Swapping subject and predicate, preserving truth, four quantified forms and guided practice Read the bilingual lesson for Simple Conversion of Propositions: Definition, Method and Rules and test your understanding with a focused quiz.
Lesson
1. From contradiction to conversion
Last lesson studied contradiction. Now we ask a different question: can a proposition yield another true proposition by exchanging its subject and predicate?
Example: Every human is an animal.
Does this imply every animal is human? No; animals include nonhuman species. This lesson explains when the exchange works, when quantity must change, and when no generally valid exchange exists.
2. The book’s definition
The source defines simple conversion by making the first component of a proposition the second, and the second component the first. But mere word reversal is insufficient: truth must be preserved, and an affirmative remains affirmative while a negative remains negative. Simple conversion therefore includes both exchanging subject and predicate and choosing a form that follows logically.
3. Identify the components
Proposition: Every human is an animal.
Subject: human.
Predicate: animal.
Quantifier: every, applying to all humans.
Quality: affirmative.
Conversion exchanges human and animal, but it does not automatically preserve the quantifier every. You must determine whether all or some is warranted.
4. First worked conversion
Original: Every human is an animal.
Step 1: Make animal the new subject.
Step 2: Make human the new predicate.
Step 3: Use some, because only some animals are human.
Valid converse: Some animals are humans.
The new claim does not extend beyond what the original can justify.
5. Why “Every animal is human” fails
Incorrect converse: Every animal is human.
Valid converse: Some animals are human.
The category animal is broader than human; horses and birds are animals too. The original proposition covers every human, not every animal. A common error is exchanging subject and predicate while automatically retaining every.
6. Rule for universal affirmatives
A universal affirmative of the form “Every S is P” converts to a particular affirmative: “Some P are S.”
Every horse is an animal → Some animals are horses.
Every rose is a flower → Some flowers are roses.
In the traditional system, the subject class is assumed to have members; in modern logic the existential assumption has to be stated.
7. Why every becomes some
Suppose all 20 students in a class can write. Writers include students, teachers, and many others. So we can infer that some writers are students, but not that every writer is a student. A predicate may cover a larger class than the original subject, forcing the converted proposition to become particular.
8. Universal negative conversion
Source example:
Original: No human is a stone.
Converse: No stone is a human.
These classes do not overlap. If nothing is both a human and a stone, swapping their names preserves the exclusion. A universal negative converts to another universal negative.
9. Another universal negative example
Original: No triangle is a circle.
Subject: triangle.
Predicate: circle.
Converse: No circle is a triangle.
The exclusion works in either direction. We exchange the terms while preserving both negation and universal quantity.
10. Particular affirmative conversion
“Some S are P” converts to “Some P are S.”
Original: Some animals are humans.
Converse: Some humans are animals.
The original says the classes overlap in at least one member. That same member witnesses the overlap regardless of which class is named first.
11. Another particular affirmative example
Original: Some students are athletes.
Converse: Some athletes are students.
Imagine Ali belongs to both groups. In the original he is a student who is an athlete; in the converse he is an athlete who is a student. The same individual establishes both claims.
12. A special rule: particular negatives
Consider the source example:
Original: Some animals are not human.
Attempted converse: Some humans are not animals.
The attempted converse does not follow: nonhuman animals exist, but humans are animals. Thus a particular negative has no generally valid simple converse.
13. Why particular negatives do not generally convert
“Some birds are not white” says there is at least one bird outside the class of white things. It does not tell us whether any white thing lies outside the class of birds. In a hypothetical domain every white thing could be a bird. So swapping terms alone does not yield a valid inference.
14. The four-rule map
Universal affirmative: Every human is an animal → Some animals are human.
Universal negative: No human is a stone → No stone is a human.
Particular affirmative: Some animals are human → Some humans are animals.
Particular negative: Some animals are not human ⇏ Some humans are not animals.
The first three have standard conversion rules; the fourth has none valid in general.
15. Quality must be preserved
Simple conversion preserves the quality of the proposition.
Original: Some flowers are fragrant.
Converse: Some fragrant things are flowers.
Not its converse: Some fragrant things are not flowers.
The last changes an affirmative into a negative; it may be separately true, but it does not follow by simple conversion.
