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

108 IMPORT OF PROPOSITIONS AND JUDGMENTS.
equiangular triangles
"
; that is, U and co are compatible.
That a) is also compatible with each of the diagrams of
2, figs. 10 to 13, is obvious.
We are therefore reduced to the five forms described
in 2, which, as indicated by the Hamiltonian symbols,
are as follows :
() If
"
some
"
Fig. 9 = U.
Fig. i o = A or 77.
Fig.
Fig.
1 1 = Y or O.
12 = 1 or O.
Fig. 13 = E.
means
"
some at least,"
not excluding
"all," then it is obvious that the eight propositions are
not independent forms. Detailed proof is unnecessary.
It has been said that in our ordinary thinking we
do occasionally quantify the predicate. It is worth
while therefore to see which of the new forms U, Y, 77,
and &>
are
found in ordinary speech. Dr Thomson,
who adopted the Hamiltonian scheme in his Laws of
Thought, admitted that 77 and w are never used, and we
have seen that co is also
entirely useless. The form
i]
is certainly never used ; but a proposition may occur
which can be expressed in that form. "Men are not
the only rational beings" expresses what is meant by
"
no men are some rationals."
"
It is equivalent to some
rationals are not
"
men (the primary implication) to
gether with
"
some men are rational." But no pro
position ever made could be adequately expressed
in the form &>. With regard to U and Y, we may
say with Dr "It Keynes, must be admitted that these
propositions are met with in ordinary discourse. We
may not indeed find propositions which are actually
written in the form all S is all P ; but we have to all