Explainable artificial intelligence (XAI) is an emerging, multidisciplinary field of research that seeks to develop methods and tools for making AI systems more explainable or interpretable. XAI researchers increasingly recognise explainability as a context-, audience- and purpose-sensitive phenomenon, rather than a single well-defined property that can be directly measured and optimised. However, since there is currently no overarching definition of explainability, this poses a risk of miscommunication between the many different researchers within this multidisciplinary space. This is the problem we (...) seek to address in this paper. We outline a framework, called Explanatory Pragmatism, which we argue has two attractive features. First, it allows us to conceptualise explainability in explicitly context-, audience- and purpose-relative terms, while retaining a unified underlying definition of explainability. Second, it makes visible any normative disagreements that may underpin conflicting claims about explainability regarding the purposes for which explanations are sought. Third, it allows us to distinguish several dimensions of AI explainability. We illustrate this framework by applying it to a case study involving a machine learning model for predicting whether patients suffering disorders of consciousness were likely to recover consciousness. (shrink)