In such instances the category of number is completely pervaded and modified by the quality of the objects it is applied to. So, in the Semitic languages, the so-called 'broken plural' is a quasi-collective, which grammatically counts as a feminine singular (like so many Latin and Greek collectives): and whereas the more regular plural is generally shown by separable affix, this quasi-collective plural enters the very body of the word by vowel-change, indicating as it were by this absorption the constitution of a specifically new view of things. On the other hand, it may be said, there is in this collective a trace of the emergence of the universal and identical element through the generalisation due to the conjunction of several similars all acting as one[2] In a true plural, on the contrary, it is required that the sign of number be clearly eliminated from any peculiarities of its special object, and be distinctly separated from the collective. And similarly the true numeral has to be realised in its abstractness, as a category _per se._ And to do this requires some amount of abstraction. In Greek, for example, we meet the distinction between numbers in the abstract, pure numbers (such as four and six), and bodily or physical numbers (such as four men, six trees)[3]. The geometrical aspect under which numbers were regarded by the Greeks, e. g. as oblong or square numbers, bears in the same direction. But another phenomenon in language tells the tale more distinctly[4]. Abundantly in Sanscrit and Greek, more rarely in Zend and Teutonic, and here and there in the Semitic languages, we meet with what is known as the dual number, a special grammatical form intended to express a pair of objects. The witty remark of Du Ponceau[5] concerning the Greek dual, that it had apparently been invented only for lovers and married people, may illustrate its uses, but hardly suffices to explain its existence in language. But a comparison of barbarian dialects serves to show that the dual is, as it were, a prelude to the plural,--a first attempt to grasp the notion of plurality in a definite way, which served its turn in primitive society, but afterwards disappeared, when the plural had been developed, and the numerals had attained a form of their own. If this be so, the dual is what physiologists call a rudimentary organ, and tells the same story as these organs do of the processes of nature.