the possession of language. In order to this, another kind of analysis is necessary, an analysis which separates the qualities of a thing from the thing itself, and contemplates them apart. The man, in short, is able to perceive, not only that three corns are more than two corns, but that three are more than two—a thing that the bird neither does nor can do. Such a perception makes language possible—for language-making is a naming of the properties of things, and of things themselves through those properties—and, combined with the other power which we have just noticed, it creates the possibility also of an indefinite progression in thinking and reasoning by means of language. Signs being found for the conceptions 'one,' 'two,' 'three,' and so on, we can proceed to build them up into any higher aggregate that we choose, following each step of combination by a sign, and with that sign associating the result of the process that made it, so as to be effectually relieved of the necessity of performing the process over again in each new case. Thus, from the recognition that three is more than two, that two and one are three, that twice two is four—all which truths are virtually within reach of the crow, since he would determine aright any practical question that involved them—we rise to the recognition that twenty is more than nineteen, that fifteen and five are twenty, that seven times seven are forty-nine, or ten times ten are a hundred: and these are truths which we could only reach by means of language; they are inferences, circuitously arrived at, and made by means of language not less manageable than the simpler truths which are matters of direct synthetic apprehension. He who, having learned only to count, constructs for his own use a multiplication-table, has to work onward from step to step in somewhat the same way as he who has no speech; but every product that he attains and fixes in memory with its factors, is an acquisition made once for all. Indefinite progress is thus ushered in; every new result of mathematical reasoning is rendered capable of being handled, and the whole career of mathematical science is initiated. Yet not to be carried on by words alone. The most skilful mathematician cannot perform any of the more complicated processes
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