Simplistic Overview

The usool of mantiq (foundations of logic) are mainly two things:

Hadd (precise description of a thing) and qiyas (reasoning).

• Hadd is what gives you a clear idea of something. It uses tools like genus (jins), differentia (fasl), species (nawʿ), common accident (ʿarad ʿamm), and property (khassa). These are called the five universals.
• Qiyas is reasoning from premises to a conclusion. It can be certain (burhani), based on agreement (jadali), common opinion (khitabi), imagination (shiʿri), or trickery (sofistaʾi).

All knowledge is either:

• Tasawwur (knowing what a thing is) – gained through hadd.
• Tasdiq (knowing if something is true) – gained through qiyas.

So, the usool of mantiq is the method of defining things properly and reasoning correctly to reach knowledge.

Ibn Taymiyyah said that the base of logic is two things: hadd (definition) and qiyas (reasoning). Knowledge is of two kinds: tasawwur (to know what a thing is) and tasdiq (to know if something is true).

Some knowledge is obvious (badihi) and some is gained by thinking (nazari). The gained kind always depends on the obvious kind, or else it would go in circles or never end.

Qiyas (syllogism): This is how tasdiq is reached. It is built from two premises (muqaddimat), each being a statement (qadiyya). A statement can be:

• Affirmative (mujiba) or negative (saliba).
• Universal (kulliyya) or particular (juzʾiyya)

Types of Qiyas by Material

• Burhani: Proof built on certain knowledge, leading to certainty.
• Jadali: Reasoning built on what is conceded or agreed upon in debate.
• Khitabi: Reasoning that uses what is commonly known or accepted among people.
• Shiʿri: Reasoning that works through imagination and imagery, like in poetry.
• Sofistaʾi: False reasoning based on deception and trickery.

Types of Qiyas by Form

• Hamli (Categorical): Reasoning through inclusion, where one idea is contained in another.
• Shartiyy Muttasil (Conditional Connected): Reasoning through entailment, “If this, then that.”
• Shartiyy Munfasil (Conditional Disjunctive): Reasoning through opposition or disjunction, “Either this or that.”

Other Kinds of Reasoning

• Shumul (Syllogism of Inclusion): Reasoning from a universal rule down to a particular case.
• Istiqraʾ (Induction): Reasoning from particular cases up to a universal rule. This can be complete if all cases are covered, or incomplete if not.
• Tamthil (Analogy): Reasoning from one particular case to another. Ibn Taymiyyah says that Shumul and Tamthil reduce to each other, so it is wrong to say that only Shumul gives certainty. Scholars also differed on how the name Qiyas should be applied.

Ibn Taymiyyah summed up the discussion in four points. It is wrong to say tasawwur (knowing what something is) can only come from hadd (definition),

and it is wrong to say tasdiq (knowing if something is true) can only come from qiyas (reasoning).

It is correct, however, that hadd (definition) can give tasawwur (knowing what something is), and qiyas (reasoning) especially burhani (demonstrative proof based on certainty) can give tasdiq (knowing if something is true).

This shows both the limits and the value of logic in gaining knowledge.

The foundations of logic and its terms

They built logic upon discussion of the hadd (definition) and its types, and the qiyas burhani (demonstrative syllogism) and its types. They said: knowledge is either tasawwur (conceptualisation) or tasdiq (assent), and each of them is either badihi (self-evident) or nazari (acquired through reasoning).

It is known that not all are self-evident, and it is not possible that all are acquired, because the acquired needs the self-evident. Otherwise, it would lead to circularity in causes or infinite regress in causes, and here the causes are the asbab al-ilm (means of knowledge), namely the adillah (proofs). Both circularity and infinite regress are impossible.

As for the nazari (acquired), it must have a path through which it is attained. The path by which tasawwur (conceptualisation) is attained is the hadd (definition), and the path by which tasdiq (assent) is attained is qiyas (syllogism).

The hadd (definition) is a comprehensive name for everything by which tasawwur is known. It is the explanatory statement. This includes the hadd haqiqi (real definition), the hadd rasmi (descriptive definition), and the hadd lafzi (verbal definition).

Or it is only the haqiqi (real) definition, to which the rasmi (descriptive) is attached, while the lafzi (verbal) is not of this kind. Or the hadd is a name for the haqiqi (real) and the rasmi (descriptive) but not the lafzi (verbal). Each of these three is an expression used by a group among them, as I have explained elsewhere and mentioned the names of those who held each view.

As for qiyas (syllogism), if its material is yaqini (certain), then it is the burhani (demonstrative). If it is musallam (conceded), then it is jadal (dialectical). If it is mashhur (well-known), then it is khitabi (rhetorical). If it is mukhayyal (imaginary), then it is shi’ri (poetic). If it is mumawwah (deceptive), then it is sawfisṭa’i (sophistical). For this reason, the burhani, khitabi, and jadal may overlap. Some people make khitabi the zanni (probabilistic), and some make it the iqna’i (persuasive).

