

Philosophy 103: Introduction to Logic
Fallacy of the Undistributed Middle Term
Abstract: The Fallacy of the
Undistributed Middle Term is discussed and illustrated.
I. We continue our study of the syllogistic fallacies with a second common fallacy. 

A. Note, how in the following argument, about the
only persons likely to be sympathetic are those who dislike Senator Jones. (Notice
that singular statements are treated as universal affirmative propositions.) 


All [Communists] are [believers
in heavy taxes].
[Senator Jones] is a [believer in heavy taxes].
[Senator Jones] is a [Communist]. 


The Venn Diagram would be sketched like this: 


B. It is fairly evident that for the conclusion
to follow logically, one would have to presuppose instead that "All believers in
heavy taxes are Communists," not "All Communists are believers in heavy
taxes." Notice that the former statement would distribute
the term "believers in heavy taxes." But this distribution is not what is
asserted in the original argument. In the original argument, the middle term is
undistributed in both premisses. 

C. Fallacy of the
Undistributed Middle Term occurs when the middle term is undistributed in both
premisses. 


1. Rule: In a valid standard form
categorical syllogism, the middle term must be distributed in at least one premiss. 


2. Reason: for the two terms of the conclusion to be
connected through the third, as in the mechanism sketched below, at least one of them must
be related to the whole of the class designated by the middle term. Otherwise, the
connection might be with different parts of the middle term, as illustrated below, and no
connection can be made. 



3. Note: Remember for the
Fallacy of the Undistributed Middle Term to occur, the middle term must be undistributed
in both premisses, not just one premiss. 

