Dempster, nicknamed Honest George, was a key figure of the Scottish Enlightenment and respected as an "independently minded, incorruptable and moderately radical MP". He dedicated the later years of his life to improving Scottish fishing and agriculture and improving the living conditions of his tenants.
George Dempster was born in 1732 in Dundee, the son of John Dempster 2nd Laird of Dunnichen, a Dundee merchant, and Isabel Ogilvie. George's date of birth is unclear, and has alternatively been given as 8 February or 8 December. He was educated at Dundee Grammar School (c1739–c1748) and possibly also at the small parish school at Leuchars, Fife. On 24 February 1748 he entered the University of St Andrews and studied there until about 1750, when he left without taking a degree and moved on to study law at the University of Edinburgh. He also studied at the Académie Royale in Brussels.
Dempster was admitted to the Faculty of Advocates in 1755; and about the same time became a member of the Select Society, later becoming a director of this pre-eminent literary and intellectual society of the Scottish Enlightenment. In 1762 he joined the Poker Club of Edinburgh, and may have been a co-founder of this influential body,
He, Andrew Erskine, and James Boswell were joint authors and a "triumvirate of wit", although he later regretted at least one of their attacks, the Critical Strictures on the New Tragedy of Elvira, as he believed the tragedy was better than anything he or his co-authors could have done.