Consider:
No cat is a fish.
All cats are animals.
The premises do not establish either “All fish are animals” or “No fish are animals.” There is no affirmative link placing any fish under the middle term cat and thus within the major premise.
The error is to treat a shared subject as if it supplied an instance of the minor predicate. The first premise excludes fish from cats; it does not provide fish to which the second premise may be applied.
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The Third Figure: Conditions and Six Productive Moods
Consider:
No cat is a fish.
All cats are animals.
The premises do not establish either “All fish are animals” or “No fish are animals.” There is no affirmative link placing any fish under the middle term cat and thus within the major premise.
The error is to treat a shared subject as if it supplied an instance of the minor predicate. The first premise excludes fish from cats; it does not provide fish to which the second premise may be applied.