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

128 MEDIATE INFERENCE
does not forbid us to take less. There is no illicit
process when a term is distributed in the premise and
undistributed in the conclusion as in the :
; following
"All M is P, all S is M; .-. some S is P."
The fifth rule states that one premise, at least, must
be affirmative ; or, which is the same thing in different
words, from two negative premises there can be no
conclusion. A negative major premise is equivalent to
a denial of any connection between the major term and
the middle ; a negative minor premise is equivalent to
a denial of any connection between the minor term and
the middle. Hence there is no means of comparing the
major and minor terms : there is no middle term, and
the condition of a valid syllogism does not exist.
Jevons, in his Elementary Lessons in Logic, has given
the following explanation of the case, not of uncommon
occurrence, where from two apparently negative prem
ises we obtain a valid conclusion. "It must not, how
ever, be supposed that the mere occurrence of a negative
"
"
particle not or
("
no ") in a proposition renders it nega
tive in the manner contemplated by this rule. Thus the
argument
What is not compound is an element,
Gold is not compound ;
Therefore gold is an element,
contains negatives in both premises, but is nevertheless
valid, because the negative in both cases affects the middle
"
term, which is really the negative term not-compound.
Now this explanation applies to an example which Jevons
himself gives, in his Principles of Science, as a case where
two really negative premises give a valid conclusion. The
example is
"Whatever is not metallic is not capable of powerful
magnetic influence,
Carbon is not metallic ;
Therefore carbon is not capable of powerful magnetic
influence."