ABSTRACT

The logical syntax of inductive support-functors will be taken to define a general class of inductive functions, a sub-class of which is constituted by the support-functions invoked in experimental science, just as the mathematical calculus of probabilities may be taken to define a general class of syntactically similar, though semantically dissimilar, probability-functions. The distinction between the syntax and semantics of inductive support-functors may be illuminated by comparison with the corresponding distinction in the case of probability-functions. The most direct way of doing this is to hold that inductive support-functions have precisely the syntax of probability-functions. One possibility worth considering is that a conjunction principle can be established for universal propositions that in appropriate conditions produce the same probability-resistant structure as. Philosophers have often treated inductive support as being a function of certain probabilities rather than a probability itself.