in.] PROPOSITIONS. 43 



Thus we may say, with some approximation to truth, that 

 " Large plants are plants devoid of locomotive power." 



A barrister may make numbers of most general state- 

 ments concerning the relations of persons and things in the 

 course of an argument, but it is of course to be understood 

 that he speaks only of persons and things under the 

 English Law. Even mathematicians make statements 

 which are not true with absolute generality. They say 

 that imaginary roots enter into equations by pairs ; but this 

 is only true under the tacit condition that the equations in 

 question shall not have imaginary coefficients. 1 The uni- 

 verse, in short, within which they habitually discourse 'is 

 that of equations with real coefficients. These implied 

 limitations form part of that great mass of tacit knowledge 

 which accompanies all special arguments. 



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. 2 



It is worthy of inquiry whether all identities are not 

 really limited to an implied sphere of meaning. When we 

 make such a plain statement as " Gold is malleable " we 

 obviously speak of gold only in its solid state ; when we 

 say -that " Mercury is a liquid metal " we must be under- 

 stood 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 substance, not. in- 

 cluding that basis of heat, light, and electrical undulations 

 which occupies space and possesses many wonderful me- 

 chanical properties, but not gravity. The proposition then 

 is really of the form 



Material substance = Material gravitating substance. 



Negative Propositions. 



In every act of intellect we are engaged with a certain 

 identity or difference between things or sensations compared 

 together. Hitherto I have treated only of identities ; and 

 yet it might seem that the relation of difference must be 



1 De Morgan On the Root of any Function. Cambridge Philo- 

 sophical Transactions, 1867, vol xi. p. 25. 



2 Syllabus of a proposed tiystem of Logic, 122, 123. 



