i: 31 



SECTION III. 



ANY given reminiscence may have a place in an 

 indefinite number of trains of thought which we 

 may picture to ourselves as intersecting one another 

 in that reminiscence. Hence, by continual crossing 

 and recrossing, our syntaxes form a sort of network, 

 the different threads of which must fit one to 

 another at each point of intersection if the whole 

 structure is to be logically satisfactory when re- 

 garded as a single comprehensive syntax. For 

 example, a seaman in sight of land may calculate 

 his position in at least three different ways, namely, 

 by astronomical observation, by dead-reckoning, and 

 by the appearance of the coast. Here the different 

 lines of thought converge towards the determination 

 of the position of the ship. Evidently they cannot 

 all be satisfactory unless they be compatible one 

 with another in respect of their point of convergence, 

 or intersection ; that is to say, unless they all indi- 

 cate the same position. The establishment of such 

 compatibility tends to increase confidence both in 

 the correctness of the result, and in the validity of 

 the various steps of the syntaxes by which this 

 result was obtained. Again, we know that Ptolemy 

 had appreciated some of the advantages of an 



