Judgment and propositions are important concepts in logic. Judgment is an act of the mind asserting or denying a relationship between two concepts. A proposition expresses a judgment as a declarative sentence. There are different types of propositions including categorical and non-categorical. A categorical proposition uses a subject, predicate, and copula, and can be affirmative or negative in quality and universal or particular in quantity. The subject and predicate terms of a proposition have specific universal or particular quantities depending on the type of proposition.

2. Judgment is one of the three material objects
of logic or three mental actions and another
important part of an argument.
Judgment is an act of the mind asserting or
denying the union or relation of the two
concepts.

3. Example:
The man is a driver.
(The mind affirms the union of the two
concepts.)
The man is not a driver.
(The mind negates or denies the union of the
two concepts.)

4. The sensible expression of which is
known as a proposition or premise.
We may define proposition in a
simplest way as a sensible expression
of a judgment.

5. A premiss (or proposition) then is a
sentence affirming or denying one
thing of another. “…Therefore a
syllogistic premiss without
qualification will be an affirmation or
denial of something concerning
something else…
- Aristotle: Prior Analytic. Book 1 # 1

6.  Sentence and Proposition
Proposition is essentially a declarative
sentence. Other sentences that are not
declarative are not Proposition.
Non-Proposition
1. Have you taken your dinner?
2. Oh my God!
3. For God sake!
4. Look at that.

7.  Sentence and Proposition
Proposition is essentially a declarative sentence.
Other sentences that are not declarative are not
Proposition.
Proposition
1. War is a huge business for armed manufacturers.
2. Some American bankers are funding terrorism.
3. Some students will not have a date this Valentines
day.

8.  Categorical and Non-Categorical Propositions
Non-categorical propositions are also declarative
sentences that do not use copula (to be discussed
later).
Non-Categorical
Some Americans bankers have had funded terrorism.
Categorical
Some Americans bankers are funding terrorism.

9. Further Examples:
Some teachers did not go to sleep last night.
Some Teachers were not sleeping last night.
Some students can learn Logic.
Some students are capable of learning Logic.
All normal people have two eyes.
All normal people are having two eyes.

10.  The Other Forms of Non-Categorical Proposition
Hypothetical Proposition
1. Conditional Proposition
“If it were a cat, then it is an animal.”
2. Disjunctive Proposition
“Either it is evening in Cuba now or morning.”
3. Conjunctive Proposition
“A person cannot be a man and a woman at the same
time.”

11.  The Standard Categorical Proposition
The components of standard form categorical
proposition are;
1. Quantifier
2. Subject Term
3. Predicate Term
4. Copula.

12.  The Standard Categorical Proposition
Example:
All nurses are medical practitionersAll nurses are medical practitioners.
- Quantifier
All nurses are medical practitioners.
- Subject Term
All nurses are medical practitioners.
- Prediacate Term
All nurses are medical practitioners.
- Copula

13.  The Standard Categorical Proposition
Quantifier:
1. No doctors are illiterate.
2. All doctors are not illiterate.
3. Some medical practitioners are not doctors.
4. Not all medical practitioners are doctors.
5. Some surgeons are doctors.
 The Standard Categorical Proposition
Quantifier:
1. No doctors are illiterate.
2. All doctors are not illiterate.
3. Some medical practitioners are not doctors.
4. Not all medical practitioners are doctors.
5. Some surgeons are doctors.

14.  The Standard Categorical Proposition
Copula:
1. No doctors are illiterate.
2. All doctors are not illiterate.
3. Some medical practitioners are not doctors.
4. Not all medical practitioners are doctors.
5. Some surgeons are doctors.
 The Standard Categorical Proposition
Copula:
1. No doctors are illiterate.
2. All doctors are not illiterate.
3. Some medical practitioners are not doctors.
4. Not all medical practitioners are doctors.
5. Some surgeons are doctors.

15.  The Standard Categorical Proposition
Subject Term:
1. No doctors are illiterate.
2. All doctors are not illiterate.
3. Some medical practitioners are not doctors.
4. Not all medical practitioners are doctors.
5. Some surgeons are doctors.
 The Standard Categorical Proposition
1. No doctors are illiterate.
2. All doctors are not illiterate.
3. Some medical practitioners are not doctors.
4. Not all medical practitioners are doctors.
5. Some surgeons are doctors.

