PROBLEMS EMPHASIZED BY PRAGMATISM 403 



whatever which has a definite meaning permits you to draw from it an 

 infinite number of deductive inferences, all of which are possible with- 

 out formulating any other basis for the deductions in question than 

 the assertion of the original proposition and the synthetic power which 

 one indeed has in his hands who is capable of understanding certain 

 simple processes of the construction of relations. Let me mention the 

 instance, famous in modern logic, which De Morgan first formulated; 

 and which as it stands may appear trivial enough. If a horse is an 

 animal, you can deduce from that hypothesis the conclusion that the 

 owner of a horse is the owner of an animal, that the friend of the 

 owner of a horse is the friend of the owner of an animal, and so on. 

 Such deductions in an individual case such as that of the assertion 

 about a horse may seem and are trivial enough. But they have the char- 

 acter of novelty: That is, the conclusion does not follow from the prem- 

 ises by the process of first stuffing a vast number of cases into a bag 

 and then pulling them out one by one. But the process of deduction 

 thus illustrated can be used and is used as an instrument of enormous 

 power in those branches of mathematics in which one builds one system 

 of relations upon another system. The number of ways whereby such 

 deductive processes can be accomplished is presumably very great. And 

 it is because such processes are possible that mathematical reasoning 

 possesses its great fecundity. 



And now since such fecundity, such proof of novelties, is the essence 

 of the live process of deduction as it exists in the deductive sciences, 

 why should not psychologists study that live process instead of study- 

 ing the dead body which some text-books have called the syllogism? 

 And if they must study the syllogism as the supposed typical example 

 of deductive reasoning, why should they confine their attention to con- 

 sidering the most traditional and trivial aspect of it? 



As modern logic has shown, the really essential feature of the 

 syllogism lies in the fact that what the logicians call the Illative Eela- 

 tion (that is, the relation which is in mind when you consider one 

 proposition as true in case another is true) is a relation which has the 

 property of so-called transitivity. That is, the essence of the syllogism 

 may be stated by saying that from the pair of propositions " A implies 

 B," and " B implies C" taken together you can deduce the conclusion 

 " A implies C." In other words, it is of the nature of the illative rela- 

 tion that it permits the use of what James called the principle or 

 axiom of skipped intermediaries. I can not pause to show why this 

 account of the essence of the syllogism is logically correct. But the 

 mere mention of this fact shows that those who analyze the process 

 of deduction, supposing it to be represented by the traditional syllogism, 

 and interpreting the traditional syllogism in the way in which Pro- 

 fessor Pillsbury interprets it, simply miss the most interesting feature 

 of syllogistic reasoning. 



