Chapter Two: Propositions, Categorical and Conditional Forms, and Their Parts

1. Chapter two: the study of propositions

The earlier chapters developed the means of conception through universals, predicables and definitions. Chapter two turns to an instrument of judgment: the proposition, through which something is asserted about something else.

“Human” provides a concept. “A human is an animal,” however, makes an assertion about humans that may be evaluated as true or false. The analysis of propositions therefore concerns the relation expressed between concepts, not merely the words themselves.

This lesson develops the definition of a proposition, the distinction between categorical and conditional propositions, and the components of each.

2. The textbook definition of a proposition

«القضية قول يحتمل الصدق والكذب»
A proposition is a statement capable of being true or false.

Capability of truth or falsity means that the statement has the kind of content whose correspondence with reality can be assessed. It does not mean the same definite proposition must actually be both true and false; rather, a particular proposition may be true or false and is open to such evaluation.

“Zayd is present” is a proposition because we can investigate whether he is actually present.

3. An alternative phrasing in the source

«هو قول يقال لقائله إنه صادق فيه أو كاذب»
It is a statement about which its speaker may be said to be speaking truthfully or falsely.

This formulation focuses on the speaker's assertion: may the speaker be called truthful or mistaken on the basis of what was said? If someone states “It is raining,” we can check that claim against the weather.

The two formulations point to the same feature. The first describes truth-aptness; the second connects that truth-aptness to the person's assertion.

4. Questions, commands, and propositions

“Where is Zayd?” seeks information and does not itself assert a fact about his location, so the question as such is not a proposition.

“Close the door” is a command. Its purpose is to direct an action, not to assert the existence or nonexistence of a state of affairs.

“The door is closed” does assert something that can be checked.

An intelligible and complete expression is therefore not necessarily a proposition: the decisive criterion is whether truth or falsity can be predicated of its content.

5. The two main kinds of propositions

«وهي قسمان: حملية، وشرطية»
And propositions are of two kinds: categorical and conditional.

A categorical proposition directly affirms or denies a predicate of a subject. A conditional proposition expresses a relation between two propositional contents, often by means of a condition.

“Zayd is standing” — categorical.
“If the sun has risen, then daylight exists” — conditional.

Both can be true or false; they differ in the structure of the judgment.

6. Definition of the categorical proposition

«فهو ما حكم فيها بثبوت شيء لشيء أو نفيه عنه»
It is a proposition in which something is affirmed of a thing or denied of it.

In “Zayd is standing,” standing is affirmed of Zayd. In “Zayd is not standing,” standing is denied of him. In either case, Zayd is directly the subject of the predication.

Thus categorical propositions need not be affirmative. Both affirmation and denial occur within the categorical form.

7. Affirmative categorical propositions

«الحملية ضربان: موجبة»
Categorical propositions are of two types, the first being affirmative.

«وهي التي حكم فيها بثبوت شيء لشيء»
This is one in which something is affirmed of something else.

«الإنسان حيوان»
The human is an animal.

Animality is affirmed of the human. In logic, “affirmative” does not mean praise or approval; it is the technical term for affirming a predicative relation.

8. Negative categorical propositions

«وسالبة: وهي التي حكم فيها بنفي شيء عن شيء»
And the second is negative, in which something is denied of something else.

«والإنسان ليس بفرس»
And the human is not a horse.

Here “human” is the subject and “horse” the predicate, but the predication is denied rather than affirmed. “Negative” does not mean meaningless or false: “A human is not a horse” can be a true negative proposition.

Affirmative and negative are distinguished by the affirmation or denial of the predicative connection, not by approval or disapproval.

9. Polarity and truth are separate questions

Whether a categorical proposition is affirmative or negative concerns the form of its judgment; whether it is true or false concerns the correctness of its content. These are independent questions.

“A human is an animal” — affirmative and true.
“A human is a stone” — affirmative but false.
“A human is not a horse” — negative and true.
“A human is not an animal” — negative but false.

Thus affirmative propositions need not be true and negative propositions need not be false.

10. Three components of a categorical proposition

«الحملية تلتئم من أجزاء ثلاثة»
A categorical proposition consists of three components.

«أحدها المحكوم عليه، ويسمى موضوعاً»
The first is what is judged about, called the subject.
«والثاني المحكوم به، ويسمى محمولاً»
The second is what is predicated, called the predicate.
«والثالث الدال على الرابط، ويسمى رابطة»
The third indicates their connection, called the copula or link.

In “Zayd is standing,” Zayd is the subject, standing the predicate, and “is” indicates their affirmative connection.

11. The subject: what is being judged about?

The subject is the thing or concept about which something is asserted. In “Zayd is learned,” the subject is Zayd; learning is what is asserted of him.

“The tree is tall” — subject: the tree.
“A human is an animal” — subject: human.
“This book is not old” — subject: this book.

A subject may be expressed by one word or a multiword phrase. Identify it by asking what the judgment concerns, not by counting words.

12. The predicate: what is affirmed or denied?

The predicate is what is affirmed or denied of the subject. In “Zayd is present,” the predicate is “present,” because presence is affirmed of Zayd.

In “Zayd is not present,” the relevant predicate is still presence, but its connection to Zayd is denied. Do not confuse the predicate with the affirmative or negative character of the judgment.

“The student is diligent” — predicate: diligent.
“This water is not warm” — predicate: warm, which is denied.

A predicate may express a quality, species, genus or another predicable concept.

13. The copula connects subject and predicate

The copula indicates the predicative relation between subject and predicate. In “Zayd is standing,” “is” relates standing to Zayd in an affirmative judgment.

«زيد هو قائم»
Zayd is standing.

