Skip to main content
SpringerLink
Log in

The Hypothetical Logic

  • Chapter
  • First Online:
Arabic Logic from al-Fārābī to Averroes

Part of the book series: Studies in Universal Logic ((SUL))

  • 487 Accesses

Abstract

The Arabic logicians include the study of the hypothetical syllogisms in their counterparts of the Prior Analytics, that is, in the treatises called al-Qiyās. In al-Fārābī’s frame, they are also evoked in al-Maqūlāt (the counterpart of the Categories ).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    See [59] for a fuller analysis of the conditional in al-Fārābī’s theory.

  2. 2.

    The expression “qad yakūn” has been translated in several ways. W. Hodges translates it as “sometimes”, K. El-Rouayheb translates it as “Once”.

  3. 3.

    See [70, 71] for a different interpretation of these conditional propositions and [91, 132, 142] for a discussion of these interpretations.

  4. 4.

    See also [57] for an analysis of these propositions and the conditional ones, and [134] for a modal interpretation of the disjunctive and conditional propositions.

  5. 5.

    See also ([128], 42).

  6. 6.

    This formula and all formulas below are expressed by considering only one situation. But they are also valid with two or more situations.

  7. 7.

    We could also add “p” to “p ⊃ q”, since it is also a universal proposition and for the symmetry of the whole formula, but this addition is not required to validate the mood, for the “augment” (as Professor Wilfrid Hodges calls it) added to the first proposition is sufficient to validate it.

  8. 8.

    All these are equivalent to “P ≡ Q” too, but Avicenna does not mention that in this part of the text.

  9. 9.

    Here the word ‘not’ is added by N. Shehaby .

  10. 10.

    This rule is stated as follows (for First-Order Logic ) by contemporary logicians: “If a sentence φ can be inferred in FOL from a set Γ of premises , then it can also be inferred from any set Δ of premises containing Γ as a subset” (See [20]).

  11. 11.

    Some followers of Avicenna have also been shown by Wilfrid Hodges to use modern “Model-Theoretic” methods . See [88] for more details.

  12. 12.

    Avicenna adds the conditions “as long as it is C” and “as long as it is A” to the propositions of this mood in his full analysis of the proof (pp. 114–115), but this does not alter the whole structure of the proof, which is the usual presentation of the reductio ad absurdum.

References

  1. Al-Fārābī, Abū Naṣr. 1986. Kitāb al-Qiyās. In Al-Manṭiq ‘inda al-Fārābī, vol. 2, ed. Rafik Al Ajam, 11–64. Beirut: Dar el Machriq.

    Google Scholar 

  2. Al-Fārābī, Abū Naṣr. 1988. Al-Maqūlāt. In Al-Manṭiqiyāt li-al-Fārābi, vol. 1, texts published by Mohamed Teki Danesh Pazuh, Edition Qom, 41–82.

    Google Scholar 

  3. Al-Fārābī, Abū Naṣr. 1988. Kitāb al Qiyās. In Al-Manṭiqiyāt li-al-Fārābi, vol. 1, texts published by Mohamed Teki Danesh Pazuh, Edition Qom, 115–151.

    Google Scholar 

  4. Al-Fārābī, Abū Naṣr. 1988. Al-Qiyās al-Ṣaghīr. In Al-Manṭiqiyāt li-al-Fārābi, vol. 1, texts published by Mohamed Teki Danesh Pazuh, Edition Qom, 152–194.

    Google Scholar 

  5. Antonelli, Aldo. Non-monotonic logic. In Stanford Encyclopedia of Philosophy, ed. E.N. Zalta. http://plato.stanford.edu/entries/logic-nonmonotonic/.

  6. Aristotle. 1991. Prior Analytics. In The complete works of Aristotle, the Revised Oxford Edition, ed. Jonathan Barnes, vol. 1.

    Google Scholar 

  7. Averroes. 1982. Talkhīṣ Manṭiq Arisṭu (Paraphrase de la logique d’Aristote), volume 1: Kitāb Al-Maqūlāt, 3–77, Kitāb al-‘Ibāra, 81–141, Kitāb al-Qiyās, 143–366, ed. Gérard Jehamy, Manshūrāt al-Jāmi‛a al-lubnānīya, al-Maktaba al-sharqiyya. Beirut.

    Google Scholar 

  8. Avicenna. 1964. Al-Shifā’, al-Manṭiq 4: al-Qiyās, ed. S. Zayed, rev. and intro. I. Madkour. Cairo.

    Google Scholar 

  9. Avicenna. 1971. Al-Ishārāt wa l–tanbīhāt, with the commentary of N. Ṭūsi, intro. Dr. Seliman Donya, Part 1, 3rd ed. Cairo: Dar al Ma’arif.

    Google Scholar 

  10. Bobzien, Susanne. 2006. Ancient Logic. In Stanford encyclopedia of philosophy, ed. Edward N. Zalta. http://plato.stanford.edu/entries/logic-ancient/.

  11. Chatti, Saloua. 2014. Syncategoremata in Arabic logic, al-Fārābi and Avicenna. History and Philosophy of Logic 35 (2): 167–197.

    Article  MathSciNet  Google Scholar 

  12. Chatti, Saloua. 2016. Avicenna (Ibn Sīnā): Logic. Encyclopedia of logic, internet Encyclopӕdia of philosophy. College Publications. www.iep.utm.edu/av-logic/.

