Page:Carroll - Euclid and His Modern Rivals.djvu/254

216 particular instance,' which practice, he says, makes the study of Geometry 'unnecessarily stiff, obscure, tedious and barren.'

''Euc. One advantage of making a general statement, and afterwards referring to it instead of repeating it, is that you have to go through the mental process of affirming or proving the truth once for all: apparently Mr. Wilson would have you begin de novo'' and think out the truth every time you need it! But the great reason for always referring back to your universal, instead of affirming the particular (Mr. Wilson is merely starting the old logical hare 'Is the syllogism a Petitio Principii?'), is that the truth of the particular does not rest on any data peculiar to itself, but on general principles applicable to all similar cases; and that, unless those general principles prove the conclusion for all cases, they cannot he warranted to prove it for any one selected case. If, for instance, I see a hundred men, and am told that some assertion is true of ninety-nine of them, but am not told that it is true of all, I am not justified in affirming it of any selected man; for he might chance to be the excepted one. Now the assertion, that the truth of the particular case under notice depends on general principles, and not on peculiar circumstances, is neither more nor less than the assertion of the universal affirmative which Mr. Wilson deprecates.

§ 4. Euclid's Style.

Min. Quite satisfactory. I will now take the third heading, namely 'Style.'