48 SCIENCE AND METHOD. 



follow. We shall be capable of grasping each of the 

 syllogisms, and it is not in the passage from premises 

 to conclusion that we are in danger of going astray. 

 But between the moment when we meet a proposition 

 for the first time as the conclusion of one syllogism, 

 and the moment when we find it once more as the 

 premise of another syllogism, much time will some- 

 times have elapsed, and we shall have unfolded many 

 links of the chain ; accordingly it may well happen 

 that we shall have forgotten it, or, what is more serious, 

 forgotten its meaning. So we may chance to replace 

 it by a somewhat different proposition, or to preserve 

 the same statement but give it a slightly different 

 meaning, and thus we are in danger of falling into 

 error. 



A mathematician must often use a rule, and, natur- 

 ally, he begins by demonstrating the rule. At the 

 moment the demonstration is quite fresh in his 

 memory he understands perfectly its meaning and 

 significance, and he is in no danger of changing it. 

 But later on he commits it to memory, and only 

 applies it in a mechanical way, and then, if his 

 memory fails him, he may apply it wrongly. It is 

 thus, to take a simple and almost vulgar example, 

 that we sometimes make mistakes in calculation, 

 because we have forgotten our multiplication table. 



On this view special aptitude for mathematics 

 would be due to nothing but a very certain memory 

 or a tremendous power of attention. It would be a 

 quality analogous to that of the whist player who 

 can remember the cards played, or, to rise a step 

 higher, to that of the chess player who can picture 

 a very great number of combinations and retain them 



