Page:Carroll - Euclid and His Modern Rivals.djvu/124

86 the condition here laid down—of bringing them 'together into the same position'—you make the thing impossible, whether they have size or not.

I have often found it the best way for exhibiting the unsoundness of an argument, to make another exactly like it, but leading to an absurd conclusion. I will try it here. You grant that a cubic foot can be made up of cubic inches?

Nie. Certainly.

Min. Well, I will prove to you that it cannot; and I will do so by an argument just as good as Mr. Henrici's. 'If we bring different cubic inches together into the same position they will never give us anything but a cubic inch; we never obtain any extension—'

Nie. That won't do! You have the 'extension' of one cubic inch.

Min. Yes, but you had that to begin with. You don't 'obtain' any extension by squeezing in other cubic inches, do you?

Nie. No, I suppose not.

Min. Then the argument is sound so far. And now comes my triumphant conclusion, à la Henrici. 'We cannot, therefore, say that a cubic foot is made up of cubic inches.'

Nie. I see your meaning now. I give up the words 'into the same position.'

Min. I haven't quite done with points yet. I find an assertion that they never jump. Do you think that arises from their having 'position,' which they feel might be compromised by such conduct?