Logic in Islamic philosophy

Islamic logic was inspired primarily by Aristotle's logical corpus, the Organon (which according to a late Greek taxonomy also included the Rhetoric and Poetics). Islamic authors were also familiar with some elements in Stoic logic and linguistic theory, and their logical sources included not only Aristotle's own works but also the works of the late Greek Aristotelian commentators, the Isagog of Porphyry and the logical writings of Galen. However, most of the logical work of the Islamic philosophers remained squarely within the tradition of Aristotelian logic, and most of their writings in this area were in the form of commentaries on Aristotle. For the Islamic philosophers, logic included not only the study of formal patterns of inference and their validity but also elements of the philosophy of language and even of epistemology and metaphysics. Because of territorial disputes with the Arabic grammarians, Islamic philosophers were very interested in working out the relationship between logic and language, and they devoted much discussion to the question of the subject matter and aims of logic in relation to reasoning and speech. In the area of formal logical analysis, they elaborated upon the theory of terms, propositions and syllogisms as formulated in Aristotle's Categories, De interpretatione and Prior Analytics. In the spirit of Aristotle, they considered the syllogism to be the form to which all rational argumentation could be reduced, and they regarded syllogistic theory as the focal point of logic. Even poetics was considered as a syllogistic art in some fashion by most of the major Islamic Aristotelians. Since logic was viewed as an organon or instrument by which to acquire knowledge, logic in the Islamic world also incorporated a general theory of argumentation focused upon epistemological aims. This element of Islamic logic centred upon the theory of demonstration found in Aristotle's Posterior Analytics, since demonstration was considered the ultimate goal sought by logic. Other elements of the theory of argumentation, such as dialectics and rhetoric, were viewed as secondary to demonstration, since it was held that these argument forms produced cognitive states inferior in certitude and stability to demonstration. The philosopher's aim was ultimately to demonstrate necessary and certain truth; the use of dialectical and rhetorical arguments was accounted for as preparatory to demonstration, as defensive of its conclusions, or as aimed at communicating its results to a broader audience.

1. The subject matter and aims of logic

As was their custom in discussing all the branches of philosophy, the Islamic philosophers devoted considerable attention to identifying the subject matter studied by logic and the aims at which logical studies are directed. Al-Farabi, whose logical and linguistic writings comprise the majority of his philosophical output, epitomizes the approach to logic that is characteristic of Islamic Aristotelianism. In his Ihsa' al-'ulum (Enumeration of the Sciences), he defines logic as an instrumental, rule-based science aimed at directing the intellect towards the truth and safeguarding it from error in its acts of reasoning. He defends the need for such a science of reasoning on the grounds that it is possible for the mind to err in at least some of its acts, for example, in those in which the intelligibles sought are not innate, but are rather attained discursively and empirically 'through reflection and contemplation'. Al-Farabi compares logic to tools such as rulers and compasses, which are used to ensure exactness when we measure physical objects subject to the errors of sensation. Like these tools, logical measures can be employed by their users to verify both their own acts of reasoning and the arguments of others. Indeed, logic is especially useful and important to guide the intellect when it is faced with the need to adjudicate between opposed and conflicting opinions and authorities.

Al-Farabi's view of logic as a rule-based science which governs the mind's operations over intelligibles is repeated in many of his introductory logical works, and it formed the foundation for Ibn Sina's later refinements (see Ibn Sina). In the opening chapters of his al-Madkhal (Introduction), the first logical book of his encyclopaedic work al-Shifa' (Healing), Ibn Sina describes the purpose of logic as one of enabling the intellect to acquire 'knowledge of the unknown from the known'. Like al-Farabi, he defends the need for logic by arguing that the innate capacities of reasoning are insufficient to ensure the attainment of this purpose, and thus they require the aid of an art. While there may be some cases in which innate intelligence is sufficient to ensure the attainment of true knowledge, such cases are haphazard at best; he compares them to someone who manages to hit a target on occasion without being a true marksman. The most important and influential innovation that Ibn Sina introduces into the characterization of logic is his identification of its subject matter as 'second intentions' or 'secondary concepts', in contrast to 'first intentions'. This distinction is closely linked in Ibn Sina's philosophy to his important metaphysical claim that essence or quiddity can be distinguished from existence, and that existence in turn can be considered in either of its two modes: existence in concrete, singular things in the external world; or conceptual existence in one of the soul's sensible or intellectual faculties (see Existence).

