Contradiction and the Eight Conditions

Matching subject, predicate, place, time, actuality, condition, whole/part and relation with worked examples Read the bilingual lesson for Contradiction and the Eight Conditions and test your understanding with a focused quiz.

Lesson

1. Why study contradiction?

You already know propositions and their types. Now ask: when do two statements oppose each other so completely that exactly one must be true?
Example 1: Zayd is present.
Example 2: Zayd is not present.
These look contradictory. Yet if the first concerns morning and the second evening, both could be true. Logic therefore requires us to compare the complete meaning and circumstances of each proposition.

2. The definition of contradiction

Contradiction occurs when one proposition affirms precisely what another denies, with matching relevant circumstances, so that one is true exactly when the other is false.
Example: At the same time and in the same respect, 'This door is open' and 'This door is not open.'
The textbook identifies eight required identities to prevent the appearance of contradiction where the assertions actually differ in meaning.

3. The truth test

For a genuine contradictory pair there are only two possibilities:
Case 1: The first statement is true and the second false.
Case 2: The first is false and the second true.
They cannot both be true or both false.
For the same specified integer, 'This integer is even' and 'This integer is not even' satisfy this test.

4. A negative word is not enough

Negation alone does not guarantee contradiction. The subject, predicate, and relevant context must match.
Pair 1: Zayd is a teacher / Zayd is not a teacher — contradictory if qualifications match.
Pair 2: Zayd is a teacher / Amr is not a teacher — different subjects.
Pair 3: Zayd is a teacher / Zayd is not a poet — different predicates.

5. Overview of the eight identities

The source requires identity in eight respects:
1. Subject.
2. Predicate.
3. Place.
4. Time.
5. Potentiality versus actuality.
6. Condition.
7. Whole versus part.
8. Relational standpoint.
These are safeguards: without them, apparent opposition may concern different propositions.

6. Identity of subject

The subject is what the proposition is about. Both propositions must concern the same subject.
Example 1: Zayd is learned.
Example 2: Amr is not learned.
Both may be true because they concern different people. Replace Amr with Zayd and, provided the other respects are identical, direct contradiction becomes possible.

7. Identity of predicate

The predicate is what is affirmed or denied of the subject.
Example 1: Zayd can write.
Example 2: Zayd cannot swim.
These can both be true; writing and swimming are different attributes. Only when the very same predicate is both affirmed and denied, with the remaining circumstances fixed, is contradiction possible.

8. Identity of place

Location must match when location is part of what is asserted.
Example 1: Zayd is sitting at home.
Example 2: Zayd is not sitting in the mosque.
Both can be true. A direct contradictory pair instead says that Zayd is and is not sitting in the same room at the same time and in the same respect.

9. Identity of time

A subject can change over time.
Example 1: Zayd was present yesterday.
Example 2: Zayd is not present today.
These do not contradict. Contrast 'Zayd was present at 9 a.m. today' with 'Zayd was not present at 9 a.m. today,' with all other circumstances fixed.

10. Identity of potentiality and actuality

Potentiality means the capacity for something; actuality means its present realization.
Example 1: This dry wood is capable of burning.
Example 2: This dry wood is not burning now.
Both can be true. Contradiction requires the same level of assertion, such as 'the wood is burning now' and 'the wood is not burning now.'

11. The source illustration of potentiality

The textbook illustrates the potential/actual distinction by discussing an intoxicating substance and the manifestation of its effect.
A thing's capacity to produce an effect is different from that effect actually occurring at a given moment. This is a point about logical predication, not an endorsement or practical instruction about the substance.

12. Identity of condition

When assertions depend on a condition, the condition must be kept the same.
Example 1: If the door is locked, Zayd will not enter.
Example 2: If the door is unlocked, Zayd will enter.
Different conditions allow both statements to hold. Genuine contradiction denies the same complete conditioned claim, rather than merely changing the condition.

13. Negating a whole conditional

Additional logical clarification: the denial of 'If it rains, the courtyard gets wet' is not simply the new conditional 'If it rains, the courtyard does not get wet.' The original conditional is false specifically if rain occurs while the courtyard does not get wet.
This distinguishes denying a whole conditional proposition from merely reversing its consequent.

14. Identity of whole and part

A predicate can apply to a whole in one sense but not to every part individually.
Example 1: The wall looks white overall.
Example 2: One corner of the wall is not white.
Both may be true. By contrast, 'Every part of the wall is white' and 'At least one part is not white' form a genuine contradictory pair.

15. Identity of relational standpoint

Some predicates are relational. A person may be someone's father but not another person's father.
Example 1: Zayd is Amr's father.
Example 2: Zayd is not Bakr's father.
Both may be true. A contradictory pair holds the relation fixed: 'Zayd is Amr's father' and 'Zayd is not Amr's father.'

