Born in Independence, Missouri to Kenneth T. and Evelyn, he was a precocious child.
A pupil of Solomon Feferman at Stanford University, Barwise started his research in infinitary logic. After positions as assistant professor at the Universities of Yale and Wisconsin, during which time his interests turned to natural language, he returned to Stanford in 1983 to direct the Center for the Study of Language and Information. He began teaching at Indiana University in 1990. He was elected a Fellow of the American Academy of Arts and Sciences in 1999.
Barwise contended that, by being explicit about the context in which a proposition is made, the situation, many problems in the application of logic can be eliminated. He sought ... to understand meaning and inference within a general theory of information, one that takes us outside the realm of sentences and relations between sentences of any language, natural or formal. In particular, he claimed that such an approach resolved the liar paradox. He made use of Peter Aczel's non-well-founded set theory in understanding "vicious circles" of reasoning.
Barwise, along with his former colleague at Stanford John Etchemendy, was the author of the popular logic textbook Language, Proof and Logic. Unlike the Handbook which was a survey of the state of the art of Mathematical Logic c. 1975, this work targeted elementary logic. The text is notable for including computer-aided homework problems, some of which provide visual representations of logical problems. During his time at Stanford, he was also the first Director of the Symbolic Systems Program, an interdepartmental degree program focusing on the relationships between cognition, language, logic, and computation. The K. Jon Barwise Award for Distinguished Contributions to the Symbolic Systems Program has been given periodically since 2001.
He was diagnosed with colon cancer in 1999 and throughout the rest of his life made an exhaustive exploration of his condition both through conventional and alternative medicine, and by articulating his own emotional experience. The Ting-sha Institute in Inverness, California played an important part in his journey. He died in 2000 in Bloomington, Indiana. Indiana University School of Informatics has named a fellowship for Master's and doctoral degree students in his honor.
- Barwise, J, (1975) Admissible Sets and Structures. An Approach to Definability Theory ISBN 0-387-07451-1
- Barwise, J, Editor (1977) Handbook of Mathematical Logic. ISBN 0-7204-2285-X
- Barwise, K. J. (1988) The Situation in Logic ISBN 0-937073-32-6
- Barwise, K. J. & Etchemendy, J. (1987) The Liar: An Essay in Truth and Circularity ISBN 0-19-505944-1
- Barwise, K. J. & Moss, L. (1996) Vicious Circles. On the Mathematics of Non-Wellfounded Phenomena ISBN 1-57586-008-2
- Barwise, K. J. & Perry, John (1983) Situations and Attitudes. Cambridge: MIT Press. ISBN 1-57586-193-3
- Barwise, K, J. & Seligman, J. (1997) Information Flow: the Logic of Distributed Systems ISBN 0-521-58386-1
- Barwise, K. J. & Etchemendy, J. (2002) Language, Proof and Logic ISBN 1-57586-374-X
See also 
- In Memoriam: Kenneth Jon Barwise by Solomon Feferman The Bulletin of Symbolic Logic vol. 6(4) Dec. 2000, pp505–8 (PostScript)
- K. Jon (Kenneth) Barwise at the Mathematics Genealogy Project