In al-Madkhal, Ibn Sina argues that logic differs from the other sciences because it considers not conceptual existence as such (this would be psychology), but rather the accidents or properties that belong to any quiddity by virtue of its being conceptualized by the mind. These properties, according to Ibn Sina, include such things as essential and accidental predication, being a subject or being a predicate, and being a premise or a syllogism (see Logical form §1). It is these properties that allow the mind to connect concepts together in order to acquire knowledge of the unknown; they provide the foundation for the rules of reasoning and inference that logic studies. They are moreover formal properties in the sense that, as properties belonging to all concepts in virtue of their mental mode of existence, they are entirely independent of the content of the thought itself; they are indifferent to the intrinsic natures of the quiddities which they serve to link together.

In the Ilahiyyat (Metaphysics) of al-Shifa', Ibn Sina introduces the terminology of first and second 'intentions' or concepts in order to express the relation between the concepts of these quiddities themselves - which are studied in the theoretical sciences - and the concepts of the states and accidents of their mental existence which logic studies: 'As you know, the subject matter of logical science is second, intelligible intentions (al-ma'ani al-ma'qula al-thaniyya) which are dependent upon the primary intelligible intentions with respect to some property by which they lead from the known to the unknown' (Ilahiyyat Book 1, ch. 2, in Anawati and Zayed 1960: 10-11). For example, the second intentions of 'being a subject' and 'being a predicate' are studied in logic independently of whatever first intentions function as the subject and predicate terms in a given proposition, for example, 'human being' and 'rational animal' in the proposition 'a human being is a rational animal'. The logical second intentions depend upon the first intentions because the first intentions are the conceptual building blocks of the new knowledge which second intentions link together: but logic studies the second intentions in abstraction from whatever particular first intentions the logical relations depend upon in any given case.

2. Logic, language and grammar

The attention that Ibn Sina and al-Farabi devote to the proper characterization of the subject matter of logic stems in part from a concern to distinguish logic from grammar. In the ancient and medieval traditions, the study of logic was closely tied to the philosophical consideration of language (see Language, medieval theories of; Logic, ancient; Logic, medieval), and for this reason many Arabic grammarians - whose linguistic theories were developed to a high degree of complexity and sophistication - were contemptuous of the philosophers for importing Greek logic, which they saw as a foreign linguistic tradition, into the Arabic milieu. This attitude toward Greek logic is epitomized in a famous debate reported to have taken place in Baghdad in 932 between the grammarian Abu Sa'id al-Sirafi and Abu Bishr Matta, a Syriac Christian who translated some of Aristotle's works into Arabic and is purported to have been one of al-Farabi's teachers. The extant account of the debate is heavily biased towards al-Sirafi, who attacks logical formalism and denies the ability of logic to act as a measure of reasoning over and above the innate capacities of the intellect itself. His principal claims are that philosophical logic is nothing but Greek grammar warmed over, that it is inextricably tied to the idiom of the Greek language and that it has nothing to offer speakers of another language such as Arabic.

It is against the background of such attacks that the discussions of the relations between logic, language and grammar by al-Farabi, Ibn Sina and al-Farabi's pupil Yahya ibn 'Adi (also a Syriac Christian and translator), are to be understood. Al-Farabi and Yahya both present essentially the same perspective on the relations between logic and language, a moderate perspective which Ibn Sina later rejects. In the Ihsa' al-'ulum, al-Farabi argues that logic and grammar both have some legitimate interest in language, but whereas grammatical rules primarily govern the use of language, logical rules primarily govern the use of intelligibles:

