Some quantifiers require two-predicate scopes (Q1090330)

Let \(M^ 2x(Px,Qx)\) mean that the cardinality of the set \(\{\) x: Px\&Qx\(\}\) is greater than that of \(\{\) x: Px\&\(\sim x\}\), and let \(M^ 1xPx=M^ 2x(true,Px)\). The author seems to claim that \(M^ 2\) is not first order definable in terms of \(M^ 1\), but proves only that \(M^ 2x(Px,Qx)\) cannot be expressed as \(M^ 1x(c(Px,Qx))\) for any binary propositional connective c.