CATEGORICAL JUDGMENTS AND PROPOSITIONS. 189 



All, as a sign of the general proposition, must be used dis- 

 tributively (pmnes) : not collectively (cunctt) in the sense of &quot; all 

 together &quot;. When it is used in the latter sense, it is not regarded as 

 an ordinary sign of quantity, attached extrinsically to the subject 

 to distribute it, but as incorporated with the latter to constitute 

 it, and as equivalent to &amp;lt;( a (or the, or some, or any) COLLECTION of 

 . . . ,&quot; being merely used as a substitute for a collective name. 

 Whether, then, such a collective proposition will be general, 

 singular, or particular, will depend altogther on whether the 

 predication is made about the whole class of such &quot;alls &quot; or &quot;col 

 lections,&quot; or about some definite individual collection, or about 

 an indefinite number of such collections. For example, the 

 collective proposition &quot; All the angles of a triangle are equal to 

 two right angles &quot; is a general proposition, because the predication 

 is made of any and every such collection of angles &quot;All the 

 angles of a (i.e. any or every) triangle . . . &quot;. The collective 

 proposition &quot; All the books in the British Museum would fit in 

 Westminster Abbey &quot; is singular, because the predication is made 

 about the whole denotation of the singular subject the said 

 denotation being unity. So, too, is the collective proposition, 

 &quot; The Romans conquered Gaul,&quot; because the predication is made 

 about that one individual people or nation collectively. But the 

 collective proposition &quot; All the books of some public libraries 

 would not weigh a ton &quot; is a particular proposition, because the 

 predication is made indefinitely, about &quot; some &quot; collections of 

 books. A collective proposition, therefore, maybe either general, 

 singular, or particular, whether its subject be a collective term 

 like army, navy, etc. or a collection formed by a distributive 

 class name qualified by &quot; all &quot; in the sense of &quot; all together &quot;. 



Owing to the ambiguity arising from this double use of &quot;all &quot; it would be 

 preferable to use &quot; every &quot; as the logical sign of the general proposition. 

 However, long usage is not easily discontinued. &quot;All&quot; is to be interpreted 

 distributively wherever the collective use is not obvious from the context, or 

 otherwise expressly indicated. The symbolic form &quot; All S s are P &quot; is free 

 from the ambiguity ; not so the form &quot; All S is P &quot;. 



Neither is the sign &quot;any &quot; free from ambiguity. It is usually equivalent 

 to &quot;every,&quot; &quot;all&quot; (distributively) ; for we cannot predicate P about any unit 

 taken at random from the denotation of 5, unless we can predicate it of all the 

 S s, of each and every S. But &quot; any &quot; sometimes introduces an indefinite 

 singular proposition which should be classified as a particular [see (b)\ For 

 example, &quot;Anyone who wins this race will receive a silver cup &quot; is particular, 

 because it refers to some as yet undetermined individual &quot; winner of the 



