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

AND THE ARISTOTELIAN SYLLOGISM. 129
The form of this argument appears to be
No not-M is P (E),
S is not M (E) ; ~
. . S is not P (E).
The same explanation holds ;
the minor premise asserts the
absence of metallic characteristics from carbon. In other
words, the middle is the negative term
M .
The logical form of the syllogism is
M eP,
SaM ;
. . SeP.
"
not-metallic," or
The sixth rule says that if one premise is negative,
the conclusion must be negative, and vice versti. For,
if one premise is negative, the other must be affirmative
(by rule 5). The affirmative premise asserts some
amount of coincidence between one extreme and the
middle term, that all or part of it is in the middle
term ; the negative premise says that all or part of
the other extreme is outside the middle term. Hence
the only conclusion can be, that all or part of this
second extreme is outside the area of coincidence of
the first extreme and the middle term. This is a
negative conclusion. Further, a negative conclusion
implies a negative premise. For it asserts that one
extreme is wholly or partly outside the other; and
this result is reached by comparing both extremes with
the middle term. Hence one of the extremes must
be wholly or partly outside the middle term, that
is, one of the premises must be negative.
The seventh rule says that from two particular
be deduced
premises there is no conclusion. This may
from the preceding rules.
tions are I and O and as ;
The only particular proposi
each of them may be either
major or minor premise, there are four possible cases,