On the Surprising In Science and Logic

QUINE'S DOCTRINE of the indeterminacy of translation is made possible by the principle of substitution characteristic of extensional logic. The same characteristic makes it impossible, in philosophy of science, to choose among theoretical models no one of which is obviously best suited to explain the facts. Hilary Putnam achieved a sort of closure to the problem of reference in philosophy of science, when he pointed out the implications of the Skolem-Löwenheim theorem. He said that besides the facts a theory is designed to explain, there are any number of unintended interpretations of the same theory that assign the correct truth values to all sentences of the theory. There can be no sound basis for deciding upon the sole interpretation for a theory. Following Putnam, some philosophers have abandoned the problem of reference in the context of axiomatic systems. Ian Hacking, for instance, prefers a notion of reference "that is not tied by any specific, binding theory about what is referred to." He has turned to the study of approximations and practical models, spurred on by the difficulty of reconciling axiomatic systems to scientific practice.