Predication, Types of Categorical Proposition and Negated Terms

1. The central question of predication

The previous lesson classified categorical propositions by quantity and quality: all or some instances, affirmation or negation. We now examine predication (ḥaml) itself: in what sense may a predicate be affirmed of a subject?

In “Zayd is a writer,” Zayd means a particular person whereas writer conveys an attribute. The meanings differ, yet both can apply to one and the same person.

We shall first examine the relation between subject and predicate, then several independent classifications of categorical propositions. One proposition can fall under more than one classification because each asks a different question.

2. The textbook definition of predication

«الحمل في اصطلاحهم: اتحاد المتغايرين في المفهوم بحسب الوجود»
In the logicians’ terminology, predication is the unity in existence of two items whose concepts differ.

Difference in meaning means subject and predicate convey distinct concepts. Unity in existence means that they can be truly applied to the same referent.

Thus Zayd and writer are conceptually different; if Zayd writes, both descriptions refer to the same existing person. The definition resolves the apparent puzzle of how distinct meanings can be joined in one predication.

3. Worked source example: Zayd is a writer

«زيد كاتب»
Zayd is a writer.

Subject: Zayd, a determinate person.
Predicate: writer, a person who writes.
Predicative relation: affirmation of being a writer of Zayd.

Grasping the two concepts separately does not yet affirm anything. When the statement attributes authorship or writing to Zayd, the subject and predicate are brought together in one referent. That is the structure of predication here.

4. Worked source example: Amr is a poet

«وعمرو شاعر»
And Amr is a poet.

Amr is a proper name; poet denotes a quality or ability. The concepts differ, but if Amr is a poet the quality is realized in that person.

Invalid inference: Everyone who is a poet must be Amr.
Valid interpretation: The predication concerns Amr; the concept poet may also apply to many other persons.

Identity of referent in a true predication does not establish synonymy or make every bearer of the predicate identical with the subject.

5. What differs and what unites

The definition mentions both difference and unity, but in different respects. If subject and predicate were wholly separate in every respect, predication would fail. If they had to be identical in every respect, informative predication would be undermined.

In “A human is an animal”:
Human — the concept of a rational animal.
Animal — a broader genus of sentient living beings.

The concepts are different while every human individual is also an animal. Keeping conceptual difference alongside referential unity is essential.

6. Direct predication: ḥaml bi-l-muwāṭaʾah

«الحمل بالمواطأة، نحو عمرو طبيب، وبكر فصيح»
Direct predication, such as “Amr is a physician” and “Bakr is eloquent.”

In ḥaml bi-l-muwāṭaʾah, the predicate is directly said of the subject. “Amr is a physician” attributes physicianhood to Amr himself; “Bakr is eloquent” attributes eloquence to Bakr himself.

This is commonly understood as an “is-a” form of predication: the bearer of the attribute is directly described by the predicate. A paraphrase involving “has” may be related in meaning but is not the same direct expression.

7. Derivative predication: ḥaml bi-l-ishtiqāq

«والمال لزيد، وخالد ذو مال»
And the property belongs to Zayd, and Khalid possesses property.

In derivative predication (ḥaml bi-l-ishtiqāq), the subject–predicate relation is expressed through a mediator such as fī, the possessive lām, or dhū (“possessing”).

“The property belongs to Zayd” states ownership; it does not identify the property with Zayd. “Khalid possesses property” gives Khalid a relation to wealth, not an identity with wealth. The intermediary matters to the claim's structure.

8. Location as mediated predication

«زيد في الدار»
Zayd is in the house.

The preposition fī conveys a locative relation. The sentence does not call Zayd a house; it locates him in one.

Subject: Zayd.
What is expressed: being in the house.
Mediator: fī, which carries the locative relation.

Replacing it with “Zayd is a house” destroys the intended claim. This contrast makes the role of an intermediary in derivative predication clear.

9. Direct and derivative predication contrasted

Both kinds say something about a subject, but the manner of attribution differs.

Direct: “Amr is a physician” — physician is predicated directly of Amr.
Derivative: “Zayd is in the house” — location is expressed with fī.
Derivative: “The property belongs to Zayd” — possession is expressed by lām.

The presence of the English verb “is” or Urdu “ہے” does not settle the classification; one must inspect the predicative relation.

10. A second axis: what kind of subject existence?

«تقسيم آخر للحملية»
Another division of categorical propositions.

