By Raimo Tuomela (auth.)

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Let us now go on to describe Craig's general replacement programme in detail (d. CRAIG (1953) and (1956)). We still have to sharpen our tools somewhat. Let us first list some conditions that all our theories (deductive systems) have to satisfy (d. CRAIG (1956)): (i) The set of applications of a rule of inference is effectively defined. (ii) The set of logical axioms is effectively defined. (iii) The set of extralogical axioms is effectively defined. (iv) The set of formulas is effectively defined.

A satisfactory elimination programme shows how this can be done. It is no wonder that in trying to establish the premises of the theoretician's dilemma instrumentalists commonly refer either to Craig's or to Ramsey's elimination technique. It is condition (4) of the theoretician's dilemma that concerns us in the first place (see Chapter I). We shall here consider the following modification of it (d. also CORNMAN (1972), p. 85): (4') If the theoretical terms of a theory T establish observational scientific systematization, then the Craigian transcription of T preserves its observational scientific systematization.

It can be argued that explanation and prediction are subactivities of scientific systematization, broadly understood (d. HEMPEL (1958), p. 174). Scientific systematization consists of deductive and inductive systematization. These notions will be defined below. Later we shall be concerned with the role of theoretical concepts in scientific explanation (and, to some extent, in prediction as well). It will indeed then be seen that at least some interesting aspects of explanation and prediction are special cases of our broad notion of scientific systematization.

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