Carnap’s Early Semantics

Schiemer, Georg

doi:10.1007/s10670-012-9365-8

Cited by 13 publications

(18 citation statements)

References 24 publications

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“…However, and as shown by Awodey and Carus (2007), this situation changed in the early 1930s, specifically after Carnap's exchange with Gödel on the notion of analyticity. In particular, Carnap's understanding of "metatheoretic" statements at that point becomes similar to the semantic reconstruction given here, as argued in Schiemer (2013). 24 This interpretive issue has been much debated in the secondary literature on Carnap's early semantics.…”

Section: Models and Domain Variationsupporting

confidence: 55%

“…Loeb's discussion focuses on examples of axiomatic theories where a domain predicate is introduced into the language in terms of an explicit definition from the theory's primitive signs. These defined domain predicates provide further confirmation for the interpretation of Carnap's conception of model given in Schiemer (2013), given that in most cases a model domain is explicitly specified as the domain or range or field of a given primitive relation. Nevertheless, Loeb holds that "the domains-as-fields conception is too strict to describe Carnap's practice."…”

Section: Consequence and Derivabilitymentioning

confidence: 62%

“…14 What exists of part two of Untersuchungen is documented in Carnap's Nachlass (RC 081-01-01 to 081-01-33). See Schiemer (2012bSchiemer ( , 2013 for a detailed discussion of its contents. "extremal axioms", i.e., axioms (such as Peano's induction axiom in arithmetic and Hilbert's axiom of completeness in geometry) that impose a minimality or maximality constraint on the models of a theory.…”

Section: Axiomatic Theories and Carnap's Model Theorymentioning

confidence: 99%

“…This view has recently been corrected in work by Schiemer, Reck, and Loeb. In that work, it is shown that Carnap was well aware of the importance of capturing the notion of domain variability for his metatheoretic work and was not without resources to do so. See Loeb (2014a,b), Schiemer (2012bSchiemer ( , 2013, and Schiemer and Reck (2013).…”

Section: Models and Domain Variationmentioning

confidence: 99%

“…In them, not only the limitations of his approach were acknowledged, but also its innovative aspects and its significant influence on later developments in metalogic (Awodey and Reck 2002a;Reck 2004;Goldfarb 2005;Reck 2007). The third phase consists in fairly recent scholarship in which attention is drawn to previously neglected details of Carnap's early model theory and in which its role in the development of metalogic is spelled out more (Reck 2011;Schiemer 2012bSchiemer ,a, 2013Schiemer and Reck 2013;Loeb 2014a,b).…”

Section: Introductionmentioning

confidence: 99%

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Carnap’s early metatheory: scope and limits

2015

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In his Untersuchungen zur allgemeinen Axiomatik (1928) and Abriss der Logistik (1929), Rudolf Carnap attempted to formulate the metatheory of axiomatic theories within a single, fully interpreted type-theoretic framework and to investigate a number of meta-logical notions in it, such as those of model, consequence, consistency, completeness, and decidability. These attempts were largely unsuccessful, also in his own considered judgment. A detailed assessment of Carnap's attempt shows, nevertheless, that his approach is much less confused and hopeless than it has often been made out to be. By providing such a reassessment, the paper contributes to a reevaluation of Carnap's contributions to the development of modern logic.

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Section: Models and Domain Variationsupporting

confidence: 55%

Section: Consequence and Derivabilitymentioning

confidence: 62%

Section: Axiomatic Theories and Carnap's Model Theorymentioning

confidence: 99%