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Hugh Maccoll and the Birth of Logical Pluralism

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Hugh Maccoll and the Birth of Logical Pluralism HUGH MACCOLL AND THE BIRTH OF LOGICAL PLURALISM Shahid Rahman and Juan Redmond INTRODUCTION Hugh MacColl (1837-1909) was a mathematician and logician who was born, raised and educated in Scotland and after a few years working in different areas of Great Britain moved to Boulogne-sur-Mer (France), where he developed the greater part of his work and went on to become a French citizen. Hugh MacColl was well known in his time for his innovative contributions to logic. Despite the fact that one can hardly say that his work satisfies the standards of rigour of Frege's phi- losophy of mathematics and logic it might represent one of the first approaches to logical pluralism. His first contribution to the logical algebras of the 19 th century was that his calculus admits not only a class interpretation (as in the algebra of Boole) but also a propositional one. Moreover, MacColl gave preference to the propositional interpretation because of its generality and called it pure logic. The main connective in his pure logic is the conditional and accordingly his algebra contains a specific operator for this connective. In Symbolic Logic and its Applica- tions (1906) MacColl published the final version of his logic(s) where propositions are qualified as either certain, impossible, contingent, true or false. After his death his work suffered a sad destiny. Contrary to other contemporary logicians such as L. Couturat, G. Frege, W.S. Jevons, J. Venn, G. Peano, C. S. Pierce, B. Russell and E. Schr5der, who knew MacColl's work, his contributions seem to have received neither the acknowledgement nor the systematic study they certainly deserve. Moreover, many of his ideas were attributed to his successors; the most notorious examples are the notion of strict implication, the first formal approach to modal logic and the discussion of the paradoxes of material implication normally attributed to C. I. Lewis. The same applies to his contributions to probability logic (conditional probability), (relational) many-valued logic, relevant logic and connexive logic. Less known is the fact that he also explored the possibilities of building a formal system able to handle reasoning with fictions. The latter seems to be linked to his formal reconstruction of Aristotelian Syllogism by means of connexive logic. Two main factors might have been determinant for the fact that his work fell into oblivion. One is related to technical issues and the other to his philosophical position. Handbook of the History of Logic. Volume 4: British Logic in the Nineteenth Century. Dov M. Gabbay and John Woods (Editors) @ 2008 Elsevier BV. All rights reserved. 534 Shahid Rahman and Juan Redmond The strong influence of the logistic methodology triggered by the work of Frege immediately after MacColl's death accounts for the first factor. Indeed, the logistic methods of presenting a logical system as a set of axioms closed under a conse- quence relation initiated by Frege and further developed by Peano, Russell and others rapidly replaced the algebraic methods of calculation of the 19 th century employed by MacColl. The second factor relates to his philosophy of logic. MacColl's philosophical ideas were based on a kind of instrumentalism which was extended beyond both of the mainstream paradigms of formal logic in the 19 th century, namely math- ematics as logic (logicism) and logic as algebra (Boole's algebraic approach). It is interesting to note that his philosophical position could be linked to French conventionalism and instrumentalism such as developed by his younger contempo- raries Henri Poincar~ and Pierre Duhem and the American pragmatism of Charles Saunders Peirce rather than to empiricism or logicism. MacColl was probably the first to explicitly extend conventionalism and instrumentalism to logic. Beyond his scientific contributions, MacColl had literary interests. Following the spirit of the century, he published two novels, Mr. Stranger's Sealed Packet (1889) and Ednor Whitlock (1891) and the essay Man's Origin, Duty and Destiny (1909). The first is a novel of science fiction, namely a voyage to Mars. In fact it was the third novel about Mars to be published in English. In his two last works MacColl discusses the conflicts between science and religion and the related problems of faith, doubt, and unbelief. It is impossible to resist the temptation to compare MacColl's contributions to science with his literary incursions. MacColl penned both one of the most conservative Victorian books on science fiction of his time and one of the most innovative proposals on logic of the 19 th century. Let us trace back, briefly, the revival of the interest in MacColl's work. During the nineteen-sixties Storrs McCall (1963-1967) drew attention to MacColl's work particularly in relation to the paradoxes of material implication, connexive logic and MacColl's reconstruction of Aristotle's Syllogism. 