemble Logical Syntax at all, at least on the surface. Wherein, then, did the momentous insight of 21 January 1931 consist? We seek to answer this question by placing Carnap’s shorthand manuscript in the context of his previous efforts to accommodate scientific theories and meta- linguistic claims within Wittgenstein’s Tractatus theory of meaning. The breakthrough of January 1931 consists, from this viewpoint, in the rejection of the Tractatus theory in favor of the meta-mathematical perspective of Hilbert, Gödel, and Tarski. This was not yet the standpoint of the published Logical Syntax, as we show, but led naturally to the “principle of tolerance” and thus to Carnap’s mature philosophy, in which the inconsistencies between this first view and the principle of tolerance, which survived into the published Syntax, were overcome.
This paper concerns the recent debate on the nature and motivations of the epistemological project advanced in Rudolf Carnap's (18911970) Aufbau. Much of this debate has been initiated by Michael Friedman and Alan Richardson who argue (against the received view of the Aufbau as a foundationalist defense of empiricism) that Carnap's epistemological project is located in the tradition of neo-Kantian epistemology. On this revisionist reading of the Aufbau, Carnap's project is not motivated to address traditional empiricist problems regarding the justification of knowledge, but rather to show how objective knowledge is possible. A central aspect of the Aufbau that is neglected in the revisionists' analysis is the role of epistemic justification in Carnap's project. The aim of the present study is to argue that although the general epistemology in the Aufbau can be cast as neo-Kantian, Carnap's method of construction theory (or rational reconstruction) is formulated precisely as an empiricist method for the justification of conceptual knowledge. Construction theory radically redefines `empirical justification' into a formal-conventional notion, and is part of Carnap's more general agenda of redefining epistemology as a purely formal discipline.
This paper concerns the debate on the nature of Rudolf Carnap''sproject in his 1928 book The Logical Structure of the Worldor Aufbau. Michael Friedman and Alan Richardson haveinitiated much of this debate. They claim that the Aufbauis best understood as a work that is firmly grounded inneo-Kantian philosophy. They have made these claims in oppositionto Quine and Goodman''s ``received view'''' of the Aufbau. Thereceived view sees the Aufbau as an attempt to carry out indetail Russell''s external world program. I argue that both sidesof this debate have made errors in their interpretation ofRussell. These errors have led these interpreters to misunderstandthe connection between Russell''s project and Carnap''s project.Russell in fact exerted a crucial influence on Carnap in the1920s. This influence is complicated, however, due to the factthat Russell and Carnap disagreed on many philosophical issues. Iconclude that interpretations of the Aufbau that ignoreRussell''s influence are incomplete.
The two most popular approaches to Carnap's 1928 Aufbau are the empiricist reading of Quine and the neo-Kantian readings of Michael Friedman and Alan Richardson. This paper presents a third "reserved" interpretation that emphasizes Carnap's opposition to traditional philosophy and consequent naturalism. The main consideration presented in favor of the reserved reading is Carnap's work on a physical construction system. I argue that Carnap's construction theory was an empirical scientific discipline and that the basic relations of its construction systems need not be eliminated.
"Homage to Rudolph Carnap."--Hempel, C. G. Rudolf Carnap, logical empiricist.--Wedberg, A. How Carnap built the world in 1928.--Eberle, R. A construction of quality classes improved upon the Aufbau.--Carnap, R. Observation language and theoretical language.--Kaplan, D. Significance and analyticity: a comment of some recent proposals of Carnap.--Wójcicki, R. The factual content of empirical theories.--Williams, P. M. On the conservative extensions of semantical systems: a contribution to the problem of analyticity.--Winnie, J. A. Theoretical analyticity.--Wedberg, A. Decision and belief in science.--Bohnert, H. G. Carnap's logicism.--Hintikka, J. Carnap's heritage in logical semantics.--Partee, B. H. The semantics of belief-sentences.--Kasher, A. Pragmatic representations and language-games.--Carnap, R. Notes on probability and induction.--Jeffrey, R. C. Carnap's inductive logic.--Hilpinen, R. Carnap's new system of inductive logic.--Kuipers, T. A. F. A generalization of Carnap's inductive logic. Essler, W. K. Hintikka versus Carnap.--Hintikka, J. Carnap and Essler versus inductive generalization.--Shimony, A. Carnap on entropy, introduction to "Two essays on entropy" by Rudolf Carnap.
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