 This second strategy might itself be developed in two distinct ways, in an effort to show its compatibility with the broad sweep of Lewis’s theory. First, it could be admitted that there is no prior L with respect to which the conventions of truthfulness and trust both hold. The conventions hold, however, with respect to their passing theories. Participants arrive at these passing theories from their (potentially divergent) prior theories plus some general intelligence. Compositionality, moreover, also plays an essential role in the extraction of passing theories from prior theories, with the conventions of truthfulness and trust being observed in the resulting passing L. However, the principle of compositionality would have to be weakened so as to not consider the strictly linguistic process it describes as fully determining meaning, thus leaving room for extra elements to take part. Alternatively, there could be truthfulness and trust in prior L if Lewis’s fine-grained individuation of languages is rejected. On this second version of the theory, one and the same L may sometimes have different sentence-to-meaning mappings; alternatively, it could be claimed that the conventions hold with respect to different common Ls or a set of sufficiently similar such languages.