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Two Squares of Opposition in Two Arabic Treatises: al-Suhrawardī and al-Sanūsī

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Abstract

The square of opposition has never been drawn by classical Arabic logicians, such as al-Fārābī and Avicenna. However, in some later writings, we do find squares, which their authors call rather ‘tables’ (sing. lawḥ). These authors are Shihāb al-Dīn al-Suhrawardī and Muhammed b. Yūsuf al-Sanūsī. They do not pertain to the same geographic area, but they both provide squares of opposition. The aim of this paper is to analyse these two squares, to compare them with each other and with the traditional square of opposition drawn by Apuleius and Boethius, with regard to their particular structure and their vertices and to evaluate their validity. We will show that both squares are different from each other and from the traditional square both with regard to their vertices, and to the arrangements of the oppositional relations. In addition, while al-Suhrawardī uses the notion of matter modalities to define the oppositions, al-Sanūsī relies rather on al-Rāzī’s and al-Khūnajī’s distinctions. Both authors agree, however, on the fact that affirmatives have an import while negatives do not. For this reason, their squares are valid from a logical viewpoint. As diagrams, these squares are nevertheless entirely original, due to the particular arrangements of their oppositional relations. Our analysis shows also that the later author does not seem to know the square drawn by the earlier one and that both authors do not seem to know Apuleius’ or Boethius’ squares.

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Notes

  1. See [13] and [12, 16] and Chatti, [18].

  2. These letters are not in Aristotle’s text. They are due to the medieval logicians who use them for practical reasons.

  3. This figure is drawn in Apuleius’s treatise ‘On Interpretation’ (see[8] Apulée, L’interpretazione, text established, translated and commented by M. Baldassarri, Côme, Quaderni del Liceo A. Volta, 1986).

  4. See, for instance, Saloua Chatti, “Logical Oppositions in Arabic Logic, Avicenna and Averroes” (2012) [13], Saloua Chatti and Fabien Schang [20] “The Cube, the Square and the problem of Existential Import” (2013), Stephen Read [26] “Aristotle and Łukasiewicz on Existential Import” (2015), and Terence Parsons “The Traditional Square of Opposition” (2017) [25].

  5. There are other ways to validate the square of opposition, as shown in [20], but they are less natural than the traditional one and they require a formal language to express symbolically the propositions, something that was not available in Ancient and Medieval times.

  6. See [11] Avicenna, al-’Ibāra, pp. 46–47 and [13], pp. 22–25, for an analysis of the oppositions and the table presenting all the truth values of the quantified propositions as they are presented by Avicenna.

  7. al-Fārābī, [1] al-Qawl fi al-’Ibāra (1988); [2] Kitāb al-’Ibāra (R. Al-Ajam, ed.) and [3] Kitāb al-Qiyās, Sect. 5. See also Hodges [22] ‘Introduction’, in [19], pp. 36–38, where Wilfrid Hodges analyses what he calls the “semantic square of opposition” (p. 38) endorsed by al-Fārābī, in which the oppositions are characterized by means of the truth values of the propositions.

  8. This example is given by al-Fārābī in [3] al-Qiyās, Sect. 3, p. 15. See also [19] Chatti, S. and Hodges, W. (eds), ‘al-Fārābī, Syllogism: An Abridgement of Aristotle’s Prior Analytics’, p. 120.

  9. This expression has also been used by Averroes (d. 1198), who lived at the same period as al-Suhrawardī but pertained to a different geographic area, since he was Andalusian.

  10. See, for instance, Chatti and Schang ([20]), p. 113.

  11. Note that this definition is less precise than Avicenna’s one, for unlike Avicenna, al-Suhrawardī omits to say that in the possible matter, the particular should be true in order for subalternation to hold.

  12. See also Fig. 4 below, which translates in English the linguistic content of this Fig. 3

  13. Note, here, that what is written in Arabic, in the text, can be translated as ‘Not some C is B’ and not, as one reviewer suggests, as ‘Some C is not B’, since the word ‘laysa’ (= not) is indeed written before the word ‘ba’d’ (= some), and not after it. This is why we have kept this translation, despite its strangeness from a logical viewpoint, as rightly stressed by the reviewer, since its logical structure makes it closer to ‘\(\sim \) I’ (= E). It does not seem, however, that the editor or even Avicenna interprets it as ‘\(\sim \) I’, for ‘\(\sim \) I’ is more adequately expressed in Arabic by ‘lā aḥada’ (= no one), where the word used to express the particular is ‘aḥad’ or ‘wāḥid’, not the word ‘some’. So it seems that for them, ‘Not some C is B’ is just another usual way to express O in the Arabic language. In addition, ‘Some C is not B’ expresses a particular negative proposition which has an import, while ‘Not every C is B’ is clearly without import. This makes both expressions of the O proposition different from each other.

  14. See also El-Rouayheb, K. The Development of Arabic Logic, 1200-1800, Shwabe Verlag, Basel, 2019, pp. 134–135.

  15. See [10] Avicenna, al-Ishārāt wa al-Tanbīhat, p. 250, in particular the explanations of Naṣīr al-Dīn al-Tūsī in that page, which clarify the meanings of the three disjunctions.

  16. Ibn ’Arafa provides also extensional definitions of the conditional as has been shown in Chatti, which was not the case with his predecessors, whose definitions of the conditional were as intensional as Avicenna’s ones.

  17. This distinction has been introduced by al-Rāzī in his Mulakhkhasò (see [27] Tony Street Afḍal al-Dīn al-Khunājī on the conversion of modal propositions”, 2014, p. 461).

  18. For an analysis of these readings of the categorical propositions, see, for instance, [27], pp. 454–513 and also [17] Saloua Chatti ‘Existential Import in Avicenna’s Modal Logic’, Arabic Sciences and Philosophy, 2016, in particular pp. 66–68.

  19. See, for instance [15], Saloua Chatti ‘The Logic of Avicenna between al-Qiyās and Mantiq al Mashriqiyīn’, Arabic Sciences and Philosophy, 29 (2019): 109–131.

  20. Professor Wilfrid Hodges told me that he saw a square drawn in one treatise of Bahmanyār, a student of Avicenna (personal communication).

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Chatti, S. Two Squares of Opposition in Two Arabic Treatises: al-Suhrawardī and al-Sanūsī. Log. Univers. 16, 545–580 (2022). https://doi.org/10.1007/s11787-022-00312-w

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