David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Bulletin of Symbolic Logic 8 (4):478-515 (2002)
In papers published between 1930 and 1935. Zermelo outlines a foundational program, with infinitary logic at its heart, that is intended to (1) secure axiomatic set theory as a foundation for arithmetic and analysis and (2) show that all mathematical propositions are decidable. Zermelo's theory of systems of infinitely long propositions may be termed "Cantorian" in that a logical distinction between open and closed domains plays a signal role. Well-foundedness and strong inaccessibility are used to systematically integrate highly transfinite concepts of demonstrability and existence. Zermelo incompleteness is then the analogue of the Problem of Proper Classes, and the resolution of these two anomalies is similarly analogous
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Silvia De Bianchi (2015). When Series Go in Indefinitum, Ad Infinitum and in Infinitum Concepts of Infinity in Kant’s Antinomy of Pure Reason. Synthese 192 (8):2395-2412.
Heinz-Dieter Ebbinghaus (2006). Zermelo: Boundary Numbers and Domains of Sets Continued. History and Philosophy of Logic 27 (4):285-306.
Similar books and articles
Kevin C. Klement (2009). A Cantorian Argument Against Frege's and Early Russell's Theories of Descriptions. In Nicholas Griffin & Dale Jacquette (eds.), Russell Vs. Meinong: The Legacy of. Routledge
Heinz-Dieter Ebbinghaus (2003). Zermelo: Definiteness and the Universe of Definable Sets. History and Philosophy of Logic 24 (3):197-219.
Gregory H. Moore (1978). The Origins of Zermelo's Axiomatization of Set Theory. Journal of Philosophical Logic 7 (1):307 - 329.
Richard Pettigrew (2010). The Foundations of Arithmetic in Finite Bounded Zermelo Set Theory. Cahiers du Centre de Logique 17:99-118.
A. R. D. Mathias (2001). Slim Models of Zermelo Set Theory. Journal of Symbolic Logic 66 (2):487-496.
R. Gregory Taylor (2008). Symmetric Propositions and Logical Quantifiers. Journal of Philosophical Logic 37 (6):575 - 591.
Gregory H. Moore (1980). Beyond First-Order Logic: The Historical Interplay Between Mathematical Logic and Axiomatic Set Theory. History and Philosophy of Logic 1 (1-2):95-137.
Added to index2009-01-28
Total downloads18 ( #172,644 of 1,777,935 )
Recent downloads (6 months)2 ( #206,198 of 1,777,935 )
How can I increase my downloads?