|Abstract||The Barcan formula made its ﬁrst appearance in  as ♦(∃x)Φ 3 (∃x)♦Φ, in the logic S2. This logic, S2, despite interesting properties, is not much seen these days, and the Barcan formula itself has been simpliﬁed to ♦(∃x)Φ ⊃ (∃x)♦Φ. The paper  was one of the earliest serious investigations of ﬁrst-order modal logic and, of necessity, it was axiomatic since a ﬁrst-order modal semantics was still some years away. In the system as formulated, the converse of the Barcan formula was provable, but the Barcan formula itself was not. Consequently the Barcan formula was added as an axiom schema because it enabled an interesting development that otherwise seemed impossible.|
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