Meredith Williams thinks that what she calls the 'background Understanding' in later Wittgenstein can be used to refute W. V. Quine's theses of the indeterminacies of translation and reference. For this she first points out that the so-called basic judgments of sameness, unlike other judgments, are not interpretable, hence not subject to Quine's indeterminacies. She also thinks that the background understanding can help us single out from among other alternatives what our words really refer to. In this paper we will argue that the basic judgments of sameness, due to their sharing of words with other judgments, are subject to interpretation, hence to Quine's indeterminacies. We will also point out that the background understanding can in no way privilege a certain ontology as the actual or intended ontology of our language. So, contrary to what Williams would want us to believe, there is no direct route from the background understanding to a refutation of Quine's indeterminacy theses.