 We have the same set of contradictions we derived earlier in “Frege’s puzzle.” Because both (31) and (33) are true of Pierre at the same time and they appear to involve attribution to Pierre of belief in a proposition and its negation, it would seem that Pierre is irrational. Intuitively Pierre is free of irrationality in his beliefs. (31) and (35) seem to be, themselves, mutually inconsistent. Yet we derived them using the same basic principles driving Frege’s puzzle. Because we nowhere employed the thesis of direct reference nor a substitution principle seemingly entailed by the thesis of direct reference, Kripke concludes that simply denying the thesis of direct reference is not sufficient for solving the original Frege puzzle. After all, we get the very same set of problems without that thesis.