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Confirming Inexact Generalizations

Published online by Cambridge University Press:  31 January 2023

Ernest W. Adams
Ernest W. Adams*
Affiliation:
University of California-Berkeley
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An inexact generalization like ‘ravens are black’ will be symbolized as a prepositional function with free variables thus: ‘Rx ⇒ Bx.’ The antecedent ‘Rx’ and consequent ‘Bx’ will themselves be called absolute formulas, while the result of writing the non-boolean connective ‘⇒’ between them is conditional. Absolute formulas are arbitrary first-order formulas and include the exact generalization ‘(x)(Rx → Bx)’ and sentences with individual constants like ‘Rc & Bc.’ On the other hand the non-boolean conditional ‘⇒’ can only occur as the main connective in a formula. We shall also need to consider formulas with more than one free variable such as ‘xHy ⇒ xTy,’ which might express ‘if x is the husband of y then x is taller than y.’ Though it is inessential, it will simplify things to work in ‘n-languages’ with a finite number of individual constants c1,…, cn, which are interpreted as denoting the elements of the domains of the ‘n-models’ to be described below.

Type
Part I. Confirmation and Scientific Laws
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1988 , Issue 1: Volume One: Contributed Papers 1988 , 1988 , pp. 10 - 16
Copyright
Copyright © Philosophy of Science Association 1988

References

Adams, E.W. (1975). “The Logic of ‘Almost all’.” Journal of Philosophical Logic 3: 3–17.CrossRefGoogle Scholar
Adams, E.W. (1986). “Continuity and Idealizability of Approximate Generalizations.” Synthese 67: 439–376.CrossRefGoogle Scholar
Adams, E.W. and Carlstrom, I.R. (1979). “Representing Approximate Ordering and Equivalence Relations.” Journal of Mathematical Psychology 19: 182–207.CrossRefGoogle Scholar
Carlstrom, I.F. (1975). “Truth and Entailment for a Vague Quantifier.” Synthese 30: 461–495.CrossRefGoogle Scholar
Carnap, R. (1950). The Logical Foundations of Probability. Chicago: University of Chicago Press.Google Scholar
Goodman, N. (1955). Fact, Fiction, and Forecast. Cambridge: Harvard University Press.Google Scholar
Hardy, G.H., Littlewood, J.E. and Polya, G. (1952). Inequalities 2nd. edition. Cambridge: The University Press.Google Scholar
Hempel, C.G. (1945). “Studies in the Logic of Confirmation.” Mind 54: 1–26 and 97-121.CrossRefGoogle Scholar
Hintikka, J. (1966). “A Two-Dimensional Continuum of Inductive Methods.” In Aspects of Inductive Logic. Edited by Hintikka, J. and Suppes, P. Amsterdam: North-Holland Publishing Company, pp. 113–132.CrossRefGoogle Scholar
Hoover, D.N. (1978). “Probability Logic.” Annals of Mathematical Logic 14: 287–313.CrossRefGoogle Scholar
Hoover, D.N. (1982). “A Normal Form Theorem for Lw, with Applications.” The Journal of Symbolic Logic 47: 605–624.CrossRefGoogle Scholar
Lukasiewicz, J. (1913). “Die Logische Grundlagen der Wahrscheinlichkeits-rechnung.” Reprinted as “Logical Foundations of Probability Theory” in Jan Lukasiewicz Selected Works. Edited by Borkowski, L.. Amsterdam: North-Holland.Google Scholar
Rosenkrantz, R.D. (1977). Inference, Method and Decision. Dordrecht: Reidel Publishing Company.CrossRefGoogle Scholar
Russell, B. (1912). “On Induction.” Chapter VI of The Problems of Philosophy. London: Oxford University Press.Google Scholar
Suppes, P. (1966). “A Bayesian Approach to the Paradoxes of Confirmation.” In Aspects of Inductive Logic. Edited by Hintikka, J. and Suppes, P. Amsterdam: North-Holland Publishing Company, pp. 198–207.CrossRefGoogle Scholar