In this Arabic construction, “هو” makes the connection explicit. Arabic may omit an overt copular expression, as in “زيد قائم,” while the affirmative relation remains understood.

The copula does not contribute a new defining property; it indicates the act of predication.

14. An expressed or an understood copula

«وقد تحذف الرابطة في اللفظ دون المراد»
The copula may be omitted in the wording without being absent from the intended meaning.

«زيد قائم»
Zayd is standing.

The overt Arabic words are only “Zayd” and “standing,” yet the sentence is not two unrelated names: the mind understands the predicative connection.

Therefore categorical analysis distinguishes three functional elements even though not every language must express all three through separate words.

15. Copulas and temporal expression

The source notes that a copula may take different verbal forms. Some constructions use “هو” to show a non-temporal relation; “كان” can express a predication located in the past.

“زيد قائم” — Zayd is standing.
“كان زيد قائماً” — Zayd was standing.

Both attribute standing to Zayd, but the second explicitly adds temporal orientation. The point here is not to teach the grammar of past-tense verbs; it is to distinguish the logical function of connection from the linguistic form in which it appears.

16. A categorical with a complex part

«زيد أبوه قائم»
Zayd's father is standing.

The presence of more than one noun or an internal relation does not automatically mean that two independent propositions have been asserted. The sentence makes one complete judgment concerning the standing of Zayd's father.

The commentary considers an analysis in which removing a linking element leaves a simple concept “Zayd” and another expression such as “his father is standing,” which has propositional form. We must distinguish an internally complex expression from the complete judgment actually made.

17. Why a categorical does not resolve into two propositions

«والحملية ما لا ينحل إلى قضيتين»
A categorical proposition is one that does not resolve into two propositions.

In “Zayd is standing,” we may distinguish the concepts Zayd and standing; but “Zayd” alone is not a complete assertion, nor is “standing” in this context an independent statement.

Dividing words or concepts and dividing complete propositions are different operations. A categorical expresses one central judgment uniting its subject and predicate. That is what distinguishes its structure from a conditional.

18. The essential shape of the conditional

«وأما الشرطية: فما لا يكون فيه ذلك الحكم»
A conditional proposition is one in which that direct categorical judgment is not made in the same way.

The primary judgment in a conditional does not simply affirm “the sun has risen” or “daylight exists” in isolation. It asserts a relation between two propositional contents.

“If the sun rises, daylight exists” links one statement to another conditionally. That link itself may be correct or incorrect, making the entire expression a proposition.

19. The original conditional example

«إن كانت الشمس طالعة فالنهار موجود»
If the sun has risen, daylight exists.

The expression contains two propositional components:
“الشمس طالعة” — The sun has risen.
“النهار موجود” — Daylight exists.

The construction “إن ... فـ” places them in a conditional relation. Its point is the connection between sunrise and daylight, not a separate assertion that the sun has already risen at the moment of speaking.

Recognizing both components reveals the structure of the conditional.

20. A conditional resolves into two propositions

«وقيل: الشرطية ما ينحل إلى قضيتين»
It is also said that the conditional is what resolves into two propositions.

Removing the conditional particles from “If the sun has risen, daylight exists” produces two statements that can each be evaluated:
“The sun has risen.”
“Daylight exists.”

This analysis does not equate the original conditional with an unconnected pair of assertions. The conditional relation is essential; the analysis shows that each side has propositional content.

21. Antecedent and consequent

«للشرطية أيضاً أجزاء»
A conditional also has components.

«ويسمى الجزء الأول منها مقدماً، والجزء الثاني منها تالياً»
The first component is called the antecedent and the second the consequent.

“If the sun rises, daylight exists” consists of:
Antecedent: The sun rises.
Consequent: Daylight exists.

The antecedent occupies the conditional position and the consequent the related result position. “Antecedent” refers to its logical or verbal position; it need not always mean that one event happened earlier in time.

22. The link in a conditional proposition

«والرابطة هي الحكم بينهما»
And the link is the judgment between the two components.

In a categorical, the copula connects subject and predicate. In a conditional, the relation connects antecedent and consequent. This distinction is fundamental to their logical analysis.

“If water freezes, its temperature will be consistent with the freezing point” relates two propositions through a conditional connection.

Not every conditional in every language must use the exact words “if” and “then,” but these words make the connection easy to see in the source's examples.

23. Negation of a conditional relation

«وليس البتة إذا كانت الشمس طالعة فالليل موجود»
It is by no means the case that if the sun has risen, night exists.

The negation targets the relation claimed between antecedent and consequent. The sentence does not simply negate “the sun has risen”; it rejects the connection asserted between sunrise and the presence of night.

It must not be confused with “If the sun has not risen, it is night,” which would have a different antecedent and would express another conditional proposition.

24. Truth of the conditional versus truth of its parts

“If the lamp is on, the room will be illuminated” is a conditional. We need not establish that the lamp is currently on in order to understand the claim; the main issue is the asserted connection between illumination and a lit lamp.

Even when the lamp is off, we can grasp the conditional's meaning and discuss whether the stated relation holds.

Thus hearing the antecedent in a conditional is not the same as asserting that it is actual. This distinction later matters in conditional reasoning and inference.

25. Consolidation and preparation for the next chapter section

A proposition is a statement that may be true or false. Its two principal types here are categorical and conditional.

A categorical affirms or denies a predicate of a subject. Its components are subject, predicate and copula. Affirmatives assert the connection and negatives deny it; either type may be true or false.

A conditional states a relation between two propositional contents, called antecedent and consequent. Negating the conditional connection must not be confused with negating its antecedent.

The next lesson examines classifications based on the subject and the scope of the judgment over individuals.