Communication and Strong Compositionality

1. Cognitive and epistemic asymmetry Suppose that you are given the task of translating ten words from English to Swedish. You know English and you don’t know Swedish, but you have an English-Swedish dictionary. Given the dictionary, you easily accomplish what was asked for. But then you are given a more difficult task. You are now to translate ten new words from Swedish to English, say ‘låtsas’, ‘dimma’, ‘ofog’, ‘färdig’, ‘dumheter’, ‘glömska’, ‘om’, ‘springa’, ‘tryck’, and ‘tillbringare’. The reason this is more difficult is that you have to do it with the same tool as last time, the English-Swedish dictionary. The dictionary contains all translation pairs you need, but they are listed alphabetically according to the English members of the pairs. So you know where to find any English word in the list, but you don’t know where to find the Swedish words (unless you already know the translation, which you don’t). So in order to find the translation of ‘ofog’ you simply have to search through the dictionary, in whatever order you prefer, until you happen to find the word. You don’t know how long it will take. Because of this, the dictionary translation method is cognitively asymmetric. It defines a relation between the Swedish and English vocabularies, but it provides an efficient (e.g. as measured by average time needed) method only for one direction, not for the other. The hypothesis that a bilingual speaker’s translation capacity is subserved by a mental English-Swedish dictionary can explain the speaker’s ability of English-Swedish translation, but it cannot explain his ability of Swedish-English translation. We can make things worse by two changes to this scenario. Suppose, first, that the list of words is infinite1, and, second, that the strings of letters you are served need not be part of the vocabulary. In the English-to-Swedish task the increase in difficulty is not great. Given an arbitrary string of letters you know where to find it: if there is no such string at the determined position, it isn’t a word in the English vocabulary. Hence, you have a decision method for determining wordhood, and what the translation is, if the word exists. By contrast, in the Swedish-to-English task, where you don’t know where in the list to find the string, you only know that if there is a word, and you search systematically, you will sooner or later find it, even though not when. If the string (e.g. ‘bab’)