 Quine suggested, in effect, that we tentatively suppose that \(\phi \equiv \phi^+\) for all \(\phi\) ; it is not just the case that if we can prove \(\phi\), we can prove \(\phi^+\), but that the truth values of these sentences are the same. It then becomes strongly tempting to identify \(\{x^n \mid \phi \}^{n+1}\) with \(\{x^{n+1} \mid \phi^{+}\}^{n+2}\), since anything we can say about these two objects is the same (and our new assumption implies that we will assign the same truth values to corresponding assertions about these two objects).