The Fallacy of the Undistributed Middle

The fallacy of the undistributed middle is a formal logical fallacy. It occurs when the middle term in a categorical syllogism isn't distributed in either the major premise or the minor premise. It makes an erroneous connection between two categories that are separately linked to a common category but don't necessarily relate to each other.

In simpler terms, it's when we mistakenly assume that because two things share a common property, they must be related or equivalent in some significant way.

The general structure of the fallacy is:

1. All A are B.

2. All C are B.

3. Therefore, all A are C.

Example:

1. All dogs are animals.

2. All cats are animals.

3. Therefore, all dogs are cats.

The conclusion doesn't follow from the premises. Just because dogs and cats art mean all dogs are ca’all dogs are cats.