Craig's theorem

A theorem in mathematical logic, held to have implications in the philosophy of science. The logician William Craig at Berkeley showed how, if we partition the vocabulary of a formal system (say, into the T or theoretical terms, and the O or observational terms), then if there is a fully formalized system T with some set S of consequences containing only O terms, there is also a system O containing only the O vocabulary but strong enough to give the same set S of consequences. The theorem is a purely formal one, in that T and O simply separate formulae into the preferred ones, containing as non-logical terms only one kind of vocabulary, and the others. The theorem might encourage the thought that the theoretical terms of a scientific theory are in principle dispensable, since the same consequences can be derived without them. However, Craig's actual procedure gives no effective way of dispensing with theoretical terms in advance, i.e. in the actual process of thinking about and designing the premises from which the set S follows. In this sense O remains parasitic upon its parent T .