n.] THE INDIRECT METHOD OF INFERENCE. 113 



reasoning have now been attained, although they were 

 unknown to Aristotle and his followers. The time must 

 come when the inevitable results of the admirable 

 investigations of the late Dr. Boole must be recognised 

 at their true value, and the plain and palpable form in 

 which the machine presents those results will, I hope, hasten 

 the time. Undoubtedly Boole's life marks an era in the 

 science of human reason. It may seem strange that it had 

 remained for him first to set forth in its full extent the 

 problem of logic, but I am not aware that anyone before 

 him had treated logic as a symbolic method for evolving 

 from any premises the description of any class whatsoever 

 as defined by those premises. In spite of several serious 

 errors into which he fell, it will probably be allowed that 

 Boole discovered the true and general form of logic, and 

 put the science substantially into the form which it must 

 hold for evermore. He thus effected a reform with which 

 there is hardly anything comparable in the history of logic 

 between his time and the remote age of Aristotle. 



Nevertheless, Boole's quasi- mathematical system could 

 hardly be regarded as a final and unexceptionable solution 

 of the problem. Not only did it require the manipulation 

 of mathematical symbols in a very intricate and perplexing 

 manner, but the results when obtained were devoid of 

 demonstrative force, because they turned upon the employ- 

 ment of unintelligible symbols, acquiring meaning only by 

 analogy. I have also pointed out that he imported into 

 his system a condition concerning the exclusive nature of 

 alternatives (p. 70), which is not necessarily true of logical 

 terms. I shall have to show in the next chapter that logic 

 is really the basis of the whole science of mathematical 

 reasoning, so that Boole inverted the true order of proof 

 when he proposed to infer logical truths by algebraic 

 processes. It is wonderful evidence of his mental power 

 that by methods fundamentally false he should have 

 succeeded in reaching true conclusions and widening the 

 sphere of reason. 



The mechanical performance of logical inference affords 

 a demonstration both of the truth of Boole's results and 

 of the mistaken nature of his mode of deducing them. 

 Conclusions which he could obtain only by pages of intri- 

 cate calculation, are exhibited by the machine after one or 



I 



