§ 579. Hence in applying these axioms it is necessary to bear in mind the rules for the distinction of terms. Thus from
All B is A,
No C is B,
the only inference which can be drawn is that Some A is not C (which alters the figure from the first to the fourth). For it was only part of A which was known to agree with B. On the theory of the quantified predicate we could draw the inference No C is some A.
§ 580. It is of course possible for terms to agree with different parts of the same third term, and yet to have no connection with one another. Thus
All birds fly.
All bats fly.
But we do not infer therefrom that bats are birds or vice versâ.
§ 581. On the other hand, had we said,—
All birds lay eggs,
No bats lay eggs,
we might confidently have drawn the conclusion
No bats are birds