David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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History and Philosophy of Logic 23 (1):1-30 (2002)
This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully extend the usual set-theoretic semantics so as to shed new light on the relevant strengths and limits of higher-order logic
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Iulian D. Toader (2013). Concept Formation and Scientific Objectivity: Weyl's Turn Against Husserl. Hopos 3 (2):281-305.
Georg Schiemer (2012). Carnap on Extremal Axioms, "Completeness of the Models," and Categoricity. Review of Symbolic Logic 5 (4):613-641.
Sébastien Gandon (2005). Pasch Entre Klein Et Peano: Empirisme Et Idéalité En Géométrie. Dialogue 44 (4):653-692.
George Weaver (2011). A General Setting for Dedekind's Axiomatization of the Positive Integers. History and Philosophy of Logic 32 (4):375-398.
John Symons (2008). Book Reviews. [REVIEW] Studia Logica 89 (2):285-289.
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