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Abstract |
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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Keywords | completeness categoricity |
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Reprint years | 2002 |
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Citations of this work BETA
Carnapian Explication, Formalisms as Cognitive Tools, and the Paradox of Adequate Formalization.Catarina Dutilh Novaes & Erich Reck - 2017 - Synthese 194 (1):195-215.
Frege or Dedekind? Towards a Reevalaution of Their Legacies.Erich H. Reck - 2013 - In The Historical Turn in Analytic Philosophy. London: Palgrave-Macmillan. pp. 139-170.
The Methodological Roles of Tolerance and Conventionalism in the Philosophy of Mathematics: Reconsidering Carnap's Logic of Science.Emerson P. Doyle - 2014 - Dissertation, University of Western Ontario
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