28 SIGNS AND THEIR LAWS. [CHAP. II. 



It is clear also, that to the above class we must refer any sign 

 which may conventionally be used to express some circumstance 

 or relation, the detailed exposition of which would involve the 

 use of many signs. The epithets of poetic diction are very fre- 

 quently of this kind. They are usually compounded adjectives, 

 singly fulfilling the office of a many- worded description. Homer's 

 " deep-eddying ocean" embodies a virtual description in the single 

 word jSafluSi'i'Tjc- And conventionally any other description ad- 

 dressed either to the imagination or to the intellect might equally 

 be represented by a single sign, the use of which would in all es- 

 sential points be subject to the same laws as the use of the ad- 

 jective " good" or " great." Combined with the subject " thing," 

 such a sign would virtually become a substantive ; and by a single 

 substantive the combined meaning both of thing and quality 

 might be expressed. 



6. Now, as it has been defined that a sign is an arbitrary 

 mark, it is permissible to replace all signs of the species above 

 described by letters. Let us then agree to represent the class of 

 individuals to which a particular name or description is appli- 

 cable, by a single letter, as x. If the name is " men," for instance, 

 let x represent "all men," or the class "men." By a class is 

 usually meant a collection of individuals, to each of which a 

 particular name or description may be applied ; but in this work 

 the meaning of the term will be extended so as to include the 

 case in which but a single individual exists, answering to the 

 required name or description, as well as the cases denoted by 

 the terms " nothing" and " universe," which as " classes" 

 should be understood to comprise respectively " no beings," 

 " all beings." Again, if an adjective, as "good," is employed 

 as a term of description, let us represent by a letter, as ?/, all 

 things to which the description " good" is applicable, i. e. " all 

 good things," or the class "good things." Let it further be 

 agreed, that by the combination xy shall be represented that 

 class of things to which the names or descriptions represented by 

 x and y are simultaneously applicable. Thus, if x alone stands 

 for "white things," and y for " sheep," let xy stand for " white 

 sheep ;" and in like manner, if z stand for " horned things," and 

 x and y retain their previous interpretations, let zxy represent 



