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The Probable and The Provable$
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L. Jonathan Cohen

Print publication date: 1977

Print ISBN-13: 9780198244127

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780198244127.001.0001

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Probability as Gradation of Provability

Probability as Gradation of Provability

Chapter:
(p.13) 2 Probability as Gradation of Provability
Source:
The Probable and The Provable
Author(s):

L. Jonathan Cohen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198244127.003.0003

This chapter discusses the probability as gradation of provability. It is stated that probability is to be viewed as a generalization on the notion of provability. Proof-criteria that are general, necessary, and extensional generate probabilities that are appropriate to games of chance. Proof-criteria that are general, contingent, and extensional produce the probabilities that are appropriate to empirical statistics. In addition, proof-criteria that are general, contingent, and non-extensional generate probabilities that are appropriate to the measurement of causal propensities. Moreover, proof-criteria that are singular and necessary generate probabilities like those of Carnapian confirmation-theory, and proof-criteria that are singular and contingent generate probabilities appropriate to subjectivist, or personalist theory. Finally, probability-statements are evaluations of inferential soundness, and cannot be elucidated as acts of guarded assertion.

Keywords:   probability, provability, proof-criteria, empirical statistics, causal propensities, Carnapian confirmation-theory, personalist theory

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