International Journal of Theoretical Physics

, Volume 42, Issue 2, pp 301–307 | Cite as

Explicit Finitism

  • András Kornai


This paper takes the first steps in developing a theory of “explicit finitism” which puts explicit limits on the size of finite objects. We provide motivation in the “physics of computation” sense, survey some of the difficulties and describe the appropriate computing machinery. We introduce the subset J of the real numbers that is the central mathematical object emerging from considerations of explicit finitism, and take the first steps in studying its properties.

explicit finitism physics of computation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Friedman, H. (1999). Enormous Integers in Real Life. EnormousInt.12pt.6_1_00.docGoogle Scholar
  2. Lloyd, S. (2002). Computational capacity of the universe. Physical Review Letters 88, 237901.Google Scholar
  3. Montague, R. (1974). Deterministic theories. In Formal Philosophy, pp. 303-360, R. H. Thomason, ed., Yale University Press, New Haven, CT.Google Scholar
  4. Raatikainen, P. (1998). On interpreting Chaitin's incompleteness theorem. Journal of Philosophical Logic 27, 569-586.Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • András Kornai
    • 1
  1. 1.Metacarta Inc.CambridgeMassachusetts

Personalised recommendations