Since 2015, Cappelen has been Professor at the University of Oslo, where he co-directs CSMN's ConceptLab. He is running, with Øystein Linnebo and Camilla Serck-Hanssen, a project on conceptual engineering funded by a Toppforsk award from the Research Council of Norway. Prior to that, he was, since 2007, Professor and Arché chair at the University of St Andrews. He has previously held positions at Somerville College, Oxford, University of Oslo, and Vassar College. He has been the Director of the Arché Philosophical Research Centre and was co-investigator of two research projects funded by longterm AHRC grants: "Contextualism and Relativism" and "Intuitions and Philosophical Methodology". Cappelen was one of the original applicants for the research center Centre for the Study of Mind in Nature at the University of Oslo. Cappelen has been a member of the Norwegian Academy of Science and Letters since 2008.
Work
Cappelen's most influential work is the 2004 book, Insensitive Semantics. The book defends a minimal role for context in semantics and advocates speech act pluralism. It is one of the most cited works in philosophy within the last 10 years. Cappelen has argued that the role of intuition in Western analytic philosophy is overstated. His 2012 book, Philosophy without Intuitions, argues that intuition plays a minor role - or no role at all - in most modern philosophy, and the fear that intuition is widespread has been damaging. His claim that the role of intuitions is overstated is controversial, and has been hotly debated. Along with Josh Dever, Cappelen has argued that the notion of perspective is unimportant for the philosophy of language, thought, and action. Their 2013 book The Inessential Indexical argues that the phenomena which, for example, John Perry and David Lewis think show the importance of indexical representation of the self and time can be accounted for using resources already available in the philosophy of language and thought. Cappelen has also authored, or co-authored, important books on the debate between contextualists and relativists, and on quotation. Some of his papers co-written with Ernie Lepore are collected in Liberating Content. He is currently writing a series of philosophy of language textbooks with Josh Dever, the first of which, Context and Communication was released in 2016. In 2018, his monograph Fixing Language: An Essay On Conceptual Engineering was released. It surveys both historical and contemporary work on conceptual engineering, and presents a theory of its nature and limitations.