Non distributio medii

Logical fallacy that occurs in categorical syllogisms when the middle term (the term that appears in both premises) is not distributed, meaning it does not refer to all members of the category it describes. This fallacy leads to incorrect conclusions because the shared term does not adequately link the two premises.

In syllogistic reasoning, a valid argument must distribute the middle term at least once, meaning it must refer to all members of the category it represents in at least one premise. When the middle term is not distributed, it creates a logical gap, leading to a faulty conclusion. The fallacy of the undistributed middle occurs because the premises share a common term, but that term does not establish a proper link between the premises, resulting in an invalid inference.

Recognizing this fallacy is crucial for evaluating the validity of categorical arguments and ensuring that conclusions are logically sound and properly supported by the premises.

Examples:

Animals:
Premise 1: All cats are animals.
Premise 2: All dogs are animals.
Conclusion: Therefore, all dogs are cats.
This conclusion is incorrect because the middle term "animals" is not distributed; it does not refer to all animals in the premises.

People and Attributes:
Premise 1: All fools act stupid.
Premise 2: You acted stupid.
Conclusion: Therefore you are a fool.
Again, this conclusion is fallacious because the middle term "stupid" does not connect the premises correctly.

Food Preferences:
Premise 1: All elephants are big
Premise 2: Some boys are big.
Conclusion: Therefore some boys are elephants.
This conclusion is incorrect because the middle term "big" is not distributed; it does not refer to all big things in the premises.