ordinate or cointesive with A. And supposing that there is a
symbol which denotes any sum of symbols, there will be a
symbol C to which both A and B are subordinate in extension.
Hence, they will both be superordinate to it in intension and will have
in common the intension of C. Hence they will intersect in intension.
If on the other hand we had added to A an intension excluded
from B we should have diminished the extension of A without
leaving it subordinate superordinate or coextensive with B. And
supposing that any sum of intensions has some symbol to connote it,
there will be a symbol C to which both A and B are subordinate in
intension. Hence they will both be superordinate to it in extension
or will intersect it in extension.
4. Next suppose that from the extensions of both A and B
we take away that from which they have in common. This will
only add to the intension of both as they cannot be subordinate
superordinate or cointensive, they will still intersect in intension.
Or suppose they are made to exclude each other in intension
then by the same reasoning, they would intersect in extension.
Hence since intersection in either quantity by (3) implies intersection
in both it follows that when the suppositions of (3) there
can be no exclusion either in extension or intension. But if
there is no exclusion there is no coincidence or subordination
since these imply exclusion (?) and hence nothing but intersection.
EN