180 SCIENTIFIC METHOD IN PHILOSOPHY 



thinking of the infinite as the " unended." It is odd that 

 he did not see that the future too has one end at the 

 present, and is precisely on a level with the past. His 

 regarding the two as different in this respect illustrates 

 just that kind of slavery to time which, as we agreed in 

 speaking of Parmenides, the true philosopher must learn 

 to leave behind him. 



The confusions introduced into the notions of philoso- 

 phers by the so-called " true " infinite are curious. They 

 see that this notion is not the same as the mathematical 

 infinite, but they choose to believe that it is the notion 

 which the mathematicians are vainly trying to reach. 

 They therefore inform the mathematicians, kindly but 

 firmly, that they are mistaken in adhering to the " false ' 

 infinite, since plainly the " true " infinite is something 

 quite different. The reply to this is that what they call the 

 " true " infinite is a notion totally irrelevant to the problem 

 of the mathematical infinite, to which it has only a fanci- 

 ful and verbal analogy. So remote is it that I do not 

 propose to confuse the issue by even mentioning what 

 the " true " infinite is. It is the " false " infinite that 

 concerns us, and we have to show that the epithet " false ' 

 is undeserved. 



There are, however, certain genuine difficulties in 

 understanding the infinite, certain habits of mind derived 

 from the consideration of finite numbers, and easily 

 extended to infinite numbers under the mistaken notion 

 that they represent logical necessities. For example, 

 every number that we are accustomed to, except o, has 

 another number immediately before it, from which it 

 results by adding i ; but the first infinite number does 

 not have this property. The numbers before it form an 

 infinite series, containing all the ordinary finite numbers, 

 having no maximum, no last finite number, after which 



