# The Logical Syntax of Inductive Probability-gradings

# The Logical Syntax of Inductive Probability-gradings

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 S_{4}.

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

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