He made rapid progress at school (first Kinbuck then Dunblane), and began his religious studies in the University of Glasgow at the age of 14.
In this year, the Duke of Atholl offered Finlayson a position as minister of Dunkeld, which he declined, as Sir William Murray had informed him that an arrangement had been proposed to procure for him the chair of logic in the University of Edinburgh.
He therefore dedicated much of his leisure to study the laws, constitution, and history of the Scottish church, and began to take an active part in the details of its political government.
In 1799, on a vacancy occurring in the High Church of Edinburgh, he was chosen by the town council to fill that charge.
The latter is considered the most honourable appointment in the Church of Scotland, and it was, at the time, rendered more desirable from the circumstance that he had for his colleague Hugh Blair, whose funeral sermon he was called upon to preach in little more than a year.
Finlayson established his ascendency on the wisdom of his councils and his knowledge of the laws and constitution of the church, and among his own party his sway was unlimited.
In 1807, he was constrained to accept the assistance of one of his earliest friends, Principal George Husband Baird, who taught the class during the remainder of that session.
On his deathbed, the senatus academicus of the university and the magistrates of Edinburgh waited on him and asked him to name the successor to his chair.