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Logical Consequence in Avicenna’s Theory

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Abstract

In this paper I examine Avicenna’s conception of the consequence relation. I will consider in particular his categorical and hypothetical logics. I will first analyse his definition of the implication and will show that this relation is not a consequence relation in his frame. Unlike the medieval logicians, he does not distinguish explicitly between material and formal consequences. The arguments discussed in al-Qiyās, where the conclusion is true only in some matters, and would seem close to a material consequence for that reason, are rejected explicitly as not syllogistic. He also rejects the ‘enthymemes’ unless they are complemented by their missing premise and the superfluous premises which, according to him, should promptly be ruled out. It seems then that the consequence relation in his theory is formal. It can be characterized as being ‘productivity in all matters’ or ‘necessary truth preserving’. It is illustrated by some (but not all) single premise arguments, and above all by all kinds of syllogisms which, in his theory, are more numerous and various than in Aristotle’s one. The syllogism may contain two or more premises, including disjunctive ones. When it is hypothetical, it may lead to several conclusions. The premises may be in conflict, but then, the conclusion is false. He thus rejects the principle according to which ‘anything follows from a contradiction’. But, unlike what some scholars say, he does not admit any connexive principle. In the compound syllogisms, the conclusion follows by steps, each step taking two premises at once.

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Acknowledgments

I would like to thank an anonymous reviewer for his very detailed and fruitful comments, criticisms and suggestions about an earlier version of this paper, which improved it in several ways. I am equally very grateful to Prof. Wilfrid Hodges for his invaluable and precious help and suggestions and also for having procured me many useful documents. Thanks also to Prof. Stephen Read and all the participants of the workshop ‘Medieval Logic’ at UNILOG 2015 for their valuable questions and remarks and to Prof. Jean-Yves Beziau for his help and patience.

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  1. Department of Philosophy, Faculty of Human and Social Sciences, University of Tunis, 94, boulevard du 9 avril 1938, 1007, Tunis, Tunisia

    Saloua Chatti

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Chatti, S. Logical Consequence in Avicenna’s Theory. Log. Univers. 13, 101–133 (2019). https://doi.org/10.1007/s11787-018-0210-y

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