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He began his career as a hardware merchant. In 1779, he was clerk of the Court of Quarter Sessions in Philadelphia, and a member of the Pennsylvania Constitutional Convention of 1787. Baker was elected alderman from 1789 to 1796, and elected mayor in 1796. He was re-elected in 1797, but died in the 1798 yellow fever outbreak in Philadelphia, where he was buried in Laurel Hill Cemetery.
- Casstevens, Frances H. (Oct 31, 2006). Tales from the North and the South: Twenty-Four Remarkable People and Events of the Civil War. McFarland. ISBN 978-0-7864-2870-0. Retrieved 18 April 2019.