The source example, premises and conclusion, valid and invalid inferences, with guided exercises Read the bilingual lesson for Ḥujjah: Deriving a Conclusion from Known Judgments and test your understanding with a focused quiz.
Lesson
1. From conceptions to judgments
The earlier part examined how a concept is understood and defined. The book now opens the section on judgments. Its first concern is how already understood and accepted propositions can lead to another proposition. Understanding “human” is conception; grasping “humans are living beings” is judgment; deriving “humans have bodies” from further known propositions belongs to the discussion of argument.
2. What the text means by ḥujjah
The source explains ḥujjah or dalīl as arranging two or more already known judgments in order to obtain knowledge of a further judgment. The known judgments are accepted or established propositions; the previously unknown judgment is the claim whose basis we seek. “Unknown” need not mean that the sentence has never been heard: what matters is that its justification has not yet been established for the learner.
3. The textbook example in three steps
The book’s example runs as follows:
Known statement 1: Humans are living beings.
Known statement 2: Every living being has a body.
Conclusion: Therefore humans have bodies.
The first statement places humans among living beings; the second attributes a body to every member of that broader class. Together they support the conclusion.
4. What does the first premise establish?
“Humans are living beings” places humans within the living-beings class. By itself it does not assert anything about bodies. An accepted statement used to support a conclusion is called a premise (muqaddimah). This explanatory label helps analyze the book’s two known judgments.
5. Why the second premise matters
“Every living being has a body” is universal. Since the first premise places humans among living beings, the universal predicate applies to humans. Replacing “every” with “some” would not justify the same conclusion, because we would not know whether humans fall within the selected subset. Logical scope matters.
6. The connection from known to unknown
The inferential path is: human → living being; every living being → embodied; therefore human → embodied. “Living being” serves as the connecting concept between the two premises. The source’s requirement that judgments be suitably arranged matters: simply placing unrelated statements next to each other does not yield a conclusion.
7. Identify premises and conclusion
Use three checks: What is already known? Which additional statement links it to a broader rule? What new proposition follows? In the textbook example the two premises concern humans as living beings and all living beings as embodied; the conclusion concerns humans as embodied. This method makes an argument visible rather than merely memorized.
8. How argument differs from definition
The preceding lesson used “rational animal” to explain the concept human. Here two propositions are arranged to justify a further proposition. Definition principally clarifies a concept; argument principally supports a judgment. A definition may help us understand the terms of a premise, but the two operations have distinct goals.
9. A worked example: apple and fruit
Premise 1: Every apple is a fruit.
Premise 2: This object is an apple.
Conclusion: This object is a fruit.
The general rule and the specific classification work together. Neither premise on its own provides the same conclusion about the identified object.
10. A worked example from numbers
Premise 1: Every number divisible by 4 is divisible by 2.
Premise 2: 12 is divisible by 4.
Conclusion: 12 is divisible by 2.
The middle property—divisibility by 4—connects the particular number to a more general rule. The same inferential structure applies in different domains.
11. Changing “every” to “some” changes the inference
Premise 1: Some fruits are sweet.
Premise 2: Apples are fruits.
Unsupported conclusion: All apples are sweet.
The premises never establish that apples are among the sweet fruits, much less that all of them are. A conclusion must not claim more than the premises warrant.
12. An invalid argument with a shared attribute
Premise 1: All birds are living beings.
Premise 2: All cows are living beings.
Invalid conclusion: All cows are birds.
Both classes belong to a broader class, but this does not make them identical or make one a subset of the other. A repeated middle term alone does not ensure a valid link.
13. Do not reverse a one-way implication
Premise 1: Every teacher is a human.
Premise 2: Ahmad is human.
Unsupported conclusion: Ahmad must be a teacher.
The first claim is one-directional: teacher → human. It does not license human → teacher. Recognize the direction of the stated relationship before drawing a conclusion.
14. Two true statements do not justify any conclusion
Statement 1: Lahore is in Pakistan.
Statement 2: Under suitable conditions, water may freeze at zero degrees Celsius.
