Levinson started his studies in 1965 at the Massachusetts Institute of Technology, where he gained a BS Degree in Philosophy and Chemistry in 1969.
[3] He earned his Ph.D. in philosophy at the University of Michigan in 1974, under the supervision of Jaegwon Kim and Kendall Walton,[4] his dissertation covering the topic of "Properties, Qualities, and Categoriality".
He has also held visiting appointments in other countries, such as England (University of London and University of Kent), New Zealand (University of Canterbury), France (Université de Rennes), Belgium (Université Libre de Bruxelles), Portugal (Universidade de Lisboa) and Switzerland (Conservatorio della Svizzera Italiana).
During 2010-2011 he held an International Francqui Chair [8] at the Katholieke Universiteit Leuven (Belgium), and in 2011 received the Premio Internazionale of the Società Italiana d'Estetica.
In 2003, Levinson co-directed a National Endowment for the Humanities Summer Institute, Art, Mind, and Cognitive Science, and during 2001-2003 was President of the American Society for Aesthetics.