Further Conditional Divisions, Quantification and Conditional Quantifiers

1. A further division of disjunctive conditionals

The previous lesson distinguished genuine disjunction, exclusion of joint truth, and exclusion of joint falsehood by testing which combinations can occur. A second question now arises: what grounds the incompatibility being asserted?

«المنفصلة بأقسامها الثلاثة قسمان: عنادية واتفاقية»
Each of the three disjunctive forms is divided into oppositional (ʿinādiyya) and coincidental (ittifāqiyya).

The first three kinds measure the extent of exclusion, while the new division identifies its basis. The commentary also notes a third, unqualified (muṭlaqa) consideration.

2. Defining the oppositional disjunction

«والعنادية: عبارة عن أن يكون فيه التنافي بين الجزئين لذاتهما»
An oppositional disjunction is one in which the incompatibility of the two components arises from what they themselves signify.

For example, a whole number is even or odd, and no such number can be both. That incompatibility follows from the meanings of evenness and oddness, not from circumstances on a particular day.

Li-dhātihimā identifies the ground of opposition; it does not merely mean that two different words or objects have been mentioned.

3. A second oppositional example: tree and stone

Take the claim about one object: “It is a tree or a stone.” A thing genuinely classified as a tree is not, in the same respect, a stone.

This can be an exclusion-of-joint-truth: the object cannot be both, yet a book may be neither. Viewed by the source of incompatibility, it is also oppositional because the contrast follows from the concepts.

These are not competing labels on a single axis. One identifies what is excluded, the other why the exclusion holds.

4. Defining coincidental disjunction

«والاتفاقية: عبارة عن أن يكون فيه التنافي بمجرد الاتفاق»
A coincidental disjunction expresses incompatibility grounded in contingent circumstances, rather than in the inherent meanings of its components.

Suppose the rules of a competition reserve exactly one seat for exactly one of Zayd or Amr. In that setting we say: “The seat will go either to Zayd or to Amr.” The opposition comes from the contest rule. There is no essential contradiction between the two people's names.

The claimed exclusivity therefore depends on the stipulated arrangement, not on a universally necessary opposition of concepts.

5. What “mere coincidence” does and does not mean

Coincidental does not mean that the components must be false or that the statement is carelessly made. It means that the present exclusion does not follow from the very meanings of the components.

Suppose a room has a rule that only one of two machines may operate today. Under that rule they cannot run together, although simultaneous operation is not logically contradictory in their natures.

The distinction is one of grounds: conceptual incompatibility in the oppositional form and a contingent arrangement in the coincidental form.

6. The marginal note on unqualified disjunction

The main text classifies disjunction into oppositional and coincidental forms. The marginal commentary adds an unqualified (muṭlaqa) consideration, where neither an intrinsic nor a contingent ground of exclusion is specified.

Under this additional consideration, each of the three main disjunctive kinds can be viewed as oppositional, coincidental, or unqualified. That is why the note mentions nine combinations.

Unqualified does not mean the relevant exclusion disappears. It means that the source of that exclusion has not been expressly determined.

7. How the two disjunctive classifications intersect

To classify a disjunction accurately, ask two separate questions.
Question 1: Can the alternatives both be true or both be false? This establishes genuine disjunction, exclusion of joint truth, or exclusion of joint falsehood.
Question 2: Does the relevant exclusion follow from the meanings, or from contingent circumstances? This establishes oppositional or coincidental disjunction.

“An integer is even or odd” is both genuine and oppositional.
“This is a tree or a stone” is, in the stated sense, both exclusion-of-joint-truth and oppositional.

Answering both questions yields a more complete analysis of the same proposition.

8. Quantification of conditionals concerns suppositions

In categorical propositions a quantifier normally ranges over instances of the subject: “Every human is an animal.” In conditionals the concern is the scope of suppositions or circumstances in which the antecedent and consequent are considered.

“Whenever the sun rises, daylight exists” extends the connection beyond today's particular sunrise to the relevant cases generally.

Thus conditionals also admit singular, quantified, and indefinite forms, but their quantification must be analyzed in the appropriate domain.

9. The textbook divides conditionals by quantity

«كما تنقسم الحملية إلى الشخصية والمحصورة والمهملة، كذلك الشرطية تنقسم إلى هذه الأقسام»
Just as categorical propositions are divided into singular, quantified, and indefinite, conditional propositions are divided into the same kinds.

