Dugald Stewart's father was Matthew Stewart who was Professor of Mathematics at the University of Edinburgh at the time Dugald was born. Matthew Stewart had married Marjorie Stewart, the only daughter of Archibald Stewart, writer to the signet, on 20 May 1750. Dugald was their only child who survived beyond childhood.
Dugald Stewart 's ama ay Matthew Stewart na ay Propesor ng Matematika sa Unibersidad ng Edinburgh sa oras Dugald ay ipinanganak. Matthew Stewart had kasal Marjorie Stewart, ang tanging anak na babae ng Archibald Stewart, writer sa mga selyo, sa 20 Mayo 1750. Dugald lamang ay ang kanilang mga anak na lampas sa pagkabata survived.