David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
References found in this work BETA
No references found.
Citations of this work BETA
Iulian D. Toader (2013). Concept Formation and Scientific Objectivity: Weyl's Turn Against Husserl. HOPOS 3 (2):281-305.
George Weaver (2011). A General Setting for Dedekind's Axiomatization of the Positive Integers. History and Philosophy of Logic 32 (4):375-398.
Sébastien Gandon (2005). Pasch Entre Klein Et Peano: Empirisme Et Idéalité En Géométrie. Dialogue 44 (4):653-692.
Georg Schiemer (2012). Carnap on Extremal Axioms, "Completeness of the Models," and Categoricity. Review of Symbolic Logic 5 (04):613-641.
John Symons (2008). Book Reviews. [REVIEW] Studia Logica 89 (2):285-289.
Similar books and articles
Dirk Schlimm (2011). On the Creative Role of Axiomatics. The Discovery of Lattices by Schröder, Dedekind, Birkhoff, and Others. Synthese 183 (1):47-68.
Steve Awodey & Erich H. Reck, Completeness and Categoricity, Part I: 19th Century Axiomatics to 20th Century Metalogic.
Steve Awodey & Erich H. Reck (2002). Completeness and Categoricity, Part II: Twentieth-Century Metalogic to Twenty-First-Century Semantics. History and Philosophy of Logic 23 (2):77-94.
Steve Awodey & Erich H. Reck, Completeness and Categoricty, Part II: 20th Century Metalogic to 21st Century Semantics.
Steve Awodey & Erich H. Reck, Completeness and Categoricity: 19th Century Axiomatics to 21st Century Senatics.
Stephen Read (1997). Completeness and Categoricity: Frege, Gödel and Model Theory. History and Philosophy of Logic 18 (2):79-93.
Dirk Schlimm, Axiomatics and Progress in the Light of 20th Century Philosophy of Science and Mathematics.
Ugo Perone (2010). The Risks of The Present. Symposium 14 (2):19-34.
S. Awodey & A. W. Carus (2001). Carnap, Completeness, and Categoricity:The Gabelbarkeitssatz OF 1928. [REVIEW] Erkenntnis 54 (2):145-172.
Mojżesz Presburger & Dale Jabcquette (1991). On the Completeness of a Certain System of Arithmetic of Whole Numbers in Which Addition Occurs as the Only Operation. History and Philosophy of Logic 12 (2):225-233.
Added to index2010-08-10
Total downloads26 ( #56,547 of 1,089,153 )
Recent downloads (6 months)5 ( #20,087 of 1,089,153 )
How can I increase my downloads?