404 TEE POPULAR SCIENCE MONTHLY 



Nor is the aspect of the syllogistic reasoning which this emphasizes, 

 the only one to which modern logic calls attention. Mrs. Ladd-Franklin 

 long ago pointed out that the entire theory of the syllogism could be 

 stated as a sort of comment upon the fact that a triad of propositions 

 which she called "a triadic inconsistency" has, when considered as a 

 triad, a certain set of logical properties. These logical properties, 

 belonging to such a triad of propositions, can be observed by a process 

 which is of the nature widely illustrated throughout the whole realm 

 of mathematics; but this is certainly not the synthesis that Professor 

 Pillsbury has in mind when he analyzes what he supposes to be a typical 

 process of deductive reasoning. 



Still more unfortunate for the study of the psychology of the reason- 

 ing process is that misunderstanding of the nature of deduction which 

 supposes that the principal use of a deduction is to bring to pass a 

 belief in a certain conclusion by virtue of an appeal to a belief in 

 certain premises. This assumption, common in the recent literature of 

 pragmatism, is false to the most essential use of deduction in the exact 

 sciences. Mr. Russell has well emphasized the fact that, in mathematical 

 science, just in so far as it is pure mathematics, you are not concerned 

 with producing belief in the conclusions themselves. Your interest in 

 pure mathematics, that is to say in that science which deals with deduc- 

 tion proper, lies simply in showing that certain premises do imply 

 certain conclusions. That is, you show that "p implies q," where p and 

 q are propositions. The importance of mathematics for the empirical 

 sciences is due to the fact that it gives you a means for testing the 

 hypotheses by first finding out what are their logical consequences. 

 Now it is essential for the fair and unprejudiced testing of an hypothe- 

 sis, that you should not be too much disposed to believe in it before 

 you test it. It is very important, when you do not believe an hypothesis, 

 or when your mind is still perfectly open upon the subject, to find out 

 with exactness what would he true if the hypothesis were true. Your 

 purpose in deduction is therefore not to establish belief in certain 

 consequences by virtue of a previous belief in the hypothesis upon which 

 they depend. Your great interest is to produce no belief whatever 

 either in the hypothesis or in the conclusions from the hypothesis, until 

 the logical issues arc precisely defined for empirical confirmation; and 

 then you are ready to appeal to the confirming or refuting experience. 

 It is a strange misunderstanding of the nature of the deductive process 

 to suppose that its principal interest is an interest in producing belief 

 in consequences. The sole logical interest of the deductive inquirer 

 lies in his discovery that certain premises imply certain conclusions. 



To sum up, then, this sketch : I assert that in the recent psycliolog}' 

 of reasoning, the nature of the deductive process and its principal pur- 

 pose have leen equally misunderstood. Deduction in its more developed 



