Kivy earned master's degrees in both philosophy (University of Michigan, 1958) and musicology (Yale University, 1960). He earned his PhD at Columbia University in 1966. He joined the faculty at Rutgers the following year, and became full professor in 1976. He taught there for his whole career except one year as a visiting professor at University of California, Santa Barbara.
His early work was on the 18th-century British aesthetics, and was influenced by Francis Hutcheson. From there he developed an interest in analytic aesthetics. From the late 1970s on, he had been interested mainly in music philosophy. His book The Corded Shell made him a central figure in music aesthetics.
One preoccupation of his had been the problem of what it means for instrumental music to "express" an emotion. His answer is that common emotions have physical behavioral expression in people that can be understood by appearance and imitated in music; thus, music cannot express more complex emotions that do not have an obvious behavioral expression. A similar position is followed by Stephen Davies.
Some criticism of Kivy's ideas is available in Music, Philosophy, and Modernity (2007) by Andrew Bowie and Filosofía de la Música. Respuestas a Peter Kivy (2017, published in Spanish) by James O. Young.
- Speaking of Art (1973).
- Francis Hutcheson's Inquiry Concerning Beauty, Order, Harmony, Design (ed., 1973).
- Thomas Reid's Lectures on the Fine Arts (ed., 1973).
- The Seventh Sense: A Study of Francis Hutcheson's Aesthetics, and its Influence in Eighteenth-Century Britain (1976, 2nd ed. 2003).
- The Corded Shell: Reflections on Musical Expression (1980).
- Sound and Semblance: Reflections on Musical Representation (1984, 2nd ed. 1991).
- Osmin's Rage: Philosophical Reflections on Opera, Drama and Text (1988, 2nd ed.).
- Sound Sentiment: An Essay on Musical Emotions (1989).
- Music Alone: Philosophical Reflections on the Purely Musical Experience (1990).
- Essays on the History of Aesthetics (ed., 1992)
- The Fine Art of Repetition: And Other Essays in the Philosophy of Music (collection, 1993)
- Authenticities: Philosophical Reflections on Musical Performance (1995).
- Philosophies of Arts: An Essay in Differences (1997).
- New Essays on Musical Understanding (collection, 2001)
- The Possessor and the Possessed: Handel, Mozart, Beethoven and Idea of Musical Genius (2001).
- Introduction to a Philosophy of Music (2002).
- The Blackwell Guide to Aesthetics (ed., 2004)
- The Performance of Reading: an Essay in the Philosophy of Literature (2006).
- Music, Language, and Cognition: And Other Essays in the Philosophy of Music, further collected essays of Peter Kivy (collection, 2007).
- Antithetical Arts: On the Ancient Quarrel Between Literature and Music (2009).
- Sounding Off: Eleven Essays in the Philosophy of Music (2012).
- Douglas Dempster. "How Does Debussy's Sea Crash? How Can Jimi's Rocket Red Glare?: Kivy's Account of Representation in Music." Journal of Aesthetics and Art Criticism 52/4 (Autumn 1994): 415-428.
- Kelly Dean Jolly. "(Kivy on) The Form-Content Identity Thesis." British Journal of Aesthetics 48/2 (April 2008): 193-204.