And this art [of logic] is analogous to the art of grammar, in that the relation of the art of logic to the intellect and the intelligibles is like the relation of the art of grammar to language and expressions. That is, to every rule for expressions which the science of grammar provides us, there is a corresponding [rule] for intelligibles which the science of logic provides us. (Ihsa' al-'ulum, in Amin 1968: 68)

More precisely, al-Farabi explains that although grammar and logic share a mutual concern with expressions, grammar provides rules that govern the correct use of expressions in a given language, but logic provides rules that govern the use of any language whatsoever in so far as it signifies intelligibles. Thus, logic will have some of the characteristics of a universal grammar, attending to the common features of all languages that reflect their underlying intelligible content. Some linguistic features will be studied in both logic and grammar, but logic will study them as they are common, and grammar in so far as they are idiomatic. On the basis of this comparison with grammar, then, al-Farabi is able to complete his characterization of the subject matter of logic as follows: 'The subject-matters of logic are the things for which [logic] provides the rules, namely, intelligibles in so far as they are signified by expressions, and expressions in so far as they signify intelligibles' (Ihsa' al-'ulum, in Amin 1968: 74).

Like al-Farabi, Yahya ibn 'Adi, in a treatise entitled Maqala fi tabyin al-fasl bayna sina'atay al-mantiq al-falsafi wa-al-nahw al-'arab (On the Difference Between Philosophical Logic and Arabic Grammar), makes his case for the independence of logic from grammar based upon the differences between the grammar of a particular nation and the universal science of logic. He argues that the subject matter of grammar is mere expressions (al-alfaz), which it studies from the limited perspective of their correct articulation and vocalization according to Arabic conventions. The grammarian is especially concerned with language as an oral phenomenon; the logician alone is properly concerned with 'expressions in so far as they signify meanings' (al-alfaz al-dalla 'ala al-ma'ani) (Maqala fi tabyin, in Endress 1978: 188). To support this claim, Yahya points out that changing grammatical inflections do not affect the basic signification of a word: if in one sentence a word occurs in the nominative case, with the appropriate vocalization, its signification remains unchanged when it is used in another sentence in the accusative case and with a different vocal ending.

In Ibn Sina's view, however, such accounts of the logician's interest in language and its differences from that of the grammarian did not go far enough. In keeping with his own understanding of logic as the science which studies second intentions, Ibn Sina criticized such earlier attempts to introduce linguistic concerns into the subject matter of logic. In al-Madkhal, Ibn Sina labels as 'stupid' those who say that 'the subject matter of logic is speculation concerning expressions in so far as they signify meanings (ma'ani)'. However, Ibn Sina does not deny that the logician is sometimes or even often required to consider linguistic matters; his objection is to the inclusion of language as an essential constituent of the subject matter of logic. The logician is only incidentally concerned with language because of the constraints of human thought and the practical exigencies of learning and communication. Ibn Sina goes so far as to claim that, 'if logic could be learned through pure thought so that meanings alone could be attended to in it, then it would dispense entirely with expressions'; but since this is not in fact possible, 'the art of logic is compelled to have some of its parts come to consider the states of expressions' (al-Madhkal, in Anawati et al. 1952: 22-3). For Ibn Sina, then, logic is a purely rational art whose purpose is entirely captured by its goal of leading the mind from the known to the unknown; only accidentally and secondarily can it be considered a linguistic art.

3. Conceptualization and assent

While the close links between logic and linguistic studies emerge in the Islamic philosophers' consideration of the subject matter of logic, the links between logic and epistemology come to the fore in the consideration of the divisions within logic and the order of the books within Aristotle's Organon. All the principal Islamic Aristotelians organize their understanding of the divisions of logic around the epistemological couplet of tasawwur (conceptualization), and tasdiq (assent), which constitute for them the two states of knowledge that logic aims to produce in the intellect.

Conceptualization is the act of the mind by which it grasps singular (though not necessarily simple) essences or quiddities, such as the concept of 'human being'. Assent, by contrast, is the act of the intellect whereby it makes a determinate judgment to which a truth-value can be assigned; in fact, conceptualization is defined in Islamic philosophy principally by contrast with assent. Thus, any act of knowledge that does not entail the assignment of a truth-value to the proposition that corresponds to it will be an act of conceptualization alone, not assent. More specifically, the Islamic philosophers link assent to the affirmation or denial of the existence of the thing conceived, or to the judgment that it exists in a certain state, with certain properties. Thus, assent presupposes some prior act of conceptualization, although conceptualization does not presuppose assent.

