Introduction

The expression ‘Arabic logic’ is used by scholars to cover a tradition of writing over a period stretching from the eighth century to the present day. The treatises and handbooks that belong to this tradition were written in various languages, including Arabic, Persian, Turkish, Hebrew, and Urdu. The central figures are Alfarabi (d. 950), Avicenna (d. 1037) and Averroes (d. 1198) (Street 2013a, introduction). Because of limitations of space, this chapter will omit Alfarabi, discussing only Avicenna and some of the more significant thinkers (including Averroes) whose work is based on, or reacts against, the latter's logical theories.

Avicenna

Avicenna uses the term ‘necessary’ to mark out (a) a class of beings, and (b) a class of propositions. His doctrine of the unique Necessary Being from which all contingent beings are derived is well known. Contingent beings are described as ‘possible’; but ‘possible’ here means two-sided possibility. A contingent being is one that can either exist or not exist. Whether it exists depends on a cause external to it. A necessary existent is one that cannot not exist, because its existence does not depend on anything external:

What is the connection between the usage of ‘necessary’ as a predicate of beings and its usage as a predicate of propositions? There is some evidence that, in Avicenna's view, the first usage is a particular case of the second – that to say a being is necessary is to say that the proposition expressing the being's existence is a necessary proposition. Avicenna's standard example of a proposition which is absolutely necessary is a proposition about the Necessary Being, namely, the proposition ‘God exists’ (Street 2004, 551).

INTRODUCTION

The logical analysis of modalities, as initiated in Aristotle's On Interpretation and Prior Analytics, focused on the inferential relations among modal propositions, i.e. propositions concerning necessity, possibility and contingency. The Aristotelian legacy of modal logic underwent major transformations in medieval times, in both the Arabic and the Latin traditions. But these transformations took very different forms in the two traditions. The corpus of Aristotle's works was available in Arabic translation at a very early stage as a result of the translation movement that flourished under the ʿAbbāsid caliphate in eighth- to tenth-century Baghdad. Crucial works for modal logic such as Aristotle's On Interpretation and Prior Analytics, as well as texts of indirect but equally significant relevance from the physical and metaphysical corpus were known to logicians in this tradition from the very start. In the Latin tradition, a comprehensive response to Aristotle's writings on the logic of modality had to await the rediscovery in the late twelfth century of the full text of Prior Analytics. The early availability of the key Aristotelian texts to the Arabic world sparked an interpretive effort whose primary concerns were to understand those texts and to resolve the difficulties which they posed. The first fruits of this effort were the commentaries of al-Fārābī (d. 950), whose long commentary on Prior Analytics has, sadly, not survived. The commentatorial tradition in the Arabic-Islamic world reached its apogee in the works of Averroes (d. 1198). The earliest Latin commentary on Prior Analytics, an anonymous and incomplete work, dates from the late twelfth century. The earliest known complete Latin commentary is that of Robert Kilwardby (d. 1279), although, as we shall see below, some of his ideas about the meaning of modal sentences have precedents in the writings of Peter Abelard (d. 1142).

Long before Kilwardby's time, modal logic had received an extraordinary impulse in the Arabic-Islamic world, in the figure of Avicenna (d. 1037), who developed a new and original system that departed from Aristotle in crucial ways. Avicenna's system in effect relegated Aristotle's modal logic to a purely marginal role. The work of the post-Avicennan logicians, particularly in the twelfth- and thirteenth-century Eastern tradition, evolved in ways that are entirely independent of Aristotle and seem to be motivated exclusively by the need to go beyond Avicenna's system (Rāzī d. 1210; Khūnajī d. 1248; Kātibī d. 1276) or to defend it (Ṭūsī d. 1274).

Every medieval logic compendium, and every medieval commentary on Aristotle's Analytics, has something to say about the syllogism. While there is a core of standard logical syllogistic theory that is unchanging across the Middle Ages, there are also significant theoretical differences from one author to another. Some of these concern the very definition of the syllogism. Aristotle had crafted the classic definition; but at different times during the Middle Ages, and in different traditions, opinions differed on how much of the Aristotelian definition should be retained, and how the retained clauses should be interpreted. In this chapter, we examine some of the more interesting transformations that the definition of the syllogism underwent in the Arabic and Latin Middle Ages.

Conceptions of the syllogism undergo transformations over time. But the syllogism itself, as a logical structure, is also capable of certain types of transformation. One of these gives rise to what Aristotle called conversive syllogisms (Aristotle 1965, 59b1), and we will consider some medieval analyses of this type of transformation. We will also look at a related form of argument, the syllogism through the impossible. And these investigations will lead us back to the question of the nature of the syllogism.

INTRODUCTION

The Aristotelian theory of the syllogism makes use of technical terminology that was to become standard in both the Arabic and Latin traditions. A categorical proposition contains two terms – a subject and a predicate. Such a proposition states that the predicate applies to all, or to none, or to some, or to not all of the subject. Propositions of the first two of these types are universal, those of the last two types particular; these two attributes give a proposition's quantity. Propositions of the first and third types are affirmative, those of the second and fourth negative; these attributes give a proposition's quality. A valid inference from two categorical propositions (the premises) to a third (the conclusion) is a syllogism only if its two premises share a term (the middle term), and each premise shares a term with the conclusion. The predicate of the conclusion is the major term, and its subject the minor term. Three different arrangements of the middle, minor and major terms were standardly recognised, and these arrangements were called the figures of the syllogism. In the first figure, the middle term is subject in one premise and predicate in the other.