Types of Qiyas: Istithna’i and Iqtirani

Conditional and disjunctive inference, valid and invalid patterns, and categorical syllogism Read the bilingual lesson for Types of Qiyas: Istithna’i and Iqtirani and test your understanding with a focused quiz.

Lesson

1. Two principal forms of qiyas

The preceding lesson showed how a qiyas uses premises to yield a conclusion. This lesson distinguishes two patterns: istithna’i, which uses a conditional or disjunctive proposition along with an explicit affirmation or denial, and iqtirani, which combines premises without repeating the conclusion or its negation in that way.

2. First recognize the textbook classification

The seventh lesson names two forms of qiyas: istithna’i and iqtirani. Here istithna’ is a technical logical term, not merely the everyday idea of making an exception. One premise is conditional or disjunctive, and the next explicitly affirms or denies a component. Iqtirani instead joins premises to derive a conclusion.

3. The structure of an istithna’i syllogism

An istithna’i argument contains a conditional or disjunctive premise and another premise that explicitly affirms or denies a component. Example:
Conditional: If it rains, the courtyard becomes wet.
Second premise: It is raining.
Conclusion: Therefore the courtyard becomes wet.
The inference follows provided that the conditional and the second premise hold.

4. Antecedent and consequent in a connected conditional

In “If the sun rises, then daytime exists,” the antecedent (muqaddam) is “the sun rises” and the consequent (tali) is “daytime exists.” These are parts of one conditional proposition. Do not confuse muqaddam, the antecedent, with the word muqaddamah meaning a whole premise.

5. Valid form one: affirm the antecedent

If the accepted conditional is “If the sun rises, it is daytime,” and the next premise affirms that the sun has risen, then daytime follows. Form:
1. If P, then Q.
2. P.
3. Therefore Q.
The conclusion depends on the conditional link, not on a shared word by itself.

6. Valid form two: deny the consequent

Given “If P, then Q,” denying Q allows us to deny P. Example:
If the sun has risen, it is daytime.
It is not daytime.
Therefore the sun has not risen.
This form is called denying the consequent (modus tollens). It relies on the conditional relation remaining in force.

7. The two valid conditional patterns

Two standard valid moves with a conditional are:
Affirm P: If rain then wet ground; rain occurred; therefore wet ground.
Deny Q: If rain then wet ground; the relevant ground is not wet; therefore that rain did not occur.
Both require the conditional to apply to the same place, time, and circumstances.

8. A common error: affirming the consequent

Invalid pattern: If it rains, the road becomes wet; the road is wet; therefore it rained. Other causes, such as washing the road, can explain the wetness. “If P then Q” does not mean “Q only if P.” This is the fallacy of affirming the consequent.

9. Another error: denying the antecedent

Invalid pattern: If it rains, the road becomes wet; it did not rain; therefore the road is not wet. The road might still be wet for another reason. Denying the antecedent is not a valid general inference.

10. Four moves with a conditional

Assume “If P then Q.” Four possible moves are:
1. P; therefore Q — valid.
2. Not Q; therefore not P — valid.
3. Q; therefore P — not generally valid.
4. Not P; therefore not Q — not generally valid.
For the invalid forms, consider an alternative way Q could occur.

11. The conditional premise itself needs scrutiny

A formally valid pattern does not guarantee a true conclusion when its premises are false. Example:
If every bird is a fish, a sparrow is a fish.
Every bird is a fish.
Therefore a sparrow is a fish.
The inference has a valid form, but a premise is false. Validity and soundness are different assessments.

12. Istithna’i with a disjunctive proposition

Disjunctive istithna’i reasoning uses an either/or premise. For an integer:
Premise 1: It is either even or odd.
Premise 2: It is even.
Conclusion: It is not odd.
The conclusion follows because an integer cannot be both even and odd.

13. Exclusive and exhaustive alternatives

“An integer is either even or odd” is both exclusive (not both) and exhaustive (not neither). This is the haqiqiyyah form previously studied. Exclusivity permits inferring the negation of the other alternative from an affirmation; exhaustiveness permits inferring the other alternative from a denial.

14. Haqiqiyyah: affirmation eliminates the other

For a given integer:
Either even or odd.
It is even.
Therefore it is not odd.
Likewise:
Either even or odd.
It is odd.
Therefore it is not even.
These deductions rely on the impossibility of both alternatives holding together.

15. Haqiqiyyah: denial establishes the other

For an integer:
Either even or odd.
It is not even.
Therefore it is odd.
Similarly:
Either even or odd.
It is not odd.
Therefore it is even.
These inferences rely on the fact that both alternatives cannot be false.

