Logic in the Islamic Legacy: a General Overview

Dissention from Aristotelian Legacy

The Avicennan Tradition of the Twelfth Century

Avicenna (d. 1037) was beginning his career far away in the east, in Khurasan (Persia). Led by his Intuition, he presented himself as an autodidact able to assess and repair the Aristotelian tradition. Here is what he says in the Syllogism of the Cure, written about midway through his career:

'You should realize that most of what Aristotle's writings have to say about the modal mixes are tests, and are not genuine opinions - this will become clear to you in a number of places…' (Avicenna (1964), Qiyâs 204.10-12)

Of all his many works, it is Avicenna's Pointers and Reminders that had most impact on subsequent generations of logicians. From it we may note a few broad but typical differences from the Prior Analytics in the syllogistic. First, the “absolute” (mutlaqât , often translated “assertoric”) propositions have truth-conditions stipulated somewhat like those stipulated for possibility propositions (so that, for example, the contradictory of an absolute is not an absolute, absolute e-propositions do not convert, second-figure syllogisms with absolute premises are sterile). Secondly, Avicenna begins to explore the logical properties of propositions of the form every J is B while J. Thirdly, Avicenna divides syllogistic into connective (iqtirânî ) and repetitive (istithnâ'î ) forms, a division which replaces the old one into categorical and hypothetical (Avicenna (1971) al-Ishârât 309, 314, 374). We may call a logician “Avicennan” if he adopts these doctrines.

Avicennan logicians embarked upon repairing and reformulating Avicenna's work. Just as Avicenna had declared himself free to rework Aristotle as Intuition dictated, so too Avicenna's school regarded itself free to repair the Avicennan system as need arose, whether from internal inconsistencies, or from intellectual requirements extrinsic to the system. A major early representative of this trend is ‘Umar ibn Sahlan as-Sawi (d. 1148) who began, in his Logical Insights for Nasîraddîn, to rework Avicenna's modal syllogistic. It was to be his students and their students, however, who would go on to make the final changes to Avicennan logic that characterized the subject that came to be taught in the madrasa.

Tûsî and the Neo-Avicennan Response

The great Shî‘î scholar Nasiraddîn at-Tûsî (d. 1274) explains why Avicenna explores it the way he does:

What spurred him to this was that in the assertoric syllogistic Aristotle and others sometimes used contradictories of absolute propositions on the assumption that they are absolute; and that was why so many decided that absolutes did contradict absolutes. When Avicenna had shown this to be wrong, he wanted to give a way of construing those examples from Aristotle (Tusi (1971) Sharh al-Isharat 312.5-7).

Revisionist Avicennan Logicians

By and large, the Revisionists adopt most of Avicenna's distinctions and stipulations. But - on their preferred reading of the proposition - they reject, among other inferences. If every J is possibly B, and every B is necessarily A, it doesn't follow that every J actually becomes B such that it is necessarily A. Kâtibî does not ampliate the subject term to the possible (so that it would be understood as every possible B is necessarily A), nor does he read each proposition as being embedded in a necessity operator. Rather, he understands the possibility proposition as follows: there are Js, and whatever is at one time J is possibly B. This means that Kâtibî and the other Revisionists have a modal syllogistic that differs significantly from Avicenna's. The way the Revisionists put this difference is as follows:

Our statement every J is B is used occasionally according to the essence (hasab al-haqîqa ), and its meaning is that everything which, were it to exist, would be a J among possible individuals would be, in so far as it were to exist, a B; that is, everything that is an implicand of J is an implicand of B. And occasionally [it is used] according to actual existence (hasab al-khârij ), and its meaning is that every J actually (fî l-khârij ), whether at the time of the judgment or before it or after it, is B actually (fî l-khârij ).

The distinction between the two considerations is clear. Were there no squares actually (fî l-khârij ) it would be true to say a square is a figure under the first consideration and not the second; and were there no figures actually other than squares, it would be correct to say every figure is a square under the second consideration but not the first (Kâtibî (1948) Shamsiyya 91.1-4, 96.12-14).

