An Easy Summary of Logic

A student wrote that he encounters considerable difficulty in grasping the discussions of manṭiq and wishes to have a brief and simple outline of its foundational topics placed before him. I advised him to study my concise book ‘Mabādiʾ fī al-Manṭiq’; I hope it will assist him in understanding the fundamental terms and discussions of logic. Nevertheless, in view of his question, it seems appropriate to present a summary introduction to the science of manṭiq together with an outline of its principal topics, so that the basic structure and purposes of this discipline become clear at a glance.

The importance and need of logic
For centuries Greek logic exercised a profound influence over the scholarly world, and even today its effects remain, in one form or another, within various intellectual traditions and systems of thought. The Islamic sciences—especially ʿilm al-kalām, uṣūl al-fiqh, philosophy and other rational disciplines—have made use of the terminology of logic and its manner of reasoning. For this reason the curricula of the dīnī madāris have consistently included the teaching of this science.

In recent times, however, the share of logic within the curricula of the madāris has been gradually contracting. A large number of ʿulamāʾ hold reservations about this discipline, and indeed some consider its teaching unnecessary. Without doubt certain discussions in logic are open to critique and one may disagree with some of its theories; but disagreement with particular aspects of a science cannot serve as a basis for denying the need to study that science. The truth is that, for the correct utilisation of the Islamic scholarly heritage, the classical sources and the various intellectual traditions, familiarity with the fundamental discussions of logic is indispensable. Even to subject the theories of logic to critical scrutiny and refutation requires a sound understanding of them. Before demolishing a building one must know its blueprint and structure; likewise, in order to criticise an intellectual theory one must comprehend its foundations and argumentative framework.

Logic, in essence, is a rule for organising thought and presenting reasoning in a correct arrangement and form. It does not by itself discover any truth, nor does it guarantee the veracity of any claim; rather, it explains how a conclusion is to be drawn from a premise and under what principles a claim is to be advanced, so that a methodological error does not occur in reasoning. In other words, manṭiq does not show the path to reality; it provides discipline to the mind in walking upon that path. In this respect it is termed manṭiq ṣūrī (formal logic).

The foundational discussions of logic may be understood under three broad headings: the classification of things and concepts, their correct definition and delimitation, and reasoning and proof for the establishment of claims. These three discussions correspond, in fact, to the three basic stages of any scholarly discourse: first, to determine what the matter under discussion is and to which class it belongs; then to clarify its meaning; and finally to present evidence for the judgement or claim made about it.

1. Classification of things and concepts
The first fundamental discussion of logic concerns the classification of things and concepts. Its purpose is to determine to which class or category a thing or idea belongs and what relationship it bears to other concepts. The material and immaterial entities of the world are divided into various categories and grades. Every thing belongs to some species, and above it there exist one or several broader genera.

In the terminology of logic, the specific and determinate class of a thing is called its nawʿ (species), whilst the broader common class is called its jins (genus). The genus immediately above the species is the jins qarīb (proximate genus), and those still wider are the jins baʿīd and the jins abʿad.

For example, Zayd, Bakr, Fāṭimah and ʿĀʾishah are individuals of the human species. The proximate genus of the human species is ḥayawān (animal), its distant genus is jism nāmī (living body) and a still wider genus is jism muṭlaq (body, without qualification). Thus one and the same thing can, in relation to a lower class, be a species and, in relation to a higher class, be a genus.

This principle may be understood from everyday and scholarly examples alike. Lucknow is a city, Uttar Pradesh is a state and Hindustān is a country. Likewise, Nadwat al-ʿUlamāʾ is a religious educational institution, dīnī madāris are a kind of educational institution and educational institutions are part of a broader educational system.

The classification of the sciences follows the same principle. For instance, rafʿ, naṣb and jarr are kinds of iʿrāb; iʿrāb is one of the discussions of ʿilm al-naḥw; and ʿilm al-naḥw is a branch of the ʿulūm ʿarabiyyah. Similarly, in fiqh, bayʿ and qarḍ are different forms of financial transactions, while financial transactions are included in the broader discussions of fiqh islāmī.

Ignorance of this classification of things and sciences is a significant cause of scholarly confusion and intellectual disorder. When a matter is viewed apart from its original field of discussion and scholarly rank, misunderstandings arise concerning it. Scholarly concepts are also like the branches of an organised tree; each branch is connected to a larger branch and each larger branch to the main trunk. If their mutual relations are ignored, the entire scholarly landscape appears fragmented. Therefore, before engaging in any academic discourse, it is necessary to determine to which category the issue belongs, what its broader meaning is and what kind of relation it bears to other concepts.