16. Apply the eight identities together

Pair: Zayd was actually teaching a lesson as a teacher in this room at the specified time this morning / Zayd was not teaching a lesson in the same capacity, room, and time.
Subject, predicate, time, place, actuality, conditions, whole/part reference, and relational standpoint all match. Consequently the second denies exactly what the first affirms.

17. Worked example: different subject

Statement 1: This horse runs fast.
Statement 2: That horse does not run fast.
Not necessarily contradictory: two different horses may be intended. Both can be true. If the very same horse, speed criterion, and circumstances are fixed, affirmation and denial of the same predicate do contradict.

18. Worked example: different time

Ayesha was ill on Monday / Ayesha was not ill on Thursday are compatible: recovery is possible. Replace Thursday with Monday, keep the same sense of illness and relevant circumstances, and you obtain genuine contradiction. The negative word was unchanged; the time reference determined the difference.

19. Contradictory versus contrary

Contradictories cannot both be true or both false:
Every student is present / At least one student is not present.
Contraries can both be false:
Every student is present / No student is present.
If some students are present and others absent, both universal claims are false. This distinction is an additional clarification using standard logical examples.

20. Negating quantified propositions

To deny 'Every student has read the book,' it suffices to establish 'At least one student has not read the book.' 'No student has read the book' is a stronger claim and not the contradictory. Similarly, the negation of 'At least one student is present' is 'No student is present.' This is added practice extending the source's definition of contradiction.

21. Opposition in conditional statements

The whole conditional 'If electricity is supplied, the fan runs' is false when electricity is supplied and the fan does not run. Merely saying 'If electricity is supplied, the fan does not run' forms a different conditional claim, not automatically the logical negation of the entire first conditional. Deny the complete assertion, not simply one clause.

22. Five worked classification pairs

Classify each pair using the identity test:
1. The book is on the table / is not on the table — contradictory if the book, table, and time match.
2. Zayd is in Lahore / not in Islamabad — not necessarily contradictory.
3. The child can read / is not reading now — capacity versus actuality.
4. Fatima is Ahmad's sister / is not Ahmad's sister — contradictory if the relation is fixed.
5. Every bird in the specified group is in the cage / one is not — contradictory for the same group and time.

23. Common pitfalls

Do not infer contradiction from a negative word alone. Do not confuse 'not everyone' with 'no one.' Do not confuse capacity with actual performance. Do not switch between individuals, times, places, parts, or relations without noticing. The opposing statements must refer to precisely the same assertion in the same respect.

24. Further exercise: look-alike propositions

Compare the full meaning of each pair:
1. Every human is living / At least one human is not living — contradictories.
2. Every horse is living / Some living things are not horses — not contradictories; subject scope differs.
3. Amr is in the mosque / Amr is not at home — compatible.
4. At least one student is present / No student is present — contradictories.
Always identify the subject's scope, relevant relation, and exact denial.

25. A practical three-step test

Step 1: Identify precisely the subject and predicate of each claim.
Step 2: Check identity of time, place, potentiality/actuality, condition, whole/part reference, and relational standpoint.
Step 3: Ask whether both statements could be true or both could be false in some permitted situation. If so, they are not genuine contradictories.
Contradiction is the affirmation and denial of exactly the same proposition in the same respects.

Practice questions

Question 1

What is the truth relation between genuine contradictories?

Both always true
Both always false
Exactly one is true
No relation

Question 2

How many identities does the source list?

Question 3

Why are Zayd is learned / Amr is not learned not contradictory?

Same predicate
Different subjects
Both affirmative
Time not given

Question 4

Which identity is missing between Zayd can write / Zayd cannot swim?

Predicate
Subject
Time
Relation

Question 5

Classify Zayd was present yesterday / absent today.

Necessarily contradictory
Not contradictory; time differs
Both false
Different subjects

Question 6

Why can Zayd sits at home / does not sit at the mosque both be true?

Different locations
Different subjects
Different predicates
Neither asserts

Question 7

What differs in the wood can burn / is not burning now?

Subject
Potentiality versus actuality
Nothing
Relation

Question 8

Which identity differs between if locked no entry / if unlocked entry?

Subject
Length
Condition
Predicate name

Question 9

What differs between Zayd is Amr’s father / is not Bakr’s father?

Whole/part
Relational standpoint
Place
Potentiality

Question 10

Why can a class be strong overall while one member is weak?

Subject changed
Whole versus part
Time necessarily changed
Both just concepts

Question 11

What contradicts “The door is open” in the same respects?

