Skip to main content

Philosophical Applications of Kolmogorov’s Complexity Measure

  • Chapter
Logic and Philosophy of Science in Uppsala

Part of the book series: Synthese Library ((SYLI,volume 236))

Abstract

The basic question of how people choose theories to explain observations has justifiably drawn much attention and received numerous and various possible answers. In particular, it will certainly not be a shockingly new idea to suggest that people opt for the simplest possible theory, i.e., the simplest theory out of those that are compatible with accumulated evidence. (As an explicitly descriptive theory this idea dates back to Wittgenstein (1922) at the latest, while with a slightly more normative flavor it is often attributed to William of Occam —see, e.g., Russell (1945, pp. 468–473), and Sober (1975) for additional references.)

The process of induction is the process of assuming the simplest law that can be made to harmonize with our experience.

(Wittgenstein (1922, Proposition 6.363))

I would like to thank many teachers. colleagues, friends and family members for numerous discussions which motivated and refined these notes, for the encouragement to write them down, and for comments and references.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Dubins, L. E. and L. J. Savage (1965), How to Gamble if You Must, New York: McGraw Hill.

    Google Scholar 

  • Carnap, R. (1923), “Uber die Aufgabe der Physik und die Andwednung des Grundsatze der Einfachstheit,” Kant-Studien, 28, 90–107.

    Google Scholar 

  • de Finetti, B. (1949), “Sull Impostazione Assiomatica del Calcolo delle Probabilita,” Annali Triestini, 19, 29–81.

    Google Scholar 

  • de Finetti, B. (1950), “Aggiunta alla Nota sull’ Assiomatica della Probabilita,” Annali Triestini, 20, 5–22.

    Google Scholar 

  • Fine, T. L. (1973), Theories of Probability, New York: Academic Press.

    Google Scholar 

  • Gilboa, I. and D. Schmeidler (1989), “Infinite Histories and Steady Orbits in Repeated Games,” forthcoming in Games and Economic Behavior.

    Google Scholar 

  • Goodman, N. (1965), Fact. Fiction and Forecast, 2nd edition, Indianapolis: BobbsMerrill.

    Google Scholar 

  • Kolmogorov, A. (1963), “On Tables of Random Numbers,” Sankhya Ser. A, 369–376.

    Google Scholar 

  • Kolmogorov, A. (1965), “Three Approaches to the Quantitative Definition of Information,” Problems of Information Transmission (translated from Problemy Peredaci Informacii), 1, 1–7.

    Google Scholar 

  • Loveland, D. W. (1969), “A Variant of the Kolmogorov Concept of Complexity,” Information and Control, 15, 510–526.

    Article  Google Scholar 

  • Martin-Lof, P. (1966), “The Definition of Random Sequences,” Information and Control, 9, 602–619.

    Article  Google Scholar 

  • Pager, D. (1969), “On a Problem of Finding Minimal Programs for Tables,” Information and Control, 14, 550–554.

    Article  Google Scholar 

  • Popper, K. R. (1934), Logik der Forschung; English edition (1958), The Logic of Scientific Discovery, London: Hutchinson and Co. Reprinted ( 1961 ), New York: Science Editions.

    Google Scholar 

  • Russel, B. (1945), A History of Western Philosophy, New York: Simon and Schuster.

    Google Scholar 

  • Sober, E. (1975), Simplicity, Oxford: Clarendon Press.

    Book  Google Scholar 

  • Suppe, F. (1974), The Structure of Scientific Theories (edited with a critical introduction by F. Suppe), Urbana, Chicago, London: University of Illinois Press.

    Google Scholar 

  • Turing, A. M. (1956), “Can a Machine Think?”, in The World of Mathematics, Vol. IV, 2099–2123, New York: Simon and Schuster.

    Google Scholar 

  • Wittgenstein, L. (1922), Tractatus Logico Philosophicus, London: Routledge and Kegan Paul; fifth impression, 1951.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Gilboa, I. (1994). Philosophical Applications of Kolmogorov’s Complexity Measure. In: Prawitz, D., Westerståhl, D. (eds) Logic and Philosophy of Science in Uppsala. Synthese Library, vol 236. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8311-4_13

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-8311-4_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4365-8

  • Online ISBN: 978-94-015-8311-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics