CHAPTER THREE
PROPOSITION
➔A proposition is an expression of judgment. It may be something that is stated for the purpose of discussion or
something to be dealt with as a statement of fact or truth.
➔It is a statement in which something is affirmed or denied.
➔A proposition is different from a sentence because a sentence is a word or a group of words expressing a
complete thought. An example of a sentence is “RUN!” This is a single word expressing a complete thought
and therefore a sentence.
Therefore, all propositions are sentences but not all sentences are propositions.
“RUN!” is not a proposition because it does not express a judgment.
A. CATEGORICAL PROPOSITION
Elements of a Categorical Proposition
1. Quantifier➔ part of the CP that tells the quantity of the proposition
2.) Subject and Predicate Terms➔matter of the proposition
➔materials from which the proposition is made
3.) Copula➔bonding verb- form of the CP
➔Unifying principle that maintains the structure of the proposition
Quality of a Proposition
1.) Affirmative➔ the predicate is affirmed of the subject
➔from the Latin word affirmo which means “I agree”. The first 2 vowels of the word are A and I. They are the
affirmative propositions.
Example: GMA is the president of the Philippines
2.) Negative➔ the predicate is denied of the subject.
➔from the Latin word nego which means “I deny”. The two vowels of the word are E and O. They are the negative
propositions.
Example: ERAP is not the President of the Philippines.
Quantity of a Proposition
1.) Universal➔the predicate is affirmed or denied of the whole of the subject.
Example: All mothers are loving parents.
2.) Particular➔ the predicate is affirmed or denied of only part of the subject.
Example: Some politicians are corrupt officials.
4 TYPES OF CATEGORICAL PROPOSITION
1. Universal Affirmative (A)
All lawyers are politicians.
2. Universal Negative (E)
No lawyers are politicians.
3. Particular Affirmative (I)
Some lawyers are politicians.
4. Particular Negative (O)
Some lawyers are not politicians.
B. LOGICAL OPPOSITIONS
1. Contradiction/Contradictories
➔ when two propositions using the same subject and predicate terms oppose each other owing to their differences in
both quantity and quality.
➔A and O/ E and I
Examples:
“All men are mortal beings” and “Some men are not mortal beings” are contradictory propositions.
“All men are not emotional” and “Some men are emotional” are contradictory propositions.
2. Contrariety/Contrary Propositions
➔when two universal propositions using the same subject and predicate terms but differ in quality.
➔A and E
Examples”
“All politicians are honest” and “No politician is honest” are contrary propositions.
“No student is intelligent” and “All students are intelligent” are contrary propositions.
3. Sub-Alternation
➔when two propositions using the same subject and predicate terms but differ in quantity with the same quality.
➔A and I/ E and O
Examples:
“All men are liars” and “Some men are liars” are sub-alternating propositions.
“Some students are not absent” and “No student is absent” are sub-alternating propositions.
4. Sub-Contrariety
➔when two particular propositions using the same subject and predicate terms but differ in quality.
➔I and O
Examples:
“Some buildings are houses” and “Some buildings are not houses” are contrary propositions.
“Some criminals are not harmful” and “Some criminals are harmful” are contrary propositions.
THE SQUARE OF OPPOSITION
All S are P. No S is P.
A CONTRARIETY E
C
O
S N N S
U T O U
B R I B
A A T A
L D C L
T I T
E D C E
R A T R
N R I N
A T O A
T N N T
I O I
O C O
N N
I S U B- C O N T R A R I E T Y O
Some S are P. Some S are not P.
C. FOUR LAWS GOVERNING LOGICAL OPPOSITIONS
1. Law of Contradiction 3. Law of Sub-Alternation
2. Law of Contrariety 4. Law of Sub-Contrariety
1. Law of Contradiction
➔Two contradictory propositions cannot be both true and both false at the same time.
* If A is true, O is false * If A is false, O is true
* If O is true, A is false * If O is false, A is true
* If E is true, I is false * If E is false, I is true
* If I is true, E is false * If I is false, E is true
2. Law of Contrariety
➔States that two contrary propositions cannot be both true but they may be both false at the same time.
* If A is true, E is false
* If E is true, A is false
* If A is false, E is doubtful
* If E is false, A is doubtful
3. Law of Sub-Alternation
a) States that the truth of the universal carries or implies the truth of the particular but not vice versa.
* If A is true, I is true
* If E is true, O is true
* If I is true, A is doubtful
* If O is true, E is doubtful
b) States that the falsity of the particular carries or implies the falsity of the universal but not vice
versa.
* If I is false, A is false
* If O is false, E is false
* If A is false, I is doubtful
* If E is false, O is doubtful
4. Law of Sub-Contrariety
➔States that two contrary propositions can not be both false but they maybe both true at the same time.
* If I is false, O is true
* If O is false, I is true
* If I is true, O is doubtful
* If O is true, I is doubtful
RULES IN TRANSLATING ORDINARY STATEMENTS INTO THE STANDARD
FORM OF CATEGORICAL PROPOSITION
1. Translate universal statements as universal propositions unless the statement points to a particular usage.
Examples:
Dogs bark.
➔ All dogs are barking animals.
Filipinos are hospitable people.
➔Some Filipinos are hospitable people
Men are stronger than women.
➔Some men are people stronger than women
2. Add the missing complement to an adjective or to a describing phrase to show that they refer to classes/terms.
Examples:
All lions are fierce.
➔All lions are fierce animals.
Mothers love their children.
➔Some mothers are children lovers.
3. Singular statements should be treated as universal statements.
Examples:
The first lady is very extravagant person.
➔The first lady is very extravagant person.
A proposition
The author of Don Quijote is a good writer.
➔The author of Don Quijote is a good writer.
A proposition
This student is not lazy.
➔ This student is not a lazy guy. E proposition
4. Quantifiers that refer to universal or particular should be replaced by: all, no or some respectively.
Examples:
Almost 50% of the students in logic are members of the debate team.
➔ Some students in logic are members of the debate team.
Most of the teachers are nationalists.
➔ Some teachers are nationalists.
Every student is a learner.
➔ All students are learners.
5. Exclusive statements should be translated into universal statements by reversing the order of the original
statement.
Examples:
None but men are priests.
➔All priests are men.
Only voters are citizens.
➔ All citizens are voters
6. Exceptive statements should be translated to an E statement.
Examples:
All except seminarians are members of the club.
➔No seminarian is a member of the club.
Everybody except the judges are members of the administration
➔ No judge is a member of the administration.
7. “Not all” should be translated as an O proposition
Examples:
Not all applicants are qualified workers.
➔Some applicants are not qualified workers.
Not all politicians are liars.
➔Some politicians are not liars.