In fact, the Revisionists are prepared to accept the Avicennan inferences given an essentialist reading of the propositions, but this is a half-hearted concession never pursued in their treatises. The question is why, and I conclude this section by speculating as to the answer.

Both groups, the Avicennan and the Revisionists, want to be able not only to trace valid inferences, they want also to use the system they produce for extra-logical purposes. They want arguments that are not only valid, but also sound, that is, arguments that are not only formally perfect, but that have true premises. To use the essentialist reading to say every cow is necessarily four-stomached, as an Avicennan would, is to claim necessarily, every cow is necessarily four-stomached; this is much stronger in one important respect than the Revisionist claim that there are actually cows, and everything that's actually a cow is necessarily four-stomached.

Ghazâlî and Logic

The twelfth century is one of the most complex periods of transformation in Muslim intellectual history. This period has been called the Golden Age of Arabic philosophy. The growth of logic in the preceding two centuries was concordant with the advance of the medical sciences and consequently it gained support with a wider audience. The century before had seen the advent of the madrasa as the prime institution of learning in the Islamic world (Makdisi (1981) 27-32), and Abu Hamid al-Ghazali (d. 1111) had been appointed to the most prestigious of these new institutions. Ghazali had successfully introduced logic into the madrasa which attracted much more gifted logicians (Gutas (2002). al-Ghazali took up Alfarabi's arguments in support of the utility of logic for theology and law, especially in his last juridical summa, Distillation of the Principles of Jurisprudence, a text which soon became a mainstay of the madrasa.

It is in this period that the major change in the coverage and structure of Avicennan logic occurred. The late twelfth century also saw Averroes produce what was effectively the last of the work in the Farabian tradition of logic, work which was to be translated into Hebrew and Latin but which was neglected by Arabic logicians. Finally, through the course of the twelfth century, the modified Avicennan logic that would be adopted by the logic texts of the madrasa began to emerge.

Ghazali argued that, properly understood, logic was entirely free of metaphysical presuppositions injurious to the faith. This meant that logic could be used in forensic reasoning:

We shall make known to you that speculation in juristic matters (al-fiqhiyyât ) is not distinct from speculation in philosophical matters (al-‘aqliyyât ) in terms of its composition, conditions, or measures, but only in terms of where it takes its premises from (Ghazâlî (1961) Mi‘yâr 28.2-4).

Ghazali tended to an even stronger position towards the end of his life: more than being merely harmless, logic was necessary for true knowledge. However for all his historical importance in the process of introducing logic into the madrasa, the logic that Ghazâlî defended was too dilute to be recognizably Farabian or Avicennan.

AI-Ghaziili's position was largely formed by both his philosophical preparation and his theological convictions. al-Ghazali as a jurist/theologian was very much interested in the logical questions that legal discussions could comprise. The attraction that the foreign sciences held for al-Ghazali was in direct relation to their usefulness in furthering the cause of theology. AI-Ghazali raised the possibility that these sciences could be demonstrably true and that they might have some bearing on religion, i.e., that when the specialized sciences (mainly logic and physics) offered demonstrations which conflicted with the literal readings of scripture, the latter must alter their status to one of metaphor. And because al-Ghazali held the view that God could not actuate something self-contradictory, literal readings should therefore be subjected to demonstrable proofs where and when they appear to exist. For example, when dealing with some of the well established facts of cosmology such as eclipses he writes: "thus, when one who studies these demonstrations and ascertains their proofs, deriving thereby information

about the times of the two eclipses, their extent and duration, is told that this is contrary to religion, he will not suspect this science, but only religion.

However, al-GhazalI also wanted to maintain that logic and the sciences were doctrinal1y neutral, particularly where the world of natural causation was concerned, and especially where they attempted to redefine the ontological stature of the Qur'an. He states:

"As for logical sciences, none of these relates to religion either by way of denial or by affirmation. They are no more than the study of the methods or proof and standards of reasoning, the conditions of the premises of demonstration and the manner of their ordering, the conditions of correct definition and the manner of its construction.

