ich men" evidently
contains the smaller Proposition "_Some_ bankers are rich men".]

The question now arises "What is the _rest_ of the information which
this Proposition gives us?"

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 '=equivale