, Volume 53, Issue 1–2, pp 147–154 | Cite as

On The Untenability Of Nelson's Predicativism

  • St. Iwan


By combining some technical results from metamathematicalinvestigations of systems of Bounded Arithmetic, I will givean argument for the untenability of Nelson's finitistic program,encapsulated in his book Predicative Arithmetic.


Technical Result Bounded Arithmetic Predicative Arithmetic Finitistic Program 
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  1. Hájek, P. and P. Pudlák: 1993, Metamathematics of First-Order Arithmetic, Springer, Berlin.Google Scholar
  2. Kalsbeek, M.: 1989, ‘An Orey Sentence for Predicative Arithmetic', Technical Report X-89–01, ITLI, University of Amsterdam, Holland.Google Scholar
  3. Nelson, E.: 1986, Predicative Arithmetic, Princeton University Press, Princeton.Google Scholar
  4. Parikh, R.: 1971, ‘Existence and Feasibility in Arithmetic', The Journal of Symbolic Logic 36, 494–508.Google Scholar
  5. Paris, J. and C. Dimitracopoulos: 1983, ‘A Note on the Undefinability of Cuts', The Journal of Symbolic Logic 48, 564–9.Google Scholar
  6. Paris, J. and A. Wilkie: 1987, ‘On the Scheme of Induction for Bounded Arithmetic Formulas', Annals of Pure and Applied Logic 35, 261–302.Google Scholar
  7. Pudlák, P.: 1985, ‘Cuts, Consistency Statements and Interpretations', The Journal of Symbolic Logic 50, 423–41.Google Scholar
  8. Visser, A.: 1990, ‘Interpretability Logic', in P. Petkov (ed.), Mathematical Logic, Proceedings of the Heyting 1998 Summer School in Varna, Bulgaria, pp. 175–209.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • St. Iwan
    • 1
  1. 1.Institut für Theoretische Informatik und MathematikUniversität der Bundeswehr MünchenNeubibergGermany

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