ARTHUR LEEEVRE PEDAGOGICAL NOTE OH MENSURATION. 41 
knowledge of a^thing is an isolated, mechanical fact. Bnt knowledge 
is not to be explained in any snch mechanical fashion; bnt rather con- 
sists in relating a thing to its intellectual conditions, and so assigning 
its place in the intelligible world. To quote a brief dictum, “difference 
is no less essential to a judgment than identity/ 5 
Out of the perennial and many sided controversy to which funda- 
mental views on this question have reference, there seems to have come 
at least one clear upshot, namely, that the extremes of Realism and 
Nominalism are equally wrong, with the conclusion that between the 
concept and the particular object exists some intimate relation of 
thought, and that it is necessary for all reasoning that the general and 
the particular go hand in hand. There is an essential correlation of the 
particular facts and the general grounds, and knowledge is realized only 
in the union of the universal and the particular. The one element is 
not apart from the other, and every way in which knowledge is formed 
in us presents this twofold aspect.* 
Recognition of these fundamental principles in the theory of knowl- 
edge underlies all clearly thougbt-qut teaching. It illuminates every 
step. It would pacify, for example, the inane logomacies so prevalent 
concerning induction and deduction, analysis and synthesis, by display- 
ing them as the complemental, inseparable rhythm of thought. In fine, 
in every form and degree of knowledge there is a double aspect, one 
turning upon essential connections, the other looking to the detached 
facts in which those connections are manifested. 
Such considerations ought to establish the inherent .propriety, and 
therefore the pedagogic utility of comparison and generalization. Any 
other way leads to the husks, not to the kernel of knowledge. The 
chief desiderata of enlightened and skillful teachers are concerned with 
the difficulty of providing at various points grounds for, illuminating 
comparisons. For example, it is wasteful seriously to study grammar, 
the logical analysis of language, until the student has some acquaint- 
ance with more than his mother tongue. A single language may, of 
course, be studied advantageously from aesthetic standpoints, because in 
this case other media for the expression of the true, the beautiful, and 
the good afford the requisite grounds of artistic comparison; yet even 
here there is perhaps no way for the acquisition of a pure style so safe 
and ready as translation. The commonplace essay, as a discipline in 
the vernacular, is too often a stultifying copy in expression as well as 
in matter. Translation into the mother tongue frankly takes the matter 
as- given, while for the composition it throws the student in a most 
stimulating manner upon his own resources, with no more than a de- 
*Cf. Logic , Adamson, Ency. Brit. 