Unsupported conclusion: It is snowing in Lahore today.
Even true statements fail to establish an unrelated conclusion. Good argument requires an appropriate inferential connection, not merely a collection of true statements.
15. Inference pattern versus truth of premises
Two questions should be kept distinct: If the premises were true, would the conclusion follow? And are the premises actually true? “All flowers are stones; all roses are flowers; therefore all roses are stones” follows the same general inclusion pattern but starts from a false premise. The structure does not make the conclusion factually established.
16. What if the conclusion is already familiar?
A learner may know that 12 is even without understanding a proof. Showing that every multiple of 4 is even, and that 12 is a multiple of 4, clarifies why. The status of a proposition as familiar should not be confused with having understood its justification. The book’s “unknown judgment” refers to what the proof is meant to establish for the learner.
17. Guided practice: four-sided shape
Premise 1: Every quadrilateral has four sides.
Premise 2: The shape shown is a quadrilateral.
Conclusion: The shape shown has four sides.
First identify the universal statement, then the specific classification, then apply the universal rule. Also check the truth of the premises and whether key terms retain their meanings.
18. Four classification exercises
1. All roses are flowers; this is a rose; therefore it is a flower — follows.
2. All roses are flowers; this is a flower; therefore it is a rose — does not follow.
3. Some students are athletes; Zayd is a student; therefore Zayd is an athlete — does not follow.
4. Every multiple of 10 is a multiple of 5; 30 is a multiple of 10; therefore 30 is a multiple of 5 — follows.
Explain the connection, not merely the answer.
19. Five checks for assessing an argument
Identify the conclusion, identify the premises, find the connecting concept, inspect scope words such as “all,” “some,” and “not,” and test whether the conclusion follows if the premises are granted. Then separately investigate whether those premises are true. This method distinguishes the inference pattern from the factual support for its statements.
20. Full analysis of the source example
Premise 1 places humans among living beings. Premise 2 states that every living being has a body. The connecting term is “living being”; therefore the body predicate applies to humans. The important lesson is not the word order alone, but the explicit route from accepted propositions to the new judgment.
21. Lesson summary and what follows
A ḥujjah or dalīl arranges already known propositions so that another judgment is established. Premises supply the support; the conclusion is what they are meant to establish; an appropriate inferential connection makes the reasoning work. Recall the textbook example about humans, living beings, and bodies. The next source lesson classifies the propositions that can function in arguments.
Practice questions
Question 1
What is the first topic in the textbook’s section on judgments?
- Argument (ḥujjah)
- Five predicables
- Complete essential definition
- Verbal signification
Question 2
What is the principal operation in a ḥujjah?
- Count letters in words
- Derive a further judgment from known judgments
- Display the visible shape of everything
- Alter word morphology
Question 3
What is the first known statement in the book’s example?
- Humans are living beings
- Humans are stones
- Every human is a teacher
- Living beings are disembodied
Question 4
What is the second premise in the source example?
- Every living being has a body
- Every body is human
- Every stone is living
- Some humans are stones
Question 5
What conclusion follows in the textbook example?
- Every living being is human
- Humans have bodies
- Every body is living
- Every body is human
Question 6
What concept connects the two premises?
- Living being
- Stone
- Bird
- Pronoun
Question 7
What is a premise?
- The claim being established
- A statement supplied as support
- Only an interrogative
- Only a name
Question 8
What is a conclusion?
- The heading of an argument
- A judgment derived from the premises
- Any long sentence
- Any unrelated statement
Question 9
What follows from “Every apple is fruit; this object is an apple”?
- This object is a fruit
- Every fruit is an apple
- This object is sweet
- All fruits are sweet
Question 10
What conclusion is NOT justified by “All apples are fruits; this is a fruit”?
- This is an apple
- This is a fruit
- Apples are fruits
- Nothing is known
Question 11
Why does “some fruits are sweet” not establish “all apples are sweet”?
- All fruits lack flavor
- Some does not warrant a claim about all apples
- Apples are not fruits
- A conclusion is always a question
Question 12
What is not established by “All teachers are human; Ahmad is human”?
