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Deductions and Reductions Decoding Syllogistic Mnemonics

Year 2018, Volume: 2 Issue: 1, 5 - 39, 08.07.2018

Abstract

The syllogistic mnemonic known by its first two words Barbara Celarent introduced a constellation of terminology still used today. This concatenation of nineteen words in four lines of verse made its stunning and almost unprecedented appearance around the beginning of the thirteenth century, before or during the lifetimes of the logicians William of Sherwood and Peter of Spain, both of whom owe it their lasting places of honor in the history of syllogistic. The mnemonic, including the theory or theories it encoded, was prominent if not dominant in syllogistics for the next 700 years until a new paradigm was established in the 1950s by the great polymath Jan Łukasiewicz, a scholar equally at home in philosophy, classics, mathematics, and logic. Perhaps surprisingly, the then-prominent syllogistic mnemonic played no role in the Łukasiewicz work. His 1950 masterpiece does not even mention the mnemonic or its two earliest champions William and Peter. The syllogistic mnemonic is equally irrelevant to the post-Łukasiewicz paradigm established in the 1970s and 1980s by John Corcoran, Timothy Smiley, Robin Smith, and others. Robin Smith’s comprehensive 1989 treatment of syllogistic does not even quote the mnemonic’s four verses. Smith’s work devotes only 2 of its 262 pages to the mnemonic. The most recent translation of Prior Analytics by Gisela Striker in 2009 continues the post-Łukasiewicz paradigm and accordingly does not quote the mnemonic or even refer to the code–although it does use the terminology. Full mastery of modern understandings of syllogistic does not require and is not facilitated by ability to decode the mnemonic. Nevertheless, an understanding of the history of logic requires detailed mastery of the syllogistic mnemonic, of the logical theories it spawned, and of the conflicting interpretations of it that have been offered over the years by respected logicians such as De Morgan, Jevons, Keynes, and Peirce. More importantly, an understanding of the issues involved in decoding the mnemonic might lead to an enrichment of the current paradigm–an enrichment so profound as to constitute a new paradigm. After presenting useful expository, bibliographic, hermeneutic, historical, and logical background, this paper gives a critical exposition of Smith’s interpretation.

References

  • Aristotle. Prior Analytics. Trans. Robin Smith. Indianapolis: Hackett Publishing Company, 1989.
  • Aristotle. Prior Analytics Book I. Trans. Gisela Striker. Oxford: Oxford University Press, 2009.
  • Bocheński, Joseph. History of Formal Logic. Trans. Ivo Thomas. Notre Dame: University of Notre Dame Press, 1961.
  • Cohen, Morris and Ernest Nagel. Introduction to Logic. Ed. John Corcoran. Indianapolis: Hackett Publishing Company, 1993.
  • Corcoran, John and Idris Samawi Hamid. “Investigating Knowledge and Opinion.” The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, vol. I. Eds. Arnold Koslow and Arthur Buchsbaum. Dordrecht: Springer, 2014: 95-125.
  • Corcoran, John and Kevin Tracy. “Review of Joray, Pierre, ‘A Completed System for Robin Smith's Incomplete Ecthetic Syllogistic’,” Mathematical Reviews, MR3681098, 2018.
  • Corcoran, John. “Argumentations and Logic.” Argumentation 3, 1989: 17-43.
  • Corcoran, John. “Aristotle’s Prototype Rule-Based Underlying Logic.” Logica Universalis 12, no. 1-2, 2018: 9-35.
  • Corcoran, John. “Aristotle's Demonstrative Logic.” History and Philosophy of Logic 30, 2009: 1-20.
  • Corcoran, John. “Deduction and Reduction: Two Proof-Theoretic Processes in Prior Analytics I.” Journal of Symbolic Logic 48, 1983: 906
  • Corcoran, John. “Completeness of an Ancient Logic.” Journal of Symbolic Logic 37, 1972: 696-702.
  • De Morgan, Augustus. Formal Logic or The Calculus of Inference, Necessary and Probable. London: Taylor and Walton, 1847.
  • De Rijk, Lambertus Marie. Logica Modernorum, vol. I. Assen: Koninklijke Van Gorcum & Company, 1962.
  • De Rijk, Lambertus Marie. Logica Modernorum, vol. II. Assen: Koninklijke Van Gorcum & Company, 1967.
  • Eaton, Ralph. General Logic: An Introductory Survey. London: Charles Scribners' Sons, 1931.
  • Jevons, W. Stanley. Elementary Lessons in Logic: Deductive and Inductive. London: Macmillan, 1870.
  • Keynes, John Neville. Studies and Exercises in Formal Logic. London: Macmillan & Co., 1906.
  • Kneale, William and Mary Kneale. Development of Logic. London: Clarendon Press, 1962.
  • Łukasiewicz, Jan. Aristotle's Syllogistic: From the Standpoint of Modern Formal Logic. London: Clarendon Press, 1951.
  • Parsons, Terence. Articulating Medieval Logic. Oxford: Oxford University Press, 2014.
  • Peirce, Charles Sanders. Writings of Charles S. Peirce: Chronological Edition. Volume 5 (1884-1886). Eds. Nathan Houser et al. Bloomington: Indiana University Press, 1993.
  • Rini, Adriane. “Aristotle’s Logic.” The History of Philosophical and Formal Logic: From Aristotle to Tarski. Eds. Alex Malpass and Marianna Antonutti Marfori. London: Bloomsbury Academic, 2017: 29-49.
  • William of Sherwood. Manuscript of Introduction to Logic. Paris: Bibliothèque Nationale MS. Lat. 16617, more briefly, BN 16617.
  • William of Sherwood. William of Sherwood’s Introduction to Logic. Trans. Norman Kretzmann. Minneapolis: University of Minnesota Press, 1966.
Year 2018, Volume: 2 Issue: 1, 5 - 39, 08.07.2018

