52 THE PRINCIPLES OF SCIENCE. 



The universe, in short, within which they habitually dis- 

 course, is that of equations with real coefficients. These 

 implied limitations form part of that great mass of tacit 

 knowledge which accompanies all special arguments. 



It is worthy of inquiry whether almost all identities 

 are not really limited to an implied sphere of meaning. 

 When we make such a plain statement as ' Gold is mal- 

 leable ' we obviously speak of gold only in its solid state ; 

 when we say that ' Mercury is a liquid metal ' we must 

 be understood to exclude the frozen condition to which it 

 may be reduced in the Arctic regions. Even when we 

 take such a fundamental law of nature as ' All substances 

 gravitate/ we must mean by substance, material sub- 

 stance, not including that basis of heat, light and electrical 

 undulations which occupies space and possesses many 

 mechanical properties, but not gravity. The proposition 

 then is really of the form 



Material substance = Material gravitating substance. 



To De Morgan is due the remark, that we do usually 

 think and argue in a limited universe or sphere of notions 

 even when it is not expressly stated f . 



Negative Propositions. 



In every act of intellect, as we have seen, we are en- 

 gaged with a certain degree of identity or difference 

 between certain things or sensations compared together. 

 Hitherto I have treated only of identities ; and yet 

 it might seem that the relation of difference must be 

 infinitely more common than that of likeness. One 

 thing may resemble a great many other things, but 

 then it differs from all remaining things in the world. 

 Difference or diversity may almost be said to constitute 

 life, being to thought what motion is to a river. The 



f 'Syllabus of a Proposed System of Logic,' 122, 123. 