One conditional connection may be asserted for one specified occasion, all or some relevant occasions, or without an expressed quantifier. The scope changes, while the core antecedent–consequent meanings may remain the same.

This classification applies to both connective and disjunctive conditionals. Quantified cases can be further universal or particular.

10. Why the natural proposition is absent here

«إلا أن القضية الطبيعية لا تتصور ههنا»
The natural proposition is not conceived here.

In a categorical proposition, a natural proposition concerns a universal nature as such. A conditional proposition, however, primarily judges a relation between its component propositions, and its scope is treated in terms of suppositions.

The book therefore carries over singular, quantified, and indefinite forms, but not the natural form in the same way. The classifications are not identical across categorical and conditional propositions.

11. The singular conditional: one specified occasion

«إن جئتني اليوم أكرمك»
If you come to me today, I shall honor you.

This is the source's singular conditional. The antecedent is coming today; the consequent is being honored. The judgment is restricted to a specified occasion today, not to every possible visit.

A singular conditional is not defined merely by mentioning an individual. What matters is the particular supposition or setting for which the connection is asserted.

12. Universal quantified conditional: all relevant cases

«كلما كانت الشمس طالعة كان النهار موجودا»
Whenever the sun has risen, daylight is present.

The expression kullamā extends the claim from one occasion to all relevant suppositions. Whenever the antecedent obtains in the intended domain, the consequent is asserted.

It is an affirmative universal connective conditional: connective because a link is asserted, affirmative because the link is affirmed, and universal because the scope covers the relevant cases generally.

13. Particular quantified conditional: some cases

«قد يكون إذا كان الشيء حيوانا كان إنسانا»
In some cases, when something is an animal, it is human.

Qad yakūn limits the judgment to some suppositions rather than all animal cases. Being human is found within the category of animals but does not follow for every animal.

Universal versus particular is determined by the scope of the conditional judgment, not merely by the words composing its antecedent.

14. The indefinite conditional omits its quantifier

«إن كان زيد إنسانا كان حيوانا»
If Zayd is human, he is an animal.

The antecedent and consequent are present, but no explicit expression such as “every time” or “in some cases” quantifies the conditional judgment. In that respect the statement is indefinite (muhmala).

Indefinite does not mean meaningless or false. It means that the quantity has not been expressly stated. The essential truth of the humanity–animality link and the presence of an explicit quantifier are separate matters.

15. Three universal affirmative connective markers

«سور الموجبة الكلية في المتصلة لفظ «متى»، و«مهما»، و«كلما»»
The universal affirmative connective markers are matā, mahmā, and kullamā.

Matā — whenever / at whatever time.
Mahmā — whenever or in whatever case, as context requires.
Kullamā — every time that.

«كلما كانت الشمس طالعة كان النهار موجودا»
Whenever the sun rises, daylight exists.

These markers do more than identify the clauses: they assert that the positive conditional judgment extends across the relevant cases.

16. The universal affirmative disjunctive marker

«وفي المنفصلة «دائماً»»
For the affirmative universal disjunction, the marker is dāʾiman (“always”).

For example, within the domain of whole numbers:
«دائماً هذا العدد إما زوج أو فرد»
This integer is always either even or odd.

Here dāʾiman marks the range of the disjunctive relation. Do not conflate this quantified disjunction with the distinct modality of a predicate's permanence discussed in the chapter on modal propositions.

17. Universal negative: laysa al-batta

«وسور السالبة الكلية في المتصلة والمنفصلة «ليس ألبتة»»
The universal negative marker for both connective and disjunctive conditionals is laysa al-batta.

Laysa al-batta indicates a universal denial of the relevant relation in the intended domain. In a negative connective it denies the claimed connection; in a negative disjunction it denies the claimed incompatibility.

The negation takes scope over the conditional relation. It need not independently deny every statement inside the antecedent or consequent.

18. Particular affirmative: qad yakūn

«وسور الموجبة الجزئية فيهما «قد يكون»»
For an affirmative particular conditional—connective or disjunctive—the marker is qad yakūn.

Its role here is to affirm the relevant judgment for some suppositions. A relation holding in some cases does not, merely for that reason, establish that it holds universally.

Thus qad yakūn is not simply a conversational hesitation. In this logical classification it functions as the marker of particular affirmative quantity.

