Logical connectives are one of the building blocks of human formal thought along with number and geometry. 170 years ago the British logician Boole formulated Boolean logic, arguing that ‘or’ corresponds to the ‘|’ operator and that ‘and’ corresponds to the ‘&’ operator. Boolean logic is ubiquitous in math, computer science and other fields, even though Boole’s goal was never to provide evidence that and and or really are primitives of thought. Much of the later formal linguistic work has been biased by virtue of being studied from a Eurocentric perspective, where the mapping between natural language and logic is deceptively straightforward. Yet there are reasons to question the Boolean picture. For example, Boolean laws tell us that once we have negation in the system we only need one of the two connectives to derive the other, so we might expect only conjunction, or only disjunction, to be a primitive, and yet that has not been borne out in the well-studied languages of Europe.
Moving away from the Indo-European languages, to date, no in-depth cross-linguistic study has been conducted that not only documents all the different ways a single language may express coordination, but also describes the differences among these constructions with respect to their semantic and morphosyntactic distribution. One would expect that it should be pretty trivial to detect how a language expresses concepts as basic as and and or, yet there are languages that lack conjunction altogether, i.e. they have no single morpheme that can be reliably translated as and across all contexts. Such languages, as it turns out, recycle disjunction to express conjunctive meanings (e.g. Warlpiri, American Sign Language). On the flip side, there are languages where expressing disjunction involves an appeal to what is otherwise used to express conjunction in that language (e.g. Cheyenne where disjunction is built off of the conjunctive element).
This project constitutes the first serious contribution to this formal study of the matches and mismatches between natural language and Boolean logic, as it is underpinned by a strong cross-linguistic investigation. The develop- ment of frameworks that enable us to conceptualize the strategies for forming conjunctive and disjunctive meanings and the dimensions along which such strategies may vary is fairly recent, making this project well timed. The three main ways we will proceed with this investigation are the following: (i) interaction between connectives and negation and identifying mismatches between the predicted interpretation of the Boolean connective and the actual natural language interpretation, (ii) the function of complex connectives as opposed to simplex connectives, and (iii) the extent of the poly-functionality of connectives.
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