# Hugh MacColl

**Hugh MacColl** (1831–1909) was a Scottish mathematician, logician and novelist.

## Contents

## Life[edit]

MacColl was the youngest son of a poor Highland family that was at least partly Gaelic-speaking. Hugh's father died when he was still an infant, and Hugh was educated largely thanks to the efforts of his elder brother Malcolm MacColl, an Episcopalian clergyman and friend and political ally of William Ewart Gladstone.^{[1]} Early in his acquaintanceship with Gladstone, Malcolm MacColl persuaded the Liberal politician to provide funds for Hugh's education at Oxford. It was proposed to send him to Oxford University's St. Edmund Hall, but Gladstone made this conditional on Hugh MacColl agreeing to take orders in the Church of England.^{[clarification needed]} Hugh MacColl refused this condition and, as a result, never obtained a university education, which may have limited his contribution to philosophy, and certainly prevented him from ever obtaining a formal academic position.^{[2]}

After a few years working in different areas of Great Britain, MacColl relocated to Boulogne-sur-Mer, in France on the Channel, where he developed the greater part of his work and became a French citizen. MacColl was not obscure during his time. He was a lifelong regular contributor to the *Educational Times*. His correspondents included the logicians William Stanley Jevons and Charles Sanders Peirce. He also corresponded, and argued in print, with the young Bertrand Russell, and reviewed Alfred North Whitehead's 1898 *Universal Algebra* for *Mind* magazine.

## Works[edit]

He is known for three main accomplishments:

- During 1877-79, while working out a problem involving integration, he published a four-part article establishing the first known variant of the propositional calculus, terming it the "calculus of equivalent statements", preceding Gottlob Frege's
*Begriffschrifft*. He subsequently published 11 articles in*Mind*magazine, during the period 1880–1908, and a text,^{[3]}^{[4]}in an effort to attract the attention of philosophers to his work. - Clarence Irving Lewis credited MacColl's late work on the nature of implication as the source of the basic ideas of Lewis's innovative work in modal logic.
- MacColl's work represents one of the first treatments of logical pluralism where he explores the possibilities of modal logic, logic of fiction, connexive logic, many-valued logic and probability logic.

MacColl also published two novels, *Mr. Stranger's Sealed Packet* (1889), concerning a journey to Mars and a utopian Martian society, and *Ednor Whitlock* (1891), dealing with a crisis of faith occasioned by exposure to new scientific ideas. While described by a recent critic as "best left unread",^{[5]} the novels reveal social and moral values to which the author gave full expression in his 1909 publication *Man's Origin, Destiny, and Duty*, an apology for Christianity.

## Legacy[edit]

There is presently a long-term MacColl Project, a joint venture of Greifswald University in Germany and the University of Oslo, which intends to publish a critical edition of his work. Furthermore, the group of logic and epistemology at the University of Lille (France) develop MacColl's suggestions for a dynamic free logic. The December 1999 issue of the magazine *Nordic Journal of Philosophical Logic* published the proceedings of a 1998 conference devoted to MacColl's work.

## References[edit]

**^**Lee, Sidney, ed. (1912). .*Dictionary of National Biography, 1912 supplement*.**2**. London: Smith, Elder & Co. p. 508.**^**Source: Gladstone-MacColl Correspondence, British Library**^***Symbolic Logic and Its Applications*, 1906. Longmans, Green**^**Wilson, Edwin Bidwell (1908). "Review:*L'Algèbre de la Logique*, par Louis Couturat;*Symbolic Logic and its Applications*, by Hugh MacColl;*The Development of Symbolic Logic*by A. T. Shearman" (PDF).*Bull. Amer. Math. Soc*.**14**(4): 175–191. doi:10.1090/S0002-9904-1908-01573-8.**^**Stein Haugom Olsen, "Why Hugh MacColl is not, and will never be, part of any literary canon" in*The Quality of Literature: Linguistic Studies in Literary Evaluation*, ed. Willie van Peer, John Benjamins Publishing Company, 2008.

- Rahman, S. & Redmond, J., 2008. "Hugh MacColl and the Birth of Logical Pluralism". In:
*Handbook of History of Logic*. Elsevier, vol. 4. Discusses MacColl's contributions to philosophy of language and logic including modal logic, logic of fictions and modal logic. - Rahman, S. & Redmond, J., 2007.
*Hugh MacColl. An Overview of his Logical Work with Anthology*. College Publications. Contains a long introduction to MacColl's logic and reprints of his main logical work. - Kneebone, G., 2001 (1963).
*Mathematical Logic and the Foundations of Mathematics*. Dover. Contains a brief introduction to the "calculus of equivalent statements." - Rahman, S.; Rückert, H. (2001). "Dialogical Connexive Logic".
*Synthese*.**127**(1–2): 105–139. doi:10.1023/a:1010351931769. - Ivor Grattan-Guinness, 2000.
*The Search for Mathematical Roots 1870-1940*. Princeton Uni. Press.