Abstract

References

  • Aristotle. Prior Analytics. Trans. Robin Smith. Indianapolis: Hackett Publishing Company, 1989.
  • Aristotle. Prior Analytics Book I. Trans. Gisela Striker. Oxford: Oxford University Press, 2009.
  • Bocheński, Joseph. History of Formal Logic. Trans. Ivo Thomas. Notre Dame: University of Notre Dame Press, 1961.
  • Cohen, Morris and Ernest Nagel. Introduction to Logic. Ed. John Corcoran. Indianapolis: Hackett Publishing Company, 1993.
  • Corcoran, John and Idris Samawi Hamid. “Investigating Knowledge and Opinion.” The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, vol. I. Eds. Arnold Koslow and Arthur Buchsbaum. Dordrecht: Springer, 2014: 95-125.
  • Corcoran, John and Kevin Tracy. “Review of Joray, Pierre, ‘A Completed System for Robin Smith's Incomplete Ecthetic Syllogistic’,” Mathematical Reviews, MR3681098, 2018.
  • Corcoran, John. “Argumentations and Logic.” Argumentation 3, 1989: 17-43.
  • Corcoran, John. “Aristotle’s Prototype Rule-Based Underlying Logic.” Logica Universalis 12, no. 1-2, 2018: 9-35.
  • Corcoran, John. “Aristotle's Demonstrative Logic.” History and Philosophy of Logic 30, 2009: 1-20.
  • Corcoran, John. “Deduction and Reduction: Two Proof-Theoretic Processes in Prior Analytics I.” Journal of Symbolic Logic 48, 1983: 906
  • Corcoran, John. “Completeness of an Ancient Logic.” Journal of Symbolic Logic 37, 1972: 696-702.
  • De Morgan, Augustus. Formal Logic or The Calculus of Inference, Necessary and Probable. London: Taylor and Walton, 1847.
  • De Rijk, Lambertus Marie. Logica Modernorum, vol. I. Assen: Koninklijke Van Gorcum & Company, 1962.
  • De Rijk, Lambertus Marie. Logica Modernorum, vol. II. Assen: Koninklijke Van Gorcum & Company, 1967.
  • Eaton, Ralph. General Logic: An Introductory Survey. London: Charles Scribners' Sons, 1931.
  • Jevons, W. Stanley. Elementary Lessons in Logic: Deductive and Inductive. London: Macmillan, 1870.
  • Keynes, John Neville. Studies and Exercises in Formal Logic. London: Macmillan & Co., 1906.
  • Kneale, William and Mary Kneale. Development of Logic. London: Clarendon Press, 1962.
  • Łukasiewicz, Jan. Aristotle's Syllogistic: From the Standpoint of Modern Formal Logic. London: Clarendon Press, 1951.
  • Parsons, Terence. Articulating Medieval Logic. Oxford: Oxford University Press, 2014.
  • Peirce, Charles Sanders. Writings of Charles S. Peirce: Chronological Edition. Volume 5 (1884-1886). Eds. Nathan Houser et al. Bloomington: Indiana University Press, 1993.
  • Rini, Adriane. “Aristotle’s Logic.” The History of Philosophical and Formal Logic: From Aristotle to Tarski. Eds. Alex Malpass and Marianna Antonutti Marfori. London: Bloomsbury Academic, 2017: 29-49.
  • William of Sherwood. Manuscript of Introduction to Logic. Paris: Bibliothèque Nationale MS. Lat. 16617, more briefly, BN 16617.
  • William of Sherwood. William of Sherwood’s Introduction to Logic. Trans. Norman Kretzmann. Minneapolis: University of Minnesota Press, 1966.
There are 24 citations in total.

Details

Primary Language English
Journal Section Article
Authors

John Corcoran This is me

Daniel Novotný This is me

Kevin Tracy This is me

Publication Date July 8, 2018
Published in Issue Year 2018 Volume: 2 Issue: 1

Cite

Chicago Corcoran, John, Daniel Novotný, and Kevin Tracy. “Deductions and Reductions Decoding Syllogistic Mnemonics”. Entelekya Logico-Metaphysical Review 2, no. 1 (May 2018): 5-39.