192 THE SCIENCE OF LOGIC. 



may call the modal or connotative expression J of the latter class 

 of judgments that gives us an insight into their nature and the 

 grounds of our assent to them ; whereas these latter points are 

 rather concealed by the denotative or quantitative form of expres 

 sion, which would rather lead us to believe (erroneously) that such 

 judgments are reached, like concrete singular and general judg 

 ments, through experience and enumeration of instances. If a 

 formal distinction in expression be sought for the two classes, 

 the concrete universals might, perhaps, be appropriately expressed 

 by &quot; All S s are P,&quot; the abstract by &quot; S is P&quot; or &quot; 5 as such is 

 /*,&quot; with the corresponding negatives. 



One point in the expression of the universal negative calls for special 

 notice. The proper form for expressing judgments of this class is &quot; No 5 s 

 are P &quot; or &quot; No 5 is P &quot;. The form &quot; All (or Every) 5 is not P &quot; (or &quot; All 

 S s are not P&quot;} is ambiguous. Although it could, absolutely speaking, be 

 interpreted as expressing the universal negative, the contrary of &quot;All (or 

 Every) 5 is P&quot; nevertheless the &quot;not&quot; is usually interpreted as qualifying 

 the &quot; //&quot; instead of the copula, &quot; is &quot; or &quot; are &quot; ; so that the form is the same 

 as &quot; Not all (or &amp;lt; Not every ) 5 is P? which really means &quot; Some S (or 5 s) 

 is (or are) not P &quot;. That is to say, such propositions are really particular 

 negative (or O) propositions; e.g. &quot;All is not gold that glitters&quot; means 

 &quot;Some glittering things are not gold&quot;; &quot;All men are not saints&quot; means 

 &quot; Some men are not saints &quot;. The universal negative cannot, therefore, be 

 safely expressed in this form. Only when &quot;All&quot; is used in a singular 

 collective, can the form &quot;All 5 is not P&quot; be appropriately used to deny 

 the form &quot;All S is P &quot; : &quot;All the books in the British Museum would 

 not fit in a small room&quot; is the denial of &quot;All the books in the British 

 Museum would fit in a small room &quot;. But in the case of the general collec 

 tive, the use of the form remains ambiguous ; &quot;All the interior angles of a 

 triangle are not equal to two right angles &quot; might be (erroneously) interpreted 

 as a particular negative, meaning &quot; Some triangles have not all their interior 

 angles equal to two right angles &quot;. 



(b) Singular Propositions are usually regarded in logic as a 

 sub-class of universal propositions (A or \E\ on the ground that 

 the subject is a single individual and that the predication is made 

 definitely about that one individual, about the whole denotation 

 of the subject which is unity. Some authors, however, classify 

 them as particulars, on the ground that the predication is made 

 about a portion namely, the least possible portion of the deno 

 tation of the subject class. 2 As a matter of fact, some singular pro 

 positions must be classed as universal, others as particular. It is 



1M Virtue ought to be esteemed&quot;; &quot;An event must have a cause&quot;; &quot;Man 

 necessarily desires happiness &quot; ; etc. 

 a C/. CLARKE, Logic, p. 274. 



