Chapter

Probability as Gradation of Provability

L. Jonathan Cohen

in The Probable and The Provable

Published in print December 1977 | ISBN: 9780198244127
Published online October 2011 | e-ISBN: 9780191680748 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780198244127.003.0003

Series: Clarendon Library of Logic and Philosophy

Probability as Gradation of Provability

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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

Chapter.  8019 words. 

Subjects: Metaphysics

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