130 THE PRINCIPLES OF SCIENCE. 



2. The more immediate importance of the machine 

 seems to consist in the unquestionable proof which it 

 affords that most comprehensive views of the principles 

 of reasoning have now been attained, although they were 

 almost wholly unknown to Aristotle and his followers. 

 The time must come when the inevitable results of the 

 admirable writings of the late Dr. Boole must be re- 

 cognised at their true value, and the plain and palpable 

 form in which the machine presents those results will, 

 I hope, hasten the time. Undoubtedly his life marks 

 an era in the high 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 any one 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. His quasi-mathematical system indeed 

 could not be regarded as a final and complete solution 

 of the problem. Not only did it require the manipula- 

 tion 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 employment of unintelligible symbols, acquiring mean- 

 ing only by analogy. I have also pointed out that he 

 imported into his system a condition concerning the 

 exclusive nature of alternatives (p. 83), 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 completely inverted the true order of proof 

 when he proposed to infer logical truths by algebraic 

 processes. It is a wonderful evidence of his mental 

 power that by methods fundamentally false he should 

 have succeeded in reaching true conclusions and widen- 

 ing the sphere of reason. 



