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

elusion is
THE VALIDITY OF THE SYLLOGISM. 221
"
something new," although the major states
a mere collective fact, which (for those who know, but
not for me) already contains the conclusion.
NOTE A.
ON SYLLOGISMS INVOLVING NUMERICAL PROPOSITIONS.
These were elaborately investigated by De Morgan in his
Formal Logic. He pointed out that the following represents
a very common type of argument :
"
If the majority of a
public meeting vote for the first resolution, and a majority
also vote for the second, it follows necessarily that
who voted for the first voted also for the second."
some
And
from such instances De Morgan argued that two particular
premises may give a valid conclusion if the actual quantities
of the two terms are stated, and if, when added together,
they exceed the quantity of the middle term. This is a
misleading way of describing such arguments ; for the
premises are not "particular" in the logical sense, and the
inference from them differs in principle from syllogistic
inference. They depend on comparison of numerical rela
tions, and they are at bottom cases of counting. They are
no more and no less syllogistic than any other kind of cal
culation is.
As examples of such inferences, where the propositions are
numerical but not definite, the student may examine the
following, and consider what conclusion, if any, can be
drawn from each set of premises : "
(i) Few
of the members
were not present, but very few of them took part in the
debate." (2)
" None but members were present ; some
persons who were present did not take part
in the debate."
are not
"
(3) Every member of the society is present ; you
"
a member of the society." (4) No A are B no B are
;
other than C some C are D."
; (5) "Few A are not B;
"
few A are not C." (6) Most A are B most B are C."
;
He should also find whether a conclusion can be drawn, in
any of these examples, according to syllogistic rules.