ON THE NATURAL DOMAIN OF GRAMMAR

The domain of an empirical scientific theory is the set of objects or events whose properties are explained by the theory and in respect to which all theorems of the theory are jointly verifiable. In principle, there are an infinite number of possible domains for theories, but only a very small subset of these would ever be considered empirically significant, independent, or natural in any sense. Thus it is certainly equally possible to construct a theory about all animals or a theory about the circulatory systems of all two-week-old Siamese cats, aAhough our knowledge of the world immediately tells us that the latter theory is arbitrary and accidental in a sense in which the former is not, and that the domain of the former is compatible with a much more systematic and coherent partition of the real world than is that of the latter. We also know, of course, that any theory about animals is more general than any possible theory about cats or the organs of cats, and that any of these latter theories would in fact be derivable from the former and thus wholly reducible to it. This proportional relation between the rdative naturalness of domains as intuitively recognized and the relative generality of their theories appears to hold for all clear cases; the principled reduction of one theory to another can thus appropriately serve as the formal characterization of the naturalness of the reducing theory rdative to the one that is reduced to it. A natural theory, then, will be one