Leonardowerkstatt

191 Syllogisms 2

into the formal fallacy of THE UNDISTRIBUTED MIDDLE TERM. So, in the example:

rich

poor

people

  1. All rich people are taxable. ~

taxable 2. Some taxable people are poor; ~

people

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:

  1. Some violent anarchists are animal lovers. v 2. All cat lovers are animal lovers. .. Al cat lovers are violent anarchists x

animal Lovers

cat lovers

violent anarchists

A good way to differentiate between syllogisms is to draw a logical diagram. In many cases a simple glance can quickly expose a fallacy.

Cats

Cats

Above, and facing page: Euler diagrams are a quick way to see what’s going on

in a logical situation.

Fur

Pets

Gats

Fur

Pets

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:

  1. All cats have fur. 2. Some pets are cats. :: Some pets have fur.

Fur

Pets

LOGIC

191