ii.] TEEMS. 33 



symbolic language we may similarly hold that .A A is iden- 

 tical with A, or 



A = AA = AAA = &c. 



The late Professor Boole is the only logician in modern 

 times who has drawn attention to this remarkable property 

 of logical terms ; l but in place of the name which he gave 

 to the law, I have proposed to call it The Law of "Simpli- 

 city. 2 Its high importance will only become apparent 

 when we attempt to determine the relations of logical and 

 mathematical science. Two symbols of quantity, and only 

 two, seem to obey this law ; we may say that I x I = I, 

 and oxo = 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, how- 

 ever, 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." 3 Ancient discussions 

 about the doctrine 'of the Trinity drew more attention 

 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 com- 

 bination is a matter of indifference. " Kich 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 expression. 

 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 simply 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 between the things and 

 their qualities there need be no such, relation of order in 



1 Mathematical Analysis of Logic, Cambridge, 1847, p. 17. ^ 

 Investigation of the Laws of Thought, London, 1854, p. 31. 



2 Pure Logic, p. 15. 



3 " Velut si dicam, Sol, Sol, Sol, non tres soles effecerim, sed unc 

 toties prsedicaverim." 



O 



