ABSTRACT

Suppose that the unit (arbitrary) of pleasure is denoted by A, Tristram Shandy, by neglecting, in this ethical discussion, to introduce negative quantities (Kant's pamphlet advocating this introduction into philosophy was made subsequently3), apparently made 15A to result, and this can hardly be maintained to be the half of 10A. It is possible, however, that Tristram Shandy succeeded in proving the apparently paradoxical equation

by remarking that the axiom " the whole is greater than the part " does not always hold. This remark follows at once from what Mr. Russell 3 has called " The Paradox of Tristram Shandy." This paradox is described by Mr. Russell as follows :

" Tristram Shandy, as we know, took two years writing the history of the first two days of his life, and lamented that, at this rate, material would accumulate faster than he could deal with it, so that he could never come to an end. Now I maintain that, if he had lived for ever, and

not wearied of his task, then, even if his life had continued as event fully as it began, no part of his biography would have remained unwritten/'

This paradox is strictly correlative to the well-known paradox of Zeno about Achilles and the Tortoise.4 " 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.