40 THE PRINCIPLES OF SCIENCE. 



two, seem to obey this law ; we may say that i.i = i, and 

 o.o = o (taking o to mean absolute zero or i i) ; there 

 is apparently no other number which combined with itself 

 gives an unchanged result. I shall point out, however, in 

 the chapter upon Number, that in reality all numerical 

 symbols obey this logical principle. 



It is curious that this Law of Simplicity, though almost 

 unnoticed in modern times, was known to Boethius, who 

 makes a singular remark in his treatise ' De Trinitate 

 et Unitate Dei' (p. 959). He 'says, ' If I should say sun, 

 sun, sun, I should not have made three suns, but I should 

 have named one sun so many times d .' Ancient discussions 

 concerning the doctrine of the Trinity drew more atten- 

 tion to subtle questions concerning the nature of unity 

 and plurality than has ever since been given to them. 



It is a second law of logical symbols that order of 

 combination is a matter of indifference. 'Rich and rare 

 gems ' are the same as ' rare and rich gems/ or even as 

 ' gems, rich and rare.' Grammatical, rhetorical or poetic 

 usage may give considerable significance to order of ex- 

 pression. The limited power of our minds prevents our 

 grasping many ideas at once, and thus the order of 

 statement may produce some effect, but not in a strictly 

 logical manner. All life proceeds in the succession of 

 time, and we are obliged to write, speak, or even think of 

 things and their qualities one after the other ; but be- 

 tween the things and their qualities there need be no such 

 relation of order in time or space. The sweetness of sugar 

 is neither before nor after its weight and solubility. The 

 hardness of a metal, its colour, weight, opacity, mallea- 

 bility, electric and chemical properties, are all coexistent 

 and coextensive, pervading the metal and every part of it 



d ' Velut si dicam Sol, Sol, Sol, non tres soles effecerim, sed uno toties 

 prsedicaverim.' 