16. Four valid outcomes for haqiqiyyah

For an integer, all four hold:
1. Even -> not odd.
2. Odd -> not even.
3. Not even -> odd.
4. Not odd -> even.
They work because the two alternatives are both exclusive and exhaustive. Mere use of the word “or” does not guarantee both properties.

17. Not every either/or is exclusive and exhaustive

The textbook uses an alternative such as “this object is a tree or a stone.” To treat it as an exhaustive division, one must first restrict the possibilities to those two; not every object in the world is a tree or a stone. Likewise, passing Arabic or logic is not automatically an exclusive division: a student may pass both. If the student passes neither, the disjunctive assertion is false. Always test the scope and relationship of the alternatives.

18. What follows from mani‘at al-jam‘?

In mani‘at al-jam‘, both alternatives cannot be true, but both can be false. Example: the object is a tree or a stone, understood as mutually exclusive possibilities, not an exhaustive list; it may be iron. Affirming tree rules out stone. Denying tree does not prove stone.

19. What follows from mani‘at al-khulu?

In mani‘at al-khulu, both options cannot be false, but both may be true. For real numbers: “The number is greater than 2 or less than 4.” Every number satisfies at least one, while 3 satisfies both. Denying one proves the other; affirming one does not deny the other.

20. Compare the three disjunctive patterns

Haqiqiyyah: neither both true nor both false.
Mani‘at al-jam‘: not both true; both may be false.
Mani‘at al-khulu: not both false; both may be true.
Thus haqiqiyyah permits both kinds of inference. Mani‘at al-jam‘ supports affirmation-to-denial; mani‘at al-khulu supports denial-to-affirmation.

21. Definition of iqtirani qiyas

The textbook’s second type is iqtirani qiyas: the conclusion or its negation is not repeated verbatim among the premises; the premises are composed to derive it. Example:
Every human is an animal.
Every animal is a body.
Therefore every human is a body.
The entire conclusion is absent from either premise individually.

22. The middle term in iqtirani reasoning

In the same iqtirani syllogism:
Minor term: human — subject of the conclusion.
Major term: body — predicate of the conclusion.
Middle term: animal — links the premises.
The middle term appears in the premises but not as a separate term in the conclusion.

23. How to distinguish the two forms

Compare:
A. If the sun rises, it is day; the sun has risen; therefore it is day — istithna’i.
B. Every human is an animal; every animal is a body; therefore every human is a body — iqtirani.
An isolated “if” statement is not a complete argument, and a random pair of statements does not automatically yield a syllogism.

24. Diagnosing a faulty inference

To check an argument: (1) identify the premises, (2) identify whether its pattern is istithna’i or iqtirani, and (3) ask whether the conclusion must follow if the premises are true. “If fire then heat; heat; therefore fire” fails because heat may have other causes. The flaw is in the inference, not its length.

25. Review and readiness for the next lesson

Istithna’i reasoning explicitly affirms or denies a component of a conditional or disjunctive premise. In connected conditionals, affirming the antecedent and denying the consequent are valid core patterns. With disjunctions, rules depend on whether options are exclusive, exhaustive, or both. Iqtirani reasoning links premises to produce a conclusion not stated verbatim in them. The next lesson covers induction and analogy.

Practice questions

Question 1

Which two kinds of qiyas does the book describe?

Istithna’i and iqtirani
Conception and judgment
Genus and differentia
Universal and particular

Question 2

What is the first premise usually like in istithna’i qiyas?

An isolated term
A conditional or disjunctive proposition
A personal name
A definition

Question 3

In “If the sun rises, it is daytime,” which is the antecedent?

It is daytime
The sun rises
The entire conclusion
The minor premise

Question 4

What is the consequent in that sentence?

The sun rises
If
It is daytime
The sun alone

Question 5

If rain makes the ground wet, and it rained, what follows?

It did not rain
The ground is wet
The ground is dry
Nothing follows

Question 6

If P then Q; P. What follows?

Q
Not Q
Not P
Neither P nor Q

Question 7

If P then Q; not Q. What follows?

P
Not P
Q
Nothing follows about P

Question 8

If P then Q; Q. Must P hold?

Always
No; Q may occur for another reason
P must be false
Both must be false

Question 9

If P then Q; not P. Must not Q hold?

Yes
No
Only with conjunction
This is simple conversion

Question 10

What is wrong with “The road is wet, therefore it rained”?

Road is not a noun
Other causes of wetness are possible
Rain is a particle
The inference is always valid

Question 11

What does affirming the antecedent do?

Establishes the then-part from the if-part
Proves the if-part from the then-part
Negates the antecedent
Eliminates all possibilities

Question 12

What fallacy appears in “If fire then heat; heat; therefore fire”?

