Examples
For example:
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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
Specifically, the structure of this example results in affirming the consequent.
However, if the latter two statements were switched, the syllogism would be valid:
- All students carry backpacks.
- My grandfather is a student.
- Therefore, my grandfather carries a backpack.
In this case, the middle term is the class of students, and the first use clearly refers to 'all students'. It is therefore distributed across the whole of its class, and so can be used to connect the other two terms (backpack carriers, and my grandfather). Again, note below that "student" is distributed:
- grandfather is a student and thus carries a backpack
Read more about this topic: Fallacy Of The Undistributed Middle
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