Zermelo's Cantorian theory of systems of infinitely long propositions
Bulletin of Symbolic Logic 8 (4):478-515 (2002)
| Abstract | 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 | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,709 |
| External links |
  Try with proxy. |
| Through your library | Configure |
Similar books and articlesKevin 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 "on Denoting". Routledge.
R. Gregory Taylor (2008). Symmetric Propositions and Logical Quantifiers. Journal of Philosophical Logic 37 (6).
A. R. D. Mathias (2001). Slim Models of Zermelo Set Theory. Journal of Symbolic Logic 66 (2):487-496.
Richard Pettigrew (2010). The Foundations of Arithmetic in Finite Bounded Zermelo Set Theory. Cahiers du Centre de Logique 17:99-118.
Gregory H. Moore (1978). The Origins of Zermelo's Axiomatization of Set Theory. Journal of Philosophical Logic 7 (1):307 - 329.
Heinz-Dieter Ebbinghaus (2003). Zermelo: Definiteness and the Universe of Definable Sets. History and Philosophy of Logic 24 (3):197-219.
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.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads6 ( #145,761 of 550,917 )Recent downloads (6 months)1 ( #63,425 of 550,917 )How can I increase my downloads? |
My notes
Discussion
