 Anderson and Zalta prove then that \(\top\) and \(\bot\) are indeed truth values and, moreover, that there are exactly two such objects. The latter result is expected, if one bears in mind that what the definitions above actually introduce are the classical truth values (as the underlying logic is classical). Indeed, \(p\leftrightarrow q\) is classically equivalent to \((p\wedge q)\vee(\neg p\wedge \neg q)\), and \(\neg(p\leftrightarrow q)\) is classically equivalent to \((p\wedge \neg q)\vee(\neg p\wedge q)\). That is, the connective of material equivalence divides sentences into two distinct collections. Due to the law of excluded middle these collections are exhaustive, and by virtue of the law of non-contradiction they are exclusive. Thus, we get exactly two equivalence classes of sentences, each being a hypostatized representative of one of two classical truth values.