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Undistributed Middle Fallacy

Updated Apr 1, 2023

Understanding the Undistributed Middle Fallacy: A Logical Pitfall to Avoid


Logic plays a fundamental role in our everyday lives, helping us make sound arguments and draw valid conclusions. However, even the most astute logicians can sometimes fall into the trap of committing logical fallacies. One such fallacy that often catches people off guard is the undistributed middle fallacy. In this article, we will explore what the undistributed middle fallacy is, provide examples to illustrate its occurrence, and discuss ways to avoid this common logical pitfall.

What is the Undistributed Middle Fallacy?

The undistributed middle fallacy, also known as the fallacy of the excluded middle or the fallacy of the unshared middle, is an error in deductive reasoning that occurs when a middle term within a syllogism's premises is not distributed (i.e., it does not refer to all members of the class it represents). This fallacy wrongly assumes that two separate terms have something in common based solely on their shared relationship with a third, undistributed term.

Examples of the Undistributed Middle Fallacy

To better understand this fallacy, let's consider a couple of examples:

Example 1:

Premise 1: All cats are animals. Premise 2: All dogs are animals. Conclusion: Therefore, all cats are dogs.

In this syllogism, the undistributed middle fallacy occurs when the term "animals" is not distributed. While both cats and dogs are animals, it does not mean that cats are necessarily dogs. The middle term "animals" is undistributed, leading to an erroneous conclusion.

Example 2:

Premise 1: All pianos are musical instruments. Premise 2: All guitars are musical instruments. Conclusion: Therefore, all pianos are guitars.

Similar to the previous example, this syllogism commits the undistributed middle fallacy. While both pianos and guitars fall under the category of musical instruments, it does not logically follow that all pianos are guitars. Again, the middle term "musical instruments" is undistributed, resulting in an incorrect conclusion.

Avoiding the Undistributed Middle Fallacy

To avoid falling into the trap of the undistributed middle fallacy, it is essential to ensure that the middle term is properly distributed in the premises. Here are some strategies to employ:

  1. Carefully examine the premises: Analyze each premise to ensure that the middle term is distributed. If it is not, then the argument is susceptible to the undistributed middle fallacy.

  2. Use precise language: Avoid vague or ambiguous language that can lead to an undistributed middle. Clearly define the terms and make sure they are applicable to all members of the class they represent.

  3. Check the validity of the conclusion: Double-check the conclusion to see if it logically follows from the premises. If it relies on an undistributed middle term, the argument is invalid.

  4. Study logic: Familiarize yourself with various logical fallacies, including the undistributed middle fallacy. By understanding these fallacies, you can better identify and avoid them in your own arguments.


In the realm of logic, the undistributed middle fallacy serves as a reminder that we must tread carefully when making arguments. By ensuring that the middle term is properly distributed and avoiding the trap of assuming shared qualities between unrelated terms, we can strengthen our reasoning and arrive at more accurate conclusions. So, let's be mindful of this fallacy and strive for logical precision in our everyday discourse.

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