16. Quantity may change while quality stays
Quantity is signaled by words such as every, no, and some. Simple conversion does not require preserving quantity in every case:
Every S is P → Some P are S.
No S is P → No P is S.
Some S are P → Some P are S.
Some S are not P → no general simple converse.
Always verify the logical consequence and the preserved affirmative/negative quality.
17. Truth versus valid consequence
A valid converse is guaranteed to be true whenever the original proposition is true, under the textbook’s assumptions.
Every rose is a flower → Some flowers are roses.
But “Every flower is a rose” does not follow. Distinguish establishing that a premise is factually true from establishing that a conclusion follows from it logically.
18. Source exercise: Every human is a body
Original: Every human is a body.
Form: universal affirmative.
Subject: human; predicate: body.
Valid converse: Some bodies are humans.
“Every body is human” would be too broad. The book uses body as a general term in its traditional classification.
19. Source exercise: No donkey is rational
Original: No donkey is rational.
Form: universal negative.
Subject: donkey; predicate: rational.
Converse: No rational being is a donkey.
The point is exclusion between the two classes, not any evaluative meaning in the words.
20. Source exercise: Every worshipper prostrates
Original: Every person performing prayer is a person who prostrates.
Form: universal affirmative.
Converse: Some who prostrate perform prayer.
“Everyone who prostrates performs prayer” is stronger than the premise and is not justified by conversion alone.
21. Source exercise: Some Muslims do not pray
Original: Some Muslims do not perform prayer.
Form: particular negative.
Tempting converse: Some non-prayers are not Muslims.
The original gives no information that guarantees the second statement. We are classifying the argument form, not making a judgment about any named individual.
22. Test a conversion with a counterexample
Imagine a garden where all roses are red.
Original: Every rose is red.
Valid converse: Some red things are roses.
Invalid: Every red thing is a rose.
A red chair shows why the last claim can fail while the original remains true. A counterexample is a powerful test of an alleged inference.
23. A four-question conversion method
For any proposition ask:
1. What are its subject and predicate?
2. Is it universal affirmative, universal negative, particular affirmative, or particular negative?
3. After exchanging the terms, which quantity is warranted?
4. Does the proposed converse really follow?
A grammatically complete sentence is not automatically a valid logical converse.
24. Six self-check examples
1. Every goat is an animal → Some animals are goats: valid.
2. No stone is a tree → No tree is a stone: valid.
3. Some teachers are poets → Some poets are teachers: valid.
4. Every fish is an animal → Every animal is a fish: invalid.
5. Some animals are not birds → Some birds are not animals: does not follow.
6. No goat is a horse → Some horses are not goats: not the specified standard converse; use No horse is a goat.
25. Recap and next topic
Simple conversion exchanges subject and predicate while preserving valid consequence and affirmative/negative quality.
Universal affirmative → particular affirmative.
Universal negative → universal negative.
Particular affirmative → particular affirmative.
Particular negative → no generally valid converse.
A mechanically reversed sentence is not necessarily a valid conversion. The next textbook topic examines modalities or jihāt of propositions.
Practice questions
Question 1
Which two parts are exchanged in simple conversion?
- Agent and object
- Subject and predicate
- Particle and verb
- Time and place
Question 2
What is essential to a valid converse?
- If the original is true the converse follows
- The converse must be longer
- Every must always remain
- Negation must become affirmation
Question 3
What type is “Every human is an animal”?
- Universal negative
- Particular affirmative
- Universal affirmative
- Particular negative
Question 4
Valid converse of “Every human is an animal”?
- Every animal is human
- Some animals are human
- No animal is human
- Some humans are not animals
Question 5
Why is “Every animal is human” not a valid converse?
- It contains a negation
- It asserts too much
- It lacks the word human
- It is a question
Question 6
What is the traditional simple converse of A?
Question 7
Valid converse of “Every rose is a flower”?
- Some flowers are roses
- Every flower is a rose
- No flower is a rose
- Some roses are not flowers
Question 8
What follows from “Every student can write”?
- Every writer is a student
- Some writers are students
- No students can write
- No writer is a student
Question 9
Type of “No human is a stone”?
- Universal negative
- Universal affirmative
- Particular negative
- Particular affirmative
Question 10
Converse of “No human is a stone”?
- Some stones are humans
- Every stone is human
- No stone is a human
- Every human is a stone
Question 11
How does E convert?
