The project developed a full-fledged theory of rejection, expanding and modifying extant models of conversation to take into account the fact that speakers not only assert or accept what is being asserted but often reject. Paying close attention to the linguistic phenomena, we identified and studied weak, moderate and strong forms of assertion and rejection. We then used these weak, moderate and strong forms of assertion and rejection to develop what we call a ‘multilateral logic framework’, a logical framework which has the resources to handle not only assertion (like standard logical systems) but also other speech acts. The mathematical properties of this framework were extensively studied and extensions of the framework involving speech acts other than strong, moderate and weak forms of assertion and rejection were developed.
The project used the theories and logics developed to establish a novel approach to natural language semantics, inferential expressivism, which explains the meaning of an expression in terms of the inferences we draw involving the attitudes we express. This approach combines elements of the expressivist and inferentialist programmes in semantics. We showed that inferential expressivism has the resources to address the main challenges faced by expressivism and inferentialism respectively, in particular the so-called Frege-Geach Problem and the problem of limited applicability. Moreover, we demonstrated the fruitfulness of the inferential expressivist approach by applying it to a wide range of linguistic phenomena including negation, epistemic modals (e.g. expressions such as `might’ in `Elizabeth Warren might win the Democratic primaries’), moral vocabulary (e.g. expressions such as `wrong’), vague expressions (such as `red'), semantic vocabulary (such as 'true'), conditionals and probabilistic operators (e.g. expressions such as 'It is unlikely that Jorgensen will win the presidential elections').
In the context of language evolution, we used game theory and computational techniques to show that the presence of rejection explains the emergence of negation (whose presence is effectively universal in human languages). One key result in this part of the project is the development of a new model of linguistic interactions which we call the Rejection Game.
The interplay between philosophical and linguistic analysis, logical methods and computational techniques proved particularly fruitful. The output of the work includes numerous articles in top logic (Journal of Philosophical Logic, Review of Symbolic Logic), linguistics (Semantics and Pragmatics, Linguistics and Philosophy) and philosophy (Mind, Journal of Philosophy, Philosophical Quarterly, British Journal for the Philosophy of Science, Erkenntnis) journals and a monograph (Oxford University Press). Several events were organized, including a weekly reading group, a seminar with invited speakers, three international workshops and a three-day conference. The project's findings were also advertised on social media, magazines and blogs.
