The Completeness Issue
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.
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