When people say that such-and-such a thing “is non-existent” they usually mean that there is not any “thing” of the kind spoken of. Venn meant this when he described[67] his encounter with what he imagined to be a very ingenious tradesman: “I once had some strawberry plants furnished me which the vendor admitted would not bear many berries. But he assured me that this did not matter, since they made up in their size what they lost in their number. (He gave me, in fact, the hyperbolic formula, xy = c, to connect the number and magnitude.) When summer came, no fruit whatever appeared. I saw that it would be no use to complain, because the man would urge that the size of the non-existent berry was infinite, which I could not see my way to disprove. I had forgotten to bar zero values of either variable.”

It is to be regretted that this useful note was omitted in the second edition of Venn’s book; one can imagine that it might have protected Mr. MacColl and Herr Meinong (who believed, unlike Alice in what may be called her first theory,[68] in round squares and fabulous monsters) against the dishonest practices of traders who were too ready with promises. For the death-blow to this kind of trade was not given until 1905, when Mr. Russell published his article “On Denoting,”[69] and took up the position of the White King in opposition to Alice’s later assertions.[70]

Venn’s experience illustrates another characteristic of mathematical logic. It is necessary, in order to make our arguments conclusive, to devote great care to the elimination of difficulties which rarely occur. The White Knight—who was like Boole in being a pioneer of mathematical logic in this way, and yet seems to have held, like Boole, those philosophical opinions which would base logic on psychology—recognized the necessity of taking precautions against any unusual appearance of mice on a horse’s back.[71]

CHAPTER XXVI