The new criterion is the perspective from which the subject and the judgment are considered: subject existing externally, subject considered in the mind, or the subject as determined in reality itself.

The resulting categories are external (khārijiyyah), mental (dhihniyyah), and real (ḥaqīqiyyah). Unlike quantity-based classification, this is not just the question “How many members?” but concerns how the domain of the judgment is understood.

11. The external proposition

«إن كان موجودا في الخارج»
If the subject exists outside the mind.

A categorical judgment considered with reference to an externally existing subject is called external (khārijiyyah). “External” distinguishes actual existence from a merely mental concept.

«الإنسان كاتب»
A human is a writer.

The book uses this to illustrate consideration of humans as externally existing. This does not establish that every human actually writes; the proposition’s quantity and factual truth are separate matters.

12. The mental proposition

«وإن كان موجودا في الذهن»
And if the subject exists in the mind.

A proposition treating a concept precisely as a concept in the intellect is called mental (dhihniyyah).

«الإنسان كلي»
Human is universal.

Universality here does not belong to a particular human as an external characteristic. Zayd and Amr are individuals, not universals in their own persons. Being universal is a logical feature of the mentally considered human concept.

13. Mental and natural: related but distinct

“Human is a species” was a natural proposition in the earlier distinction, because its predicate concerns a nature itself. “Human is universal” now illustrates a mental proposition, because universality pertains to a concept considered in the intellect.

Both concern something other than humans taken one by one as individuals, but the questions differ.

Natural: Is the judgment about the nature itself or its instances?
Mental: Is the judgment made concerning the concept as mental rather than external?

The two labels should not be treated as automatically synonymous.

14. The real proposition

«وإن كان الحكم باعتبار تقرره في الواقع»
And if the judgment is made with reference to its establishment in reality.

A real (ḥaqīqiyyah) proposition treats the subject and judgment in reality as such, without restricting the claim to some particular externally existing object or merely to the concept as mental.

«أربعة زوج»
Four is an even number.

The evenness of four is not created by drawing four objects. It belongs to numerical reality whether we consider four in thought or count four things outside the mind.

15. A second source example of real predication

«والستة ضعف الثلاثة»
And six is twice three.

“Six” and “twice three” have different conceptual expressions but refer to the same numerical quantity. The truth is not confined to any one actual occasion of counting.

Six books can be twice a set of three books, but the relation did not come into being because those particular books were counted. The basis of the proposition is the numerical relation itself, which makes this a real proposition in the textbook's sense.

16. Comparing external, mental and real propositions

The three categories answer: In what respect is the judgment made?

External: “This book is open” — an externally existing book and its condition.
Mental: “Human is universal” — the universal concept in the intellect.
Real: “Four is even” — a property rooted in numerical reality.

A common error is to interpret “real” merely as “true.” Ḥaqīqiyyah is a technical classification, not another name for every true proposition. External and mental propositions can also be true.

17. A new division: where negation is placed

«القضية الموجبة وكذا السالبة تنقسمان إلى معدولة وغير معدولة»
Affirmative and likewise negative propositions divide into metathetic (maʿdūlah) and non-metathetic forms.

The new issue is not merely whether the entire judgment is affirmative or negative. Ask whether the negative particle is built into the subject term or predicate term, or instead negates the predicative connection itself.

In a maʿdūlah, negation forms part of the subject, predicate, or both; in a non-maʿdūlah, it does not. Counting a visible negative word is not enough.

18. The original definition of maʿdūlah

«فالمعدولة: ما يكون فيه حرف السلب جزء من الموضوع، أو من المحمول، أو كليهما»
A metathetic proposition is one in which the negative particle is part of the subject, or the predicate, or both.

Negated subject: the negative component belongs to the subject term.
Negated predicate: it belongs to the predicate term.
Both terms negated: it belongs to each side.

In all three cases negation helps form a complex term. It need not mean that the entire predicative relation is itself being denied.

19. Negation as part of the subject

«اللاحَيُّ جماد»
The non-living is inanimate.

The subject “al-lā-ḥayy” is a compound conception including negation of being living. The predicate “inanimate” is nevertheless affirmed of that subject.

Subject: the non-living.
Predicate: the inanimate.
Judgment: an affirmative predication of the subject.

Negation within the subject term does not, by itself, turn the entire judgment into a negative proposition.

20. Negation as part of the predicate

«زيد لا عالم»
Zayd is a non-scholar.