One of the purposes of including a consideration of the tasawwur-tasdiq dichotomy in introductory discussions of the purpose of logic is to provide an epistemological foundation for the two focal points of Aristotelian logic, the definition and the syllogism (see Logical form §1). The purpose of the definition is identified as the production of an act of conceptualization, and the purpose of the syllogism is identified as causing assent to the truth of a proposition. However, since the definition and the syllogism are both considered in the Prior and Posterior Analytics and the works that come after them in the Organon, the study of the ways of producing conceptualization and assent presupposes as its foundation the study of single terms and propositions in the Categories and De interpretatione.

4. Predicables, categories and propositions

In keeping with the ancient Greek tradition, the Islamic philosophers considered the books of the Organon to be an ordered series which begins with the study of the signification of simple terms in the Categories and then proceeds to the study of propositions in the De interpretatione. In addition to these two Aristotelian texts, a work of the Neoplatonist Porphyry, known as the Isagog (Introduction), was appended to the beginning of this series as an introduction to the study of the Categories (see Aristotle §7). It was concerned with the five predicables: genus, species, difference, property and accident. While all of the Islamic Aristotelians wrote commentaries on the Isagog and utilized its grouping of the predicables, not all were convinced of its utility as an introduction to Aristotle. Ibn Rushd openly expresses such doubts in the introduction to his Talkhis kitab al-maqulat (Middle Commentary on the Categories), where he indicates that his original intention was to omit the Isagog entirely from his series of middle commentaries on the Organon. At the end of his work on the Isagog itself, he explains bluntly that he does not believe that Porphyry's text is a helpful introduction to the study of logic and questions whether it is really a logical text at all. His sole reason for completing the commentary, he tells us, was to comply with a request made by his friends.

The logical character of the Categories presented a related problem for other Islamic philosophers. In the introduction to his Sharh al-'ibarah (Great Commentary on the De interpretatione), al-Farabi rehearses some of the controversies inherited from the Greek tradition over the relations between the Categories and the De interpretatione. As al-Farabi points out, the De interpretatione can be understood quite well without a prior knowledge of the Categories, and the former work makes no explicit references to the latter. Moreover, the De interpretatione is principally concerned with the formal relations amongst propositions, such as contradiction and contrariety, whereas the Categories is concerned with the signification or meaning of terms as such. Furthermore, in its opening chapters, the De interpretatione considers in formal terms the simple parts of which propositions are composed, that is, the noun and the verb. Despite these concerns, however, al-Farabi opts for the traditional ordering of these books on the grounds that the Categories is relevant to the whole of logic, since it studies 'the simplest of the subject matters in which logic actualizes itself'. In his Falsafa Aristutalis (Philosophy of Aristotle), al-Farabi opts for a similar solution to the logical status of the Categories, explaining that it comprises an investigation and classification of 'the instances of being from which the first premises are compounded', which are 'the primary significations of the expressions generally accepted by all' (Falsafa Aristutalis, in Mahdi 1969: 82-3).

Al-Farabi's misgivings in both of these texts stem from the largely ontological focus of the Aristotelian Categories, which calls into question its placement within the Organon. This concern was echoed later by Ibn Sina, who points out that many of the discussions in the Categories would be better placed in metaphysics or psychology, since they pertain to the study of expressions as directly signifying external or mental beings, in other words, to first rather than to second intentions. But since the Categories is useful in instructing us how to formulate definitions - which is one of the principal goals of logic - its placement in the Organon can be justified on practical grounds.

Islamic philosophers viewed De interpretatione as a study of the composition and truth-values of categorical propositions. Thus al-Farabi, in his great commentary on this text, explains that the term 'interpretation' used in the title of the work means 'complete statement' (al-qawl al-tamm). A complete statement, according to al-Farabi, must be one which causes a complete understanding in the mind; in other words, one in which assent occurs along with conceptualization. This is achieved principally by a simple, predicative, categorical statement (al-qawl al-jazim al-hamli al-basit) which affirms or denies a predicate of its subject.

