PROPOSITIONS. 57 



Venus, and Venus must differ from Mars. The Earth 

 differs from Jupiter in density ; therefore Jupiter must 

 differ from the Earth. Speaking generally, if A ^ B we 

 shall also have B * A, and these two forms may be con- 

 sidered expressions of the same difference. But the 

 reader will notice that the relation of differing things 

 is not wholly reciprocal. The density of Jupiter does 

 not differ from that of the Earth in the same way that 

 that of the Earth differs from that of Jupiter. The change 

 of sensation which we experience in passing from Venus 

 to Mars is not the same as what we experience in passing 

 back to Venus, but just the opposite in nature. The 

 colour of the sky is lighter than that of the ocean ; 

 therefore that of the ocean cannot be lighter than that 

 of the sky, but darker. In these and all similar cases 

 we gain a notion of direction or character of change, 

 and results of immense importance may be shown to 

 rest on this notion. For the present we shall be 

 concerned with the mere fact of identity existing or 

 not existing. 



Twofold Interpretation of Propositions. 



Terms, as we have seen (p. 31), may have a meaning 

 either in extension or intension ; and according as one 

 or the other meaning is attributed to the terms of a 

 proposition, so may a different interpretation be assigned 

 to the proposition itself. When the terms are abstract 

 we must read them in intension, and a proposition con- 

 necting such terms must denote the identity or non- 

 identity of the qualities respectively denoted by the 

 terms. Thus if we say 



Equality = Identity of magnitude, 

 the assertion means that the circumstance of being equal 



