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  1. The development of mathematical logic from Russell to Tarski, 1900-1935.Paolo Mancosu, Richard Zach & Calixto Badesa - 2011 - In Leila Haaparanta (ed.), The development of modern logic. New York: Oxford University Press.
    The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...)
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  • Ramified structure.Gabriel Uzquiano - 2022 - Philosophical Studies 180 (5-6):1651-1674.
    The Russell–Myhill theorem threatens a familiar structured conception of propositions according to which two sentences express the same proposition only if they share the same syntactic structure and their corresponding syntactic constituents share the same semantic value. Given the role of the principle of universal instantiation in the derivation of the theorem in simple type theory, one may hope to rehabilitate the core of the structured view of propositions in ramified type theory, where the principle is systematically restricted. We suggest (...)
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  • The Fact Semantics for Ramified Type Theory and the Axiom of Reducibility.Edwin D. Mares - 2007 - Notre Dame Journal of Formal Logic 48 (2):237-251.
    This paper uses an atomistic ontology of universals, individuals, and facts to provide a semantics for ramified type theory. It is shown that with some natural constraints on the sort of universals and facts admitted into a model, the axiom of reducibility is made valid.
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  • Leon Chwistek on the no-classes theory in Principia Mathematica.Bernard Linsky - 2004 - History and Philosophy of Logic 25 (1):53-71.
    Leon Chwistek's 1924 paper ?The Theory of Constructive Types? is cited in the list of recent ?contributions to mathematical logic? in the second edition of Principia Mathematica, yet its prefatory criticisms of the no-classes theory have been seldom noticed. This paper presents a transcription of the relevant section of Chwistek's paper, comments on the significance of his arguments, and traces the reception of the paper. It is suggested that while Russell was aware of Chwistek's points, they were not important in (...)
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  • Propositional function.Edwin Mares - 2014 - Stanford Encyclopedia of Philosophy.
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