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]
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]
FOOTNOTES:
[67] _S. L._, 1881, p. 339, note.
[68] See Appendix N.
[69] _Md._, N. S., vol. xiv., October 1905, pp. 479-93.
[70] See Appendix N.
[71] See Appendix O.