He became a naturalized citizen of the United States in 1930, after immigrating to the country in 1923. In 1937, he graduated from the College of St. Thomas. He received a Ph.D. in 1942 from the University of California, Los Angeles. He was assistant professor at New York University from 1940-1945. He then returned to the University of California, Los Angeles as assistant professor for the next four years of his life, and associate professor for three years after that. Kaplan became a professor of philosophy in 1952, and stayed there for twelve years. He was also chair of the department for those twelve years, along with two years past that.
He taught at the University of Michigan from 1962 to 1972 as well. Then in 1978 he moved to teaching at University of Haifa in Israel. Kaplan also taught at Harvard University, California Institute of Technology, California State Polytechnic University, Pomona, and several other schools. He was also president of the American Philosophical Association from 1947 to 1958.
Kaplan was named one of the top ten teachers in the United States in 1966 by Time magazine. He also traveled to India, Israel, and Japan to study their cultures and beliefs.
On November 17, 1939, Abraham Kaplan married Iona Judith Wax, a child psychologist. and they had two children: Karen Eva Kaplan Diskin and Jessica Aryia Kaplan Symonds.