He became house surgeon and later clinical tutor to Thomas Annandale, the Regius professor of clinical surgery and was elected a fellow of the Royal College of Surgeons of Edinburgh in 1891. He was awarded the degree of M.D. by the University of Edinburgh in 1894. Having decided on a career in ear, nose and throat surgery he was appointed surgeon for diseases of the ear, nose and throat to the Deaconess Hospital, and in 1903 he became an assistant surgeon at the newly built Ear, Nose and Throat Pavilion at Edinburgh Royal Infirmary of Edinburgh, graduating to full surgeon in 1906. During the First World War he served in the Royal Army Medical Corps acting as laryngologist to the Second Scottish General Hospital in Edinburgh, which later became the Western General Hospital. Turner was editor of the University of Edinburgh Journal for ten years, from 1928 to 1937. His textbook Diseases of the Nose, Throat and Ear was first published in 1924. This proved so popular that it ran to several editions during Turner's lifetime which he continued to edit. An 11th edition, now entitled Logan Turner's Diseases of the Nose, Throat and Ear, Head and Neck Surgery was published in 2015. His collection of pathological specimens was donated to Surgeon's Hall Museum in Edinburgh and is known as the Arthur Logan Turner Collection.
Medical historian
After retiring from his surgical career Turner devoted much of his time and energy to the history of medicine. He wrote the definitive biography of his father Sir William Turner, K.C.B. : A Chapter in Medical History which was published in 1919. To commemorate the 100th anniversary of the birth of Joseph Lister he edited a memorial work, Joseph, Baron Lister, A Centenary Volume, 1827-1927. In 1933 when the University of Edinburgh celebrated the 350th anniversary of its foundation Turner produced The History of the University of Edinburgh, 1883-1933, a continuation of the history of that institution by Sir Alexander Grant which had been published fifty years earlier.
Awards and recognition
In 1905 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Daniel John Cunningham, George Chrystal, James Geikie and Henry Littlejohn. He served as Vice President of the Society 1930 to 1933. As his father had been before him he was elected President of the Royal College of Surgeons of Edinburgh in 1925 in succession to Professor Harold Stiles. In recognition of his academic contributions he received the degree of LLD from the University of Edinburgh. He was President of the Medico-Chirurgical Society of Edinburgh in 1927 and President of the Sections of Laryngology and Otology in the Royal Society of Medicine, London. President of the Section of Laryngology at the British Medical Association Meeting in Edinburgh in 1927. He was made a corresponding Fellow of the American Laryngological Association, an honorary Member of the Austrian Otological Society and a corresponding Member of the French Society of Otology and Laryngology.
Turner never married. He died in Edinburgh on 6 June 1939. He is buried with his parents in Dean Cemetery. The grave lies in the north section, backing onto the dividing wall with the original cemetery.