https://youtu.be/VQpQtVgxWjI?si=oa7yHFFd8d2AS1hqForms of logic
Logic appears in four main forms. The first is Aristotelian logic as written by Aristotle, which contains both discussions concerned with matter and discussions concerned with form.
The second is Stoic logic, which is a formal logic that focuses on the structure of arguments and does not concern itself with their material content.
The third is modern mathematical logic, which is also a formal logic and is regarded as an extension of Stoic logic in its concern with pure form.
Among the deviated muslims there was a developed and modified version of Aristotelian logic. It is strongly influenced by Aristotle, but it also carries Stoic elements and contributions from later commentators, such as those of Alexandria.
It was taken up by the Asharis, the Muʿtazilah, the Shia and others. To distinguish this from pure Aristotelian logic, it is called here traditional logic.
Aristotelian logic, formal logic, and Greek logic usually point to this traditional logic in a general way, even though the details are not identical to Aristotle himself. Most of this traditional logic consists of formal discussions, while some material discussions were dropped in the shorter summaries.
Subject matter of mantiq: concepts and assents
The subject matter of mantiq is two kinds of information. The first is conceptual information, which concerns simple concepts in the mind. The second is assent based information, which concerns judgements that affirm or deny something. Each of these has foundations and aims.
The foundations of concepts are the five universals, and their aim is definition, which is called the explanatory statement.
The foundations of assents are propositions and their rulings,and their aim is syllogism, which is the structure by which one judgement leads to another.
Signification and the link between words and meanings
Signification is defined as the state of a thing such that knowing it leads to knowing another thing. The first is called the sign, the second is called the signified, and the link between them is the signification. An example is knocking at a door, which serves as a sign that someone is present behind it.
There are conditions for signification. One must know that there is a necessary connection between sign and signified, such as between smoke and fire, and the sign itself must actually exist. Signification is divided in several ways.
There is rational signification, natural signification and conventional signification, and each of these can be verbal or non verbal. From another angle, signification can be divided into verbal and non verbal, and both of these may again be rational, natural or conventional.
Within verbal conventional signification there are three well known kinds. Signification by conformity is when a word points to the whole of its meaning, as when the word masjid points to the entire building with its main elements.
Signification by inclusion is when a word points to part of its meaning, as when masjid points only to the mihrab. Signification by implication is when a word points to something that is not explicitly in the meaning but is closely connected to it, such as the name Hatim indicating generosity.
Mantiq is concerned with verbal conventional signification, because its task is to treat words as signs of meanings and to analyse those meanings and the judgements built on them.
Concept and instance
The central concern of mantiq is meaning, not bare sounds or letters. Meaning, in relation to its existence, is of two kinds. If it exists in the mind, it is called a concept. If it exists outside, in concrete reality, it is called an instance.
The mental concept can be the image of fire, or the concept of a human being. The instance is the actual fire burning in front of you, or a particular human being in the external universe. Thus the concept is the meaning in the mind, and the instance is the concrete thing outside the mind.
Universal and particular
The mental meaning is then divided into universal and particular. A universal is that whose concept does not prevent many individuals from sharing in it. For example, the concept of human being is one meaning that can be shared by Zayd, Amr, Ahmad, Muhammad and many others. A particular is that whose concept does prevent such sharing.
The concept of Zayd is tied to the specific features of that single person and does not extend to another individual.
It is important to note that universality and particularity belong to meanings, not to words. The word human being is not universal in itself; rather it is the meaning of human being which is universal and which can have multiple instances in reality. This confirms that mantiq studies meanings as they are signified by expressions.
Univocal and gradational universals
After dividing meaning into concept and instance, and the concept into universal and particular, the universal is further divided into univocal and gradational, also known as mushakkik.
A univocal universal is a universal that applies to its instances equally. The concept human being applies to Zayd and Amr in the same way. Zayd is not less human than Amr, nor is Amr more human than Zayd. With respect to the concept, their share in humanity is equal.
A gradational universal is a universal that applies to its instances with variation in degree. Whiteness is a gradational universal. Two objects can both be white, but one may be whiter than the other.
A remote control and a book may both be white, although the whiteness of a book may be clearer and stronger than the whiteness of the remote control. The same holds for existence when comparing the existence of a contingent being with the existence of the Necessary Being; there is a clear disparity between the two.
The way to distinguish a univocal universal from a gradational universal is to look at how the universal applies to its instances in external reality. If all instances have equal participation in that universal, it is univocal. If they differ in degree, it is gradational.
The common division among the logicians is that every universal is either univocal or gradational, although Shaykh al Islam Ibn Taymiyyah has another way of dividing them that will be discussed elsewhere.
Real and relative particulars
The particular, when contrasted with the universal, is the real particular. This is a concept whose very grasp blocks the possibility of multiple individuals sharing in it. Zayd, Muhammad, and a specific copy of a book are real particulars. The concept of this particular book includes its title, cover, author and contents, and that full meaning is not shared by any other book.
From another angle, the particular is divided into real particular and relative particular. The real particular is looked at in itself, as to its own meaning, without relation to anything above it. The relative particular is a universal concept that falls under a wider universal.
For example, human being in itself is a universal, because its concept can be shared by many individuals. When human being is viewed under the more general concept animal, it becomes a particular relative to that wider universal. In itself it remains a universal, but, in relation to what is above it, it is described as a relative particular.
In truth, the only particular that stands opposite the universal in the main division is the real particular. The relative particular is still a universal that has been placed under a more general universal. The overall understanding is that meaning in the mind is the concept.
This concept, with respect to its application in reality, either has a single instance and is then a real particular, or has many instances and is then a universal. That universal is then either univocal or gradational.
The four relations between universals
Between universal meanings there are four main relations, which are studied in terms of the instances that fall under them in external reality. The focus is not on universals merely as meanings in the mind, but on how their instances overlap or do not overlap.
The first relation is equivalence. This is when each of two universal meanings applies to every instance to which the other applies. The pattern here is all and all. An example given is the relation between human being and rational.
Every instance that is a human being is rational, and every instance that is rational is a human being, so the two universals are equivalent with respect to their instances.
The logicians also mention human being and laughing in this way, saying that every human being is laughing in potential and that everything to which laughing applies is a human being, although this claim is open to criticism.
The second relation is absolute generality and particularity. This is when one universal applies to all the instances of the other, while the second universal applies only to some of the instances of the first. The pattern here is all and some.
For example, every bird is an animal, but not every animal is a bird. Likewise, every human being is an animal, but not every animal is a human being. The narrower universal is particular in relation to the wider one, yet all its instances fall under the wider universal.
The third relation is generality and particularity from one respect. This is when each of the two universals applies to some of the instances of the other, and each also applies to instances to which the other does not apply.
The pattern here is some and 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, or disjointness. This is where no instance that falls under one universal falls under the other. There is no overlap at all. An example is animal and inanimate object. Nothing that is an animal is inanimate, and nothing that is inanimate is an animal. The relation between stone and human being is also of this kind.
These four relations always hold between universals that differ in meaning, such as human being and rational.
The logicians also say that although these concepts are distinct as meanings in the mind, they may coincide, include one another, partially intersect, or be mutually exclusive at the level of instances. The same terminology of absolute generality and particularity and generality and particularity from one respect appears constantly in usul al fiqh, kalam, grammar.