5. Theory of argumentation

For the entire Islamic tradition, the crowning glory of Aristotelian logic is the syllogistic theory outlined in the Prior and Posterior Analytics, especially the latter. The purpose of logic is to provide the means whereby knowledge is to be acquired, and the most valuable type of knowledge is that which is certain and necessary, that is, knowledge gained according to the paradigm of demonstrative science laid out in the Posterior Analytics. This part of logic, in the words of al-Farabi's Ihsa' al-'ulum, is 'the strongest and pre-eminent in dignity and authority. Logic seeks its primary aim in this part alone, and the rest of its parts are only for its sake' (Ihsa' al-'ulum, in Amin 1968: 89). Even the formal study of the syllogism itself is primarily undertaken for the sake of its employment in demonstrations.

In their formal syllogistic theory, the Islamic Aristotelians mainly follow Aristotle's Prior Analytics. While they are aware of the fourth figure traditionally ascribed to Galen, the tendency is to dismiss this figure as superfluous and intuitively implausible, as Ibn Sina does in the seventh method of his al-Isharat wa-'l-tanbihat (Remarks and Admonitions); or to ignore it entirely, as al-Farabi does in his Kitab al-qiyas (Book on the Syllogism). Similarly, the Arabic philosophers knew of the alternative propositional logic of the Stoics and incorporated elements of it in their discussions of conditional or hypothetical (shartiyyah) syllogisms (see Logic, ancient). However, they did not accept the Stoic inference schemata, nor did they treat conditional connectives as truth-functional, since they did not consider the parts of conditional statements to be complete propositions in their own right. Moreover, for the Islamic logicians 'conditional' was a generic term which included both 'conjunctive' (al-muttasilat) conditionals (of the form, 'if... then') and 'disjunctive' (al-munfasilat) conditionals (of the form, 'either... or'). Conditional syllogisms of both sorts were viewed as relying upon a process of 'reiteration' or 'repetition' (istithna'), a term which referred to the repetition of the antecedent or the consequent, or one of the two disjuncts, in so far as it formed the second premise of a syllogism. Thus in the conjunctive conditional syllogism, 'If it is daytime, then it is light; but it is daytime, therefore it is light', 'it is daytime' would be labelled the mustathna' or reiterated premise, since it is by its restatement that the syllogism reaches its conclusion.

When we turn to the specific application of syllogistic theory to particular types of argumentation, the epistemological concerns of Islamic logic surface once more. In particular, the Islamic philosophers explained the primacy of demonstration, and the ancillary role of dialectical, rhetorical, poetic and sophistical syllogisms, by reference to the epistemic status of the premises used in each type of syllogism, and the type of assent they could produce to the conclusion of the syllogisms in which they were employed. The classification of syllogisms and their premises according to the nature of their assent is found in the logical writings of all the major Islamic philosophers, but the most complete and systematic classification of premises occurs in three of Ibn Sina's works, al-Burhan (Demonstration), in al-Shifa', al-Najah (Deliverance) and al-Isharat wa-'l-tanbihat (Remarks and Admonitions). Although these three accounts differ somewhat in the number and variety of the premises listed in each, generally they present a single and consistent theory. Demonstrative syllogisms are composed of premises which necessitate assent and include self-evident first principles as well as sensible, empirically evident propositions. Dialectical syllogisms are based upon generally accepted beliefs (al-mashhurat), which are equivalent to the endoxa of Aristotle's Topics; on premises granted for the purposes of dialectical debate; and in general, on all premises assented to because they are universally accepted by all people, or by people deemed authoritative. Rhetorical syllogisms are similar to dialectical ones, except that they are accepted unreflectively and on the basis of a more limited authority, relative, for example, to a particular group or sect; as such, they are only supposed or presumed to be 'generally-accepted beliefs'. Sophistical premises are those accepted because of some misleading resemblance to another type of premise, and poetic premises are those that produce a motion in the faculty of imagination (al-takhyil), not an act of intellectual assent.

