Logic in the Islamic Legacy: a General Overview

The Aristotelian Expositors


Al-farabi was the outstanding contributor to the Aristotelian project, though not as a translator. Al farabi claimed that logic was indispensable for analyzing the argument-forms used in jurisprudence and theology, a claim that was to be taken up a century later by Abu Hamid al-Ghazali (d. 1111), thereby introducing the study of logic into the madrasa. To support his claim, Alfarabi wrote The Short Treatise on Reasoning in the Way of the Theologians …in which he interpreted the arguments of the theologians and the analogies (qiyâsât) of the jurists as logical syllogisms in accordance with the doctrines of the ancients.

Maybe Alfarabi is the first truly independent thinker in Arabic logic, a fact commemorated by bestowing upon him 'the Second Teacher' (after Aristotle). Al farabi was the first Muslim to bring Greek thinking closer to Islamic understanding, which, then pivoted around the codification and clarification of Qur'anic expression. al-Fiarabi was first and foremost a commentator of Aristotelian texts; his commentary on Aristotle's Organon served as the work of reference for other Muslim scholars. His work, however, went further in analogical reasoning to produce unique ideas not present in the Aristotelian original, and was dedicated to the inclusion of analogical inferences (transference). AI-FarabI's original contribution to analogical inference lay in his systematization of inductive reasoning under the rubric of the categorical syllogism. His intent was to raise the strength of analogy to that of a first order Aristotelian syllogism, i.e. a syllogism which does not deviate from the Greek rendering of two premises, a middle term, and the production of new knowledge which in turn may serve as a premise for further inferences. Drawing general or universal conclusions from premises generated by the scientific study of experience bodes well with the analogical framework of likewise generating general conclusions from particular instances of human experience-foreshadowing the methods of induction not yet fully developed in Western philosophical history. This commensurability between the formal syllogism and analogy is defended by al-Farabl when he uses what he calls "inference by transfer" or, as he notes of the mutakallimiln, "inference from evidence to the absent", or, as Kant would have it, from the phenomenal to the noumenal realms. The act of transference requires that the syllogism have a middle term, what analogy calls similarity. AI-Farabi further contends that, "if we are determined to have the 'transfer' be correct it is necessary that the 'matter' which is similar in the two compared objects be investigated. He presents a case depicting the (evident) createdness of animals or plants with the (absent) notion of createdness in the sky and the stars, and sets out to establish not only a middle term that denotes similarity, but one which also speaks of relevance. If both similarity and relevance obtain, then analogical inference takes on the form and strength of a first order syllogism, and a causal connection is established.

However, problems still arise when similarity might appear to obtain, but, in fact, does not. When this happens, analogical reasoning contains at

least one faulty premise that has not been detected by those forwarding an analogical argument. AI-Farabi refers to this distinction as the method of "raising" whereby conclusions are raised but do not obtain upon further logical investigation. However, leaving room for a legitimate analogy, al-Farabi then speaks of the method of "finding". 'Simply stated, al-Farabl reminds the reader that, "if one establishes a judgment by 'raising' it does not necessarily result that when one' finds' this thing (which is 'raised') one will 'find" the judgment (to be true); rather it is the converse of this that is necessitated, namely if one 'finds' the judgment, one 'finds' (also) the thing (in question)". In this sense, al-Farabi anticipates harsh criticisms against the analogy that he does not necessarily accept. Inductive and analogical arguments were converted into syllogisms making the cause or similarity in analogy the middle term in the syllogism", which compounded the difficulty of defining and determining the exact limits of qiyas. The force of the inferences made in an analogy is identical to those of a first figure syllogism because the similarity (' illa) is the subject term in the major premise and the predicate term in the minor. If the 'illa is absent when the judgment is absent...and present when the judgment is present... the 'illa is all the more true. If one removes animality, for example, from a thing, then one removes from this thing the property of being a man. But it is not necessarily true that if one finds an animal he also finds a man. Rather the converse is true; if one finds a man it necessarily follows that one finds an animal. To establish the truthfulness of a matter by the method of non existence, it necessarily follows that when the 'illa is found the judgment is also found. In order to ensure valid conclusions from an analogy (following this reasoning) the similarity ('illa), has to be relevant to the two cases; the judgments must be true of any case if it has the same' illa; the 'illa itself must be found and verified in each of the cases considered; it must be established that the judgment exists in all cases which possess an 'illa in common.  al-Farabi's importance lies in the fact that he placed heavy emphasis on the necessity and importance of the 'illa in all inferences: "For a complete inference and for achieving a high degree of certainty he insists that an illa must accompany the judgment". AI-Fariibi's marriage of analogy to the first order syllogism exists within a neo-Platonic and Aristotelian framework of metaphysics, replete with positivistic inclinations concerning the notions of cause and effect, and its importance for both logic and onto-logic. Thus, his legal concerns cross both «Islamic and Greek boundaries at their very source, and are less tied to simply the a priori sensibilities demanded by the more literal readings of the Koran that were adhered to by the mutakallimun. AI-Farabi managed to transform analogy into a first-figure syllogism, setting a standard by which the legal process could be developed. AI-Farabi had maintained, in accordance with his Neo-Platonic Aristotelian emanative position, that Allah was the God of metaphysical (i.e. causal) statements and that the Koran had to be interpreted metaphorically. This, along with discussions on logic and other sciences, was nonetheless accused of being un-Islamic, and the theological milieu remained highly antagonistic to the Greek "foreign"/heretical sciences. They rejected the concept of natural causation (i.e., arguing from cause to effect and from

effect to cause) that maintained that phenomenal acts advance from a thing's quiddity. They held the view that only divine will held the power to cause. It was in this manner, that they upheld the concept of divine omnipotence. And later, al-Farabi would become the focus of attacks directed against the "School of Baghdad".

