An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

IMMEDIATE INFERENCE. 79
each other (figs. 3, 4, 5). In the original proposition,
called the convertend, this relation is stated from the
side of S ; in the converted proposition, called the
converse, the same relation is stated from the side of
P. Now the relation (of coincidence or exclusion) is
the same whether looked at from the side of S or the
side of P. If P coincides with S to any extent, to
the same extent S must coincide with P ; and if P is
excluded from S to any extent, S is also excluded to
the same extent from P. A glance at the diagrams
will make these facts obvious. And as coincidence in
the diagram corresponds to affirmation in the proposi
tion, and exclusion to negation, we have the first rule
of conversion : the quality (affirmative or negative) of
the original proposition is unchanged in the converse.
Again, obviously we cannot state in the converse any
more than the convertend declares to be known. Apply
this principle to the four forms.
(1) "All S is P." When we come to convert this,
P and S change places, and P has the sign of quantity
instead of S. What quantity must be given to P ?
This depends on what we know of the quantity of P in
the original proposition. Now in an A proposition we
do not know, from the form, that P is distributed ( 6) ;
we only know that some at least of P is referred to.
Hence in converting A, we must say
"
some at least of
P is or in S," the logical form, "some P is S." Thus,
"
the converse of all men are
"
fallible is
"
some fallible
beings are men." There may be
"
"
fallible beings
which are not men ; the original proposition tells us
nothing
as to this.
(2) "Some S is P." Here again we do not know,
from the form, whether P is taken in its whole extent,
is
"
distributed," or not hence we cannot distribute it in
;