The inclusion of rhetorical and poetical syllogisms in this enumeration reflects a common assumption among Islamic philosophers that Aristotle's Rhetoric and Poetics are parts of his logical Organon. This assumption was inherited by the Islamic tradition from the Greek commentators, and it was used by them in part to account for the differences between philosophical and popular modes of discourse and argumentation, particularly in the context of discussions of the relations between philosophy and religion. The Islamic philosophers held that whereas philosophers rely principally upon demonstrative and dialectical syllogisms, religious leaders and theologians generally use rhetorical and poetical syllogisms to persuade the general populace. Religion is thus viewed as an image or reflection of philosophical, demonstrative truth propounded in language and argument-forms that can be easily understood by the mass of humanity.

The place of dialectic within the theory of argumentation is perhaps the most ambivalent in Islamic logic. While dialectic is seen as inferior to demonstration, its importance for philosophy is none the less recognized. A good example of this is found in al-Farabi's enumeration in his Kitab al-jadal (Book on Dialectic) of the ways in which dialectic serves philosophers. According to al-Farabi, dialectic hones argumentative skills, introduces the principles of the special demonstrative sciences, alerts the mind to the self-evident principles of demonstration, helps to develop communicative skills and provides the means for refuting sophistry. Of these five uses, only the fourth is external to the proper aims of philosophy and closer to the tasks usually reserved to theology and religion. The other four pertain to the learning or acquisition of truly philosophical skills, even if they lie outside the strictly demonstrative aims that are the ultimate end of philosophy.

In the case of the theory of demonstration itself, Islamic logicians organized their commentaries on the Posterior Analytics around the definition and the demonstrative syllogism as the means by which both conceptualization and assent are most perfectly attained. Al-Farabi's Kitab al-burhan (Book on Demonstration) offers an excellent summary of the standard approach taken by Islamic philosophers to theory of demonstration and its epistemological aims. Just as he identified the categorical statement as the embodiment of perfect assent on the propositional level, here al-Farabi identifies demonstrative certitude as complete or perfect assent on the level of syllogistic inference. Moreover, certitude is defined by al-Farabi in terms of what we would now label 'second-order' knowledge:

Certitude is for us to believe, concerning the truth to which we have assented, that it is not possible at all for what we believe about this matter to be different from what we believe it to be; and in addition to this for us to believe, concerning our belief, that another belief is not possible - in the sense that whenever some belief about the first belief is formed, it is impossible for it to be otherwise, and so on ad infinitum. (Kitab al-burhan, in al-'Ajam and Fakhry 1986-7, 4: 20)

Certitude requires not just knowledge of a conclusion, p, but knowing that we know p. This sort of certitude al-Farabi calls 'necessary certitude'. However, he also allows for non-necessary certitude, which holds 'only at a particular time', and thus can be applied to propositions about merely contingent beings: 'Necessary certitude and necessary existence are convertible in entailment, for what is verified as necessarily certain is necessarily existent' (Kitab al-burhan, in al-'Ajam and Fakhry 1986-7, 4: 22). While al-Farabi recognizes both of these varieties of certitude to be forms of perfect assent, in his view necessary certitude alone fulfils the strict conditions of Aristotelian demonstration, since it alone will pertain to objects which cannot be other than they are.

Al-Farabi's remarks on the utility of dialectic, combined with his extension of the notion of perfect assent beyond the confines of strict and necessary demonstration, illustrate the overall breadth of the Islamic philosophers' theories of argumentation. Despite their professions of the primacy of the demonstrative paradigm within philosophy, the Islamic Aristotelians recognized a broad range of legitimate and useful argument forms and acknowledged their importance as philosophical tools leading to knowledge of the unknown.

See also: Aristotelianism in Islamic philosophy; Aristotle; al-Farabi; Ibn Sina; Logical form; Logic, ancient; Logic, medieval; Logic, philosophy of; Meaning in Islamic philosophy; Syntax