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  1.  49 DLs
    Georg Schiemer (2013). Carnap's Early Semantics. Erkenntnis 78 (3):487-522.
    This paper concerns Carnap’s early contributions to formal semantics in his work on general axiomatics between 1928 and 1936. Its main focus is on whether he held a variable domain conception of models. I argue that interpreting Carnap’s account in terms of a fixed domain approach fails to describe his premodern understanding of formal models. By drawing attention to the second part of Carnap’s unpublished manuscript Untersuchungen zur allgemeinen Axiomatik, an alternative interpretation of the notions ‘model’, ‘model extension’ and ‘submodel’ (...)
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  2.  22 DLs
    Georg Schiemer (2014). Invariants and Mathematical Structuralism. Philosophia Mathematica 22 (1):70-107.
    The paper outlines a novel version of mathematical structuralism related to invariants. The main objective here is twofold: first, to present a formal theory of structures based on the structuralist methodology underlying work with invariants. Second, to show that the resulting framework allows one to model several typical operations in modern mathematical practice: the comparison of invariants in terms of their distinctive power, the bundling of incomparable invariants to increase their collective strength, as well as a heuristic principle related to (...)
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  3.  17 DLs
    Georg Schiemer (2012). Carnap on Extremal Axioms, "Completeness of the Models," and Categoricity. Review of Symbolic Logic 5 (4):613-641.
    This paper provides a historically sensitive discussion of Carnaps theory will be assessed with respect to two interpretive issues. The first concerns his mathematical sources, that is, the mathematical axioms on which his extremal axioms were based. The second concerns Carnapcompleteness of the modelss different attempts to explicate the extremal properties of a theory and puts his results in context with related metamathematical research at the time.
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  4.  13 DLs
    Georg Schiemer & Erich H. Reck (2013). Logic in the 1930s: Type Theory and Model Theory. Bulletin of Symbolic Logic 19 (4):433-472.
    In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style of Principia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as involving a radical break that first made possible the rise of modern model theory. While comparing several early attempts to develop the semantics (...)
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  5.  5 DLs
    Georg Schiemer (2010). Fraenkel's Axiom of Restriction: Axiom Choice, Intended Models and Categoricity. In Benedikt L.öwe & Thomas Müller (eds.), PhiMSAMP. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice. College Publications 307{340.
  6.  4 DLs
    Georg Schiemer (2014). Logicism and Ramsification. Metascience 23 (2):255-261.
    This excellent book presents a collection of eleven articles, all but one of which were written by William Demopoulos over the period of the last 19 years. The book comprises eight published articles, some of which have appeared only recently, as well as three new articles. The thematic scope of the topics investigated here is broad and ranges from Frege’s original logicist program outlined in his Grundlagen der Arithmetik (Frege 1884) to Carnap’s mature work on the logical reconstruction of scientific (...)
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  7.  3 DLs
    Georg Schiemer (2012). Carnap's Untersuchungen: Logicism, Formal Axiomatics, and Metatheory. In R. Creath (ed.), Vienna Circle Institute Yearbook. Springer Verlag 13--36.
    This paper discusses Carnap’s attempts in the late 1920s to provide a formal reconstruction of modern axiomatics.1 One interpretive theme addressed in recent scholarly literature concerns Carnap’s underlying logicism in his philosophy of mathematics from that time, more specifically, his attempt to “reconcile” the logicist approach of reducing mathematics to logic with the formal axiomatic method. For instance, Awodey & Carus characterize Carnap’s manuscript Untersuchungen zur allgemeinen Axiomatik from 1928 as a “large-scale project to reconcile axiomatic definitions with logicism, and (...)
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  8.  2 DLs
    Georg Schiemer & Norbert Gratzl (forthcoming). The Epsilon-Reconstruction of Theories and Scientific Structuralism. Erkenntnis:1-26.
    Rudolf Carnap’s mature work on the logical reconstruction of scientific theories consists of two components. The first is the elimination of the theoretical vocabulary of a theory in terms of its Ramsification. The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator. This paper investigates Carnap’s epsilon-reconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of (...)
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  9.  1 DLs
    Hans-Joachim Dahms, Markus Lammenranta, Juha Manninen & Georg Schiemer (2011). Reviews. [REVIEW] Vienna Circle Institute Yearbook 15:337-349.
    As Paul Feyerabend once remarked, philosophy of science is a subject with a great past. Let me for the moment leave aside his disillusioned impression that it had only a sad present and no future and concentrate on its past. It is surprising indeed that much has been published on the history of science in the last few decades, while only very few efforts have been made to give an overall description of the history of philosophy of science. That of (...)
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