SECT. 20.] Fallacies. 351 



entirely of sequences such as fall within our experience. It 

 makes the past necessarily contain the whole, as to the qua 

 lity of its components; and judges by samples. Now the 

 least cautious buyer of grain requires to examine a handful 

 before he judges of a bushel, and a bushel before he judges 

 of a load. But relatively to such enormous numbers of com 

 binations as are frequently proposed, our experience does not 

 deserve the title of a handful as compared with a bushel, or 

 even of a single grain.&quot; 



20. The origin of this inveterate mistake is not diffi 

 cult to be accounted for. It arises, no doubt, from the exi 

 gencies of our practical life. No man can bear in mind 

 every contingency to which he may be exposed. If therefore 

 we are ever to do anything at all in the world, a large num 

 ber of the rarer contingencies must be left entirely out of 

 account. And the necessity of this oblivion is strengthened 

 by the shortness of our life. Mathematically speaking, it 

 Avould be said to be certain that any one who lives long 

 enough will be bitten by a mad dog, for the event is not an 

 impossible, but only an improbable one, and must therefore 

 come to pass in time. But this and an indefinite number 

 of other disagreeable contingencies have on most occasions 

 to be entirely ignored in practice, and thence they come 

 almost necessarily to drop equally out of our thought and 

 expectation. And when the event is one in itself of no im 

 portance, like a rare throw of the dice, a great effort of 

 imagination may be required, on the part of persons not ac 

 customed to abstract mathematical calculation, to enable 

 them to realize the throw as being even possible. 



Attempts have sometimes been made to estimate what 

 extremity of unlikelihood ought to be considered as equi 

 valent to this practical zero point of belief. In so far as 

 such attempts are carried out by logicians, or by those who 



