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The unrestricted universal, which at first sight might seem to be the only justifiable type, can now be shown to be the mathematically limiting case of a typology that is based on a single predicate. Thus, if we assert as an unrestricted universal that all languages have vowels, then there is the implicit associated typology that is constructed from a single predicate Ø, the property of having vowels. There are two typological classes, that of languages that have the property Ø and that of languages that do not. The second class is empty, since there are no languages that do not have the property of possessing vowels. This parallel the earlier result with two predicates and four logically definable classes of languages, of which one is empty; this led to the formulation of an implicational universal. We conclude that there is a reasonable basis for including implicational universals as a valid generalization about language. Further, one can point to the fact that scientific generalizations as a rule hold only under certain stated conditions, even in such advanced sciences as physics-for example, within certain limits of pressure. Indeed, conditional generalizations are, for a number of reasons, of strategic importance in the study of the general properties of human languages. They are far more numerous than unrestricted generalizations, they exhibit interrelationships among linguistic variables (for example, the dual and the plural), and they establish hierarchical relations among linguistic categories. For example, the fact that the dual implies that plural-that is, that the former cannot exist without the latter being present-while the converse does not hold, permits us to conclude that in some sense the plural is more fundamental category in human language than the dual. Most importantly, as will appear, such generalizations can often be shown to exhibit interconnections with each other, to form a structure, at least in some instances, a system in their own right, that leads to the formulation of higher-level generalizations of which the individual implications then become examples. Once we broadened the logical bases for generalizations about language, so as to include the implicational type that involves the relation of two predicates, there seems to be no reason for confining universals to the unrestricted and conditional types. The natural formulation appears to be that we will regard as a legitimate universal any statement that has as its logical scope the set of all natural languages. In terms of the symbolism employed earlier, this means that all statements are accepted that are of the type (x) e L … (for all values of x, if x is a language, then …).
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