174 THE PRINCIPLES OF SCIENCE. 



only strong and true as long as he is logical, and if 

 numbers rule the world, it is the laws of logic which rule 

 number. 



Nearly all writers have hitherto been strangely content 

 to look upon numerical reasoning as something wholly 

 apart from logical inference. A long divorce has existed 

 between quality and quantity, and it has not been un- 

 common to treat them as contrasted in nature and re- 

 stricted to independent branches of human thought. For 

 my own part, I have a profound belief that all the sciences 

 meet somewhere upon common ground. No part of know- 

 ledge can stand wholly disconnected from other parts of 

 the great universe of thought ; it is incredible, above all, 

 that the two great branches of abstract science, interlac- 

 ing and co-operating in every discourse, should rest upon 

 totally distinct foundations. I assume that a connection 

 exists, and care only to inquire, What is its nature 1 Does 

 the science of quantity rest upon that of quality ; or, vice 

 versd, does the science of quality rest upon that of 

 quantity ? There might conceivably be a third view, that 

 they both rest upon some still deeper set of principles yet 

 undiscovered, but there is an absence of any sugges- 

 tions to this effect. The late Dr. Boole adopted the second 

 view, and treated logic as a kind of algebra, a special 

 case of analytical reasoning which admits but the two 

 quantities unity and zero. He proved beyond doubt 

 that a deep analogy does exist between the forms of 

 algebraic and logical deduction ; and could this analogy 

 receive no other explanation we must have accepted his 

 opinion, however strange. But I shall attempt to show 

 that just the reverse explanation is the true one. 



I hold that algebra is a highly developed logic, and 

 number but logical discrimination. Logic resembles al- 

 gebra, as the mould resembles that which is cast in it. 

 Logic has imposed its own laws upon every branch of 



