Logical connectives in natural language: a cultural evolutionary approach
van Wijk, Maarten
This thesis attempts to explain the particular selection of the 16 logically possible truth-functional connectives that is found in human language. Only a few of these connectives, such as (AND) and (OR) are expressed using single-morpheme lexicalisations in natural language. Others, such as (NAND) and (IFF) are expressed compositionally, by combining words for other connectives or adding extra phrases specific to language. Various kinds of explanations have been put forward for this observation. Mentalist-cognitive explanations appeal to properties and limitations of the logical reasoning mechanisms of human minds. On the other hand, communicative explanations state that connectives differ in the extent to which they can be pragmatically appropriate or communicatively useful. None of the previous accounts fully answers the research question. Some of the accounts are functionalistic: they propose a cause for language’s particular set of connectives and stop there. What these accounts fail to provide is a clear mechanism that links the proposed causes to language form. The evolutionary accounts propose that cultural evolution be that mechanism. However, these accounts use a representation of language structure that is too impoverished to answer the research question. What is needed is a model of cultural evolution that addresses language surface structure in sufficient detail. Such an approach is the Iterated Learning Model of the emergence of compositionality by Kirby. This model demonstrates how, as a consequence of the transmission of language across generations of learners, frequent meanings evolve to be represented as irregular holistic phrases, whereas infrequent meanings get compositional representations. The main part of this thesis is devoted to applying this model to the problem of the connectives. Two routes to a frequency distribution of connectives were pursued. The mentalist-cognitive approach remained unsubstantiated as psychological theories of reasoning difficulty were shown to make false predictions about which connectives should be present in language and also unable to provide frequency data in general. More fruitfully, a communicative approach was pursued using a simplified model of human communication. This model consisted of agents aiming to discriminate sets of topic objects from background objects. For this purpose the agents used descriptions involving perceptual properties of the objects, conjoined by the connectives. An exploratory analysis was done of the variables influencing the frequencies of the connectives in this simulation. Analysis of the simulation results revealed a hierarchy among the 16 connectives with respect to a property of specificity, familiar from Gricean pragmatics. It was shown that in a number of situations that are, within the limited bounds of the reality of the simulation, the ones most reminiscent of human communicative situations, (AND) and (OR) are the connectives most frequently used by the agents, because they are the ones that conform best to Grice’s Maxim of Quantity. More research is needed on the external validity of the communication model used, however. A concrete application of Kirby’s model proved a bridge too far, as the model simulates the emergence of a different kind of combinatoriality than is found with connectives. Changes need to be made to the learning mechanisms implemented in this model in order to apply it to the case at hand. Despite the lack of the desired conformation by a computer simulation, connective frequency looks like a strong candidate for an explanation of language’s set of single-morpheme logical connectives. In particular, Zipf’s principle of least effort is likely to favour a system in which the most frequently needed connectives are realised as single morphemes from which all others are derived. The communication simulation in this thesis suggests that those most frequent connectives may well be (AND) and (OR) or (XOR), because of their usefulness in the communicative situations that humans tend to find themselves in.