In rejecting "the principle of necessary causal connection" which was "the cornerstone of Aristotelian demonstrative science," al-Ghazal'i entered into a paradox viz. the logical sciences to which he was committed. How can logic and science adjudicate scriptures, but remain doctrinally neutral in its first principles? al-Ghazal'i's intent was not to indicate that demonstrative logic is philosophically uncommitted. In stead, his purpose lay in the impossible attempt to prove that its philosophical commitment is not given to an Aristotelian metaphysic.

Al-Ghazal'i was evidently reacting against what was then the well established refusal at the time, to integrate useful aspects of formal logic (i.e., the syllogism) into law. Attempting to avoid a contradictory position where logic is concerned, al-Ghazal'i maintained that logic could be disengaged from the heretical metaphysical framework in which it was imbedded and be used as a tool or method in the realm of al-fiqh. Whether he did so successfully or not is questionable. The answer given by al-Ghazali is motivated by theological reasons first and foremost. It is based on the parent eternal nature of the natural world implied by emanationist (causal) theories which attempt either to lower God's eternality to the finite stature of the world, or raise the finitude of the world to God's eternality, much in the way al-Farabi attempted to move from "evidence to absence". Both would be contradictory statements about the sovereign nature of God as stated in the Qur'an. Instead, al-Ghazali attempts to jettison the metaphysical aspects of Greek thinking, while harmonizing its logical tools with Islamic law.

Al-GhazalI's reformulation of the Greeks' tools of reasoning (qiyas/syllogism) relates primarily to matters of law which denote items given to "less clear speech" as opposed to "clear speech". These ambiguous legal aspects might suggest (I) finding a text relevant to the new case in the Qur'an or HadIth; (2) discerning the essential similarities or ratio legis between two cases; (3) allowing for differences lfuruq) and determining that they can be discounted; and (4) extending or interpreting the ratio legis to cover the new case. But under the auspicious abilities of qiyas that bore some affinity with a fortiori forms of reasoning, al-Ghazali endeavored to include analogy, and argumentum a simile. Al-Ghazal'i demarcates the qiyas from analogy only on the basis that the former bears certain knowledge, while the latter renders only probable inference. AI-GhazalI's insistence on converting analogy to a first figure syllogism, a reformulation of al-FarabI's

systemization of inductive reasoning, intentionally grounded legal theory in an Aristotelian framework of knowledge. Here an awareness of the dubious relationship between analogy and the syllogism (qiyas ) uncovers an inconsistency in the metaphysical system that supported it. We can leave aside the dichotomous application of logic given by al Ghazali who found it relevant in worldly (legal) affairs, but troublesome when impinging on established metaphysical norms, or theology (viz. the circumstances of God's unlimited freedom).

In sum it was Gazali's madrasa that provided the backbone of the tradition, and a number of jurists came time and again to stress that the study of logic was so important to religion as to be a fard kifâya, that is, a religious duty such that it is incumbent on the community to ensure at least some scholars are able to pursue its study. In Gazali's words:

As for the logic that is not mixed with philosophy ….  there is no disagreement concerning the permissibility of engaging in it, and it is rejected only by he who has no inkling of the rational sciences. Indeed, it is a fard kifâya because the ability to reply to heretical views in rational theology (kalâm), which is a fard kifâya, depends on mastering this science, and that which is necessary for a religious duty is itself a religious duty.

lbn Taymiyya

lbn Taymiyya is best considered a theologian and a jurist, one who often leveled polemical accusations at Greek logic. Like al-Ghazali, lbn Taymiyya was concerned with God's unlimited power and freedom of the divine will, and so rejected causal theories which would tie God explicitly to the natural world and qualify his involvement (causality) with his world. Thus, al1 forms of unitary exposition (universals) were rejected as conventions (nominal) by lbn Taymiyya.