Averroes (Ibn Rushd) and the End of Aristotelianism

Averroes was one of the last representatives of a dying Farabian Aristotelianism. Averroes was aware of Alfarabi's attempts to make sense of the difficulties in Aristotle's texts. In one such area, the modal logic, Averroes was to return to the problems four times through his career.

Averroes' project is illustrated in his Philosophical Essays, a number of which are on logical matters. Averroes defends and refines Alfarabi's account of the conversion of modal propositions and then uses that account as the basis of a new interpretation of the modal syllogistic. A second example of the way Averroes works is his reappraisal and vindication of Aristotle's doctrines of the hypothetical syllogistic against Avicenna's alternative division into connective and repetitive syllogisms (Averroes (1983) Maqâlât essay 9, 187-207).

In his fourth attempt to interpret Aristotle's modal system Averroes differs from Avicenna first and foremost by insisting on a consideration Avicenna has been at pains to remove from his syllogistic: is the subject picked out by a term essential to it?

Averroes' final system comprises two distinct aspects. The first aspect - not original to Averroes nor apparently to the Arabic tradition - is seeing the modality of a proposition as a function of the modality of its terms, which in turn is a function of how each term picks out what it refers to. The second aspect is that different classes of modal syllogism are differentiated by the types of terms occurring in them. Rather than looking on the modality of the proposition as something which belongs irreducibly to the proposition, Averroes classifies modals in the following way:

You should know that assertoric propositions have assertoric terms, necessary propositions necessary terms. By “necessary term” I mean that the term is one per se, and these propositions are composed of a subject and an essential predicate (mahmûl jawharî) of that subject, or a subject and an inseparable accident*(‘arad lâzim* ) belonging to that subject. Those propositions with assertoric terms are those which are composed of denominative terms which are sometimes present in the denominated thing and sometimes absent (sifât tûjad lil-mahmûl târatan wa-tufqad târatan ). But when one of these denominative terms is present in the subject, there must be present another denominative term that follows on it necessarily which is the predicate, as in: everything walking is moving. For when walking is actually present the thing must be moving; and when walking is withdrawn from it (irtafa‘ minhu ), so too is movement. These are the simple assertoric premises (al-muqaddamât al-wujûdiyya al-basîta ) which are atemporal (fî ghayri zamân ), and they are what Aristotle intends firstly to talk about in this book. Their subject and predicate alike are one per accidens (wal-mawdû‘ fîhâ wâhid bil-‘arad wa-ka-dhâlika l-mahmûl ). And there exists another kind of proposition that is partly assertoric and partly

necessary (min jiha wujûdî wa-min jiha darûrî ) - that is, the subject is composed of a substance and a changeable denomination (jawhar wa-sifa mutabaddila ), from which follows a predicate composed of the substance of the denomination and its intrinsic essential attribute (sifa jawhariyya gharîziyya ). The subject here is one per accidents and the predicate is one per se, for example, when we say that everything walking is an animal. And this is assertoric on account of the denomination of the denominated subject, and necessary on account of the predicate of the denomination. For walking, when it occurs, signifies an animal by discontinuous signification (fal-mashy idhâ wujida dalla ‘alâ l-hayawân dalâlatan ghayra dâ'ima ), but for the times at which walking is present in it. The subject of walking implies being an animal always (wa-mawdû‘u l-mashy yalzamuhu wujûdu l-hayawân dâ'iman ), because the subject of walking and what is denoted by that is necessarily an animal. And this proposition is in one respect necessary and in another assertoric (darûrîya min jiha wa-wujûdîya min jiha ) - necessary per accidens and assertoric per se (darûrîya bil-‘arad wa-wujûdîya bidh-dhât ). A proposition that conversely has a necessary subject and a predicate of assertoric matter (mâdda ) is just assertoric, and is not necessary per accidens. This is a temporal assertoric, I say, where the subject implies the predicate for a specified time, and necessity is not found in it, only a connexion of the predicate and subject merely for that time. The characteristic of this [proposition] is that the predicate is not connected to the subject for all times at which the subject exists, but only for a certain specified time. And so, as Aristotle says, syllogisms in the sciences are not constructed from this type of assertoric.

With a per se necessity proposition described above, he has truth-conditions which will allow him to make sense of Aristotle's claim that every J is necessarily B converts to some B is necessarily J. In fact, Averroes is able to replicate Aristotle's results with necessity and possibility premises (Thom (2003) 199). He does so, however, at the cost of having to slide between calling a proposition of type 3 a necessity proposition or an assertoric according to the dictates of the exegetical moment.