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

70
OPPOSITION OF PROPOSITIONS.
Logic on which we are now entering. Then the pro
position A expresses the fact that the thing or class
of things denoted by the subject
is included in and
forms part of the class denoted by the predicate.
Thus (a)
"
all metals are
"
elements means, on this
interpretation,
that the class "metals" is included in
the wider class "elements," and (b) "all equilateral
triangles are equiangular" means that the class equi
lateral triangles is in the class equiangular triangles,
and here we know also, from the matter of the pro
position, not from its form,
that the former class is
identical with the latter. These two possibilities always
arise in an A proposition. The mathematician Euler
(eighteenth century) invented a method of indicating
the extent of the denotation of a term by a circle, which
is supposed to include all things denoted by the term
and nothing else. In this case the proposition A is
represented by one of the two :
following diagrams
/- \
I S and P
Fig. i. Fig. 2.
Fig. i represents propositions of which (a) is a type,
and fig. 2 those of which (b) is a type, where the classes
S and P coincide. The form of this proposition does
not tell us whether they coincide or not ;
J
it does not
tell us anything of that part of P which is outside S.
But formally the proposition is always represented by
its lowest case ; hence in operating on an A proposi
tion (e.g., in Immediate Inference) we always act as if
fig.
i represented it.