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Probabilities as Truth-Value Estimates

Published online by Cambridge University Press:  14 March 2022

Hugues Leblanc
Hugues Leblanc*
Affiliation:
Bryn Mawr College
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Abstract

The author recently claimed that Pr(P, Q), where Pr is a probability function and P and Q are two sentences of a formalized language L, qualifies as an estimate—made in the light of Q—of the truth-value of P in L. To substantiate his claim, the author establishes here that the two strategies lying at the opposite extremes of the spectrum of truth-value estimating strategies meet the first five of the six requirements (R1-R6) currently placed upon probability functions and fail to meet the sixth one. He concludes from those two results that the value for P and Q of any function satisfying R1-R5 must rate “minimally satisfactory” and the value for P and Q of any function satisfying R1-R6 must rate “satisfactory” as an estimate—made in the light of Q—of the truth-value of P in L.

Type
Research Article
Information
Philosophy of Science , Volume 28 , Issue 4 , October 1961 , pp. 414 - 417
Copyright
Copyright © Philosophy of Science Association 1961

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References

1 I made the claim in three recent papers of mine, “On chances and estimated chances of being true,” Revue Philosophique de Louvain, vol. 57 (1959), pp. 225-239, “On a Recent Allotment of Probabilities to Open and Closed Sentences,” Notre-Dame Journal of Formal Logic, vol. I (1960), pp. 171-175, and “A New Interpretation of c(h, e),” Philosophy and Phenomenological Research, vol. XXI (1961), pp. 373-376.

2 R1-R6 are an adaptation of G. H. von Wright's requirements for probability functions in The Logical Problem of Induction, New York (1957), pp. 92-93. For further details on the matter, see the author's “On Logically False Evidence Statements,” The Journal of Symbolic Logic, vol. 22 (1957), pp. 345-349.