Ibn Taymiyya's position rested on its own universal premise: that under no conditions can universals (of any kind) be established outside the mind of the one who experiences. Doubtless, the exception here is prophecy. This amounted to a rejection of universals altogether, i.e., an anti-realist and nominalist position in metaphysics which claims that where universals flourish in logical discourse, they do so only mental1y, and not (in any sense) in reality. Thus, universals can be established so long as it is understood that they function pragmatically within the specific needs of a given context, that which still demands a medium for human communication. Universals cannot obtain either metaphysically, or theologically, where there is open and full communication with God. The substance/accident debate collapses in Ibn Taymiyya's nomimalist schematic. Essence and accident are but arbitrary and relative demarcations set apart from each other in accordance with usage. Ibn Taymiyya writes: "Furthermore, there is no doubt that what the logicians held concerning the theory of definition is of their own invention...Accordingly, it is necessary for them to distinguish between what in their opinion is essential and what is not...whereby they deem one attribute, to the exclusion of the other, to be of the essence.' There is undoubtedly a strong element of relativism in Ibn Taymiyya's epistemological thinking, especially as he contends that "people differ in their faculties of perception in a way that cannot be standardized".

Ibn Taymiyya attacks the most delicate aspects of the syllogism-its definitions and concepts which support its larger (conceptual) relations. It is a strategy employed by lbn Taymiyya, simply because in order for a syllogism to function correctly (demonstrating true, false or even probable conclusions) an agreement must be reached concerning the definitional terms (i.e., the universality of its contents). Here, according to Ibn Taymiyya, philosophers and theologians, whether dealing with an analogy or a syllogism per se, assume too much in the way of universal terms that denote extra-mental realities. Ibn Taymiyya states:

"The universal exists only in the mind. If the particulars of a universal exist in the extra mental world, then this will be conducive to the knowledge that it is a universal affirmative".

The ideas penned by Ibn Taymiyya evoke Hume who also interrogated both philosophy and theology on the matter of universals and their relationship to the external world. In Book 1 (Of the Understanding) of his A Treatise of Human Nature, Hume reduces the perceptions of the human mind to what he calls impressions and ideas. Impressions are more immediate in their presence before the mind and feed our ideas that are faint and subject to greater discontinuity. Because Hume is considered an

empiricist, both impressions and ideas are necessarily derived from the external world. He writes:

"Now since nothing is ever present to the mind but perceptions, and since all ideas are derived from something antecedently present to the mind; it follows, that it is impossible for us so much as to conceive or form an idea of any thing specifically different from ideas and impressions."

As is the case with Ibn Taymiyya, ideas and impressions are unable to form universals that can be placed back upon the external world. Hume writes:

"We can never really advance a step beyond ourselves, nor can conceive any kind of existence, but those perceptions, which have appeared in that narrow compass".

The logical conclusion of this position implies that nothing new in the way of knowledge could ever arise from syllogistics. Where definitions break down, so too does the idea of advancing new knowledge. Ibn Taymiyya holds that the links logicians make between concept and definition is too pronounced. He feels that concepts that belong to this or that vocational field are nothing more than an arbitrary invention of the logician. In a rather dogmatic view of conception (which has no need of formal definitions) Ibn Taimiyyah writes:

... all the communities of scholars, advocates of religious doctrines, craftsmen, and professionals know the things they need to know, and verify what they encounter in the sciences and the professions without speaking of definitions. We do not find any of the leading scholars discussing these definitions-certainly not the leading scholars of law, grammar, medicine, arithmetic- nor craftsmen, though they do form concepts of the terms used in their fields. Therefore, it is known that there is no need for these definitions in order to form concepts.

By attacking the heart of the syllogism (identity), Ibn Taymiyya is left with the circular question of just how legitimate rational concepts are established. He might agree that this presents a problem of sorts, but it is his dogmatism (or faith) which rescues him from having to deal with the problem of phenomena more earnestly. His argumentative style appears to suggest that while definitions are necessary for the articulation of logical concepts, the necessary definitions of existence are already established within the Qur'iin and have no need of logical analysis. Ibn Taimiyyah writes:

He who reads treatises on philology, medicine or other subjects must know what their authors meant by these names and what they meant by their composite discourse; so must he who reads books on law, theology, philosophy, and other subjects. The knowledge of these definitions is derived from religion, for every word is found in the Book of God, the exalted, as well as in the Sunnah of His Messenger.