into the formal fallacy of THE UNDISTRIBUTED MIDDLE TERM. So, in the example:
- All rich people are taxable. ~
taxable 2. Some taxable people are poor; ~
people :: Al rich people are poor. x the middle term “taxable’ is undistributed since it does not in either instance encompass the total field of all taxable entities. Syllogisms with undistributed middles do not prove anything:
- Some violent anarchists are animal lovers. v 2. All cat lovers are animal lovers. .. Al cat lovers are violent anarchists x
A good way to differentiate between syllogisms is to draw a logical diagram. In many cases a simple glance can quickly expose a fallacy.
Above, and facing page: Euler diagrams are a quick way to see what’s going on
in a logical situation.
Left: A logical Venn diagram.
Statements are drawn as a pair of overlapping circles with empty areas dark and known nonempty areas lightly shaded. Statements are then combined to form the conclusion.
The syllogism illustrated is:
- All cats have fur. 2. Some pets are cats. :: Some pets have fur.