Fallacy of the undistributed middle


 
Name of fallacy Fallacy of the undistributed middle
Aliases  
Type Deductive Argument, Formal Argument
Description The middle term in a categorical syllogism is not distributed.
Example 1. All students carry backpacks.
2. My grandfather carries a backpack.
3. Therefore, my grandfather is a student.

The two premises are link by "carryinh a backpack". The middle term is the one that appears in both premises — in this case, it is the class of backpack carriers. It is undistributed because neither of its uses applies to all backpack carriers. Therefore it can't be used to connect students and my grandfather — both of them could be separate and unconnected divisions of the class of backpack carriers. Note below how "carries a backpack" is truly undistributed:

grandfather is someone who carries a backpack; student is someone who carries a backpack
Form 
Treatment This is an error in formal logic and can be delat with by showing the error as per the example above.

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