Hostname: page-component-7dd5485656-gs9qr Total loading time: 0 Render date: 2025-10-31T12:17:42.491Z Has data issue: false hasContentIssue false
  • English
  • Français

IBN SĪNĀ ON REDUCTIO AD ABSURDUM

Published online by Cambridge University Press:  17 October 2016

WILFRID HODGES
Get access Rights & Permissions [Opens in a new window]

Abstract

Ibn Sīnā (11th century, greater Persia) proposed an analysis of arguments by reductio ad absurdum. His analysis contains, perhaps for the first time, a workable method for handling the making and discharging of assumptions in a formal proof. We translate the relevant text of Ibn Sīnā and put his analysis into the context of his general approach to logic.

Information

Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 3 , September 2017 , pp. 583 - 601
Copyright
Copyright © Association for Symbolic Logic 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

BIBLIOGRAPHY

Arnauld, A. & Nicole, P. (1664). La Logique, ou l’Art de Penser. Paris: Charles Savreux.Google Scholar
Barnes, J. (1984). The Complete Works of Aristotle, Vol. 1. Princeton, NJ: Princeton University Press.Google Scholar
Besthorn, R. & Heiberg, J. (1893). Codex Leidensis 339, 1: Euclidis Elementa Ex Interpretatione Al-Hadschdschadschii cum Commentariis Al-Narizii. Copenhagen: Hegel and Son.Google Scholar
Burleigh, W. (1955). De Puritate Artis Logicae Tractatus Longior with a Revised Edition of the Tractatus Brevior. Boehner, P., editor. St. Bonaventure, NY: The Franciscan Institute.Google Scholar
De Morgan, A. (1836). The Connexion of Number and Magnitude: An Attempt to Explain the Fifth Book of Euclid. London: Taylor and Walton.Google Scholar
Frege, G. (1893). Grundgesetze der Arithmetik I. Jena: Pohle.Google Scholar
Frege, G. (1969). Logik in der Mathematik. In Hermes, H. et al., editors. Nachgelassene Schriften. Hamburg: Meiner. pp. 219–270.Google Scholar
Frege, G. (1906). Über die Grundlagen der Geometrie. Jahresbericht der Deutschen Mathematikervereinigung, 15, 293–309, 377–403, 423–430.Google Scholar
Gutas, D. (2014). Avicenna and the Aristotelian Tradition: Introduction to Reading Avicenna’s Philosophical Works (second edition). Leiden: Brill.Google Scholar
Gutas, D. (2012). The empiricism of Avicenna. Oriens, 40, 391–436.Google Scholar
Hasnawi, A. & Hodges, W. (2016). Arabic logic up to Avicenna. In Dutilh, C. and Read, S., editors. Companion to Medieval Logic. Cambridge: Cambridge University Press, pp. 45–66.Google Scholar
Hodges, W. (2008). Tarski’s theory of definitions. In Patterson, D., editor. New Essays on Tarski and Philosophy. Oxford: Oxford University Press, pp. 94–132.Google Scholar
Hodges, W. (2009). Traditional logic, modern logic and natural language. Journal of Philosophical Logic, 38, 589–606.CrossRefGoogle Scholar
Hodges, W. (2010). Ibn Sina on analysis: 1. Proof search. Or: Abstract State Machines as a tool for history of logic. In Blass, A. Dershowitz, N. and Reisig, W. editors. Fields of Logic and Computation: Essays Dedicated to Yuri Gurevich on the Occasion of his 70th Birthday. Lecture Notes in Computer Science, Vol. 6300. Berlin: Springer-Verlag, pp. 354–404.Google Scholar
Hodges, W. (2011). Ibn Sina and conflict in logic. In DeVidi, D., Hallett, M. and Clark, P., editors. Logic, Mathematics, Philosophy: Vintage Enthusiasms, Essays in Honour of John L. Bell. Western Ontario Series in Philosophy of Science. Dordrecht: Springer-Verlag, pp. 35–67.CrossRefGoogle Scholar
Hodges, W. (2012). Affirmative and negative in Ibn Sina. In Dutilh, C. and Hjortland, O., editors. Insolubles and Consequences: Essays in Honour of Stephen Read. London: College Publications, pp. 119–134.Google Scholar
Hodges, W. (2015). Notes on the history of scope. In Hirvonen, A. Kontinen, J., Kossak, R. and Villaveces, A., editors. Logic Without Borders. Berlin: De Gruyter, pp. 215–240.Google Scholar
Hodges, W. (201-). Proofs as cognitive or computational: Ibn Sīnā’s innovations. Philosophy and Technology, submitted.Google Scholar
Sīnā, Ibn (1910). Manṭiq al-mashriqiyyīn. Cairo: al-Maktaba al-Salafiyya.Google Scholar
Sīnā, Ibn (1964). Al-qiyās. Zayed, S., editor. Cairo: al-Hay’a al- c Āmma li-Shu’ūn al-Maṭābi c al-Amīriyya.Google Scholar
Sīnā, Ibn (2000). Al-’ishārāt wal-tanbīhāt. Zāre c ī, M., editor. Qum: Būstān-e Ketab-e Qom.Google Scholar
Inati, S. (1984). Ibn Sīnā Remarks and Admonitions, Part One: Logic. Toronto, ON: Pontifical Institute of Mediaeval Studies.Google Scholar
Marenbon, J. (editor) (2012). The Oxford Handbook of Medieval Philosophy. Oxford: Oxford University Press.Google Scholar
Philoponus (1905). In Aristotelis Analytica Priora Commentaria. Wallies, M., editor. Berlin: Reimer.Google Scholar
Al-Sakkākī (1987). Miftāḥ al- c ulūm. Zarzūr, N., editor. Beirut: Dār al-Kutub al- c Ilmiyya.Google Scholar
Shehaby, N. (1973). The Propositional Logic of Avicenna. Dordrecht: Reidel.Google Scholar
Tarski, A. (1931). Sur les ensembles définissables de nombres réels I. Fundamenta Mathematicae, 17, 210–239.Google Scholar
Zimmermann, F. (1981). Al-Farabi’s Commentary and Short Treatise on Aristotle’s De Interpretatione. Oxford: British Academy and Oxford University Press.Google Scholar