How we change what others think, feel, believe and do

# Undistributed Middle

Disciplines Argument > Fallacies > Undistributed Middle

## Description

All A is B. All C is B. Therefore all C is A.

B is assumed to cover all items in its category.

## Example

All Californians are beautiful. All women are beautiful. Therefore all women are Californian.

All fools act stupid. You acted stupid. Therefore you are a fool.

All elephants are big. Some boys are big. Therefore some boys are elephants.

## Discussion

The problem here is that the middle term (that connects the first two statements) is assumed to refer to the same thing -- typically all of the members in its category, yet this is seldom true. Thus, in the first example above, neither all Californians nor all women cover all of the beautiful people in the world (some British men are beautiful).

In effect, the 'reasonable' assumption is that the first two statements are of the form A=B and C=B, from which the mathematically sound conclusion is that C=A. Unfortunately, syllogisms deal with sets, not mathematical variables.

And the big
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