Predicative foundations of arithmetic
Journal of Philosophical Logic 24 (1):1 - 17 (1995)
| Abstract | Predicative mathematics in the sense originating with Poincar´ e and Weyl begins by taking the natural number system for granted, proceeding immediately to real analysis and related fields. On the other hand, from a logicist or set-theoretic standpoint, this appears problematic, for, as the story is usually told, impredicative principles seem to play an essential role in the foundations of arithmetic itself.1 It is the main purpose of this paper to show that this appearance is illusory: as will emerge, a predicatively acceptable axiomatization of the natural number system can be formulated, and both the existence of structures of the relevant type and the categoricity of the relevant axioms can be proved in a predicatively acceptable way. | |||||||||
| 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: 5,653 |
| External links |
  Try with proxy. |
| Through your library | Configure |
Similar books and articlesCharles McCarty (2013). Paradox and Potential Infinity. Journal of Philosophical Logic 42 (1):195-219.
Gottlob Frege (1953/1968). The Foundations of Arithmetic. Evanston, Ill.,Northwestern University Press.
Richard Heck (2011). Ramified Frege Arithmetic. Journal of Philosophical Logic 40 (6):715-735.
Paul Strauss (1991). Arithmetical Set Theory. Studia Logica 50 (2):343 - 350.
Solomon Feferman, Relationships Between Constructive, Predicative and Classical Systems of Analysis.
Øystein Linnebo (2004). Predicative Fragments of Frege Arithmetic. Bulletin of Symbolic Logic 10 (2):153-174.
Geoffrey Hellman (1994). Real Analysis Without Classes. Philosophia Mathematica 2 (3):228-250.
Fernando Ferreira (1999). A Note on Finiteness in the Predicative Foundations of Arithmetic. Journal of Philosophical Logic 28 (2):165-174.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads20 ( #61,410 of 548,979 )Recent downloads (6 months)1 ( #63,511 of 548,979 )How can I increase my downloads? |
My notes
Discussion
