172 THE SCIENCE OF LOGIC. 



other. 1 A proposition of the second class is said to be per aliud 

 nota ; i.e. we can know that subject and predicate agree (or dis 

 agree), not from any mere analysis of the terms or concepts 

 compared one does not necessarily involve (or exclude) the 

 other, but only by an appeal to facts. 



Of course, the predicate of a proposition may de facto be 

 necessarily connected with the subject without our being aware 

 of the existence of such a necessary connexion. But, provided 

 the necessary connexion is really there, no matter how long and 

 elaborate be the analysis required to make it explicit, Scholastic 

 logicians regard the proposition as in materia necessaria and per 

 se nota IN SE, i.e. knowable in itself, even although it be not yet 

 per se nota QUOAD NOS, i.e. known by us to be a necessary pro 

 position. Thus, all the most remote and complex conclusions 

 of the pure mathematical sciences would be no less necessary and 

 per se notae than the truth that &quot; two straight lines cannot enclose 

 a space,&quot; or the truth that &quot;two and two are four &quot;. 



The point of view from which the Scholastics, following 

 Aristotle, regarded the distinction in question, was, therefore, 

 frankly objective. Hence, they perceived and indicated various 

 ways in which the necessity of the connexion between the terms 

 might make itself manifest. They enumerated various &quot;per se 

 modes of predicating,&quot; as distinct from &quot;per accidens modes of 

 predicating &quot;. 



The first and most manifest &quot;modus dicendi per se n or 

 essential proposition , to use one of the more modern expressions 

 is that in which the predicate gives the whole or part of the 

 connotation or essence of the subject. All definitions belong to 

 this class, as also all propositions whose predicates give the genus 

 or the differentia of the subject, e.g. &quot; A square is a rectangle&quot; &quot; Man 

 is rational&quot; . We may likewise regard as included in this class 

 all synonymous, tautologous, and identical propositions whether 

 the predicate be a proper name, as &quot;Tully is Cicero,&quot; or a conno- 

 tative name, as, &quot; Veracity is truth &quot; and also all purely formal 

 propositions, such as &quot;A is A,&quot; &quot;A either is or is not B,&quot; &quot; If all 

 A is B then no not-B is A &quot;. 2 



1 Comprehension, it will be remembered, includes more than connotation : it 

 includes all the attributes which are de facto common to all members of the class. 

 It therefore includes all attributes necessarily involved in, or connected with, the 

 connotation. 



2 KEYNES, op. cit., p. 52. An apparently identical proposition is sometimes 

 used to make a real assertion, in which case it is a real or synthetic proposition ; e.g. 



