Born: October 18, 1822, Framingham, Massachusetts.
Died: December 2, 1914, at the home of his son, poet Harlan Hoge Ballard.
Buried: Pittsfield Cemetery, Pittsfield, Massachusetts.
Addison was son of John and Pamelia Bennett Ballard Addison, and husband of Julia Perkins Pratt.
He was educated at Williams College (BA 1842, DD 1867). He was a tutor at Williams (1843–44), and taught in Grand Rapids, Michigan (1845–46), and Hadley, Massachusetts.
He was ordained a Congregational minister in 1846, taught Latin (1848–52) and mathematics (1852–54) at Ohio University; was a professor of rhetoric at Williams (1854–55); and professor of logic at New York University (1893–1904).
On the Sunday morning of his 92nd birthday, he preached at the First Church of Christ in Pittsfield, Massachusetts.