Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-23T23:34:01.790Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximate Generalizations and their Idealization

Published online by Cambridge University Press:  28 February 2022

Ernest W. Adams
Ernest W. Adams*
Affiliation:
University of California, Berkeley
Get access Rights & Permissions [Opens in a new window]

Extract

This paper describes recent work on a theory of approximate generalizations which, following J.S. Mill (1895, Book III Chapter XXIII), are propositions often expressed in the form Most A's are B's, and whose degrees of truth (“probabilities’ in Mill's terms) are the proportions of A's that are B's. Earlier work by Ian Carlstrom and myself studied the logic of approximate generalizations — the theory of necessary connections among their degrees of truth — and basic ideas and results of that work will be briefly summarized here, along with a related extension of this study. However our present concern is primarily with two matters having to do with the effects of small changes in the extensions of predicates on degrees of truth. One is the question of which generalizations are continuous in that small changes in the extensions of “empirical” predicates would not entail large changes in the degrees of truth of the generalizations.

Type
Part V. Measurement, Verisimilitude and Decision
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1982 , Issue 1: Volume One: Contributed Papers 1982 , 1982 , pp. 199 - 207
Copyright
Copyright © Philosophy of Science Association 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, E.W. (1965). “Elements of a Theory of Inexact Measurement.” Philosophy of Science 32: 205–228.CrossRefGoogle Scholar
Adams, E.W. (1966). “On the Nature and Purpose of Measurement.” Synthese 16: 125–169.CrossRefGoogle Scholar
Adams, E.W. (1974). “The Logic of ‘Almost All’. “ Journal of Philosophical Logic 3: 3–17.CrossRefGoogle Scholar
Adams, E.W. and Levine, H.F. (1975). “Uncertainties Transmissible from Premises to Conclusions in Deductive Inferences.” Synthese 30: 429–460.CrossRefGoogle Scholar
Adams, E.W. and Carlstrom, I.P. (1979). “Representing Approximate Ordering and Equivalence Relations.” Journal of Mathematical Psychology 19: 182–207.CrossRefGoogle Scholar
Adams, E.W. (1981a). “Improbability Transmissibility and Marginal Essentialness of Premises in Inferences Involving Indicative Conditionals.” Journal of Philosophical Logic 10: 149–177.CrossRefGoogle Scholar
Adams, E.W. (1981b). “Contributions to a Theory of Laws Admitting Exceptions: the Monadic Case.” Project Report, University of California, Berkeley.Google Scholar
Carlstrom, I.F. (1975). “Truth and Entailment for a Vague Quantifier.” Synthese 30: 461–495.CrossRefGoogle Scholar
Craig, W. (1965). “Boolean Notions Extended to Higher Dimensions.” In The Theory of Models. Edited by Addison, J., et al. Amsterdam: North Holland Publishing Company. Pages 55–69.Google Scholar
Hoover, D.N. (1978). “Probability Logic.” Annals of Mathematical Logic 14: 287–313.CrossRefGoogle Scholar
Krantz, D. et al. (1971). Foundations of Measurement, Volume I. New York: Academic Press.Google Scholar
Mill, J.S. (1895). A System of Logic.. 8th ed. New York: Harper & Brothers.Google Scholar
Morgenstern, C.F. (1979). “The Measure Quantifier.” Journal of Symbolic Logic 44: 103–108.CrossRefGoogle Scholar
Peterson, P.H. (1979). “On the Logic of ‘few’, ‘many’, and ‘most’.” Notre Dame Journal of Formal Logic XX: 155—179.Google Scholar
Titiev, R.I. (1969). “Some Model theoretic Results in Measurement Theory.” Technical Report No. 46, Psychology Series. Institute for Mathematical Studies in the Social Sciences, Stanford University.Google Scholar