Non-classical logic concepts of Hugh MacColl
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Abstract
In this article we attempt to review the main ideas of non-classical logic of Hugh MacColl, logician, mathematician and philosopher (1837–1909). Based on the ideas of G. Boole MacColl impressively advanced in the fields of studying implication and the nature of inference. This research led the Scottish scholar to an idea that there can be more than two traditional truth-values, 1 and 0, respectively. And by the same time MacColl discovered and defined different types of modalities. Thus, his investigations were breaking-through for his time and anticipated some of milestone innovations in logic of the XX century. His works caused combative debates when released. Most famous logicians of his time criticized all his initiatives, sometimes even calling them ‘useless complication’. However, his ideas inspired C.I. Lewis for his first systems of modal logic and his strict implication. But in his later works Lewis did all not to mention MacColl. The second half of the XX century is a period of some kind of interest for the Scottish logician’s works revival. Still, the ideas of MacColl are not that familiar in Russia.
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Copyright (c) 2024 Хулербен Кок-оолович Кадыг-оол
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References
Bochenski, 1961 – Bochenski, J.M. A history of formal logic. Notre Dame, USA: Univ. of Notre Dame Press, 1961. 567 pp.
Hibben, 1907 – Hibben, J.G. “Review. Reviewed Work(s): Symbolic Logic and Its Applications by Hugh MacColl: The Development of Symbolic Logic by A.T. Shearman”, The Philosophical Review, 1907, Vol. 16, No. 2, pp. 190–194.
Grattan-Guinness, 2011 – Grattan-Guinness, I. “Was Hugh MacColl a logical pluralist or a logical monist? A case study in the slow emergence of metatheorising”, Philosophia scientiæ, 2011, Vol. 15, No. 1, pp. 189–203.
Kadyg-ool, 2013 – Kadyg-ool, Kh.K. “Osnovnye etapy razvitiya i formirovaniya sovremennoj modal’noj aleticheskoj logiki” [Main periods of modern modal alethic logic development and forming]: diss. . . . kand. filos. nauk. [Candidate of Philosophy thesis], Moscow, 2013. 111 pp. (In Russian)
Кuhn, 1977 – Kuhn, T. Struktura nauchnykh revolyutsii [The structure of scientific revolutions]. Мoscow: Progress, 1977. 300 pp. (In Russian)
Karpenko, 2007 – Karpenko, A.S. Logiki Lukasevicha i prostye chisla [Lukasiewicz logics and primes]. Moscow: LKI/URSS, 2007. 256 pp. (In Russian)
Lewis, 1918 – Lewis, C.I. A survey of symbolic logic. Berkeley: Univ. of California Press, 1918. 436 pp.
Lukasevich, 1959 – Lukasevich, Ya. Aristotelevskaya sillogistika s tochki zreniya sovremennoj formal’noj logiki [Aristotle’s syllogistic from the standpoint of modern formal logic]. Moscow: Izdatel’stvo inostrannoj literatury, 1959. 312 pp. (In Russian)
Lukasevich, 1993 – Lukasevich, Ya. “O determinizme” (per. V.L. Vasyukova) [On determinism, trans. V.L. Vasyukov] Logicheskie issledovaniya [Logical Investigations], 1993, Vol. 2, pp. 190–205. (In Russian)
MacColl, 1880 – MacColl, H. “Symbolical reasoning”, Mind, 1880, Vol. 5, No. 17, pp. 45–60.
MacColl, 1897 – MacColl, H. “Symbolical reasoning (II)”, Mind. New series, 1897, Vol. 6, No. 24, pp. 493–510.
MacColl, 1900 – MacColl, H. “Symbolical reasoning (III)”, Mind. New series, 1900. Vol. 9, No. 33, pp. 75–84.
MacColl, 1902 – MacColl, H. “Symbolical reasoning (IV)”, Mind. New series, 1902, Vol. 11, No. 43, pp. 352–368.
MacColl, 1903 – MacColl, H. “Symbolical reasoning (V)”, Mind. New series, 1903, Vol. 12, No. 47, pp. 355–364.
MacColl, 1905a – MacColl, H. “Symbolical reasoning (VI)”, Mind. New series, 1905, Vol. 14, No. 53, pp. 74–81.
MacColl, 1905b – MacColl, H. “Symbolical reasoning (VII)”, Mind. New series, 1905, Vol. 14, No. 55, pp. 390–397.
MacColl, 1906a – MacColl, H. “Symbolical reasoning (VIII)”, Mind. New series, 1906, Vol. 15, No. 60, pp. 504–518.
MacColl, 1906b – MacColl, H. Symbolic logic and its applications. New York and Bombay: Longmans, Green, and Co, 1906. 141 pp.
MacColl, 1908 – MacColl, H. “‘If’ and ‘imply”’, Mind. New series, 1908, Vol. 17, No. 67, pp. 453–455.
Nordic journal of philosophy, 1998 – “Nordic journal of philosophy”, Proceedings of the conference Hugh MacColl and the tradition of logic, Ernst-Moritz-ArndtUniversitat Greifswald, March 29 – April 1, 1998, Vol. 3, No. 1.
Peckhaus, 1998 – Peckhaus, V. “Hugh MacColl and the German algebra of logic” Nordic journal of philosophy, 1998, Vol. 3, No. 1, pp. 17–34.
Philosophia scientiæ, 2011 – “Philosophia scientiæ”, Hugh MacColl after One Hundred Years, 2011, Vol. 15, No. 1.
Rahman, Redmond, 2007 – Rahman, S., Redmond, J. Hugh Maccoll. An overview of his logical works with anthology. London: College Publications, 2007. 500 pp.
Rahman, Redmond, 2008 – Rahman, S., Redmond, J. “Hugh Maccoll and the birth of logical pluralism”, in: Handbook of the history of logic. Vol. 4. British logic in the Nineteenth Century, ed. by D.M. Gabbay, J. Woods. Amsterdam: Elsevier, 2008, pp. 533–604.
Read, 1998 – Read, S. “Hugh MacColl and the algebra of strict implication” Nordic journal of philosophy, 1998, Vol. 3, No. 1, pp. 59–83.
Rescher, 1969 – Rescher, N. Many-valued logic. New York: McGraw-Hill Book Company, 1969. 288 pp.
Russell, 1906 – Russell, B. “Review. Reviewed work: Symbolic Logic and Its Applications. Hugh MacColl”, Mind. New series, 1906, Vol. 15, No. 58, pp. 255–260.
Simons, 1998 – Simons, P. “MacColl and many-valued logic: an exclusive conjunction” Nordic journal of philosophy, 1998, Vol. 3, No. 1, pp. 85–90.
Styazhkin, 1967 – Styazhkin N.I. Formirovanie matematicheskoj logiki [Forming of mathematical logic]. Moscow: Nauka, 1967. 508 pp. (In Russian)