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

Linguistically invariant inductive logic

  • Ian Hacking


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.


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.


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Copyright information

© D. Reidel Publishing Company 1969

Authors and Affiliations

  • Ian Hacking
    • 1
  1. 1.KampalaUganda

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