The Conclusion: Subject, Principles, Problems, and Eight Introductory Headings

1. Three fundamental elements of a science

لكل علم ثلاث أمور: أحدها: الموضوع
Every science has three matters; the first is its subject.

To understand a science as an organized discipline, distinguish what it studies, which preliminary notions and propositions it uses, and which questions it attempts to establish. Classical terminology calls these subject (mawḍūʿ), principles (mabādiʾ), and problems or issues (masāʾil).

Logic does not merely memorize names. It examines conceptions and judgments so that rules of reliable thinking may be learned. These three elements explain how such study forms a coherent science.

2. What is the subject of a science?

الموضوع، وهو ما يبحث في العلم عن عوارضه ولواحقه الذاتية
The subject is that whose relevant intrinsic attributes and concomitants are investigated in a science.

A science has a focus of inquiry. It examines specified properties and relations of that focus, rather than every fact one could possibly mention about it.

Here “intrinsic attributes” does not mean that each studied property is an essential constituent like genus or differentia. It refers to properties investigated in virtue of the science's subject and proper scope.

3. The subject of medicine

كبدن الإنسان لعلم الطب
For example, the human body is the subject of medicine.

A physician studies the body in relation to health, illness, symptoms, and treatment. The same body can be discussed under other aspects by other disciplines.

Thus one external object may be considered by several sciences, each with its own respect of inquiry. Naming the object alone does not fully specify the science's concern.

4. The subject of grammar

والكلمة والكلام لعلم النحو
The word and speech are the subjects of grammar.

Grammar considers expressions in relation to inflection, construction, and the roles of sentence elements. It does not automatically turn every historical or phonetic fact about a word into a grammatical issue.

In كَتَبَ زَيْدٌ الدَّرْسَ, identifying Zayd as the agent and al-dars as the object is a grammatical inquiry. This illustrates why knowing the subject must be combined with knowing which properties are being investigated.

5. Geometry and logic as sciences

والمقدار المتصل لعلم الهندسة، والمعلوم التصوري والمعلوم التصديقي لصناعتي هذه
Continuous magnitude is the subject of geometry, while known conceptions and judgments form the central concerns of the two parts of this logical art.

Geometry treats determinate relations of magnitude and form. Logic, on the conception side, examines definitions; on the judgment side, it investigates propositions and arguments.

A science's subject thus gives its questions a coherent domain.

6. The subject itself versus its properties

وينبغي أن يعلم أنه لا يبحث عن وجود الموضوع ولا يبحث عن ماهيته في العلم الذي هو موضوع له
The existence and essence of a science's own subject are not ordinarily the questions it sets out to prove within that science.

Medicine studies health and disease of the body without having to establish the body's very existence through a new philosophical demonstration in each medical argument.

The point concerns the order of investigation: the discipline takes its subject as understood and investigates its proper predicates. Foundational questions about the subject may belong to a preliminary or another discipline.

7. Why the scope of a subject matters

فلا يبحث الطبيب عن بدن الإنسان من حيث إنه موجود
The physician does not investigate the human body merely insofar as it exists.

Existence is a very general predicate shared by countless things. That alone does not specify medical questions such as health, weakness, or disease.

Changing the respect of inquiry changes the scientific question. That is why a subject must be considered with the properties proper to its discipline.

8. Can a science have several subjects?

The commentary discusses whether the subject of a science must be one thing. A discipline may investigate several related items united by a common aspect or a coherent set of questions.

In grammar, “word” and “speech” are distinct expressions, yet both are relevant to a connected field of linguistic and grammatical relationships.

Therefore the unity of a science should not be mistaken for a requirement that it investigate only one external individual. Its unifying respect is the important point.

9. Principles on which scientific issues depend

وثانيها: مباديه، والمبادي ما يبتني عليه المسائل
The second element is a science's principles: matters on which its issues depend.

Principles are not simply preliminary vocabulary. They are concepts or premises necessary to formulate or demonstrate the questions studied by a discipline.

For example, a proof by syllogism presupposes understanding “middle term,” “minor premise,” and “major premise,” and it must also rely on appropriate propositions. These different dependencies point to two classes of principles.

10. Conceptual principles

وهي إما تصورية أي حدود تورد لموضوع الصناعة وأجزائه وجزئياته وأعراضه الذاتية
Principles may be conceptual: definitions of the science's subject, its parts, kinds, and proper attributes.

One must know what the relevant terms mean before judging propositions about them. If “proposition” and “syllogism” are not defined, the purported rules concerning them lack a fixed subject.

Conceptual principles clarify meaning and delimitation; merely giving such a definition is not yet the proof of a new declarative thesis.

11. A worked example of conceptual foundations

Knowing the definition of qaḍiyya (proposition) is preliminary to studying categorical propositions. Similarly, without grasping ḥadd awsaṭ (middle term), the conditions of the syllogistic figures cannot be stated accurately.