They also have other terms, some of which agree with the terminology of the “first teacher” Aristotle, and some of which differ from him. Many of those who authored works on this subject departed in many ways from the method of their first teacher, but the purpose here is not to expand on that.

As for the hadd (definition), it is composed of dhati (essential attributes) if it is haqiqi (real). Otherwise, it must involve a ‘aradi (accidental attribute).

Each of them may either be mushtarak (shared) with other things besides the thing defined, or mumayyiz (distinctive) for it against others. The mushtarak dhati (essential shared) is the jins (genus). The mumayyiz dhati (essential distinctive) is the fasl (differentia). What is composed of the two is the naw‘ (species). The mushtarak ‘aradi (accidental shared) is the ‘arad ‘aam (common accident). The mumayyiz ‘aradi (accidental distinctive) is the khassa (property).

Sometimes the term khassa (property) is used for what occurs to the naw‘ (species) even if it is not general to all of its individuals, but such a khassa does not provide distinction. Likewise, the term naw‘ (species) is sometimes used for relative species, which in relation to what is above it is a species, and in relation to what is below it is a genus. This and similar matters are details of logic, but that is not the intended subject here. There is another place for discussion of what they mentioned regarding jins (genus) and naw‘ (species), other than what has been briefly noted here.

These are the five universals. Opposite to the kulli (universal) is the juz’i (particular), which is that whose conception prevents sharing in it. Discussion of the murakkab (composite expression) is preceded by discussion of the mufrad (single expression) and the indication of the word upon it.

As for qiyas (syllogism), it is composed of two muqaddimat (premises). A premise is a qadiyya (proposition), which is either mujiba (affirmative) or saliba (negative), and each of them is either kulliyya (universal) or juz’iyya (particular). Therefore, one must discuss the qadiyyah (propositions), their kinds, and their modes.

They may be reasoned about by their naqeed (contradictory), by their ‘aks (conversion), and by ‘aks al-naqeed (contraposition). If they are valid, their contradictory is false, and their conversion and contraposition are true. Therefore, they discussed the tanaqud (contradiction) of propositions, their simple conversion, and their contraposition.

A qadiyya (proposition) is either hamliyya (categorical), or shartiyya muttaṣila (hypothetical conditional connected), or shartiyya munfaṣila (hypothetical conditional disjunctive).

Accordingly, qiyas (syllogism), in terms of its form, is of three kinds: qiyas tadakhul (syllogism of inclusion), which is the hamli (categorical); qiyas talazum (syllogism of entailment), which is the shartiyy muttaṣil (conditional connected); and qiyas ta‘anud (syllogism of opposition), which is the division and disjunction, the shartiyy munfaṣil (conditional disjunctive).

This is in terms of its form. As for its material, it returns to the five categories mentioned earlier. Therefore, discussion must also be had regarding the material of qiyas, which are the propositions by which one reasons to others.

All this concerns qiyas al-shumul (syllogism of inclusion). As for qiyas al-tamthil (analogy) and istiqra’ (induction), they have another ruling.

They said: reasoning from the kulli (universal) to the juz’i (particular) is qiyas al-shumul (syllogism of inclusion). Reasoning from the juz’i (particular) to the kulli (universal) is istiqra’ (induction), either complete if its inclusion of all individuals is known, or incomplete if not. Reasoning from one juz’i (particular) to another juz’i is qiyas al-tamthil (analogy).

We have explained elsewhere that every qiyas al-shumul (syllogism of inclusion) returns to tamthil (analogy), and every qiyas al-tamthil (analogy) returns to shumul (inclusion). Their making qiyas al-shumul to give certainty while qiyas al-tamthil does not is a mistake.

We have mentioned the dispute of people concerning the name qiyas: does it include both shumul and tamthil, as is the view of the majority, or is it literal in tamthil and metaphorical in shumul, as chosen by Abu Hamid al-Ghazali (d. 505 AH) and Abu Muhammad al-Maqdisi, or is it the opposite, as chosen by Ibn Hazm (d. 456 AH) and others among the logicians? The discussion of this has been expanded in other places.

The purpose here is something else. We say: the discussion is in four areas, two negative and two affirmative.

The two negatives:

One, their saying that the tasawwur (conceptualisation) sought cannot be attained except by hadd (definition).

Two, their saying that the tasdiq (assent) sought cannot be attained except by qiyas (syllogism).

The two affirmatives:

One, that the hadd (definition) provides knowledge of tasawwur (conceptualisations).

Two, that qiyas (syllogism), or the burhan (demonstrative syllogism) described, provides knowledge of tasdiqat (assents).

al-Radd ‘ala al-Manțiqiyyin Pages 46-48