1 Between the eighties and nineties at the Erlangen-Niirnberg Universitgt, Christian Thiel and his collabora- tors rediscovered the work of our author in the context of a research project on the social history of logic in the 19 th century. The project led to the first systematic historic explorations into the work of Hugh MacColl by Christian Thiel [1996], Volker Peckhaus [1966] and Anthony Christie [1986; 1990]. The Erlanger group motivated Michael Astroh to deepen the research on Hugh MacColl's logic and philosophy of language. [1993; 1995; 1996; 1999a; 1999b], as then did Shahid Rah- man [1997a; 1997b; 1999; 2000]. Together Michael Astroh and Shahid Rahman conceived a workshop, finally organized in Greifswald, on "Hugh MacColl and the Tradition of Logic" with the participation among others of Stephen Read, Peter Si- mons, Volker Peckhaus, GSran Sundholm, Christian Thiel and Ian Wolefiski. The workshop yielded a special volume of the Nordic Journal of Philosophical Logic, edited by Michael Astroh and Stephen Read [1999]. This volume constitutes the 1See too Spencer [1973]. Hugh MacColl and the Birth of Logical Pluralism 535 main secondary source of our paper. BIOGRAPHICAL NOTES !g Figure 1. MacColl in 18862 Unfortunately there are no precise records about MacColl's life. We will rely on the information contained in MacColl's second marriage contract, signed by himself. We follow here the strategy used in the biography of MacColl published in 2001 by M. Astroh, I. Grattan-Guinness and S. Read which in addition to Rahman's paper [1997b] contains the main contents of the present biographical outline. Hugh MacColl was born in Strontian, Argyllshire, on 11 or 12 January 1837. He was the son of John MacColl and Martha Macrae. Hugh was their youngest child. He had three brothers and two sisters. The father was a shepherd and tenant- farmer from Glencamgarry in Kilmalie (between Glenfinnan and Fort William) who had married Martha Macrae in the parish of Kilmalie on 6 February 1823. The early loss of Hugh's father had a strong impact on the whole family. The father was 45 and the little Hugh only three. After he passed away, the mother and all the children moved on to Letterfearn and from there to Ballachulish. It was only from that moment that the children learned English, since their mother only spoke Gaelic. In 1884 Hugh's elder brother Malcolm, then aged nine, was 2by courtesy of Michael Astroh. 536 Shahid Rahman and Juan Redmond living alone with his aunt and grandmother. Malcolm did so well at school that a wealthy lady paid for him to attend a seminary in Dalkeith, near Edinburgh, where schoolteachers were trained. He taught in different places and was ordained priest in St Mary's, Glasgow by the Bishop of Glasgow in August 1857. At this time Malcolm was supporting his younger brother Hugh in his studies. But unfortunately this aid finished before Hugh completed them: his brother became involved in a dispute which divided the Episcopal Church in 1857-1858, and since he refused to support the Bishop's position he was consequently dismissed from his post. From 1858 Hugh took up various positions as a schoolmaster in Great Britain, until he left the country a few years later. In 1865 he moved to Boulogne sur Mer (France) and settled there for the rest of his life. The reasons why he left his country are unknown but it is not difficult to imagine economic motivations. If we take account of the immense emigration from Great Britain in the 19 th century, it is not so difficult to imagine changing country a sensible option. At that time Boulogne-sur-Mer was a prospering town with close economic and cultural links with Britain. Thus, a pleasant place for people who left Great Britain. Before MacColl left he married Mary Elisabeth Johnson of Loughborough in Leicestershire. She moved with him to France, where in April 1866 their first daughter Mary Janet was born. All five children, four girls and a boy, were born there. During these years the economic situation of the MacColls was very vicissi- tudinous and often precarious. Hugh worked principally as a private instructor teaching mathematics, English and logic. In contrast with this description, an obituary published in La France du Nord on 30 December 1909 depicts MacColl as a teacher of the Coll~ge Communal. However it has not been possible to identify MacColl as one of the members of the teaching staff because he did not appear in the college's advertisements and brochures. But the economic restrictions and the growing family did not prevent him from continuing to study. He prepared for and took a BA in Mathematics as an external student at the University of London in 1876. a From his frequent publications in different scientific journals and the interchange of letters with same of the most famous men of science of his time, we can presume that MacColl hoped for recognition of his achievements in logic.
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