90 MYSTICISM AND LOGIC 



to overtake the tortoise, he would have been in more 

 places than the tortoise ; but we saw that he must, in any 

 period, be in exactly as many places as the tortoise. 

 Hence we infer that he can never catch the tortoise. This 

 argument is strictly correct, if we allow the axiom that 

 the whole has more terms than the part. As the con- 

 clusion is absurd, the axiom must be rejected, and then 

 all goes well. But there is no good word to be said for 

 the philosophers of the past two thousand years and 

 more, who have all allowed the axiom and denied the 

 conclusion. 



The retention of this axiom leads to absolute contra- 

 dictions, while its rejection leads only to oddities. Some 

 of these oddities, it must be confessed, are very odd. 

 One of them, which I call the paradox of Tristram Shandy, 

 is the converse of the Achilles, and shows that the tortoise, 

 if you give him time, will go just as far as Achilles. 

 Tristram Shandy, as we know, employed two years in 

 chronicling 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, as years went by, he would 

 be farther and farther from the end of his history. Now 

 I maintain that, if he had lived for ever, and had 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. For consider : the hundredth 

 day will be described in the hundredth year, the thousandth 

 in the thousandth year, and so on. Whatever day we 

 may choose as so far on that he cannot hope to reach it, 

 that day will be described in the corresponding year. 

 Thus any day that may be mentioned will be written up 

 sooner or later, and therefore no part of the biography 

 will remain permanently unwritten. This paradoxical 

 but perfectly true proposition depends upon the fact 



