Page:Carroll - Euclid and His Modern Rivals.djvu/128

90 absurd, and to recognise as an absurdity what he knows to be a necessary truth?

Nie. At first, Mania: ultimately. Dementia.

Min. Now read Mr. Henrici's deduction from this fearful argument, at p. 24.

'We ought, therefore, to limit the conclusion arrived at as follows:—Through three points which do not lie in a Line we may always pass a Plane. Whether a Plane may be drawn through three points which do lie in a Line, remains for the moment an open question.'

Are you prepared to back that statement? Is it an 'open question'?

Nie. I cannot say that it is.

Min. Now here is a most curious bit of bad Logic. (reads)

'If two Planes have two points, A and B, in common, they must necessarily have more points in common. For, since each extends continuously without limit, a point moving in the one Plane through A or B will cross the other Plane at this point;' (p. 25.)

I pause to ask—will it necessarily do so? How if it moved along their Line of intersection?

Nie. That is an exception, I grant.

Min. (reads) 'hence one Plane will lie partly on the one and partly on the other side of the second Plane. They must therefore intersect.'

Now the conclusion—that the Planes intersect—is undoubtedly true, so long as we assume that, by 'two planes,' the writer means 'two different Planes.' But does it follow from the premisses? Have the words 'hence' and 'therefore' any logical value?