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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 Completeness Issue

The Completeness Issue

Chapter:
(p.33) 3 The Completeness Issue
Source:
The Probable and The Provable
Author(s):

L. Jonathan Cohen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198244127.003.0004

Completeness, as a property of certain deductive systems, may be viewed as a limiting-case of probabilistic complementationality. It follows that proof criteria for incomplete systems generate probabilities that do not conform to the mathematical calculus of chance. Such probabilities measure what Keynes called ‘weight’ and have a non-complementational negation principle. One such probability is that which the consequent of any generalized conditional has on the truth of its antecedent, if this probability is equated with the level of inductive support that exists for the generalization. This concept is shown to play an important part in the way in which lay juries are expected to assess proofs of fact in Anglo-American lawcourts.

Keywords:   completeness, probabilistic complementationality, proof criteria, mathematical calculus of chance, weight, Anglo-American lawcourts

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