He was educated at the High School, and later at the University of Edinburgh. He studied for the ministry of the United Presbyterian Church of Scotland, and in 1856 was ordained pastor of the Greyfriars church, Glasgow. He also examined in mental philosophy for the University of Glasgow from 1861 to 1864, and from 1866 conducted the moral philosophy classes at that university, until in 1868 he became Professor of Moral Philosophy at Edinburgh. He was made LL.D. of Glasgow in 1865.
His first and most famous work was The Philosophy of the Infinite (1854), in which he attacked the statement of Sir William Hamilton that we can have no knowledge of the Infinite. Calderwood maintained that such knowledge, though imperfect, is real and ever-increasing; that Faith implies Knowledge. His moral philosophy is in direct antagonism to Hegelian doctrine, and endeavours to substantiate the doctrine of divine sanction. Beside the data of experience, the mind has pure activity of its own whereby it apprehends the fundamental realities of life and combat. He wrote in addition A Handbook of Moral Philosophy, On the Relations of Mind and Brain, Science and Religion, The Evolution of Man's Place in Nature.
Among his religious works the best-known is his Parables of Our Lord, and just before his death he finished a Life of David Hume in the Famous Scots Series. His interests were not confined to religious and intellectual matters; as the first chairman of the Edinburgh school board, he worked hard to bring the Education Act into working order. He published a well-known treatise on education. In the cause of philanthropy and temperance he was indefatigable. In politics he was at first a Liberal, but became a Liberal Unionist at the time of the Home Rule Bill.
He is buried in Morningside Cemetery, Edinburgh, towards the south-west. His wife Anne Hutton Leadbetter (d.1912) lies with him.
- Gilbert, W.M., editor, Edinburgh in the Nineteenth Century, Edinburgh, 1901:183
- Biography of Calderwood published in 1900 by his son W. C. Calderwood and the Rev. David Woodside, with a chapter on his philosophy by A. S. Pringle-Pattison
- Calderwood, Henry (1881). The Relations of Science and Religion. Macmillian (reissued by Cambridge University Press, 2009; ISBN 978-1-108-00015-4)
- This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). Encyclopædia Britannica (11th ed.). Cambridge University Press.