These are conceptual foundations. By contrast, the proposition that a particular figure requires a universal major premise is a judgment to be established or applied.

Within one discipline, understanding a term and proving a statement about that term are distinct stages.

12. Propositional principles

أو تصديقية وهي المقدمات التي تؤلف منها قياساته إما بديهية
Or principles may be propositional: premises from which a science forms its syllogisms; some are self-evident.

A propositional principle is an assertion used as a premise. For example, the principle that contradictories cannot both be true in the same respect can underwrite a demonstration.

This is assent to a proposition, not mere conception. If the premise is neither known nor legitimately conceded, the intended conclusion is not established at the requisite level.

13. Self-evident and accepted theoretical premises

Among propositional principles, some are self-evident and do not require a new demonstration at that point. Others are originally theoretical but are accepted as premises for a particular inquiry.

For example, a teacher may use a previously established theorem in a new proof. It functions as a premise, but that does not transform it into a self-evident axiom.

This distinction separates what is immediately evident from what is granted or already established for present purposes.

14. What makes a premise an assumed postulate?

فإن كان التسليم على سبيل حسن الظن بمن ألقاه إليه تسمى أصولا موضوعة
If the premise is granted from favorable confidence in the one who presents it, it is called an assumed principle or postulate.

The emphasis is the ground of provisional acceptance: a premise is conceded in the current inquiry even though its full proof has not been reviewed in that setting.

For example, an instructor may proceed from an earlier established result. For the current discussion it functions as a postulated basis, while its independent justification remains a distinct matter.

15. Premises granted with objection or reluctance

فإن كان التسليم مع الاستنكار تسمى مصادرة
If a premise is granted despite objection or reluctance, it is termed a muṣādara in this discussion.

A participant may allow a premise for the sake of argument while still contesting it. Such concession is not the same as self-evident certainty.

An assumed postulate is granted with confidence; a contested concession is granted despite resistance. These labels describe how a premise is received in the discussion, not an automatic verdict on its truth.

16. Comparing propositional foundations

Kind of premiseWhy it is acceptedStatus in the argument
Self-evidentImmediately evidentAvailable without a fresh proof
Assumed postulateConfidence in its presenterConceded foundation in this inquiry
Contested concessionTemporarily granted with reservationStill disputed by the interlocutor

The table classifies how premises are accepted. Their use in an argument must still meet requirements of inference and of the truth or concession relevant to its purpose.

17. The issues a science seeks to prove

وثالثها: المسائل، وهي التي يشتمل العلم عليها ويحاول إثباتها بالدليل
The third element is the issues of the science: propositions it contains and attempts to establish through proof.

A masʾala is a thesis to be demonstrated within the discipline, not simply a familiar phrase. It may require a suitable argument to attain its intended standing.

For example, “A universal negative converts to a universal negative” is a logical thesis. Definitions of proposition and conversion supply conceptual principles; applicable inference rules supply propositional foundations.

18. Why foundations are not the same as conclusions

Suppose we seek to establish “Every human is an animal.” Understanding the meanings of “human,” “animal,” and “every” provides conceptual preliminaries. Relevant accepted premises or an appropriate argument supply propositional foundations. The proposition being established is the issue.

An established result in one discipline can become an accepted premise in another. The distinction survives because the roles are relative to the inquiry at hand.

Principles allow an investigation to proceed; its issues are the claims the science aims to settle.

19. Three elements in one view

ElementGuiding questionExample from logic
SubjectProperties of what?Conceptions and judgments
Conceptual principlesWhat do the terms mean?Definitions of proposition and syllogism
Propositional principlesWhich premises are used?Established or granted principles
IssuesWhich theses need proof?Conditions of valid syllogisms

This framework shows the order of disciplined inquiry. Without definitions a question may be equivocal; without justified premises its proposed answer may lack proof.

20. Eight introductory headings

فصل في الرؤوس الثمانية
A section on the eight introductory headings.

Classical study manuals often open with eight guideposts that orient the learner before detailed treatment. They are called ruʾūs thamāniya—the eight headings.

They differ in function from subject, principles, and problems. The latter describe the science's internal structure; these headings explain its aim, use, title, author, place in study, classification, division, and methods of teaching.

21. 1. Gharad: the aim of a discipline

أحدها: الغرض، أعني العلة الغائية
The first heading is the aim—that is, the final cause for pursuing the discipline.

Gharad denotes the intended objective. In logic, this may be expressed as learning rules that protect reasoning from error. That objective explains why the study is undertaken.

The aim should not simply be equated with every benefit someone may eventually receive. The distinction between an intended end and its useful consequences leads to the next heading.

22. 2. Manfaʿa: the benefit of studying

وثانيها: المنفعة، لتسهل عليه المشقة في تحصيله
The second heading is the benefit, so that the effort of mastering the science becomes easier to bear.

