Erkenntnis 79 (2):405-429 (2014)

Iris Loeb
VU University Amsterdam
G. Schiemer has recently ascribed to Carnap the so-called domains-as-fields conception of models, which he subsequently used to defend Carnap’s treatment of extremal axioms against J. Hintikka’s criticism that the number of tuples in a relation, and not the domain of discourse, is optimised in Carnap’s treatment. We will argue by a careful textual analysis, however, that this domains-as-fields conception cannot be applied to Carnap’s early semantics, because it includes a notion of submodel and subrelation that is not only absent from Carnap’s work at that time, but even contradicts it. As a consequence, Schiemer’s defense of Carnap’s extremal axioms against Hintikka’s criticism fails. We will reconcile Carnap’s treatment of extremal axioms and Hintikka’s observation by taking into account the practice of axiomatics in the early twentieth century. If one realises that, in Carnap’s time, a predicate for the domain of discourse was often introduced in the formal theory, and that Carnap defined such predicates from the basic relations of an axiom system, the apparent disagreement between optimising relations and optimising domains disappears
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DOI 10.1007/s10670-013-9501-0
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References found in this work BETA

The Logical Syntax of Language.Rudolf Carnap - 1937 - London: K. Paul, Trench, Trubner & Co..
Der logische Aufbau der Welt.Rudolf Carnap - 1929 - Annalen der Philosophie Und Philosophischen Kritik 8:106-107.

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Hilbert's Axiomatic Method and Carnap's General Axiomatics.Michael Stöltzner - 2015 - Studies in History and Philosophy of Science Part A 53:12-22.

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