Laird was born at Durris, Kincardineshire, a parish adjacent to the birthplace of Scottish philosopher Thomas Reid.
He attended Aberdeen Grammar School and the University of Edinburgh, where in 1908 he graduated with a first class MA in philosophy.
He spent a brief time at Heidelberg before entering Trinity College, Cambridge as a Scholar.
The following year he returned to the United Kingdom as Professor of Logic and Metaphysics at Queen's University Belfast (1913–24).
In 1924 he was appointed as Regius Professor of Moral Philosophy at the University of Aberdeen, a position which he held until his death.