The logic of projectibility

Philosophy of Science 39 (3):302-314 (1972)
Abstract
Projectible conditions are (roughly) those whose universal generalizations are con firmed by their positive instances. This paper proposes certain modifications to the above definition in order to capture the pre-analytic notion it is supposed to explicate. Then we investigate what logical operations, when performed on projectible conditionals, yield new projectible conditionals. A number of surprising theorems are proven, and these theorems indicate that few conditionals having complex antecedents and consequents are projectible. It is also shown that projectibility is not closed under contraposition, and this is proposed as a solution to the Paradox of the Ravens. Finally, a general conjecture is made concerning just what conditionals are projectible, and it follows from this conjecture that although most conditionals are not projectible, they can still be dealt with inductively, but in ways more complex than recognized by classical confirmation theory
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