DISJUNCTIVE PROPOSITIONS. 85 



synonymous, at any rate an organ is a part. And it is 

 obvious that a part may be developed at the same time 

 both in an extraordinary degree and manner, although 

 such cases may be comparatively very rare. 



From a careful examination of ordinary writings, it 

 will thus be found that the meanings of terms joined by 

 ' and ' or ' vary from absolute identity up to absolute 

 contrariety. There is no logical condition of distinctness 

 at all, and when we do choose exclusive expressions, it is 

 because our subject demands it. The matter, not the form 

 of an expression, points out whether terms are exclusive e . 



The question, as we shall afterwards see, is one of the 

 greatest theoretical importance, because it furnishes the 

 true distinction between the sciences of Logic and Ma- 

 thematics. It is the very foundation of number that every 

 unit shall be distinct from every other unit ; but Dr. Boole 

 imported the conditions of number into the science of 

 Logic, and produced a system which, though wonderful in 

 its results, was not a system of logic at all. 



Laws of the Disjunctive Relation. 



In considering the combination or synthesis of terms 

 (P- 39)> we found that certain laws, those of Simplicity and 

 Commutativeness, must be observed. In uniting terms by 

 the disjunctive symbol we shall find that the same or 

 closely similar laws hold true. The alternatives of either 

 member of a disjunctive proposition are certainly commu- 

 tative. Just as we cannot properly distinguish between 

 rich and rare gems and rare and rich gems, so we must 

 consider as identical the expression rich or rare gems, and 

 rare or rich gems. In our symbolic language we may say 

 generally 



A -|. B = B .|. A. 



* ' Pure Logic,' pp. 76, 77. 



