DISJUNCTIVE PROPOSITIONS. 81 



Expression of the Alternative Relation. 



In order to represent disjunctive propositions with 

 convenience we require a sign of the alternative or dis- 

 junctive relation, equivalent to one meaning at least of 

 the little conjunction or so frequently used in common 

 language. I propose to use for this purpose the sym- 

 bol -|- . In my first logical Essay I followed the example 

 of Dr. Boole and adopted the common sign + ; but this sign 

 should not be employed unless there exists exact analogy 

 between mathematical addition and logical alternation. 

 We shall find that the analogy is of a very partial cha- 

 racter, and that there is such profound difference between 

 a logical and a mathematical term as should prevent our 

 uniting them by the same symbol. Accordingly I have 

 chosen a sign \ , which seems aptly to suggest whatever 

 degree of analogy may exist without implying more. 

 The exact meaning of the symbol we will now proceed to 

 investigate and determine. 



Nature of the Alternative Relation. 



Before treating disjunctive propositions it is indis- 

 pensable to decide whether the alternatives shall be 

 considered exclusive or unexclusive. By exclusive alter- 

 natives we mean those which cannot contain the same 

 things. Thus 



Matter is solid, or liquid, or gaseous ; 

 but the same portion of matter cannot be at once solid and 

 liquid, properly speaking ; still less can we suppose it to 

 be solid and gaseous, or solid, liquid and gaseous all at 

 the same time. Many examples on the other hand can 

 readily be suggested in which two or more alternatives 

 may hold true of the same object. Thus 



Luminous bodies are self-luminous or luminous by 

 reflection. 



G 



