Also we have been told that, in the case we are discussing, some Members of the Subject are in Class (1). What else do we need to be told, in order to know that all of them are there? Evidently we need to be told that none of them are in Class (2); i.e. that none of them are Members of the Class whose Differentia is contradictory to that of the Predicate.
[Thus, we may suppose we have been told that some bankers are in the Class “rich men”. What else do we need to be told, in order to know that all of them are there? Evidently we need to be told that none of them are in the Class “poor men”.]
Hence a Proposition of Relation, beginning with “All”, is a Double Proposition, and is ‘equivalent’ to (i.e. gives the same information as) the two Propositions
(1) “Some Members of the Subject are Members of the Predicate”;
(2) “No Members of the Subject are Members of the Class whose Differentia is contradictory to that of the Predicate”.
[Thus, the Proposition “All bankers are rich men” is a Double Proposition, and is equivalent to the two Propositions
(1) “Some bankers are rich men”;
(2) “No bankers are poor men”.]
[pg019]§ 4.
What is implied, in a Proposition of Relation, as to the Reality of its Terms?
Note that the rules, here laid down, are arbitrary, and only apply to Part I of my “Symbolic Logic.”
A Proposition of Relation, beginning with “Some”, is henceforward to be understood as asserting that there are some existing Things, which, being Members of the Subject, are also Members of the Predicate; i.e. that some existing Things are Members of both Terms at once. Hence it is to be understood as implying that each Term, taken by itself, is Real.