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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References found in this work BETA
From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s.Paolo Mancosu (ed.) - 1998 - Oxford University Press.
Begriffsschrift: Eine Der Arithmetische Nachgebildete Formelsprache des Reinen Denkens.Gottlob Frege - 1879 - L. Nebert.
Citations of this work BETA
Carnap on Extremal Axioms, "Completeness of the Models," and Categoricity.Georg Schiemer - 2012 - Review of Symbolic Logic 5 (4):613-641.
Structure and Categoricity: Determinacy of Reference and Truth Value in the Philosophy of Mathematics.Tim Button & Sean Walsh - 2016 - Philosophia Mathematica 24 (3):283-307.
Concept Formation and Scientific Objectivity: Weyl's Turn Against Husserl.Iulian D. Toader - 2013 - Hopos: The Journal of the International Society for the History of Philosophy of Science 3 (2):281-305.
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