On a Logic of Induction

1. Prelude 2. Aim of this paper 3. Tinkering with the dynamic proof theory 4. The dynamic proof theory 5. The semantics 6. Heuristic matters and further comments 7. Further research ABSTRACT. In this paper I present a simple and straightforward logic of induction: a consequence relation characterized by a proof theory and a semantics. This system will be called LI. The premises will be restricted to, on the one hand, a set of empirical data and, on the oth- er hand, a set of background generalizations. Among the conse- quences will be generalizations as well as singular statements, some of which may serve as predictions and explanations. 1. Prelude I published my first paper in English a long time ago. In the paper (Batens 1968) I compared Carnap's and Popper's approach to induction, and basically assigned each approach a context of application, except that a modification was proposed for Popper's corroboration function. I had sent the paper to Car- nap, Popper, Hempel, Kemeny, and several other famous people. With one exception, all had returned a few encouraging lines. Not long thereafter, I re- ceived a letter, in Dutch, by someone I immediately recognized as Dutch be-

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