Here “lā ʿālim” is taken as a compound predicate meaning non-scholar. This complex predicate is affirmed of Zayd in the proposition's affirmative structure.

Subject: Zayd.
Predicate: non-scholar.
Quality: affirmative predication with a negated predicate term.

If “Zayd is not a scholar” is analyzed as direct denial of the affirmative connection, its logical form is different. Denying a predicate and affirming a negative predicate-term are not the same analysis.

21. Negation within both terms

«اللاحَيُّ لا عالم»
The non-living is non-knowing.

Here both the subject “al-lā-ḥayy” and the predicate “lā ʿālim” contain a negative component, so the form is negated in both terms.

First negative: helps define the subject-term.
Second negative: helps define the predicate-term.
Judgment quality: an affirmative link between the two complex concepts.

Negation in both terms must not be confused with negation of the entire predication.

22. Simple negation versus an affirmative with a negated term

«العالم ليس بلاحي»
A knower is not non-living.

The particle laysa negates the predicative link, whereas the negative component within “bi-lā-ḥayy” helps form a negated predicate. Thus the quality of the proposition and the structure of the predicate require separate examination.

Compare:
“Zayd is a non-scholar” — an affirmative judgment with a negated predicate.
“Zayd is not a scholar” — a negative judgment denying a predicate.

Ordinary speech may bring the meanings close together, but their technical analysis asks where the negation is located.

23. Non-metathetic: muḥaṣṣalah and basīṭah

«ويسمى غير المعدولة في الموجبة بالمحصلة، وفي السالبة بالبسيطة»
A non-metathetic proposition is called muḥaṣṣalah when affirmative and basīṭah when negative.

Affirmative muḥaṣṣalah: “Zayd is learned” — an affirmative judgment, with no negative particle built into either term.
Negative basīṭah: “Zayd is not learned” — the link is denied, while the predicate learned is an unnegated term.

The names contrast with maʿdūlah. Affirmative/negative state the quality of the judgment, while metathetic/non-metathetic describe whether a negative forms part of a term.

24. How can a negative proposition also be metathetic?

Maʿdūlah does not mean that the overall proposition must be affirmative. The book explicitly divides both affirmative and negative propositions into metathetic and non-metathetic forms.

Consider “This person is not a non-scholar”:
Predicate: “non-scholar,” a negated concept.
Connection: “is not,” which denies that predicate of the subject.

Thus a negated term and a negative judgment can occur together. They are not redundant simply because both contain negation; their logical roles are different.

25. A worked contrast in the position of negation

Compare four statements by locating negation:

1. “Zayd is learned” — affirmative non-metathetic: no negation.
2. “Zayd is not learned” — simple negative: the link is denied.
3. “Zayd is a non-scholar” — affirmative with a negated predicate term.
4. “Zayd is not a non-scholar” — negative with a negated predicate term.

The point is to distinguish quality of the proposition from the structure of the terms, rather than treating both as the same question.

26. Several classifications of one proposition

Take “Every human is an animal” and ask different questions.

Quantity: universal, because “every” includes all members.
Quality: affirmative, because animality is affirmed.
Mode of predication: direct, since animal is predicated immediately of human.
Metathetic status: non-metathetic, since neither subject nor predicate contains term-negation.

Recognizing several independent classifications in one proposition is a central analytical skill in logic.

27. Introducing modality without anticipating its details

«وقد يذكر الجهة في القضية، فتسمى موجهة ورباعية أيضا»
A modality may be mentioned in the proposition, so it is also called a modal or four-part proposition.

So far we have considered subject, predicate, and their relation. Modality (jihah) further qualifies the manner in which the relation holds: for example, necessity, possibility or a specified permanence.

A proposition explicitly containing such a qualification is modal (muwajjahah). The book begins its detailed classification of modalities on the following page; their precise divisions and conditions belong to the next level.

28. Review and a practical classification checklist

Predication: distinct concepts united in reference or existence.
Direct: the predicate applies immediately to the subject.
Derivative: a mediator expresses a relation.

External, mental, real: three perspectives on the subject and its judgment.
Metathetic: negation is built into the subject term, predicate term, or both.
Non-metathetic: called muḥaṣṣalah when affirmative and basīṭah when negative.

For any new proposition ask: What is predicated? How are the terms related? In what domain is the judgment considered? Is negation part of a term or the predicative link? These questions prevent category errors.