The undistributed middle 169
are dogs. This is the simplest version of the notorious fallacy of
the undistributed middle. Both horses and dogs are indeed four-
legged, but neither of them occupies the whole of the class of
four-legged beings. This leaves convenient room for horses and
dogs to be different from each other, and from other beings
which might also without any overlap be in the four-legged class.
The 'middle' which carelessly omitted to get itself distributed
is the term which appears in the first two lines of a three-line
argument, but which disappears in the conclusion. The classic
three-liner requires that this middle term must cover the whole
of its class at least once. If not, it is undistributed.
All men are mammals. Some mammals are rabbits, therefore some men
are rabbits.
(Even though the first two lines are correct, the middle term 'mam-
mals' never once refers to all mammals. The middle term is thus
undistributed and the deduction invalid.)Common sense shows why the undistributed middle is fallacious.
The standard three-liner (called a 'syllogism') works by relating
one thing to another by means of a relationship they both have
with a third. Only if at least one of those relationships applies to
all the third thing do we know that it is certain to include the
other relationship.
We cannot say that bureaucrats are petty tyrants just because
bureaucrats are meddlesome and petty tyrants are meddlesome.
It is quite possible that gin-sodden drunks are meddlesome too,
but that does not mean that bureaucrats are gin-sodden drunks.
(Life might be more interesting if they were.) This fallacy com-
monly appears in the form of 'tarring with the same brush.'
The worst oppressors of the working class are landlords. Jones is a
landlord, so Jones is one of the worst oppressors of the working classes.