Classical Formulation
In classical syllogisms, all statements consist of two terms and are in the form of "A" (all), "E" (none), "I" (some), or "O" (some not). The first term is distributed in A statements; the second is distributed in O statements; both are distributed in E statements; and none are distributed in I statements.
The fallacy of the undistributed middle occurs when the term that links the two premises is never distributed.
In this example, distribution is marked in boldface:
- All Zs are Bs
- (All) y is a B
- Therefore
- (All) y is a Z
B is the common term between the two premises (the middle term) but is never distributed, so this syllogism is invalid.
Also, a related rule of logic is that anything distributed in the conclusion must be distributed in at least one premise.
- All Zs are Bs
- Some Ys are Zs
- Therefore
- All Ys are Bs
The middle term - Z - is distributed, but Y is distributed in the conclusion and not in any premise, so this syllogism is invalid.
Read more about this topic: Fallacy Of The Undistributed Middle
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