How to Win Every Argument: The Use and Abuse of Logic (2006)

134 How to Win Every Argument

instead four separate terms, we cannot validly draw the con-

clusion, and the quaternio terminorum is committed.

John is to the right of Peter, and Peter is to the right of Paul, so John is to

the right of Paul.

(This looks reasonable, but one line has 'to the right of Peter' where

the other one simply has 'Peter'. These are two separate terms, and

the four-terms fallacy is involved. The conclusion is not validly

established. After all, they could be sitting round a table.)

We might just as easily have said:

John is in awe of Peter, and Peter is in awe of Paul, so John is in awe of

Paul.

(The error is more obvious. John might respect Peter for his intellect,

and Peter could respect Paul for his Mercedes. Since John has a

Bentley, he might not transfer his awe from Peter to the other cheap

upstart.)

The fallacy arises because, strictly speaking, the terms in this
type of argument are separated by the verb 'to be'. Whatever
comes after it is the term. It can be 'the father of, or 'in debt to',
or many other things. Unless the whole term appears in the next
line, there is a quaternio terminorum. Of course, with four terms
we cannot deduce new relationships between terms by using a
middle term common to both - there isn't one.

John is the father of Peter, and Peter is the father of Paul, so John is the

father of Paul.

(Even your grandfather can see this is wrong.)

Now look at the example where there is a middle term repeated: