Abstract
Theλ-continuum of inductive methods was derived from an assumption, calledλ-condition, which says that the probability of finding an individual having propertyx j depends only on the number of observed individuals having propertyx j and on the total number of observed individuals. So, according to that assumption, all individuals with properties which are different fromx j have equal weight with respect to that probability and, in particular, it does not matter whether any individual was observed having some propertysimilar tox j (the most complete proof of this result is presented in Carnap, 1980).
The problem thus remained open to find some general condition, weaker than theλ-condition, which would allow for thederivation of probability functions which might be sensitive to similarity. Carnap himself suggested a weakening of theλ-condition which might allow for similarity sensitive probability functions (Carnap, 1980, p. 45) but he did not find the family of probability functions derivable from that principle. The aim of this paper is to present the family of probability functions derivable from Carnap's suggestion and to show how it is derived.
In Section 1 the general problem of analogy by similarity in inductive logic is presented, Section 2 outlines the notation and the conceptual background involved in the proof, Section 3 gives the proof, Section 4 discusses Carnap's principle and the result, Section 5 is a brief review of the solutions which have previously been proposed.
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Di Maio, M.C. Predictive probability and analogy by similarity in inductive logic. Erkenntnis 43, 369–394 (1995). https://doi.org/10.1007/BF01135379
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DOI: https://doi.org/10.1007/BF01135379