Synonymous Logics

Sometimes we have a feeling that two people or groups are \talking past one another." We feel, perhaps, that one is using a certain word A to mean X while the other uses A to mean Y, but this is compensated by the former using B to mean Y while the latter uses B to mean X. But since the people or groups don't recognize this { perhaps they can't recognize this { we see them as \doomed forever to misunderstand one another." Or, perhaps one group (\tribe") uses a certain linguistic construction to convey one type of information while another tribe uses it to convey a di erent type of information. But each tribe has some other way to convey the information which the opposed tribe uses this construction to convey. Again, the two tribes seem doomed to continual misunderstanding. This situation need not be a case where just two words or constructions merely take on the role of one another. There may be many di erent words and constructions involved, and it could even be that there is no one word or construction of the one tribe's use which corresponds to some speci c word or construction of the other tribe's use; it may instead be the cumulative interaction of many di erent words and constructions. In such a case trying to nd a way of expressing one of these words as used by the second tribe back into the language of the rst tribe would itself involve very many circumlocutions. The irony in these cases is that the two tribe can assert the same things, but they just don't realize it because they each mistakenly think the other group is using the words/constructions in the same way as they themselves do. And so they continue to \talk past one another." The preceding discussion should bring to mind Quinean doctrines about \indeterminacy of translation" ([Quine, 1960]), especially the issue of whether there can be distinct translation manuals that are \empirically adequate" but nonetheless incompatible with one another. Examples of such cases are given in [Massey, 1978], where he discusses the possibility (in a rst-order language with no singular terms) that the sets of individuals assigned to the predicates by one translation manual are the complements of the sets assigned by the