Undistributed Middle

The second rule of validity that relates to the distribution of terms is this:

A valid syllogism must distribute the middle term in at least one premise.

This syllogism, for example, breaks this rule:

All women are humans.
All men are humans.
∴ All men are women.

In the above syllogism, the middle term is “humans.” It is not distributed in either premise. That means that each premise makes a claim about only some humans rather than all humans. The problem with this is that the humans that are women is a different group than the humans that are men (Bruce/Caitlyn Jenner notwithstanding). When the middle term is undistributed in both premises, then there is no necessary connection made. But it is the middle term that connects the premises so that a conclusion can be drawn.

This is a valid syllogism:

All humans are mammals.
All women are humans.
∴ All women are mammals.

In this case, the middle term “humans” is distributed in the major premise. That means that the major premise refers to all humans, saying that all of them are mammals. Then when the minor premise says that all women are humans, then women must be connected to mammals, since all humans, including the women, are connected to mammals.

In other words, when the middle term is distributed in one premise, then that middle term will include or encompass the middle term in the other premise. This connects the premises together, allowing a conclusion to be drawn.

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