Page:Carroll - Euclid and His Modern Rivals.djvu/127

.] Min. Now read this, at p. 23.

(hands the book)

'But if C happens to lie on the Line joining A and B, then a Plane through A and B, which did not pass through C, could never be made to pass through C by being rotated about A and B; for if it did contain C in one position, it would contain it in all positions, as this point would remain fixed during rotation.' What do you say to that?

Nie. Well, it is his way of discussing your third exception. Of course, when he talks of 'a Plane through A and B, which did not pass through C,' he is describing a nonentity: but it is all logical as an argument.

Min. What kind of argument?

Nie. (doubtfully) I should call it a—kind of—Reductio ad Absurdum.

Min. I don't wonder at your hesitation. A thoughtful boy might read it thus:—'then a Plane through A and B, which did not pass through C (but no such Plane can exist!), could never be made to pass through C by being rotated about A and B (why, it needs no 'making'!); for if it did contain C in one position (which it does!), it would contain it in all positions (which also it does!)'

You and I can recognise the Reductio ad Absurdum—though so abnormal and hideous—which the writer intends. But what do you think would be the effect, on a thoughtful boy, of a course of such arguments, where he is expected to accept as data what he knows to be