62 THE PRINCIPLES OF SCIENCE. [CHAV. 



substituting for A in the second side of (i) its expression 

 in (2). We thus get 



A = ABC, 



and by repeating the process over and over again we 

 obviously set the single proposition 



A = ABCD . . JK. 



But Dr. Thomson is mistaken in supposing that we can 

 obtain in this manner a definition of copper. Strictly 

 speaking, the above proposition is only a description of 

 copper, and all the ordinary descriptions of substances in 

 scientific works may be summed up in this form. Thus we 

 may assert of the organic substances called Paraffins that 

 they are all saturated hydrocarbons, incapable of uniting 

 with other substances, produced by heating the alcoholic 

 iodides with zinc, and so on. It may be shown that no 

 amount of ordinary description can be equivalent to a de- 

 finition of any substance. 



Fallacies. 



I have hitherto been engaged in showing that all the 

 forms of reasoning of the old syllogistic logic, and an 

 indefinite number of other forms in addition, may be 

 readily and clearly explained on the single principle of 

 substitution. It is now desirable to show that the same 

 principle will prevent us falling into fallacies. So long 

 as we exactly observe the one rule of substitution of 

 equivalents it will be impossible to commit a paralogism, 

 that is to break any one of the elaborate rules of the 

 ancient system. The one new rule is thus proved to be as 

 powerful as the six, eight, or more rules by which the cor- 

 rectness of syllogistic reasoning was guarded. 



It was a fundamental rule, for instance, that two nega- 

 tive premises could give no conclusion. If we take the 

 propositions 



Granite is not a sedimentary rock, (i) 



Basalt is not a sedimentary "rock, (2) 



we ought not to be able to draw any inference concerning 

 the relation between granite and basalt. Taking our 

 letter-terms thus : 



A = granite, B = sedimentary rock, C 

 the premises may be expressed in the forms 



