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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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The Logical Syntax of Inductive Probability-gradings

The Logical Syntax of Inductive Probability-gradings

(p.217) 17 The Logical Syntax of Inductive Probability-gradings
The Probable and The Provable

L. Jonathan Cohen

Oxford University Press

This chapter elucidates the logical syntax of inductive probability-gradings. It first presents some logical similarities between inductive and mathematical probability. The inductive probability-gradings conform to quite different principles from those for mathematical probability in regard to contraposition; in regard to the relation between prior and posterior probabilities; in regard to a proposition's conjunction with other propositions; and in regard to its negation. In terms of inductive probability, it is possible to describe a generalized form of reductio ad absurdum argument. The logical structure of inductive probability cannot be mapped on to the calculus of mathematical probability. Indeed, because inductive support does not seem to be additive, inductive probabilities do not seem to be measurable — though they are rankable. Furthermore, the logical syntax of inductive probability may be deployed axiomatically within a modal logic that generalizes on Lewis' system S4.

Keywords:   inductive probability-gradings, logical syntax, inductive probability, mathematical probability, logical structure, inductive support, Lewis' system

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