Even though the Geach family is infinite, these logics do not cover the full range of logics with justification counterparts. For instance, the normal modal logic using the axiom scheme \({\square}({\square}X{\rightarrow}X)\), sometimes called shift reflexivity, is not a Geach logic, but it does have a justification counterpart. Add a one-place function symbol \(k\) to the machinery building up justification terms, and adopt the justification axiom scheme \(k(t){:}(t{:}X{\rightarrow}X)\). A Realization Theorem holds; this is shown in Fitting (2014b). We speculate that all logics axiomatized with Sahlquist formulas will have justification counterparts, but this remains a conjecture at this point.