 Together, these two theorems say that the Humean thesis (with threshold 1/2) is equivalent to deductive cogency and the weak Lockean thesis (with threshold \(\Pr(\cap\Bel)\)). Since it is always possible to satisfy HT\(^\frac{1}{2}\), Leitgeb gives us an ingenious way to reconcile deductive cogency with a version of the Lockean thesis.