16.  The Standard Categorical Proposition
Predicate Term:
1. No doctors are illiterate.
2. All doctors are not illiterate.
3. Some medical practitioners are not doctors.
4. Not all medical practitioners are doctors.
5. Some surgeons are doctors.
 The Standard Categorical Proposition
1. No doctors are illiterate.
2. All doctors are not illiterate.
3. Some medical practitioners are not doctors.
4. Not all medical practitioners are doctors.
5. Some surgeons are doctors.

17.  The Quality of Categorical Proposition
Categorical Proposition has two Qualities:
(Negative and Affirmative)
Affirmative
1. All doctors are professionals.
2. Every surgeon is a medical practitioners.
3. Some medical doctors are surgeons.
4. Some surgeons are women.

18.  The Quality of Categorical Proposition
Categorical Proposition has two Qualities:
(Negative and Affirmative)
Negative
1. All doctors are not illiterate.
2. No surgeon is a moron.
3. Some medical doctors are not surgeons.
4. Some surgeons are not women.

19.  Quantity of a Categorical Proposition
There are two Quantities of Propositions namely:
(Universal and Particular)
All Singular Propositions are treated as Universal.
Universal Proposition
1. All doctors are professionals.
2. Every surgeon is a medical practitioners.
3. No doctor is illiterate.
4. All nurses are not idiots.

20.  Quantity of a Categorical Proposition
There are two Quantities of Propositions namely:
(Universal and Particular)
All Singular Propositions are treated as Universal.
Particular Proposition
1. Not all doctors are surgeons.
2. Some surgeons are women.
3. Some women are not nurses.
4. Not all nurses are men.

21. A – Universal Affirmative
E – Universal Negative
I – Particular Affirmative
O – Particular Negative

22. Universal Affirmative
A - All nurses are professionals.
Universal Negative
E - No doctor is illiterate.
Particular Affirmative
I - Some women are nurses.
Particular Negative
O - Not all nurses are men.

23. Further Examples
1. Some doctors are not men.
2. Not all doctors are men.
3. No doctor is a moron.
4. All doctors are not moron.
5. All doctors are human beings.
6. Every doctor is a rational animal.
7. Some doctors are women.

24. Quantity of the Subject and Predicate Terms:
1. The quantity of the subject term is determined by the
quantifier. If the quantifier is universal, the subject is
also universal.
2. The quantity of the predicate term is always universal if
the proposition is negative.
3. The quantity of the predicate term of an “I”, i.e,
Particular Affirmative, proposition is always particular.
4. The quantity of the predicate term of an “A”, i.e.,
Universal Affirmative, depends on the relation of the
subject and predicate terms.

25. Quantity of the Subject and Predicate Terms:
A – Universal Affirmative
1. All doctors are professionals.
2. All women are female human beings.
U P
1. All doctors are professionals.
U U
2. All women are female human beings.

26. Quantity of the Subject and Predicate Terms:
E – Universal Negative
1. No doctor is illiterate.
2. All women are not fathers.
U U
1. No doctor is illiterate.
U U
2. All women are not fathers.

27. Quantity of the Subject and Predicate Terms:
I – Particular Affirmative
P P
1. Some women are professionals.
p P
2. Some women are doctors.

28. Quantity of the Subject and Predicate Terms:
O – Particular Negative
P U
1. Some women are not professionals.
p U
2. Some women are not doctors.

29. Quantity of the Subject and Predicate Terms:
1. All dogs are animals that bark.
2. All Dalmatians are dogs.
3. All women are human beings.
4. Some dogs are Dalmatians.
5,. Some Chihuahua are puppies.
Quantity of the Subject and Predicate Terms:
U U
1. All dogs are animals that bark.
U P
2. All Dalmatians are dogs.
U P
3. All women are human beings.
P P
4. Some dogs are Dalmatians.
P P
5,. Some Chihuahua are puppies.

30. Quantity of the Subject and Predicate Terms:
1. All dogs are not reptiles.
2. No Dalmatian is an amphibian.
3. All women are not girls.
4. Some dogs are not Dalmatians.
5. Not all Chihuahua are puppies.
Quantity of the Subject and Predicate Terms:
U U
1. All dogs are not reptiles.
U U
2. No Dalmatian is an amphibian.
U U
3. All women are not girls.
P U
4. Some dogs are not Dalmatians.
P U
5. Not all Chihuahua are puppies.

31. Prepared by:
OLIVER F. PERATER