Donald Davidson used triangulation to do everything from explicate psychological and semantic externalism, to attack relativism and skepticism, to propose conditions necessary for thought and talk. At one point Davidson tried to bring order to these remarks by identifying three kinds of triangulation, each operative in a different situation. Here I take seriously Davidson’s talk of triangular situations and extend it. I start by describing Davidson’s situations. Next I establish the surprising result that considerations from one situation entail the possibility (...) that at any one time one language is partially untranslatable into another. Because the possibility is time-indexed, it need not conflict with Davidson’s own argument against the possibility of untranslatability. I derive the result, not to indict Davidson, but to propose a new kind of triangulation, the reconciliation of untranslatability, which I investigate. Insofar as triangulation is central to Davidson’s views, getting a handle on his various triangular situations is key to getting a handle on his contributions to philosophy. Insofar as those contributions have enriched our understanding of how language, thought, and reality interrelate, extending Davidson’s model promises to extend our understanding too. (shrink)