Nature and aim of mantiq

Mantiq is a discipline that studies how the mind moves correctly from what is known to what is unknown. Its subject is two kinds of knowledge in the mind: conceptual knowledge and assent based knowledge. The benefit of mantiq is that it helps uncover unknown concepts and unknown assents, and it protects thought from error by setting clear methods that the mind follows when it judges and reasons.

Forms of logic and traditional logic in Islam

Logic appears in several forms. Aristotelian logic, as found in the Organon, contains both material discussions that deal with the subject matter of propositions and formal discussions that deal with their structure.

Stoic logic is a formal logic that looks only at the form of reasoning and does not examine the content. Modern mathematical logic is also formal and is usually seen as a continuation of Stoic logic in its strong focus on form.

A modified Aristotelian logic became widespread. It was used among the Asharis, the Mutazilah, the Shia and others. This logic is built on the basis laid by Aristotle, but it is not a simple copy of his writings.

It absorbed some Stoic elements and many points from the Alexandrian commentators on logic, and Muslim logicians added their own refinements and changes.

For this reason it is called here traditional logic (mantiq al turathi). Terms such as Aristotelian logic, formal logic and Greek logic generally refer to this traditional logic in a broad sense.

Subject matter of mantiq: concepts and assents

The material of mantiq is the information present in the mind in two forms. The first form is conceptual information, which consists of simple concepts with no judgement attached.

The second form is assent based information, which consists of judgements that affirm or deny something about something.

Each of these two has foundations and aims. For concepts, the foundations are the five universals, and the aim is definition, which is the explanatory statement that makes an unknown concept clear, either by essential attribute or by descriptive attribute, whether complete or incomplete.

For assents, the foundations are propositions and the logical rules that govern them, and the aim is syllogism, in which known propositions are ordered so that a new judgement follows from them.

Signification and the connection between words and meanings

Mantiq begins with signification, because the whole science rests on how expressions point to meanings.

Signification is the state of a thing such that knowing it leads to knowing something else. The first is the sign, the second is the signified, and the relation between them is the signification. The classic example is knocking at a door, which serves as a sign that there is a person at the door. Another example is smoke, which indicates the presence of fire.

For genuine signification two conditions are required. There must be knowledge that a necessary connection exists between the sign and the signified, as between smoke and fire.

There must also be the actual presence of the sign in reality, such as the real sound of knocking or the real appearance of smoke, so that the mind can move from it to the signified. Without both, the supposed sign does not truly point to anything.

Signification can be divided into rational, natural and conventional. Rational signification is the signification of an effect for its cause or a trace for its maker. Natural signification arises from the nature itself, such as a cry of pain or blushing that shows shyness.

Conventional signification rests on agreement and custom, as with traffic lights or written symbols for arithmetic operations. Each of these three can be verbal or non verbal, and signification can also be divided first into verbal and non verbal, with each of these then divided into rational, natural and conventional.

Within verbal conventional signification there are three standard kinds. Signification by conformity occurs when a word points to the whole meaning for which it was fixed, as the word masjid points to the entire masjid with its essential parts.

Signification by inclusion occurs when the word points to part of that meaning, as when masjid is used to intend only one section. Signification by implication occurs when the word points to something that is not part of the basic meaning for which it was fixed but is closely connected with it, such as the name Hatim indicating generosity.

The concern of mantiq is verbal conventional signification, because this is the stable way by which people use words to carry meanings, and it is on this relation between word and meaning that logical analysis is built.

Concepts, instances and the focus of mantiq

Mantiq does not stop with sounds or written forms; its focus is on meanings. A meaning, in relation to its existence, is of two kinds. When it exists in the mind, it is called a concept. When it exists outside the mind in the concrete universe, it is called an instance.

The mental representation of fire is the concept of fire. The actual burning fire is an instance. The concept human being is a mental meaning that can be present in thought without any one individual in front of the eyes, while each particular human is an instance of that concept in external reality.

The work of mantiq is built on these concepts. It studies how they are formed, how they relate to one another, how they combine in propositions, and how the mind uses them to reach new judgements.

Universal and particular concepts

Concepts are divided into universal and particular. A universal is a concept whose very meaning allows many individuals to share in it. The concept human being is one meaning, but it can apply equally to Zayd, Amr, Fatimah and countless others. A particular is a concept whose meaning blocks such sharing. The concept of one specific person, such as Zayd bin so and so, applies only to that individual.

This division belongs to meanings, not to words themselves. The word human being is not universal by its sounds. It is the meaning carried by that word in the mind that is universal. The same sounds may be used in another language or context with a different meaning, but the universality or particularity lies in the concept as it is understood.

After this, universals themselves are divided. A univocal universal is a universal that belongs to all its instances in the same way. The concept human being applies to each human without difference in degree, since one person is not more human than another.

A gradational universal, or mushakkik, is a universal that is present in its instances with different degrees of intensity. Whiteness is like this. Two objects may both be called white, but one may be clearly whiter than the other.

Existence is also mentioned as an example, when comparing the existence of contingent beings with the existence of the Necessary Being, where the difference is not only in number of instances but in rank and level of existence.

Real and relative particulars

Particular concepts can be looked at in two ways. The real particular is the particular that stands opposite the universal in the main division. Its very concept stops any sharing. The concept of Zayd as an individual, or of this particular printed copy of a book with its title, cover, author and pages, is a real particular.

From another point of view, a universal can be treated as a particular in relation to something more general. The concept human being is a universal when we consider how many individuals fall under it.

But when human being is viewed under the more general universal animal, it becomes a relative particular, because it is only one kind of animal among many. In itself it remains a universal, but in relation to the higher universal it is particular.

In summary, the basic division is between concept and instance. The concept, when compared to its instances, is either universal or real particular.

The universal is then either univocal or gradational. The relative particular is in fact a universal placed under a wider universal, and is called particular only from that relative angle.

Relations between universals

Between universal meanings there are four standard relations, studied in terms of how their instances in the external universe overlap or do not overlap.

The first relation is equivalence. Here each universal applies to all the instances to which the other applies. The pattern is all with respect to all.

An example is the relation, in the logical scheme, between human being and rational, on the assumption that every human is rational and everything rational is human.

The second relation is absolute general and particular. One universal applies to all the instances of the other, while the second applies only to some of the instances of the first. The pattern is all with respect to some. For example, all birds are animals, but only some animals are birds.

The third relation is general and particular from one respect. Each universal applies to some of the instances of the other, and each also applies to instances that do not fall under the other. The pattern is some with respect to some.

An example is black and bird. Some birds are black, and some black things are birds, but there are black things that are not birds and birds that are not black.

The fourth relation is mutual exclusion. Here no instance that falls under one universal falls under the other. There is no overlap. Animal and inanimate object are related in this way, as are stone and human being.

These relations always concern universals that differ in meaning, such as human being and rational. They are described through their instances in reality, not through their bare meanings alone.

The same language of general and particular used here in mantiq appears again in usul al fiqh, kalam, grammar and other Islamic disciplines, because it provides a common way to describe how general and specific terms relate to one another.