Door is large
Window is open
Door is not open
Door was open yesterday

Question 12

Which pair can be contradictory with all contexts held fixed?

Child can read / not reading now
Zayd home / not mosque
Amr present / Amr not present
Fatima reads / Ayesha does not

Question 13

If two propositions can both be true, what follows?

Contradictory
Not genuine contradictories
Always true
Both negative

Question 14

If two propositions can both be false, what follows?

Contradictory
Not genuine contradictories
Both simple terms
Both self-evident

Question 15

What negates “Every student is present”?

No student is present
At least one is absent
All are ill
All absent

Question 16

What negates “At least one student is present”?

All are present
Some are absent
No student is present
Names unknown

Question 17

Why are “All students present” and “No students present” not contradictories?

Both can be true
Both can be false if some are present
Different subjects
Not propositions

Question 18

Which is true about contradictory and contrary propositions?

Identical
Contradictories cannot both be false; contraries can
Contradictories can both be true
Contraries never involve opposition

Question 19

What relation must be fixed when negating “Zayd is Amr’s father”?

Sentence length
Fatherhood to Amr
Zayd’s age
Word count

Question 20

What differs between a wall white overall / one corner not white?

Whole versus part
Time
Potentiality/actuality
Condition

Question 21

Why is “Is Zayd present?” not the contradictory of “Zayd is absent”?

It is a question, not an assertion
Both true
Different subjects
No common words

Question 22

How are Zayd is seated / Zayd is not seated at the same time and place related?

Mere disjointness
Contradiction if all other respects match
Just concepts
Syllogism

Question 23

Why is can run / is not running mistaken for contradiction?

Different subjects
Capacity confused with actuality
Time mentioned
Language

Question 24

How should a whole conditional be negated?

Just reverse consequent words
Test the truth of the entire conditional
Count words
Replace subject

Question 25

What falsifies “If it rains, the courtyard gets wet”?

No rain
Rain but courtyard not wet
Rain and wet
Large courtyard

Question 26

Which is not one of the textbook’s identities?

Subject
Place
Time
Number of letters

Question 27

What check comes first when one claim concerns a group and another a member?

Whole/part identity
Color
Word frequency
Book title

Question 28

Which pair is non-contradictory because of time?

Present today / absent today
Present yesterday / absent today
Alive at same instant / not alive
Same integer even / not even

Question 29

Which pair lacks identity of predicate?

Door open / not open
Integer even / not even
Zayd learned / not a merchant
Student present / absent

Question 30

Which pair maintains subject identity?

Zayd / Amr
This bird / other bird
Fatima present / Fatima absent
One horse / another

Question 31

What contradicts “No student is present”?

All present
At least one present
All absent
No teacher present

Question 32

What is ambiguous about “Not every tree is green” in loose everyday speech?

Too long
It may be confused with no trees being green
Tree is no subject
Question

Question 33

What is the central aim of contradiction analysis?

Elegant wording
Identify affirmation and denial of same claim
Assume all opposition false
Memorize terms

Question 34

Why not treat “Humans are living” and “Zayd is not living” as immediately direct contradictories?

Language
Generic class versus individual; quantify and identify subject
Both negative
Living has no meaning

Question 35

What final test best checks genuine contradiction?

Same wording?
Can both be true or both false?
Letter count?
Who spoke first?

Question 36

What about Zayd was a teacher yesterday / not a teacher today?

Necessarily contradictory
Time differs
Both false
Only relation differs

Question 37

What contradicts “All pages of the book are complete”?

Book is old
At least one page incomplete
No words on any page
All pages blank

Question 38

What identity is missing between Zayd teaches Amr / does not teach Bakr?

Place
Relational standpoint
Necessarily time
Whole/part

Question 39

Which contradicts “Every book is useful”?

No book useful
At least one book not useful
Every book beautiful
Some books useful

Question 40

Which identities clearly match when affirming and denying the same door is open at the same time?

Relation only
Subject, predicate and time
Whole/part only
None needed

Question 41

To what must the denial apply in genuine contradiction?

Precisely the same proposition
Any other term
Unrelated person
Heading

Question 42

Different subjects do not automatically produce direct contradiction.

Question 43

Zayd was present yesterday and is absent today can both be true.

Question 44

Potentiality and actuality always mean the same thing.

Question 45

Genuine contradictories can both be false.

Question 46

One absent student is enough to refute “Every student is present.”

Question 47

Zayd is Amr’s father and Zayd is not Bakr’s father must contradict.

Question 48

Contradiction requires matching relevant meanings and respects.

Question 49

All students are present / no student is present can both be false.

Question 50

Every question contradicts a corresponding negative assertion.

Question 51

Whole-versus-part reference matters when identifying contradiction.

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