  13. Chatti, Saloua. 2017. The semantics and pragmatics of the conditional in al-Farabi’s and Avicenna’s theories. Studia Humana 6 (1): 5–17.

    Article  Google Scholar 

  14. Chatti, Saloua. 2019. Logical consequence in Avicenna’s theory. Logica Universalis 13: 101–133.

    Article  MathSciNet  Google Scholar 

  15. Dutilh Novaes, Catarina. 2011. The different ways in which logic is (said to be) formal. History and Philosophy of Logic 32 (4): 303–332.

    Article  MathSciNet  Google Scholar 

  16. Dutilh Novaes, Catarina, and Stephen Read. 2016. The cambridge companion to medieval logic. Cambridge University Press.

    Google Scholar 

  17. El-Rouayheb, Khaled. 2010. Relational syllogisms and the history of arabic logic, 900–1900. Leiden: Brill.

    Book  Google Scholar 

  18. Edgington, D. 2014. Conditionals. In Stanford encyclopedia of philosophy, ed. E.N. Zalta. http://plato.stanford.edu/entries/conditionals/.

  19. El-Rouayheb, Khaled. 2009. Impossible antecedents and their consequences: Some thirteenth-century Arabic discussions. History and Philosophy of Logic 30 (3): 209–225.

    Article  MathSciNet  Google Scholar 

  20. Hasnawi, Ahmed, Wilfrid Hodges. 2016. Arabic logic up to Avicenna. In The Cambridge companion to medieval logic, ed. Catarina Dutilh Novaes and Stephen Read, 45–66. Cambridge: Cambridge University Press.

    Google Scholar 

  21. Hodges, Wilfrid. 2017. Ibn Sīnā on reductio ad absurdum. The Review of Symbolic Logic 10 (3): 583–601.

    Article  MathSciNet  Google Scholar 

  22. Hodges, Wilfrid. 2018. Proofs as cognitive or computational: Ibn Sīnā’s innovations. Philosophy and Technology 31 (1): 131–153.

    Article  MathSciNet  Google Scholar 

  23. Hodges, Wilfrid. 2018. Two early Arabic applications of model-theoretic consequence. Logica Universalis 12 (1–2): 37–54.

    Article  MathSciNet  Google Scholar 

  24. Hodges, Wilfrid. 2017. Identifying Ibn Sīnā’s hypothetical logic I: Sentences forms. Draft, Nov 2017.

    Google Scholar 

  25. Hodges, Wilfrid. forthcoming. Mathematical background to the logic of Avicenna. Available at http://wilfridhodges.co.uk/arabic44.pdf.

  26. Lameer, Joep. 1994. Al-Fārābī and aristotelian syllogistics; greak theory and islamic practice. Brill Edition.

    Google Scholar 

  27. Largeault, Jean. 1972. Logique mathématique, textes. Paris: Armand Colin.

    MATH  Google Scholar 

  28. Łukasiewicz. 1934. Contribution à l’histoire de la logique des propositions. French translation in J. Largeault. 1972. Logique mathématique, textes. Paris: Armand Colin.

    Google Scholar 

  29. Marόth, Miklos. 1989. Ibn Sīnā und die peripatetische “Aussagenlogik”. Leiden: Brill.

    Google Scholar 

  30. Movahed, Zia. 2009. A critical examination of Ibn Sīnā’s theory of the conditional syllogism, vol. 1, no. 1, published in Sophia Perennis. www.ensani.ir/storage/Files/20120507101758-9055-5.pdf.

  31. Rescher, Nicholas. 1963. Studies in the history of Arabic logic. University of Pittsburg Press; Arabic trans. Mohamed Mahrān. 1992. Cairo.

    Google Scholar 

  32. Rescher, Nicholas. 2006. Studies in the history of logic. Ontos Verlag.

    Google Scholar 

  33. Russell, Bertrand, and Alfred NorthWhitehead. 1973. Principia mathematica. Paperback edition to *56. Cambridge University Press.

    Google Scholar 

  34. Shehaby Nabil. 1973. The propositional logic of Avicenna. A translation from al-Shifā al-Qiyās. Dordrecht Holland: Kluwer, D. Reidel.

    Google Scholar 

  35. Street, Tony. 1995. Ṭūsī on Avicenna’s logical connectives. History and Philosophy of Logic 16: 257–268.

    Article  MathSciNet  Google Scholar 

  36. Street, Tony. 2004. Arabic Logic. In Handbook of the history of logic, vol. 1, ed. Dov Gabbay and John Woods. Elsevier, BV.

    Google Scholar 

  37. Strobino, Riccardo. 2018. Ibn Sīnā’s Logic. The Stanford encyclopedia of philosophy. https://plato.stanford.edu/archives/fall2018/entries/ibn-sina-logic.

Download references

Author information

Authors and Affiliations

  1. Faculty of Human and Social Sciences, University of Tunis, Tunis, Tunisia

    Prof. Saloua Chatti

Authors
  1. Prof. Saloua Chatti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saloua Chatti .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Chatti, S. (2019). The Hypothetical Logic. In: Arabic Logic from al-Fārābī to Averroes . Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-27466-5_5

Download citation

Publish with us

Policies and ethics

Search

Navigation