According to the _Daily Mail_ of October 9, 1906, Judge Russell decided against a claim brought by an agent against his company for appointing another agent, the claim being on the ground that he was appointed as "the" agent. Most people admit that the number 2 can be added to the number 2 to give the number 4, but this is a mistake. They concede, when they use _the_, that there is only one number 2, and yet they imagine that, when they consider it apart as the first term of our above sum, they can find another to add to it, and thereby form the third term. The truth is that "2 + 2 = 4" is a very misleading equation, and what we really mean by that faultily abbreviated statement is more precisely: If _x_ and _y_ denote any things which form a class B, and _x´_ and _y´_ any other things that form a class (A) which, like that of _x_ and _y_, is a member of the class (which we call "2") of those classes which have a one-one correspondence with B (so that any member of A corresponds to one, and only one, member of B, and conversely), the class of all the terms of A and B together is a member of that class of classes which, analogously, we call "4." In this, for the sake of shortness, we have introduced abbreviations which should not be used in a rigorous logical statement. FOOTNOTES: [65] Cf. _Md._, N. S., vol. xiv., 1905, pp. 481, 484. [66] Cf. _ibid._, p. 491, note. CHAPTER XXV NON-ENTITY 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]