Due to the analogy between categorical syllogisms and mereological inferences, fallacies of distribution have mereological analogues.
Undistributed Middle
Categorical Syllogism:
All C is B
All A is B
Therefore All A is C.
Mereological Syllogism:
C is part of B
A is part of B
Therefore A is part of C.
Illicit Process of Major
Categorical Syllogism:
All C is B
No A is C
Therefore No A is B.
Mereological Syllogism:
C is part of B
A does not overlap C
Therefore A is not part of B.
Illicit Process of Minor
Categorical Syllogism:
All A is B
All A is C
Therefore All B is C.
Mereological Syllogism:
A is part of B
A is part of C
Therefore B is part of C.
The matter, of course, is quite general. For mereological propositions in the form 'A is part of B', A is distributed and B is undistributed; for the form 'A overlaps B', both are undistributed; in the form 'A is not part of B', both are distributed; in the form 'A does not overlap B', A is undistributed and B is distributed. In mereological syllogisms, the same rules for distribution apply: middle terms must be distributed, and what is distributed in the conclusion must be distributed in the premises.
None of this is particularly surprising, since historically the mereological syllogisms seem to have come first, and the concept of distribution for categorical syllogisms seems to derive from thinking about mereological syllogisms. But sometimes it's worthwhile to think about things explicitly.
