  Mathematical proof aims to deliver confident conclusions, but a very similar
process of deduction can be used to make uncertain estimates that are open to
revision. A key ingredient in such reasoning is the use of a "default" estimate
of $\mathbb{E}[XY] = \mathbb{E}[X] \mathbb{E}[Y]$ in the absence of any
specific information about the correlation between $X$ and $Y$, which we call
*the presumption of independence*. Reasoning based on this heuristic is
commonplace, intuitively compelling, and often quite successful -- but
completely informal.
  In this paper we introduce the concept of a heuristic estimator as a
potential formalization of this type of defeasible reasoning. We introduce a
set of intuitively desirable coherence properties for heuristic estimators that
are not satisfied by any existing candidates. Then we present our main open
problem: is there a heuristic estimator that formalizes intuitively valid
applications of the presumption of independence without also accepting spurious
arguments?
