Abstract
In this paper, I examine Avicenna’s and Averroes’ theories of opposition and compare them with Aristotle’s. I will show that although they are close to Aristotle in many aspects, their analysis of logical oppositions differs from Aristotle’s by its semantic character, and their conceptions of opposition are different from each other and from Aristotle’s conception. Following Al Fārābī, they distinguish between propositions by means of what they call their “matter” modalities, which are determined by the meanings of the propositions. This consideration gives rise to a precise distribution of truth-values for each kind of proposition, and leads in turn to the definitions of the logical oppositions. Avicenna admits the four traditional oppositions, while Averroes, who seems closer to Aristotle and especially to Al Fārābī, does not mention subalternation, but admits subcontrariety. Nevertheless, we can find that Averroes defends what Parsons calls SQUARE and [SQUARE], because he holds E and I-conversions and the truth conditions he admits are just those that make all the relations of the square valid, while Avicenna defends SQUARE and [SQUARE] only for the waṣfī reading of assertoric propositions. They also give a special attention to the indefinite which in Averroes’ view is ambiguous, while Avicenna treats it as a particular. Some points of their analysis prefigure the medieval concepts and distinctions, but their opinion about existential import is not as clear as the medieval one and does not really escape the modern criticisms.
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Notes
- 1.
Wilfrid Hodges in [19, p. 13] translates this passage in the following way: “We say: opposing pairs are those which don’t combine in a single subject from a single aspect at a single time together.”
- 2.
Avicenna uses also the expression ‘maḍkūrat as sūr’ and the word ‘maḥṣūra’ to designate the quantified propositions. As to Al Fārābī, he uses the expression ‘ḍawāt al aswār’ (i.e. those that contain quantifiers) [2, p. 121].
- 3.
I thank one anonymous referee who drew my attention to the fact that the word ‘sūr’ is “heir to the notion of «prosdiorismos» in the Greek commentators of Aristotle”.
- 4.
However in [14, p. 70], Avicenna says that the singular propositions which are in the future are not necessarily true or false and seems to agree with Aristotle in his treatment of the problem of the “future contingents”, although he gives more details on the possible propositions.
- 5.
The Arabic sentence is the following: “… yadūmu wa-yajibu kadhibu ījābihi…yusammā māddat al- imtinā‘.”
- 6.
We find the expression “matter modalities” in Al Fārābī’s text too and the word matter seems to have a long history starting from Aristotle and his Greek commentators. The matter (hūlē) in Aristotle is opposed to the tropos, which has a rather vague sense and could mean the form of the proposition (see [18, p. 298]). In Ammonius’ text, it is related to modalities since he says in his De Interpretatione: “These relations <between subject and predicate> they call the matter of propositions and they say they are necessary, impossible or possible” (cited in [8, p. 233]). The necessity, possibility or impossibility are, according to this author, “due to the very nature of the objects” [8, p. 233]. In Avicenna’s text, the modal sense is clear as we have seen.
- 7.
Unlike Aristotle, Avicenna does not use the word “contingency” in [14, p. 122].
- 8.
As far as I know, there is no mention of this word in Al Fārābī’s texts; Al Fārābī does not mention nor include subalternation in his treatment of oppositions.
- 9.
This observation is due to Fabien Schang. I thank him for having pointed it out to me in an informal discussion.
- 10.
The reader can check the values of this relation by himself.
- 11.
- 12.
This formalization of O comes from a suggestion made by Fabien Schang in an informal discussion. I thank him for fruitful discussion about this topic.
- 13.
The reader may check the validity of this relation and all the others by constructing truth tables with the given formulas.
- 14.
This examination is made in another article written with Fabien Schang, which is under consideration.
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Acknowledgements
I would like to dedicate this article to my colleague Dr Hatem Zeghal, recently deceased, who gave me Avicenna’s books and whose knowledge and advice were very precious to me. I am also grateful to my colleague Professor Mokdad Arfa for fruitful discussions, to Professor Jean-Yves Béziau for his precious help and advice, to Fabien Schang who read an earlier version of this paper and made very valuable remarks, to the anonymous referees for their useful and helpful comments, suggestions and criticisms, and to Amirouche Moktefi who procured me some useful references.
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Chatti, S. (2012). Logical Oppositions in Arabic Logic: Avicenna and Averroes. In: Béziau, JY., Jacquette, D. (eds) Around and Beyond the Square of Opposition. Studies in Universal Logic. Springer, Basel. https://doi.org/10.1007/978-3-0348-0379-3_2
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