Understanding logical connectives : a comparative study of language influence
Operators called 'logical connectives' convey in a precise way the logical relationships between truth functional propositions and hence determine what can be inferred from them. Mathematical reasoning therefore relies heavily on their use. Whilst the operators are free of ambiguity, this is not so for the linguistic items (called 'linguistic connectives') by which they are codified. In English, at least, there is a widely reported mismatch between the logical concepts and the 'meanings' of the linguistic connectives with which they are frequently identified. This study compares the provision for expressing logical concepts in Japanese, Arabic and English and seeks to ascertain to what extent the problems reported for English are generalisable to the other two languages. It also aims to establish whether the concepts underlying certain logical connectives are 'more readily available' or 'better established' in the speakers of one or other of these languages and, if so, whether this can be attributed to differing provision in the lexicon. Two experiments were carried out using as subjects adults who were native speakers of either English, Japanese or Arabic. One was designed to determine to what extent the appropriate linguistic connectives in each of the three languages convey the associated logical concepts. The second compared performance on five concept identification tasks where the concepts tested were conjunction, inclusive and exclusive disjunction, the conditional and biconditional. The results indicated no significant differences between language groups in the understanding of the linguistic expressions of logical connectives. However, the Japanese language group consistently outperformed the other two groups in all five concept identification tasks and also offered descriptions of these concepts which were more succinct and less variable. Possible explanations for the superior performance of the Japanese group are suggested and some implications for the teaching and learning of mathematics proposed.