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Descriptive completeness and inductive methods

Published online by Cambridge University Press:  12 March 2014

Keith Lehrer*
Affiliation:
Wayne State University

Extract

In a recent paper Professor Wesley Salmon1 has shown that a certain class of c-functions, including the c-function c*. described by Rudolph Carnap2 yield incompatible results when applied to the same sentences in two languages systems which, though they have the same individual constants, do not have the same predicates. Each c-function of the class in question is characterized by a parameter λ which is a function of the number of Q-predicates in the language system in which the c-function is used.3 Taking c* as representative of this class of c-functions, I shall argue that Professor Salmon's results do not provide a reasonable basis for rejecting such c-functions in favor of others. More specifically, I shall argue (i) that such c-functions yield incompatible results in two languages because not both of the languages are sufficiently complete, (ii) that for any two languages in which such c-functions yield incompatible results there is a rule that will select either the more complete of the two languages or a language that is more complete than either of the two languages, and (iii) that it is impossible for such c-functions to yield incompatible results in two languages that are equally complete.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1964

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References

[1]Carnap, Rudolf, Logicai Foundations of Probability, Chicago, 1950.Google Scholar
[2]Carnap, Rudolf, The Continuum of Inductive Methods, Chicago, 1950.Google Scholar
[3]Carnap, Rudolf, Meaning Postulates, Philosophical Studies, vol. III, pp. 6573.Google Scholar
[4]Salmon, Wesley, Vindication of Induction, in Current Issues In the Philosophy of Science, edited by Feigl, Herbert and Maxwell, Grover, New York, 1961.Google Scholar
[5]Kemeny, John G., Extension of the Methods of Inductive Logic, Philosophical Studies, vol. III, pp. 3842.Google Scholar