 Classical predicate logic has the desirable feature that co-extensive open formulas may be substituted for one another in any formula salva veritate—i.e., without changing that formula’s truth value. (Open formulas \(A\) and \(B\) in \(n\) free variables \(x_1 ,\ldots ,x_n\) are coextensive if and only if \(\forall x_1 \ldots \forall x_n (A \leftrightarrow B)\) is true.) But, as Lambert noted in 1974, this principle fails for nearly all free logics with identity. Consider, for example, the formula \(t=t\), where \(t\) is empty, which is an instance of the open formula \(x=x\). Now \(x=x\) is coextensive with both \((x=x \amp \rE!x)\) and \((\rE!x \rightarrow x=x)\), since all three formulas are satisfied by all members of \(\bD\). Hence if co-extensive open formulas could be exchanged salva veritate, \((t=t \amp \rE!t)\) and \((\rE!t \rightarrow t=t)\) would have the same truth value as \(t=t\). But on nearly all free logics this is not the case. Positive free logic and the supervaluations described in  Section 3.4  make \(t=t\) true and \((t=t \amp \rE!t)\) false; negative free logic makes \(t=t\) false and \((\rE!t \rightarrow t=t)\) true; and any ordinary neutral free logic whose conditionals are true whenever their antecedents are false makes \(t=t\) truth-valueless and \((\rE!t \rightarrow t=t)\) true. Many find this troubling because, since Frege, it has been widely held that (1) extensions of complex linguistic expressions should be functions of the extensions of their components (so that co-extensive components should be exchangeable without affecting the extension of the whole) and (2) the extension of a formula (or statement) is a truth value.