Biography
Probably the son of John Shaw (d. 1740) and Agnes Crawford. Possibly married to Helen Kennedy (d. 1795).1
In his journal, Boswell refers only to the Laird of Daltoune which doesn't identify Shaw with absolute certainty, but the evidence seems to fit.
Life with Boswell
Boswell met Shaw at James McAdam's on September 15, 1762. He described him as a man "who, from having a pretty fortune, is reduced to live in a cottage. He is a tall, lean man of tolerable parts, but has that happy absence of feeling which makes men easies under adverse fortune than all the reasoning of philosophy".