Page:Carroll - Euclid and His Modern Rivals.djvu/206

168 So then this is his trio:—

1. Direct. 'All X are Y.'

2. Reciprocal. 'All Y are X.'

3. Contrary. 'All not-X are not-Y.'

Here of course No. 2 and No. 3, being Contranominals, are logically deducible from each other, No. 1 having no logical connection with either of them.

And yet he calls the three 'so closely connected that either of the two latter is a consequence of the other two'! Shade of Aldrich! Have we come to this? You say nothing, mein Herr?

Nie. I say that, if you grant what you call the 'premisses,' you cannot deny the conclusion.

Min. True. It reminds me of an answer given some years ago in the Schools at Oxford, when the Examiner asked for an example of a syllogism. After much patientthought, the candidate handed in

This certainly has the form of a syllogism. Also it avoids, with marked success, the dangerous fallacy of 'four terms.' And it has the great merit of Mr. Morell's syllogism, that, if you grant the premisses, you cannot deny the conclusion. Nevertheless I feel bound to add that it was not commended by the Examiner.

Nie. I can well believe it.

Min. I proceed. 'The direct and the reciprocal proofs are generally the simpler, and do not require a fresh construction.' Why 'fresh'? The 'direct' comes first,