In order to answer this question, let us begin with the smaller Proposition, "_Some_ Members of the Subject are Members of the Predicate," and suppose that this is _all_ we have been told; and let us proceed to inquire what _else_ we need to be told, in order to know that "_All_ Members of the Subject are Members of the Predicate". [Thus, we may suppose that the Proposition "_Some_ bankers are rich men" is all the information we possess; and we may proceed to inquire what _other_ Proposition needs to be added to it, in order to make up the entire Proposition "_All_ bankers are rich men".] Let us also suppose that the 'Univ.' (i.e. the Genus, of which both the Subject and the Predicate are Specieses) has been divided (by the Process of _Dichotomy_) into two smaller Classes, viz. (1) the Predicate; (2) the Class whose Differentia is _contradictory_ to that of the Predicate. [Thus, we may suppose that the Genus "men," (of which both "bankers" and "rich men" are Specieses) has been divided into the two smaller Classes, "rich men", "poor men".] pg018 Now we know that _every_ Member of the Subject is (as shown at p. 6) a Member of the Univ. Hence _every_ Member of the Subject is either in Class (1) or else in Class (2). [Thus, we know that _every_ banker is a Member of the Genus "men". Hence, _every_ banker is either in the Class "rich men", or else in the Class "poor men".] 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?_