Recognizing benefits can sustain a student through challenging technical study. Logic is useful for organizing arguments across disciplines and detecting errors in reasoning.

Aim expresses what is intended; benefit describes practical advantage or value arising from study. They are related but not interchangeable in every discussion.

23. 3. Tasmiyah: the name of the science

وثالثها: التسمية، أعني عنوان العلم
The third heading is its designation: the science's title or name.

A title identifies the discipline under which discussions are organized. “Manṭiq” is the familiar name under which conception, judgment, syllogism, and fallacies are studied.

Knowing the name does not itself define the subject. It helps identify the field, while its subject and aim specify what the name encompasses.

24. 4. Muʾallif: identifying the author

ورابعها: المؤلف
The fourth heading is the author or compiler.

Knowing who prepared a work and its pedagogical purpose helps interpret its organization. At the end, the writer names himself Muḥammad Faḍl al-Imām al-Khayrābādī and describes gathering material from earlier writings to make the art more accessible to learners.

Identifying an author helps contextualize a textbook; it does not replace examining the definitions and arguments of each claim.

25. 5. Martaba: place in the order of learning

وخامسها: أنه في أي مرتبة هو
The fifth heading asks where the discipline stands in the order of study.

This is not merely a contest over which science has greater prestige. It concerns sequence and prerequisites: what should be studied first and what can be better understood after another discipline.

Within logic itself, basic concepts and judgments precede advanced syllogisms and fallacies. The same ordering principle applies when planning a curriculum across disciplines.

26. 6. What broader class of knowledge?

وسادسها: من أي علم هو
The sixth asks to which wider class of knowledge the discipline belongs.

Sciences may be grouped as intellectual, transmitted, instrumental, or end-directed under different systems of classification. Such labels describe a relevant aspect, not necessarily mutually exclusive essences.

Logic is often called an instrumental science because it assists inquiry elsewhere. Nevertheless, its own definitions and arguments remain worthy of systematic study.

27. 7. Qisma: division into parts

وسابعها: القسمة، وهو أبواب العلم والكتاب
The seventh heading is the division of the science and the book into parts.

Organizing the material makes the dependence among subjects visible. Al-Mirqat proceeds from conceptions, definitions, and universals to propositions, arguments, the five arts, and fallacies.

This is more than a table of contents; it maps the conceptual dependencies of the discipline—why the meaning of terms comes before evaluating propositions, and propositions before the structure of proofs.

28. 8. Anḥāʾ al-taʿlīm: methods of teaching

وثامنها: أنحاء التعليم وهي التقسيم، والتحليل، والتحديد، والبرهان
The eighth heading concerns the methods of teaching: division, analysis, definition, and demonstration.

Division displays a universal's classes; analysis resolves a composite matter into its parts or explanatory components; definition determines what a thing is; demonstration establishes a proposition from fitting premises.

These methods complement rather than replace each other. Knowing the kinds of an object does not guarantee knowing its definition or the proof of a claim about it.

29. Applying the four methods to one logical topic

Consider four ways of teaching “syllogism”:
Division: classify it as conjunctive or exceptive.
Analysis: identify the minor premise, major premise, middle term, and conclusion.
Definition: state the technical meaning of syllogism.
Demonstration: show why a particular conclusion follows from the premises.

Each method reveals a different aspect. Strong instruction combines structure, meaning, classes, and proof when appropriate.

30. A complete table of the eight headings

HeadingCentral question
1. AimWhat is intended?
2. BenefitWhy is it useful?
3. NameWhat is it called?
4. AuthorWho composed it?
5. RankWhere does it belong in the learning sequence?
6. ClassificationWhat broader kind of science is it?
7. DivisionHow are the contents organized?
8. MethodsHow should it be taught?

These eight orient learners and course planners; they are not the same classification as the three scientific constituents described earlier.

31. The author’s closing statement

هذا آخر ما أردنا جمعه وتأليفه في هذه الرسالة
This is the end of what we intended to collect and compose in this treatise.

In the closing lines, Muḥammad Faḍl al-Imām al-Khayrābādī explains that the short work gathers and simplifies material for beginning students, and he ends with a prayer for a good conclusion and benefit from learning.

The whole text thus forms a sequence from conception and judgment to definitions, arguments, and the structure of sciences: clarifying meanings, assessing claims, validating inference, and organizing knowledge.

32. The integrated outcome of Al-Mirqat

The course began by distinguishing conception from judgment, then clarified expressions, universals, predicables, and definitions. It proceeded to propositions, modalities, contradiction, and conversion.

The syllogistic figures, induction, analogy, and reductio clarified forms of reasoning. The five arts distinguished demonstration, dialectic, rhetoric, poetry, and sophistry, while the fallacies showed how reasoning fails.

The conclusion brings these strands into one organized intellectual discipline through subject, principles, problems, and introductory headings. Its enduring value lies in applying these distinctions carefully when studying other sciences.