  We examine recursive monotonic functions on the Lindenbaum algebra of
$\mathsf{EA}$. We prove that no such function sends every consistent $\varphi$
to a sentence with deductive strength strictly between $\varphi$ and
$(\varphi\wedge\mathsf{Con}(\varphi))$. We generalize this result to iterates
of consistency into the effective transfinite. We then prove that for any
recursive monotonic function $f$, if there is an iterate of $\mathsf{Con}$ that
bounds $f$ everywhere, then $f$ must be somewhere equal to an iterate of
$\mathsf{Con}$.
