Advertisement

Synthese

, Volume 20, Issue 1, pp 25–47 | Cite as

Linguistically invariant inductive logic

  • Ian Hacking
Article

Summary

Carnap's early system of inductive logic make degrees of confirmation depend on the languages in which they are expressed. They are sensitive to which predicates are, in the language, taken as primitive. Hence they fail to be ‘linguistically invariant’. His later systems, in which prior probabilities are assigned to elements of a model rather than sentences of a language, are sensitive to which properties in the model are called primitive. Critics have often protested against these features of his work. This paper shows how to make his systems independent of any choice of primitive predicates or primitive properties.

The solution is related to another criticism of inductive logic. It has been noticed that Carnap's systems are too all-embracing. Hisc(h, e) is defined for all sentencesh ande. Yet for manyh ande, the evidencee does not warrant any assessment of the probability ofh. We need an inductive logic in whichc(h, e) is defined only whene really does bear onh. This paper sketches the measure theory of such a logic, and, within this measure theory, provides ‘relativized’ versions of Carnap's systems which are linguistically invariant.

Keywords

Prior Probability Early System Measure Theory Inductive Logic Primitive Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    Max Black, ‘Notes on the Paradoxes of Confirmation’, inAspects of Inductive Logic (ed. by Jaakko Hintikka and Patrick Suppes), Amsterdam 1966, pp. 175–197.Google Scholar
  2. [2]
    Rudolf Carnap,The Continuum of Inductive Methods, Chicago 1952.Google Scholar
  3. [3]
    Rudolf Carnap,The Logical Foundations of Probability, Chicago 1950.Google Scholar
  4. [4]
    Rudolf Carnap, ‘Replies and Expositions’, V, inThe Philosophy of Rudolf Carnap (ed. by P. Schilpp), La Salle, Illinois, 1963, pp. 966–998.Google Scholar
  5. [5]
    Nelson Goodman,Fact, Fiction, and Forecast, London 1954.Google Scholar
  6. [6]
    Ian Hacking,The Leibniz-Carnap Programme, forthcoming.Google Scholar
  7. [7]
    David Hume,A Treatise on Human Nature (ed. by L. A. Selby-Bigge), Oxford, 1888.Google Scholar
  8. [8]
    Harold Jeffreys,Theory of Probability, 3rd ed., Oxford 1961.Google Scholar
  9. [9]
    C. R. Karp,Languages with Expressions of Infinite Length, Amsterdam 1964.Google Scholar
  10. [10]
    J. M. Keynes,A Treatise on Probability, London 1921.Google Scholar
  11. [11]
    Johannes von Kries,Die Principien der Wahrscheinlichkeitsrechung, Freiburg 1886.Google Scholar
  12. [12]
    P. S. de Laplace, ‘Mémoires sur la probabilité des causes par les événements’,Mémoires de l'Academie Royale des Sciences, vol.VI, 1774, pp. 621–656. In theOeuvres, vol.VIII, p. 30 ff.Google Scholar
  13. [13]
    Ernest Nagel, ‘Carnap's Theory of Induction’ inThe Philosophy of Rudolf Carnap (ed. by P. Schilpp), La Salle, Illinois, 1963, pp. 785–825.Google Scholar
  14. [14]
    W. V. Quine,Methods of Logic, Cambridge, Mass., 1950.Google Scholar
  15. [15]
    A. Renyi, ‘On a New Axiomatic Theory of Probability’,Acta Mathematica 6, 285–332.Google Scholar
  16. [16]
    W. C. Salmon, ‘Carnap's Inductive Logic’,The Journal of Philosophy 21 (1967) 725–740.Google Scholar
  17. [17]
    Dana Scott and Peter Krauss, ‘Assigning Probabilities to Logical Formulas’ inAspects of Inductive Logic (ed. by Jaakko Hintikka and Patrick Suppes), Amsterdam 1966, pp. 219–264.Google Scholar
  18. [18]
    W. Stegmüller, ‘Anhang B’ inInduktive Logik und Wahrscheinlichkeit (ed. by Rudolf Carnap and W. Stegmüller), Vienna 1958, pp. 242–252.Google Scholar

Copyright information

© D. Reidel Publishing Company 1969

Authors and Affiliations

  • Ian Hacking
    • 1
  1. 1.KampalaUganda

Personalised recommendations