Page:Carroll - Euclid and His Modern Rivals.djvu/118

80 feel that the third case' (we mean your 'case ') 'is the true one.'

Min. An appeal to sentiment! What if the reader doesn't feel it?

Nie. 'But this cannot be considered decisive;'

Min. It cannot.

Nie. 'for the two Lines may include a very small angle—'

Min. Aye, or even a large one.

Nie. 'that is, they may very nearly coincide without actually doing so. Or it may be that sometimes the one, sometimes the other, happens, according as we take the point P at a smaller or greater distance from the Line.'

Min. That seems a fair statement of the difficulty. And now, how are you going to grapple with it?

Nie. 'The only way of settling this point is to make an assumption, and to see whether the consequences drawn from it do or do not agree with our experience.'

Min. If you find a consequence not agreeing with experience, you may of course conclude that your assumption was false; but, if it does agree, what then?

Nie. Nothing, I fear, unless you can prove that this is the case with one assumption only, and that all other possible assumptions lead to absurd results.

Min. Exactly so. If, then, you want to prove case, your logical course is to assume case as true, and from that assumption to deduce some consequence which is evidently contrary to experience. And then to exclude case by a similar argument. Is that your method?

Nie. Well, hardly. We say 'The assumption to be