2. Definition and delimitation
The second fundamental discussion of logic is taʿrīf (definition). To understand a thing or concept correctly it is essential to clarify its meaning and to distinguish it from other similar things and concepts. Merely knowing the name of something is not sufficient for understanding its reality; rather, a definition is required that is both jāmiʿ (inclusive) and māniʿ (exclusive), elucidating the concept while separating it from unrelated ideas.

In the terminology of logic, the act of revealing the reality of a thing or distinguishing it from other things is called taʿrīf. In formulating a definition, jins and faṣl hold basic importance.

Jins is the general attribute that connects a thing to a broader class, while faṣl is the distinguishing attribute that sets it apart from other species within that same class. In addition, there are certain attributes that are not part of the essence of a thing yet help in distinguishing it from others; these are termed khāṣṣah in the terminology of logic.

For example, a masjid may be defined as ‘a building set apart for the worship of Allah, exalted is He.’ In this definition ‘building’ functions as the jins, while the qualification of being set apart for worship distinguishes it from other buildings.

Similarly, a fiʿl (verb) may be defined as ‘a kalimah that denotes a meaning and is associated with a tense.’ Here ‘kalimah’ is the jins, whereas denoting a meaning and having a temporal association distinguish it from the ism and the ḥarf.

In the terminology of fiqh, farḍ may be defined as ‘a sharʿī ruling the performance of which is necessary and which is established by a definitive proof.’ In this definition ‘sharʿī ruling’ is the jins, while the necessity of performance and its establishment by a definitive proof are its distinguishing characteristics.

The aim of definition is not merely an explanation of words, but to create in the mind a clear and determinate image of the concept, leaving as little room for ambiguity and confusion as possible. Just as entry into a city requires the identification of its gates and boundaries, so entry into an academic concept demands a clear knowledge of its limits and constraints. If a definition is vague, unrelated things may fall within its scope and relevant ones may remain outside it. For this reason, inclusiveness and exclusiveness possess fundamental importance in definition.

In scholarly discussions, when the definitions of basic terms are not fixed, a single word comes to be used in different senses, giving rise both to differences of opinion and to misunderstandings. Hence the correct definition of the foundational terms of any discipline is not merely an initial requirement but the very basis of correct understanding.

3. Proof, reasoning and its kinds
The third and very important discussion of logic is istidlāl (reasoning). When a person presents a claim, a theory or a judgement, it is natural to ask what evidence he has for its establishment. The evidence presented to substantiate a claim is called ḥujjah, and the process of arriving at a conclusion through evidence is termed istidlāl.

Manṭiq sets out three primary modes of reasoning: qiyās, istiqrāʾ and tamthīl.

(a) Qiyās
Qiyās is that mode of reasoning in which, on the basis of two premises, a conclusion is drawn. In it a general ruling is applied to one of its particular instances; in other words, it is a method of reasoning from the universal to the particular.

Qiyās generally comprises three elements: the minor premise (ṣughrā), the major premise (kubrā) and the conclusion (natījah). The first premise is called ṣughrā, the second kubrā, and the ruling obtained from these two premises is the natījah.

For example:
• Ṣughrā: Zayd is an ʿālim dīn.
• Kubrā: Every ʿālim dīn is acquainted with ʿilm ʿarabī.
• Natījah: Therefore Zayd is acquainted with ʿilm ʿarabī.

In this example, the attribute ‘being an ʿālim dīn’ is common to both premises. In logical terminology this is called the ḥadd awsaṭ (middle term). The middle term establishes the logical relation between the two premises but does not itself appear in the conclusion. When this common term present in both premises is removed, the ruling that remains is the conclusion.

The structure of qiyās makes it clear that a conclusion is not obtained merely by joining two sentences together; rather, a specific logical relation must exist between the two premises. The ṣughrā and the kubrā are like two pillars upon which the building of the conclusion rests; if either pillar is weak, or if the relation between them is faulty, the conclusion too will not be trustworthy. Therefore, both the soundness of the premises and their logical arrangement hold fundamental importance in qiyās.

(b) Istiqrāʾ
Istiqrāʾ is that mode of reasoning in which, after studying numerous particulars and individuals, a general ruling is established concerning them. In other words, it proceeds from the particular to the general.

For example, if the individual life circumstances of students in various dīnī madāris are examined and from this examination it emerges that they demonstrate a marked ability to face adverse conditions and difficulties, one may, on the basis of these observations, form the general judgement that students of the madāris tend to possess a greater capacity for coping with circumstances.

