The minor states “Some B are C,” so B instances are explicitly provided. The major excludes every B from A. Those same B instances that are C therefore cannot be A.
Convert the minor:
Some C are B.
No B is A.
Therefore some C are not A.
This is a valid first-figure inference. Unlike the two moods with universal minors, the existence needed for the particular conclusion is already guaranteed by the minor premise.
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The Third Figure: Conditions and Six Productive Moods
The minor states “Some B are C,” so B instances are explicitly provided. The major excludes every B from A. Those same B instances that are C therefore cannot be A.
Convert the minor:
Some C are B.
No B is A.
Therefore some C are not A.
This is a valid first-figure inference. Unlike the two moods with universal minors, the existence needed for the particular conclusion is already guaranteed by the minor premise.