THE DISCIPLINARY VALUE OF GEOGRAPHY 117 



duced steps lead forward from the postulated premises to the an- 

 nounced end. Geometry therefore corresponds — so far as a corre- 

 spondence can be traced between a mathematical and an obserrational 

 science — chiefly to that part of geological or geographical investigation 

 which is concerned with invention and deduction; for these processes, 

 like the similar processes in geometry, can be performed by mental re- 

 flection in the dark, and have no close dependence on observation. 



In observational sciences it is necessary to examine critically the 

 different degrees of agreement that may exist between the deduced 

 consequences of an hypothesis and the facts gathered by observation, 

 in order to pass a safe judgment on the value of the hypothesis from 

 which the consequences were deduced. This return to the facts is one of 

 the most important as well as one of the most characteristic elements of 

 scientific work. 



If observation has discovered but few classes of simple facts, and if 

 invention has brought forth only one hypothesis, which leads only to 

 a few simple consequences, the value of the hypothesis must remain 

 in doubt, even if its consequences agree rather closely with the facts; 

 because agreement in such a case may be a matter of chance. Here 

 no decided opinion as to the value of the hypothesis should be ex- 

 pressed; judgment must be suspended, and the mind held open for 

 further light, either from observation, invention or deduction. Again, 

 if, as above pointed out, the groups of consequences deduced from two 

 or more rival hypotheses are about equally successful in matching the 

 facts, no judgment must be pronounced in favor of either, however 

 strong the investigator's desire to reach a conclusion may be. But if 

 the peculiar and numerous consequences of a certain hypothesis agree 

 to a remarkable extent with the highly specialized groups of abundant 

 and varied facts, such an hypothesis is strongly commended thereby, 

 for the possibility of accidental agreement is greatly diminished as the 

 facts and consequences to be matched become more complicated, and 

 as the number of agreements increases. Furthermore, if the facts, as 

 at first collected, seem of arbitrary occurrence and unrelated distribu- 

 tion, and yet are afterwards found, by the suggestive aid of an hypoth- 

 esis and its deduced consequences, really to possess a previously unsus- 

 pected order and many previously unseen relationships, the hypothesis 

 which leads to this larger and clearer view is thereby greatly recom- 

 mended ; for it is highly commendable to a theory, if it leads to the dis- 

 covery of reasonable system where confusion seemed to prevail. 



But we must go f urtlier ; for it often happens that, after an hypoth- 

 esis has been invented, and after its consequences have been success- 

 fully confronted with the previously observed facts, new classes of facts 

 may be discovered for which deduction had provided no appropriate 



