  Call a formula valid if it is true at every state of every first order model with respect to every first-order valuation, as defined above. Among the validities are the usual modal candidates, such as \(\Box (X \supset Y) \supset (\Box X \supset \Box Y)\), and the usual quantificational candidates, such as \(\forall xX \supset \exists xX\). We also have mixed cases such as the Barcan and converse Barcan formulas: \(\forall x\Box X \equiv \Box \forall xX\), which are characteristic of constant domain models, as was shown in Kripke 1963. Because of the way equality is treated, we have the validity of both \(\forall x\forall y(x = y \supset \Box x = y)\) and \(\forall x\forall y(x \ne y \supset \Box x \ne y)\). Much has been made about the identity of the number of the planets and 9 (Quine 1963), or the identity of the morning star and the evening star (Frege 1892), and how these identities might behave in modal contexts. But that is not really a relevant issue here. Phrases like “the morning star” have an intensional aspect, and the semantics outlined so far does not take intensional issues into account. As a matter of fact, the morning star and the evening star are the same object and, as Gertrude Stein might have said, “an object is an object is an object.” The necessary identity of a thing and itself should not come as a surprise. Intensional issues will be dealt with shortly.