- Ahmad is a teacher
- Ahmad is human
- Teachers are human
- That teachers are human
Question 13
What is the error in “Birds and cows are living; therefore cows are birds”?
- There is none
- A shared broader property is mistaken for identity of classes
- The term living never appears
- The conclusion is not an assertion
Question 14
What follows from the given divisibility premises?
- 12 is even
- 12 is odd
- Every even number is a multiple of 4
- 12 is not a number
Question 15
Why are two true statements not automatically a sound argument for any conclusion?
- True statements always contradict
- The premises must entail or appropriately support the conclusion
- An argument must be one word
- A conclusion cannot be a proposition
Question 16
Which statement distinguishes definition from argument?
- Both merely describe spelling
- Definition clarifies conception; argument supports judgment
- Argument only gives the meaning of a word
- Definition always has two premises
Question 17
What role does a known judgment play in this lesson?
- It supports a further conclusion
- It must be false
- It is necessarily a prayer
- It is merely a word
Question 18
What is missing if the first premise is only “human”?
- Nothing; it is a full assertion
- The assertion that humans are living beings
- The conclusion follows automatically
- The second premise becomes meaningless
Question 19
Why does the distinction between all and some matter?
- They are identical
- They mark plurals only
- They change the scope of a claim
- They are conjunctions
Question 20
Which example contains an entailed conclusion?
- All roses are flowers; this is a rose; therefore this is a flower
- All roses are flowers; this is a flower; therefore this is a rose
- Some students are athletes; Zayd is a student; therefore Zayd is an athlete
- All humans live; cows live; therefore cows are human
Question 21
How should the flowers-and-stones argument be evaluated?
- All premises are true
- The inference pattern works conditionally, but the first premise is false
- Both premises are concepts only
- A conclusion cannot be assertive
Question 22
Why provide an argument for a familiar conclusion?
- To show its basis and justification
- To erase prior knowledge
- Only to add words
- To turn a judgment into a term
Question 23
What are the three visible roles in the source example?
- Subject, predicate, particle
- Two premises and a conclusion
- Singular, dual, plural
- Genus, species, differentia
Question 24
How is the body predicate applied to humans?
- From the word human alone
- Through the middle classification and universal rule
- Because human and body are the same word
- Because every living being is human
Question 25
What is a good first method of checking an argument?
- Read only its conclusion
- Judge elegance alone
- Examine premises, connection, and consequence
- Count words
Question 26
What follows for a shape classified as a quadrilateral?
- It has three sides
- It has four sides
- Every four-sided shape is a circle
- It is red
Question 27
What if a conclusion makes a broader claim than its premises justify?
- The argument grows stronger
- The conclusion may be unsupported
- It becomes a definition
- No difference occurs
Question 28
What is the source’s next topic after ḥujjah?
- Propositions (qaḍiyyah)
- Verb-nouns
- Prosody
- Types of hadith
Question 29
Why distinguish understanding a term from proving a claim?
- The first concerns conception, the second the support of judgment
- They are identical
- Only the second is a single word
- Understanding meaning is always wrong
Question 30
How many known judgments does the book mention at minimum?
Question 31
What must be checked in “All fruits are sweet; this is an apple”?
- Whether apples are included as fruits and whether the premises hold
- Its color alone
- The second statement suffices
- Sweet is universally true
Question 32
Any two propositions necessarily give a valid new conclusion.
Question 33
The source definition of ḥujjah uses two or more known judgments.
Question 34
The two source premises support the conclusion that humans have bodies.
Question 35
Premise truth and whether a conclusion follows are the same issue.
Question 36
All birds live; cows live; therefore cows are birds is valid.
Question 37
Knowing an argument for a claim differs from merely recognizing its words.
Question 38
An argument’s conclusion is always unrelated to its premises.
Question 39
Replacing some with all can invalidate an inference.
Question 40
Living being is the middle linking notion in the source example.
Question 41
Definition chiefly clarifies concepts; argument supports judgments.
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