The most common form of this fallacy is what logicians call the
‘undistributed middle’, which refers to the traditional syllogism
consisting of a premise, a middle term and a conclusion.
A valid syllogism takes the following form:
Premise : All cows are quadrupeds.
Middle term : All quadrupeds are vertebrates.
Conclusion : Therefore, all cows are vertebrates.This may be represented as:
Premise : All A is B.
Middle term : All B is C.
Conclusion : Therefore, all A is C.This is logical. The middle term is fully distributed. Everything
that applies to A also applies to B, everything that applies to B
also applies to C, therefore everything that applies to A must
apply to C.
An invalid syllogism would take the following form:
All cows are quadrupeds.
All mules are quadrupeds.
Therefore, all cows are mules.This may be represented as:
All A is B.
All C is B.
Therefore, all A is C.This is false because, although everything that applies to A and C
also applies to B, there is nothing in their relationship to B which
connects A and C together.
The difference between the true and false syllogism may be
illustrated in Figure 48.1.
In the false syllogism, A and C could be quite distinct although
still contained within B. To link them together goes beyond the
original evidence. Because two things A and B are related to
another thing, C, it does not necessarilymean that they are related
together. In forming arguments, we too often jump to the conclu-
sion that some means all.
298 How to be an Even Better Manager