392 NOTES ON BOOLE'S 



de omni et nullo, but on something of equivalent evidence. The 

 only question is whether we should be right in considering these 

 cases as exceptions, and, if they are so, to what they owe their 

 existence. One instance is the inversio relationis, e.g. Noah is 

 Shem's father, therefore Shem is Noah's son. Here we pass 

 from the idea of Shem to that of his father, and vice versa. 

 The movement of the mind is along a track distinct from that 

 which it follows, either in Algebra or what we commonly call 

 Logic. The perception of the truth of the inference depends on 

 a recognition of the correlation of the two ideas, father and son. 

 Again, take a similar instance : Prince Albert sat at the Em- 

 peror's right hand, therefore the Emperor sat at Prince Albert's 

 left, &c. &c. How shall we express such inferences sym- 

 bolically? Let S be Shem, N Noah, /father, s son ; 



N=fS, 

 sf=l. 



Eliminating /bet ween these two equations, we get 



Nothing can be simpler than this : but the symbols s, / are of a 

 distinct nature from those employed in the Laws of Thought. 

 For/4 does not denote a species of -4, but an idea standing in 

 a different relation to it. The distinction between these two 

 kinds of symbols becomes more manifest when we reflect that 

 / 2 is not identical with/ but denotes "father of father," or 

 grandfather. Now I do not see how these cases of inversion of 

 relation are to be dealt with symbolically without the introduc- 

 tion of such symbols. In the following examples I confine 

 myself to the cases afforded by relationship and the succession 

 of generations. Let A, -B, (7, denote three persons, s son, g grand- 

 son; then, if .5 is A* a son and C jB's, C is A's grandson, which 

 we may express symbolically by the following equations : 



Eliminating B, we get 



