Abstract
Ibn Sīnā (Persian, 980–1037) made a dramatic extension to Aristotle’s syllogistic by adding quantifiers over times or situations, thus introducing multiple and mixed quantification. The extension is unlike anything in the Latin Scholastic logic, but related extensions to syllogistic appear later in work of Leibniz and of Peirce’s student Mitchell. Ibn Sīnā’s version was the most integrated and systematic of these three, but at the same time it was the furthest from modern perspectives. We examine from a modern point of view the limitations, proof-theoretic and otherwise, which Ibn Sīnā’s highly original introduction of multiple quantification failed to overcome.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ahmed, A.Q.: Avicenna’s Deliverance: Logic. Oxford University Press, Oxford (2011). With introduction by T. Street
Alexander of Aphrodisias: Alexandri in Aristotelis Analyticorum Priorum Librum I Commentarium. Reimer, Berlin (1883). Ed. M. Wallies
Alexander of Aphrodisias: On Aristotle Prior Analytics 1.23–31. Duckworth, London (2006). Trans. I. Mueller
Alexander of Aphrodisias: On Aristotle Prior Analytics 1.32–46. Duckworth, London (2006). Trans. I. Mueller
Andréka, H., Németi, I., van Benthem, J.: Modal languages and bounded fragments of predicate logic. J. Philos. Log. 27, 217–274 (1998)
Beziau, J.-Y.: The relativity and universality of logic. Synthese (2014). doi:10.1007/s11229-014-0419-0. Online March 2014
Buridan, J.: Summulae de Dialectica. Yale University Press, New Haven (2001). Trans. G. Klima
Burley, W.: On the Purity of the Art of Logic: The Shorter and the Longer Treatises. Yale University Press, New Haven (2000). Trans. P.V. Spade
Dipert, R.R.: The life and logical contributions of O.H. Mitchell, Peirce’s gifted student. Trans. Charles S. Peirce Soc. 30(3), 515–542 (1994)
Gutas, D.: Avicenna and the Aristotelian Tradition: Introduction to Reading Avicenna’s Philosophical Works. Brill, Leiden (1988)
Haspelmath, M.: Indefinite Pronouns. Oxford University Press, Oxford (1997)
Hodges, W.: Traditional logic, modern logic and natural language. J. Philos. Log. 38, 589–606 (2009)
Hodges, W.: Ibn Sina, Frege and the grammar of meanings. Al-Mukhatabat 5, 29–60 (2013)
Hodges, W.: Notes on the history of scope. In: Kossak, R., Villaveces, A. (ed.) Logic Without Borders, Essays in Honour of Jouko Väänänen. De Gruyter (to appear)
Hodges, W.: Mathematical background to the logic of Ibn Sīnā. Notes at http://wilfridhodges.co.uk/arabic44.pdf
Ibn Sīnā: Manṭiq al-mašriqiyyīn (Easterners). Al-Maktaba al-Salafiyya, Cairo (1910)
Ibn Sīnā: Al-qiyās (Syllogism). Ed. S. Zayed, Cairo (1964)
Kalbfleisch, C.: Galeni Institutio Logica. Teubner, Leipzig (1896)
Kieffer, J.S.: Galen’s Institutio Logica: English Translation, Introduction, and Commentary. Johns Hopkins Press, Baltimore (1964)
Mill, J.S.: A System of Logic Ratiocinative and Inductive, Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation, 8th edn. Longmans Green, London (1872)
Mitchell, O.H.: On a new algebra of logic. In: Peirce, C.S., et al. (eds.) Studies in Logic, pp. 72–106. Little Brown and Company, Boston (1983)
Morison, B.: Logic. In: Hankinson, R.J. (ed.) The Cambridge Companion to Galen, pp. 66–115. Cambridge University Press, Cambridge (2008)
Movahed, Z.: De re and de dicto modality in Islamic traditional logic. Sophia Perennis 2, 5–14 (2010)
Mugnai, M.: Leibniz’ Theory of Relations. Franz Steiner, Stuttgart (1992)
Peirce, C.S.: On the algebra of logic. Am. J. Math. 3, 15–157 (1880)
Peirce, C.S.: On the algebra of logic: a contribution to the philosophy of notation. Am. J. Math. 7, 180–202 (1885)
Peirce, C.S.: On the algebra of logic (Second paper), Summer 1884. In: Kloesel, C.J.W., et al. (eds.) Writings of Charles S. Peirce, a Chronological Edition, Volume 5, 1884–1886, pp. 111–115. Indiana University Press, Bloomington (1993)
Reisman, D.C.: The Making of the Avicennan Tradition. Brill, Leiden (2002)
William of Ockham: Summa Logicae. University of St. Bonaventure, St. Bonaventure (1974). Ed. Philotheus Boehner et al.
William of Sherwood: Treatise on Syncategorematic Words. University of Minnesota Press, Minneapolis (1968). Trans. N. Kretzmann
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Hodges, W. (2015). The Move from One to Two Quantifiers. In: Koslow, A., Buchsbaum, A. (eds) The Road to Universal Logic. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-10193-4_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-10193-4_9
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-10192-7
Online ISBN: 978-3-319-10193-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)