Can you think of a new name for the fallacy of the undistributed middle?

Question

The fallacy itself is very easy to understand, but the term "undistributed middle" is very confusing and eludes understanding.  I think this is part of the reason that the fallacy is encountered so frequently.
Example;
All cats have tails.
Dumbo the elephant has a tail.
Therefore, Dumbo the elephant is a cat.
This is MaP, SaP, SaM.
The "a" proposition it mimics is MaP, SaM, SaP, which goes like this:
All cats have tails.
Felix is a cat.
Therefore Felix has a tail.
The middle term in MaP, SaM, SaP is cat.
A logical fallacy site we googled says that the middle term is the one that does not appear in the conclusion, so in our undistributed middle example, the middle term would be "has a tail".
According to Wikipedia, the middle term is the one that appears in both premises. Perhaps the meaning of "middle" shifts, and in the case of the undistributed middle we are not necessarily speaking of the classic "M" of MaP, SaM, SaP, but of the common term, which is the "P" term, "have tails".
I cannot understand in what sense, in the case of "all cats have tails, Dumbo the elephant has a tail, Dumbo the elephant is a cat", the term "has a tail" is "undistributed". What do you mean, "undistributed"? Can anyone explain in what sense the term is undistributed?
The word root of "distribute" is the Latin "tribus", originally meaning a third of the Roman people. The Latin "distribuere" meant to distribute or divide.  See first response for continuation.

? · Answer

Here is an example from wiki that explains what you are missing.

All students carry backpacks.    My grandfather carries a backpack.    Therefore, my grandfather is a student.       All students carry backpacks.    My grandfather carries a backpack.    Everyone who carries a backpack is a student.    Therefore, my grandfather is a student.

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

Hope this clears things up for you.

Anonymous · Answer

A good new name would be Gladys.

beingagood1 · Answer

According to Webster s,  distribute  may apply to "any manner of separating into parts, and spreading out, equally or systematically, or merely at random."
As near as I can guess, the sense of "distributed middle term" in MaP, SaM, SaP is that "having tails" is evenly distributed among the universe of "cats".
The fallacy -- easy. The name for it -- impossibly abstruse. We need a new name, by which we can teach it such that it will readily be brought to mind.
The "thinking that all must mean all and only fallcy" or something like that.

Can you think of a new name for the fallacy of the undistributed middle?

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