Question 12
Converse of “No triangle is a circle”?
- Some circles are triangles
- Every circle is a triangle
- No circle is a triangle
- Some triangles are circles
Question 13
Type of “Some animals are humans”?
- Particular affirmative
- Universal affirmative
- Universal negative
- Particular negative
Question 14
Converse of “Some animals are humans”?
- No humans are animals
- Some humans are animals
- All animals are human
- Some humans are not animals
Question 15
How does I convert?
Question 16
Converse of “Some teachers are poets”?
- Every poet is a teacher
- Some poets are teachers
- No poet is a teacher
- Some teachers are not poets
Question 17
Which form is particular negative?
- Every S is P
- No S is P
- Some S are not P
- Some S are P
Question 18
Why does O have no general simple converse?
- Too few words
- No subject exists
- Being outside P on one side does not imply reverse exclusion
- Every O statement is false
Question 19
What does NOT follow from “Some animals are not human”?
- Some animals are nonhuman
- At least one animal is not human
- Some humans are not animals
- Some of them are not human
Question 20
If the original is affirmative, the converse must remain what?
- Negative
- Affirmative
- Interrogative
- Optative
Question 21
What do every and some indicate?
- Tense
- Relation
- Quantity
- Place
Question 22
What change is needed when converting A?
- Change affirmation to negation
- Change universal to particular
- Remove subject
- Remove predicate
Question 23
Why is “Every animal is a goat” not the valid converse of “Every goat is an animal”?
- Animal is broader than goat
- Goats have no body
- It is negative
- Animal is a simple term
Question 24
Converse of “Every human is a body” in the book’s exercise?
- Every body is human
- Some bodies are human
- No body is human
- Some humans are not bodies
Question 25
Converse of “No donkey is rational”?
- No rational being is a donkey
- Some rational beings are donkeys
- Every rational being is a donkey
- Some donkeys are rational
Question 26
Converse of “All who perform prayer prostrate”?
- All who prostrate perform prayer
- Some who prostrate perform prayer
- No one who prays prostrates
- Some who pray do not prostrate
Question 27
Type of “Some Muslims do not pray”?
Question 28
Safest statement about O conversion?
- Always becomes universal
- Always becomes particular
- No converse follows in general
- Always becomes affirmative
Question 29
Converse of “Some flowers are fragrant”?
- Some fragrant things are flowers
- Some fragrant things are not flowers
- No fragrant thing is a flower
- Every fragrant thing is a flower
Question 30
What distinguishes a valid converse from reversed wording?
- Nothing
- A valid converse is logically entailed
- Reversed wording is always true
- A valid converse is always negative
Question 31
Converse of “No stone is a tree”?
- Every tree is stone
- Some trees are stones
- No tree is a stone
- Some stones are trees
Question 32
What is “Some birds are not animals” as converse of “Some animals are not birds”?
- Necessarily valid
- Not generally entailed
- Universal affirmative
- Universal negative
Question 33
If two classes are disjoint, which relation is preserved under reversal?
- No S is P
- All S are P
- Some S are P
- Every S is not P
Question 34
A shared member supports conversion of which type?
Question 35
How can a proposed converse be disproved?
- Make a longer sentence
- Find a case where the premise holds but converse fails
- Change every translation
- Delete the subject
Question 36
What assumption underlies traditional A-to-I conversion?
- The subject class has members
- The subject is meaningless
- Every predicate class is empty
- The proposition is a question
Question 37
Standard converse of “No goat is a horse”?
- Some horses are not goats
- No horse is a goat
- Some goats are horses
- All horses are goats
Question 38
Which has no generally valid simple converse?
Question 39
Simple conversion only reverses words; truth preservation is unnecessary.
Question 40
In traditional logic, A converts to I.
Question 41
Every human is an animal converts to every animal is human.
Question 42
A universal negative remains true when subject and predicate are exchanged.
Question 43
Some teachers are poets converts to some poets are teachers.
Question 44
Every particular negative has a valid simple converse.
Question 45
Conversion requires turning an affirmative into a negative.
Question 46
Some animals are not human does not imply some humans are not animals.
Question 47
No S is P must convert to some P is not S.
Question 48
A case with a true premise and false proposed converse refutes the conversion.
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