This paradox is strictly correlative to the well-known paradox of Zeno about Achilles and the Tortoise.[85] "The Achilles proves that two variables in a continuous series, which approach equality from the same side, cannot ever have a common limit: the Tristram Shandy proves that two variables which start from a common term, and proceed in the same direction, but diverge more and more, may yet determine the same limiting class (which, however, is not necessarily a segment, because segments were defined as having terms beyond them). The Achilles assumes that whole and part cannot be similar, and deduces a paradox; the other, starting from a platitude, deduces that whole and part may be similar. For common-sense, it must be confessed that it is a most unfortunate state of things." And Mr. Russell considers that, in the face of proofs, it ought to commit suicide in despair. Now, I suggest the extremely unlikely possibility that Tristram Shandy, by reflection on his own life and literary labours, was led to the correct course of accepting the paradox which resulted from this reflection and rejecting the Achilles. Thus, he concluded that an infinite whole may be similar (or, in Cantor's terminology, "equivalent") to a proper part of itself, and hence, by a confusion of similarity with identity (or equivalence with equality) which he shares with some subsequent philosophers,[86] that a whole may be equal to a proper part of itself. If A is an infinite class, it is not difficult to see that we can have 10A = 5A. In this way many have avoided an opinion which rests on no better foundation than that formerly entertained by the inductive philosophers of Central Africa, that all men are black.[87] FOOTNOTES: [82] Cf. a letter of De Morgan in Mrs. De Morgan's _Memoir of Augustus De Morgan_, p. 324. [83] Kant's tract was published in 1763, while _Tristram Shandy_ was published in 1760. [84] _P. M._, pp. 358-9 [Cf. _M._, vol. xxii., January 1912, p. 187.--ED.] [85] Cf. _P. M._, pp. 350, 358-9; _M._, vol. xxii., 1912, p. 157. [86] [Cf. for example, Cosmo Guastella, _Dell' infinito_, Palermo, 1912.--ED.] [87] Cf. Russell, _P. M._, p. 360. CHAPTER XXXII THE HARDSHIPS OF A MAN WITH AN UNLIMITED INCOME