Notes
Journal of Symbolic Logic, 16 (No. 3) : 20 5–7 (September 19 51).
Philosophical Studies, 2 (No. 5):72–75 (October 1951).
Ibid., pp. 75-80.
Actually the method accomplishes much more. It allows us to introduce any set of predicates, with any type of interdependence.
For a detailed study of these functions see Carnap'sLogical Foundations of Probability (Chicago: University of Chicago Press, 1950).
If there are infinitely many individual constants, then Camap replaces the s.d. by a class of atoms (or negations of atoms). But in inductive logic only the languages Ln with a finite number n of individual constants ever influence the calculations.
For a complete definition see the author's “Models of Logical Systems,”Journal of Symbolic Logic, 13(No. 1):16–30 (March 1948).
This function is discussed in the appendix of Carnap's book (see footnote 5).
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Kemeny, J.G. Extension of the methods of inductive logic. Philos Stud 3, 38–42 (1952). https://doi.org/10.1007/BF02333166
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DOI: https://doi.org/10.1007/BF02333166