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

AND THE ARISTOTELIAN SYLLOGISM. 125
the middle term ;
breach of rule i.
ambiguous middle is the most common
Some good examples are given by Jevons.
"
If we argue
that all metals are elements and brass is metal, therefore it
is an element, we should be using the middle term metal in
two different senses, in one of which it means the pure simple
substances known to chemists as metals, and in the other
a mixture of metals commonly called metal in the arts, but
known to chemists by the name alloy. In many examples
which may be found in logical books the ambiguity of the
middle term is exceedingly obvious, but the reader should
always be prepared to meet with cases in which exceedingly
subtle and difficult ambiguities occur. Thus it might be
argued that what is right should be enforced by law, and
that charity is right and should therefore be enforced by the
law. Here it is evident that right is applied in one case
to what the conscience approves, and in another case to
what public opinion holds to be necessary for the good of
We add one or two further examples of
"
ambigu
society."
ous middle" which the student may examine for himself.
"All criminal actions ought to be punished by law; prose
cutions for theft are criminal actions, and therefore ought to
law should
"
be punished by law (De Morgan).
"
Every good
be obeyed ; the law of gravitation is a good law, and there
fore should be obeyed" (Creighton).
"
Partisans are not to
be trusted ; the supporters of the government are partisans,
and therefore are not to be trusted."
For like reasons, if the subject, or the predicate, of the
conclusion is used in a different sense there from that which
it bears in its premise, the inference is invalid.
The violation of the third rule is called the fallacy of
undistributed middle. The rule states that the whole
extent of the middle term must be referred to universally
in one premise, if not in both. For if the middle term
is not compared in its whole extent with one at least of
the extremes, we may be referring to one part
of it in
one premise, and quite another part of it in the other ;