CATEGORICAL JUDGMENTS AND PROPOSITIONS. 191 



or empirical universals, as we may call them, 1 and of much greater 

 importance for the scientific worth of human knowledge, is what 

 we may call the necessary, abstract, or generic, universal judgment, 

 wherein the connexion between subject and predicate is asserted 

 to be not merely universally verified in fact, but to be an absolutely 

 necessary, inviolable connexion, altogether beyond exception and 

 entirely independent of any change in conditions of time or space. 

 Examples of such judgments are : &quot; Each of the interior 

 angles of any triangle is less than two right angles &quot; ; 

 &quot;No pair of parallel lines enclose a space&quot;; U A11 men desire 

 happiness &quot; ; &quot; Every virtue is to be esteemed &quot; ; &quot; Every event has 

 a cause &quot; ; &quot; No pair of contradictory judgments are either both 

 true together or both false together &quot;. Now, the characteristic of 

 the class of universal judgments illustrated by these examples is 

 this, that their universality is known not by an actual enumeration 

 of all the instances, actual or possible, not by any concrete ex 

 perience of, or any appeal to, the whole denotation of the class 

 of things about which the predication is made, but by an appeal 

 to the connotation of both subject and predicate, by such an anal 

 ysis of the ideas compared as will show us that the predicate in 

 each case is necessarily connected with (or excluded from) the 

 nature of the subject, and may therefore be predicated (affirm 

 atively or negatively) of every conceivable instance whether 

 actual or possible of this subject. In their modality, such 

 judgments are apodeictic (89). The sign of universality (&quot;all,&quot; 

 &quot;every,&quot; etc.) is here independent of all conditions of time and 

 space ; and the judgments are free from all possibility of exception 

 or change. 



Although the distinction between these two classes of universal 

 judgments 2 is of sufficiently far-reaching importance for any 

 general philosophical theory of human knowledge, yet, for our 

 present formal treatment of propositions, it need not be and 

 indeed could not conveniently be maintained. It is what we 



1 To this class belongs the singular judgment \cf. (b) below]. The distinction 

 between the abstract universal on the one hand, and the concrete universal, the singu 

 lar, and the particular, on the other hand, is indeed not properly a quantitative distinc 

 tion ; while the distinction between the three latter is often purely quantitative. Cf. 

 JOSEPH, Logic, pp. 155, 157. For the distinction between the definite and the inde 

 finite singular, see below (b). 



2 The student can scarcely fail to notice that this distinction is already familiar 

 to him, as that between judgments in materia necessaria and judgments in materia 

 contingent (85-7). 



