# Confirming Universal Generalizations}

Author: Zabell, S.L.

Source: Erkenntnis, Volume 45, Numbers 2-3, 1996 , pp. 267-283(17)

Publisher: Springer

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Abstract:

The purpose of this paper is to make a simple observation regarding the Johnson-Carnap continuum of inductive methods (see Johnson 1932, Carnap 1952). From the outset, a common criticism of this continuum was its failure to permit the {\it confirmation of universal generalizations}: that is, if an event has unfailingly occurred in the past, the failure of the continuum to give some weight to the possibility that the event will continue to occur without fail in the future. The Johnson-Carnap continuum is the mathematical consequence of an axiom termed Johnson's sufficientness postulate'', the thesis of this paper is that, properly viewed, the failure of the Johnson-Carnap continuum to confirm universal generalizations is not a deep fact, but rather an {\it immediate} consequence of the sufficientness postulate; and that if this postulate is modified in the minimal manner necessary to eliminate such an entailment, then the result is a new continuum that differs from the old one in precisely one respect: it enjoys the desideratum of confirming universal generalizations.

Document Type: Regular Paper

Affiliations: Departments of Mathematics and Statistics Northwestern University 2006 Sheridan Road Evanston, IL 60208 U.S.A E-mail: zabell@math.nwu.edu

Publication date: 1996

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