III.] propositions;. 4.1 



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

 " Larfje plants are plants devoid of locomotive power." 



A barrister may make numbers of most general state- 

 ments concernini? 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 undt-r the 

 English Law. Even matliematicians make statements 

 which are not true with absolute generality. Tliey say- 

 that imaginary roots enter mto equations by pairs ; l>ur this 

 is only true under the tacit condition that the equations in 

 question shall not have imaginary coefficients.^ The uni- 

 verse, in short, within which they habitually discourst? 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 Do Morgan is due the remark, that we do usually 

 think and argue in a limited universe or sphere of notions, 

 even when il is not expressly stated.- 



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 spnak of gold only in its solid state ; when we 

 say that " Mercury is a li([uid metal " we must be under- 

 stood to exclude the frozen c(.>ndition 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 ba3is"^of heat, light, and electrical undubitions 

 which occupies space and possesses many wonderful me- 

 chanical properties, but not gravity. The proposition! hen 

 is really of tlie form 



Material sul)Stance = Material gravitating substance. 



Negative Proportions. 



In every act of intellect we are engaged with a certain 

 identity or difference between things or sensations compared 

 togettier. Hitherto I have treated only of identities; and 

 vet it mi^ht seem that the relation of difference must be 



^ De Morj^'aii On the Hoot vf any Function. Cambrid^ii I'hilo- 

 SDpliical Transactions, 1867, vol .vi. p. 25. 



^ Syllabus 0/ a proposed .system of Logic, §§ 122, 123. 



