PROPERTIES OF CLASSES OF FUNCTIONS 5 



used in the sequel. We do not hesitate to use the exact language 

 of the above memoir when it seems best to do so for our purpose. For 

 convenience we include in the introduction a section on special types 

 of developments A. 



We follow Moore in the use of certain logical symbols which are 

 extremely convenient and almost necessary. In practice these 

 symbols mightily aid in argumentation by the complete and explicit 

 representation of the notions in thoroughly convenient and concise 

 form. We begin with a list of these symbols, and in the introductory 

 sections we translate sufficiently many of the symbolical statements 

 so that throughout the paper the reader should find no difficulty in 

 understanding the notations. 



It is with pleasure that, in concluding this preface, we express 

 our obligation to Professor Moore for aid and inspiration freely given 

 in the preparation of this paper. 



Introduction. — An exposition of certain of the fundamental notions 



of the General Analysis of Moore. The definition of certain 



special types of developments A of classes ^. §§ 1-23. 



1. List of logical symbols with interpretations.* — 

 = logical identity 

 =1= logical diversity 

 = definitional identity 

 . 3 . (for every • • ■ ) it is true that 

 ( ) implies ( ) 

 if ( ) then ( ) 

 . <= . ( ) is implied by ( ) 

 . ~ . ( ) is equivalent to ( ) 



( ) implies and is implied by ( ) 

 =) ; c ; «> implies; is implied by; is equivalent to (as relations of 

 properties) 

 3 there exists a (system; class; element; etc.) 

 9 such that ; where 

 • and 

 ..;::;.::. signs of punctuation in connection with signs of implication, 

 etc.; the principal implication of a sentence has its 

 sign accompanied with the largest number of punctu- 

 ation dots. 



* I. G. A., pp. 150. 



