Epistemology and Logic 2 7Reference to the diagrams will show that a term whose
circle is entirely shaded or entirely unshaded is a distributed
term; a term whose circle is partly shaded is an undistributed
term.
In the statement “All cows are females” we are discussing
all cows; cows is a distributed term. But we are not discuss
ing all females— only a few of them, the females that are
also cows; therefore, females is an undistributed term. A
few moments of study with the diagrams as aid will clarify
the matter of distribution of terms.
(h) Fallacy: An error in the form or process of a syllo
gism. The most common fallacies in the categorical syllo
gism are these:
(1) Undistributed middle: The middle term in a categori
cal syllogism must be distributed once— and only once.
Consider:
All x is y.
All z is y.
Therefore ...?
No valid conclusion is possible, since the middle term, y,
is undistributed in both of its appearances; it never refers to
all members of its class. Also consider:
All p is q.
No r is p.
Therefore ...?
Again, no valid conclusion is possible, since the middle
term, p, is distributed both times it appears.
(2) Four terms: Every syllogism must have three terms,
and only three. Consider:
All c is d.
All e is f.
Therefore ...?
No conclusion is possible, since the minor premise is
entirely irrelevant to the major premise.
(3) Two particulars: Every syllogism must have at least
one universal premise. Consider these:
Some Americans are men.
Some girls are Americans.
Therefore ...?
It is invalid to conclude that some girls are men, since girls
may be among the Americans not mentioned in the first