Born in Chicago, Illinois, Kalish earned his bachelor's and master's degrees in psychology and his doctorate in philosophy at the University of California, Berkeley.

As chairman of the philosophy department of UCLA, Kalish hired Marxist political activist Angela Davis, an act that drew considerable controversy at the time.

He is known for his leadership role with the Peace Action Council in a 1967 protest against President Lyndon Johnson's Vietnam policies at the Century Plaza Hotel in Los Angeles, which brought out 10,000 people.

In 1967, Kalish signed a letter declaring his intention to refuse to pay taxes in protest against the U.S. war against Vietnam, and urging other people to also take this stand.

He regularly gave his students his home phone number with the instruction that if they ever wanted to discuss an assignment, to call him anytime, day or night.