fulfilled his duty to society; and would not think himself bound to disturb himself any further.
As some readers may not be acquainted with the nature of the ophthalmoscope, I will tell my parable over again in a simpler form. Suppose there was an island, the inhabitants of which were unacquainted with the principle of numeration, and therefore could only write in numbers singly. They would be able to add and multiply numbers only so far as they could reckon. They would know what such simple numbers as "three times five" make; and very clever and persevering ones might know what twelve times twelve make. But about all large numbers they would have to guess; they would have opinions, and discuss, and generally turn out wrong. If they had a tradition among them that certain ancestors of theirs, called Moses and Isaiah, used to pronounce oracularly as to what numbers "like the trees in a forest for multitude" came to, when multiplied together, and always turned out right, they would frame a provisional working-hypothesis that Moses and Isaiah were "inspired," and would argue and jangle as to the precise nature of the " inspiration." Then suppose some islander found out how to " carry," that fortunate individual would know exactly how Moses and Isaiah made sure of their results. And of course the supporters of the rival theories about inspiration would join in calling him hard names; and equally of course he would not mind what they said, but would go on his own way, and wait till events justified his faith in Rational Arithmetic versus fanciful guesses.
Now the situation in which the modern discoverers of Mathematical Logic found themselves, was very much like that of our hypothetical new Helmholtz, or
