Conversion, obversion and contraposition
Erica Bryan
Introduction
Categorical logic involves statements that classify objects into categories
Three main logical operations
1. Conversion – Swaps subject and predicate
2. Obversion – Changes quality and negates the predicate
3. Contraposition – Swaps the subject and predicate, negating both.
These operations help analyze and transform logical statements.
Four types of categorical
propositions:
Type
Example
Standard Form
A – Universal Affirmative
All cats are animals.
All S are P
E – Universal Negative
No cats are dogs.
No S are P
I – Particular Affirmative
Some cats are pets.
Some S are P
O – Particular Negative
Some cats are not wild.
Some S are not P
Conversion – Definition
Conversion is a logical operation used to exchange the subject and predicate of a
categorical proposition. This operation works with E (Universal Negative) and I
(Particular Affirmative) propositions. It does not change the type of the sentence,
unlike obversion or contraposition, and results in an equivalent proposition.
A convertend is a standard-form categorical proposition that is converted, and the
converse is the new proposition formed by switching its subject and predicate terms.
how conversion works:
1.Swap the subject and predicate of the contrapositive statement while maintaining
truth value .
Conversion Examples
1.E Proposition (Universal Negative):
1. No dogs are cats. → No cats are dogs.
2. No birds are mammals. → No mammals are birds.
3. No teachers are doctors. → No doctors are teachers.
4. No fish are mammals. → No mammals are fish.
2.I Proposition (Particular Affirmative):
1. Some students are athletes. → Some athletes are students.
2. Some cars are electric vehicles. → Some electric vehicles are cars.
3. Some birds are pets. → Some pets are birds.
4. Some musicians are composers. → Some composers are musicians
Obversion – Definition
Obversion is a transformation used in categorical logic to change the quality
(affirmative or negative) of a statement and replace the predicate with its
complement. It works with A, E, I, and O propositions, changing an affirmative
statement into a negative one or vice versa. Obversion does not affect the logical
type of the sentence and preserves the truth value.
In logic, an obvertend is a standard-form categorical proposition that undergoes
obversion, while the resulting proposition is called the obverse.
Here’s how obversion works:
1. Change the quality of the contrapositive statement (affirmative → negative or
negative → affirmative).
2. Replace the predicate with its complement (non-P).
Obversion examples
1.A Proposition (Universal Affirmative)
All cats are animals. → No cats are non-animals.
All roses are flowers. → No roses are non-flowers
2. E Proposition (Universal Negative)
No dogs are reptiles. → All dogs are non-reptiles
No apples are oranges. → All apples are non-oranges
No men are immortals. → All men are non-immortals
3. I Proposition (Particular Affirmative)
Some students are athletes. → Some students are not non-athletes.
Some flowers are red. → Some flowers are not non-red.
4. O Proposition (Particular Negative)
Some cars are not electric. → Some cars are non-electric.
Some books are not fiction. → Some books are non-fiction
Contraposition-Definition
Contraposition is a logical operation where the subject and predicate of a categorical
proposition are swapped and both are replaced with their complements. This operation works
with A and E propositions (Universal Affirmatives and Universal Negatives), and it does not
change the type of the sentence, unlike obversion.
A contraponend is a standard-form categorical proposition subject to contraposition, and the
contrapositive is the new proposition formed by switching the subject and predicate terms
and replacing them with their complements.
In contraposition, we do the following:
1. Replace the subject with the complement of the predicate.
2. Replace the predicate with the complement of the subject.
Contraposition –Examples
A Proposition (Universal Affirmative)
All humans are mortal.
Contrapositive: All non-mortals are non-humans.
All cats are mammals
Contrapositive: All non-mammals are non-cats
O Proposition (Particular Negative)
contraponend: Some books are not fiction
Contrapositive: Some non-fiction books are non-books.
contraponend: Some trees are not deciduous.
Contrapositive: Some non-deciduous trees are non-trees.
contraponend: Some houses are not painted.
Contrapositive: Some non-painted houses are non-houses.
Practice
1.
2.
3.
4.
5.
What is the contrapositive of the statement "All men are mortal" (A proposition)?
What is the obverse of the statement "No dogs are cats" (E proposition)?
What is the converse of the statement "Some birds are parrots" (I proposition)?
What is the converse of the statement "No fish are mammals"?
What is the obverse of the statement "All roses are flowers" (A proposition)?
Answers
1.All non-mortals are non-men.
2.All dogs are non-cats.
3.Some parrots are birds.
4. No mammals are fish.
5.No roses are non-flowers.