Variety and analogy in confirmation theory

Philosophy of Science 30 (3):207-221 (1963)
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Abstract

Confirmation theorists seek to define a function that will take into account the various factors relevant in determining the degree to which an hypothesis is confirmed by its evidence. Among confirmation theorists, only Rudolf Carnap has constructed a system which purports to consider factors in addition to the number of instances, viz. the variety manifested by the instances and the amount of analogy between the instances. It is the purpose of this paper to examine the problem which these additional factors raise for confirmation theory, and to prove that, despite Carnap's claim, no confirmation function satisfying the requirements he has specified can take account of variety and analogy. This result is first proved for a special case, and then, in a subsequent section, is generalized through the introduction of a theorem (the proof of which is given in Appendix I). In the final section of the paper it is shown that, contrary to a claim which Carnap has made, not even the concept of the "logical width" of a predicate will enable confirmation functions satisfying his requirements to take adequate account of analogies between instances

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Author's Profile

Peter Achinstein
Johns Hopkins University

References found in this work

The Continuum of Inductive Methods.Rudolf Carnap - 1953 - Philosophy 28 (106):272-273.
On inductive logic.Rudolf Carnap - 1945 - Philosophy of Science 12 (2):72-97.
The Logical Foundations of Probability. [REVIEW]Rudolf Carnap - 1950 - Journal of Philosophy 60 (13):362-364.
Principles of the Theory of Probability.Ernest Nagel - 1939 - Journal of Unified Science (Erkenntnis) 8 (4):261-263.

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