The principle adopted by the muḥaddithūn that all the Ṣaḥābah, may Allah be pleased with them, are ʿudūl (upright), is likewise related to their extensive study of the companions’ lives and narrations. Similarly, many of the general rules of naḥw and ṣarf were formulated as a result of the study and analysis of linguistic usages, evidences and diverse styles.

In modern academic terminology, surveys, field research and empirical studies largely fall under this istiqarāʾī mode of investigation. Istiqrāʾ, however, has two basic forms: al-istiqarāʾ al-tām (complete induction) and al-istiqarāʾ al-nāqiṣ (incomplete induction). In complete induction all relevant individuals or particulars are examined, whereas in incomplete induction a general ruling is drawn from the study of selected individuals or samples.

Since in practical research and surveys it is generally impossible to encompass all relevant individuals, their results are usually based on incomplete induction. If the sample selection is unbalanced, or if the number and nature of samples are insufficient for drawing a general conclusion, the findings can prove unreliable, misleading or mutually contradictory. Thus the soundness of inductive conclusions depends upon the quality of the observations, the appropriateness of the samples and the research methodology.

The importance of istiqrāʾ lies in its providing a path for moulding scattered observations into a general concept. Yet, just as one cannot gauge the depth of the entire ocean by observing a few drops, so a general ruling based on limited observations calls for caution and further investigation.

(c) Tamthīl
Tamthīl is that mode of reasoning in which, on the basis of a common attribute or essential resemblance between two particular things, the ruling of one is applied to the other. In it the ruling of a known particular is inferred for another particular that resembles it.

For instance, the Qurʾān declares maysir, i.e., gambling, to be ḥarām. If, in any form of lottery, the essence of gambling and its underlying ʿillah are present, then on the basis of this common attribute the lottery too can be declared impermissible.

Likewise, if it is argued that, since both woman and man share a common humanity, they must, in terms of human dignity and basic human rights, enjoy equal status, this too is an example of tamthīl.

In a similar manner, it is contended that the teachers of dīnī madāris should receive salaries and benefits comparable to those of teachers in modern educational institutions, because the attribute of teaching is common to both groups. In this reasoning, the shared character of teaching has been made the basis of resemblance.

In uṣūl al-fiqh this type of reasoning is also called qiyās. One must, however, be mindful of the distinction that the term qiyās in the science of logic and in uṣūl al-fiqh is not used in the same sense. Logical qiyās is a systematic method of deriving a conclusion from two premises, whereas the usūlī qiyās determines the ruling of a new issue on the basis of a common effective cause with a textually addressed issue. Accordingly, it is necessary to understand the difference in the usage and meaning of this term in the two disciplines.

The basis of tamthīl is resemblance, yet not every resemblance necessarily entails uniformity of ruling. Two things may share a single attribute yet differ in other significant attributes. Therefore, in analogical reasoning it is essential to consider whether the attribute taken as common foundation is truly operative and relevant to the ruling under discussion. It is this caution that elevates tamthīl above mere superficial resemblance and renders it a credible academic argument.

These three modes demonstrate that the basic function of logic is to rescue thought from a jumble of disordered ideas and to place it upon an organised scholarly path. Qiyās teaches us the method of deriving a conclusion from premises; istiqrāʾ shows the way from particular observations to universal principles; and tamthīl teaches how to establish an argumentative connection between two issues on the basis of common attributes. Though distinct, all three serve a single academic purpose: instead of presenting a claim as a bare assertion, they cast it in the mould of evidence and reasoning.

In this light it is incorrect to regard logic as merely a collection of dry terms, difficult definitions and intricate figures. In reality, it is a skill that imparts discipline to thought, clarity to concepts and order to reasoning in accordance with logical principles. Yet one must always remember that the correctness of logical form is no guarantee of the truth of the premises. If the premises themselves are false, the conclusion reached, despite the apparent correctness of the reasoning, will not accord with reality. A beautiful building plan is useful only when its foundations are sound; similarly, logical reasoning is valid only when its premises are based upon truth.

The correct way to benefit from logic, therefore, is not to memorise its basic terms and principles merely by rote, but to understand their meanings, to acquaint oneself with their practical examples and to train oneself in their application within scholarly discussions. At the same time one must keep in view both the scope and the limits of this discipline. Logic should neither be regarded as the master key to all sciences nor dismissed as a useless intellectual exercise. Its real value becomes evident only when it is employed as an auxiliary scholarly tool that bestows order upon thought, clarity upon discourse and strength upon reasoning.