[Thus, the Proposition “Some rich men are invalids” is to be understood as asserting that some existing Things are “rich invalids”. Hence it implies that each of the two Classes, “rich men” and “invalids”, taken by itself, is Real.]
A Proposition of Relation, beginning with “No”, is henceforward to be understood as asserting that there are no existing Things which, being Members of the Subject, are also Members of the Predicate; i.e. that no existing Things are Members of both Terms at once. But this implies nothing as to the Reality of either Term taken by itself.
[Thus, the Proposition “No mermaids are milliners” is to be understood as asserting that no existing Things are “mermaid-milliners”. But this implies nothing as to the Reality, or the Unreality, of either of the two Classes, “mermaids” and “milliners”, taken by itself. In this case as it happens, the Subject is Imaginary, and the Predicate Real.]
A Proposition of Relation, beginning with “All”, contains (see [§ 3]) a similar Proposition beginning with “Some”. Hence it is to be understood as implying that each Term, taken by itself, is Real.
[Thus, the Proposition “All hyænas are savage animals” contains the Proposition “Some hyænas are savage animals”. Hence it implies that each of the two Classes, “hyænas” and “savage animals”, taken by itself, is Real.]
[pg020]§ 5.
Translation of a Proposition of Relation into one or more Propositions of Existence.
We have seen that a Proposition of Relation, beginning with “Some,” asserts that some existing Things, being Members of its Subject, are also Members of its Predicate. Hence, it asserts that some existing Things are Members of both; i.e. it asserts that some existing Things are Members of the Class of Things which have all the Attributes of the Subject and the Predicate.
Hence, to translate it into a Proposition of Existence, we take “existing Things” as the new Subject, and Things, which have all the Attributes of the Subject and the Predicate, as the new Predicate.
Similarly for a Proposition of Relation beginning with “No”.