Denying antecedent
Affirming consequent
Denying consequent
Valid negation

Question 13

Which is a suitable example of exclusive and exhaustive disjunction?

An integer is even or odd
A student passes Arabic or logic
An object is a tree or iron as an exhaustive division
Fruit is sweet or red

Question 14

If an integer is even, what follows?

It is also odd
It is not odd
It is not a number
It is not even

Question 15

If an integer is not even, what follows?

It must be odd
It must be even
It is not an integer
There is no rule

Question 16

If an integer is not odd, what follows?

It is even
It is not a number
It is odd
It is not negative

Question 17

Can even and odd both be false of an integer?

Yes
No
Both true and false
They are always both true

Question 18

Can an integer be both even and odd?

Yes
No
Only zero
Only negative integers

Question 19

What characterizes a haqiqiyyah disjunction?

Both always true
Both always false
Neither both true nor both false
One part is meaningless

Question 20

What is impossible in mani‘at al-jam‘?

Both alternatives true
Both false
Exactly one true
One false

Question 21

Can both options be false in mani‘at al-jam‘?

Yes
No
Only in haqiqiyyah
This is iqtirani

Question 22

If one alternative in mani‘at al-jam‘ is affirmed, what follows?

The other is affirmed
The other is denied
The other becomes merely possible
Everything becomes false

Question 23

Does denying one alternative in mani‘at al-jam‘ prove the other?

Always
No, both could be false
Not even for even/odd
It is not a judgment

Question 24

What is impossible in mani‘at al-khulu?

Both alternatives false
Both true
One true
One denied

Question 25

Can both alternatives be true in mani‘at al-khulu?

Yes
No
Only for zero
Only in induction

Question 26

In mani‘at al-khulu, denying one option allows what conclusion?

Affirming the other
Denying the other
Nothing ever follows
Both false

Question 27

Does affirming one option in mani‘at al-khulu disprove the other?

Always
No, both could be true
That is the middle term
Only for positive numbers

Question 28

For 3, which clauses of “greater than 2 or less than 4” hold?

Both
Neither
Only the first
Only the second

Question 29

In the same example, not greater than 2 implies what?

Less than 4
Greater than 4
Neither clause
Greater than 2

Question 30

How is the conclusion related to premises in iqtirani qiyas?

It is verbatim a premise
Neither it nor its negation is stated verbatim in the premises
It is only a question
It is one word

Question 31

What type is “Every human is an animal; every animal is a body”?

Iqtirani
Disjunctive istithna’i
Mere conception
Contradiction

Question 32

What is the middle term in that syllogism?

Human
Body
Animal
Every

Question 33

What is the minor term?

Human
Animal
Body
Is

Question 34

What is the major term?

Human
Animal
Body
Every

Question 35

What follows from “Every human is an animal; every animal is a body”?

Every body is human
Every human is a body
No human is a body
Not every body is an animal

Question 36

If an argument form is valid but a premise is false, what follows?

Conclusion must be true
The form may be valid without establishing factual truth
It turns into iqtirani
The premise becomes true

Question 37

What best identifies istithna’i reasoning?

Number of letters
Explicit affirmation or denial of a conditional component
Length
Whether each word is simple

Question 38

Do two premises with a shared word automatically form a valid argument?

Yes
No, the required logical link must also hold
Only in istithna’i
The conclusion is always true

Question 39

Why not apply all even/odd inferences to every either/or sentence?

Because even and odd are Arabic words
Other alternatives may not be both exclusive and exhaustive
Every sentence has two premises
Every proposition is false

Question 40

Is a single conditional “If rain, then wet ground” itself a complete syllogism?

Yes
No, another premise and conclusion are needed
Yes, it is iqtirani
It is a definition

Question 41

Why does the middle term not appear as a term of the iqtirani conclusion?

It is meaningless
It has performed the linking role in the premises
It makes premises false
It is always negative

Question 42

If a conclusion does not follow, what should you do?

Merely change wording
Re-examine the link and possible counterexamples
Delete any premise
Treat it as haqiqiyyah

Question 43

Istithna’i reasoning explicitly affirms or denies a conditional component.

Question 44

If P then Q; Q; therefore P is always valid.

Question 45

If P then Q; not Q; therefore not P is valid.

Question 46

The integer zero is neither even nor odd.

Question 47

Both alternatives may be true in haqiqiyyah.

Question 48

Both options may be false in mani‘at al-jam‘.

Question 49

Both options may be true in mani‘at al-khulu.

Question 50

Every either/or statement is automatically haqiqiyyah.

Question 51

In iqtirani qiyas, neither the conclusion nor its negation appears verbatim as a premise.

Question 52

A valid argument form guarantees all its premises are true.

Open the interactive quiz