Potentially refers to the conflict between Thomas Chalmers and Professor John Playfair, arising after Dr. Robison's death in January 1805.

Dr. Robison, who previously held the the chair of Natural Philosophy at the University of Edinburgh, was succeeded by Dr. John Playfair, after which there was a vacancy in the mathematical professorship. Thomas Chalmers, among others, applied for the position, although he did not receive it. Alarmed that multiple clergymen had applied for a professorship in university, both Professor Stewart and Professor Playfair sent worried addresses to the Lord Provost. Chalmers took offence to the objection of Playfair, his former teacher, as Playfair argued that the professions of a professor in mathematics/science and a clergyman were incompatible. This inspired Chalmers' first publication in 1805, titled 'Observations on a Passage in Mr. Playfair's Letter to the Lord Provost of Edinburgh Relative to the Mathematical Pretensions of the Scottish Clergy'.

See Memoirs of the Life and Writings of Thomas Chalmers, D.D., LL.D., vol. 1, by William Hanna in 1852, from p.91 onwards.