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_.
[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".
A Proposition of Relation, beginning with "All", is (as shown in § 3)
equivalent to _two_ Propositions, one beginning with "Some" and the
other with "No", each of which we now know how to translate.
[Let us work a few Examples, to illustrate these Rules.
(1)
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