19. Particular negative: qad lā yakūn

«وسور السالبة الجزئية فيهما «قد لا يكون»»
For a particular negative conditional—connective or disjunctive—the marker is qad lā yakūn.

It denies the relevant conditional relation in some suppositions. This is weaker than denying it in every case, because a particular negative does not exclude the relation from the entire domain.

Qad yakūn — the relation obtains in some cases.
Qad lā yakūn — the relation fails in some cases.

The negative particle changes the quality to negative while leaving the quantity particular.

20. Negation before a universal quantifier

«وبإدخال حرف السلب على سور الإيجاب الكلي»
A negative particle may also be placed before the universal affirmative marker.

Pay attention to the scope of negation.
“Not on every occasion” denies the universal claim: at least one exception exists.
“On no occasion” denies the relation throughout the domain.

These are not equivalent. In symbolic terms, not-every is not the same as never. When explaining Arabic or Urdu conditional expressions, clearly identify whether negation applies to the universal quantifier or to each instance of the relation.

21. Not every time versus every time not

Suppose someone asserts: “Whenever a student asks, the teacher answers immediately.” Compare two denials:
“It is not true that every question receives an immediate answer.” Some questions may not receive one, while others may.
“No question receives an immediate answer.” This claims non-response on every relevant occasion.

The first does not entail the second. This difference in quantifier and negation scope is why the negative particle before a universal marker needs careful analysis.

22. Connective particles: law, in and idhā

«ولفظة «لو» و«إن» و«إذا» في الاتصال»
The particles law, in, and idhā are used for connective conditionals.

They indicate a connective construction but do not, merely by themselves, necessarily mark a universal or particular scope. Thus “If Zayd is human, he is an animal” expresses a connection without an explicit universal quantifier.

Their nuances differ in Arabic usage, including suppositional or temporal force, but the current logical discussion uses them chiefly to identify connection, not to provide a complete syntactic treatise.

23. Disjunctive particles: immā and aw

«و«إما» و«أو» في الانفصال»
The particles immā and aw are used in disjunctive propositions.

Immā … aw commonly expresses alternatives. Yet its presence alone cannot establish whether the disjunction is genuine, excludes joint truth, or excludes joint falsehood. That classification requires testing the joint truth and falsity of its components.

Without an additional quantity marker, the disjunctive particles do not by themselves assert universality. A disjunctive particle and a logical quantifier perform different functions.

24. Keep quality and quantity distinct

A conditional’s quality is whether the relation is affirmed or denied; its quantity specifies whether the judgment extends to all or some relevant cases. These are separate axes.

Universal affirmative: the relation holds in all relevant cases.
Particular affirmative: it holds in some cases.
Universal negative: it fails in all relevant cases.
Particular negative: it fails in some cases.

One must also separately determine whether the conditional is connective or disjunctive. Distinguishing kind, quality, and quantity prevents category errors.

25. Worked classification in three stages

Consider: «كلما كانت الشمس طالعة كان النهار موجودا»
Whenever the sun rises, daylight exists.

1. Structure: two propositions are connected in an if–then relation, so it is connective.
2. Quality: daylight is affirmed on the supposition of sunrise, so it is affirmative.
3. Quantity: kullamā covers all relevant cases, so it is universal.

The full analysis is an affirmative universal connective conditional. Each label has its own evidence; no single surface feature supplies the whole classification.

26. Common errors in conditional classification

Error 1: Calling every immā statement a genuine disjunction. Correction: genuine disjunction excludes both joint truth and joint falsehood.
Error 2: Treating every exclusion as oppositional. Correction: an exclusion may depend on contingent circumstances.
Error 3: Treating every “if” statement as universal. Correction: an explicit quantifier determines its stated quantity.
Error 4: Treating “not always” as “never.” Correction: denying universality does not imply a universal negative.

The guiding rule is to justify each classification by the property specific to it.

27. Synthesis and the next logical step

This lesson added a distinction between oppositional and coincidental disjunction, with an unqualified consideration in the marginal commentary. It then established conditional quantity: singular, universal quantified, particular quantified, and indefinite.

Main markers:
Universal affirmative connective — matā, mahmā, kullamā.
Universal affirmative disjunctive — dāʾiman.
Universal negative — laysa al-batta.
Particular affirmative — qad yakūn.
Particular negative — qad lā yakūn.

The next section examines the component forms of antecedent and consequent. We now have separate tools for analyzing a conditional's relation, quality, and quantity.