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

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III. Relating to quality :
MEDIATE INFERENCE
(5) From two negative premises
there can be
no conclusion. In other words : One,
at least, of the premises must be affirm
ative.
(6) If one premise is negative, the conclusion
must be negative, and vice versa.
IV. Corollaries :
(7) From two particular
no conclusion.
premises, there can be
(8) If one premise be particular, the conclusion
must be particular.
The first two rules tell us what a syllogism is. It
consists of the comparison of two propositions by
means of a common term ; and the statement of the
result in a third proposition. Hence (i) there must
be three propositions only. If there are more than
three, we have more than one syllogism ; if less than
three, we have no syllogism, but either an Immediate
Inference or a mere assertion, giving a statement as a
reason for itself :
"
I know it because I know it." Also
(2) there must be three terms only, for the two prem
ises have a common term. If there are less than
three terms, we have no syllogism ; if there are more,
we have either no syllogism or more than one :
usually
no syllogism, because the premises have no link of
connection, and contain four different terms between
them. These absurd mistakes are possible because of
the ambiguity of language. If any term is used am
biguously, it is really two terms ; hence the syllogism
containing it has at least four terms, and is not a true
syllogism at all, though at first sight it may appear to be
one. If there is ambiguity, it is most likely to occur in