368 



MEMOIRS OF THE AMERICAN ACADEMY. 



* 



between elementary relatives of the form (A:A), and those of the form (A:B). 

 These are divisions in regard to the amount of opposition between relative and cor- 

 relative. 



a. Simple relatives are in this way primarily divisible into relatives all of whose 

 elements are of the form (A: A) and those which contain elements of the form (A:B). 

 The former express a mere agreement among things, the latter set one thing over 

 against another, and in that sense express an opposition (dvTiKeta-dcu) ; I shall therefore 

 term the former concurrents, and the latter opponents. The distinction appears in this 



notation 



between relatives with a comma, such as (w,) , and 



comma, such as (w); and is evidently of the highest importance. 



itives without a 



The character 

 which is signified by a concurrent relative is an absolute character, that signified by 



an opponent is a relative character, that is, one which cannot be prescinded from 

 reference to a correlate. 



b. The second division of simple relatives with reference to the amount of opposi- 



tion between relative and correlative is into 

 in collections of squares, each square like this 



those whose elements may be arranged 



A:A 

 B:A 

 C:A 



A:B 

 B:B 



C:B 



A:C 

 B:C 



C:C 



and those whose elements cannot be so arranged. The former (examples of which 



equal 



?> 



similar 



n 



may be called copulatives, the latter non-copula 



lives. A copulative multiplied into itself gives itself. Professor Peirce calls letters 



having this property, idempotenis 



The present distinction is of course very impor 



pure algebra. All concurrents are copulat 



c. Third 



divisible into those which for every element of the form 



(A:B) have another of the form (B:A), and those which want this symmetry 

 is the old division into equiparants and (lis quipar ants* or in Professor De Morg 

 language, convertible and inconvertible relatives. Equiparants are their own con 

 tives. All copulatives are equiparant. 



This 



" Quaidam sunt relationes equiparantise, qiuedara disquiparanti*. Prim* sunt relatione similium noininum, secunds 

 relatumes d,ssimilium nominum. Exemplum primi est quando idem nomen ponitur in recto et in obliquo, sicut simile 

 umili est smnle. . . . Exemplum secundi est quando unum nomen ponitur in recto sed aliud in obliquo, sicut pater est 

 filu pater et non oportet quod sit patris pater." Ockham Quodlibetum 6, qu 20. See also his Summa Logices, pars 1, 

 cap. o2. « Relate equiparanti. : quae sunt synonyma cum suis correlativis. . . . Relativa diquiparanti* : qu* non 

 sunt synonyma cum suis correlativis." Pschlacher in Petr. Hisp. The same definitions substantially may be found in 



many late mediaeval logics. 



