Logic: Learn about Hypothetical & Modal Propositions

1. Hypothetical & Modal Propositions
Ma. Marenza “Em” D. Dangla
MBA major in Entrepreneurship
Term 1 SY 2014-2015
GS500 (St. Thomas & Critical Thinking)
Prof. Florentino T. Timbreza, PhD
University of Santo Tomas – Graduate School
Reference: Timbreza, F. T. (1992). Logic Made Simple for Filipinos. Quezon City: Phoenix Publishing House, Inc.

2. Proposition
• verbal expression of a judgment
• a statement in which something is either affirmed or denied
• a sentence
• can either be affirmative or negative
Examples: Mary is beautiful. (affirmative)
Mary is not beautiful. (negative)

3. 3 General Types of Propositions
1. Categorical Proposition
2. Hypothetical Proposition
3. Modal Proposition

4. 3 General Types of Propositions
1. Categorical Proposition
• a.k.a. Assertoric Proposition
• declares something
• gives a direct assertion of agreement or disagreement between the subject
term and predicate term
Examples: No man is perfect.
Death is certain.
2. Hypothetical Proposition
3. Modal Proposition

5. 3 General Types of Propositions
1. Categorical Proposition
2. Hypothetical Proposition
• does not declare an unconditional affirmation or denial
• expresses a relation of dependence, such as an opposition or a likeness,
between two clauses
3. Modal Proposition

6. 3 Kinds of Hypothetical Propositions
1. Conditional Proposition
2. Disjunctive Proposition
3. Conjunctive Proposition

7. 1. Conditional Proposition
• a.k.a. If-Then Proposition
Structure: If A is B, then C is D.
• expresses a condition or relation of dependence between two propositions
• points out that one proposition necessarily follows from the other because of a
definite condition
• one of the constituent proposition implies the other
• two parts are joined by if, unless, when, where suppose, in case
• 2 Component Propositions:
1. Antecedent (Implicans) - introduced by the word if or its equivalent; contains the condition
2. Consequent (Implicate) - expresses the statement that follows the acceptance of the condition;
- statement that depends upon the presence of the condition

8. 1. Conditional Proposition
Examples: If a man is farsighted, he needs eyeglasses.
If dry weather continues, the harvest will be poor.

9. 2. Disjunctive Proposition
• a.k.a. Either-Or Statement
• subject or predicate consists of parts which exclude each other
• Disjuncts (Alternants) – parts of a disjunction
• can be..
• Proper (perfect, complete, strict) - if and when the parts are mutually exclusive
1. The enumeration of the possibilities must be complete
2. There must be an exclusive opposition between or among the enumerated possibilities
• Improper (imperfect, incomplete) - parts are not mutually exclusive;
- one disjunct doesn’t necessarily exclude the other
• Broad - if and when at least one disjunct is true, but the other disjunct may also be true.

10. 2. Disjunctive Proposition
Examples: A body is either in motion or at rest. (Proper)
A man is either married or unmarried. (Proper)
Either Pedro or Juan is dishonest. (Improper, Broad)
An individual is either honest or dishonest. (Proper)
It is either raining or not raining. (Proper)
Jose is either sitting or writing. (Improper, Broad)
Either my sister or I will go. (Improper, Broad)

11. 3. Conjunctive Proposition
• denies that two contrary predicates together can be true of the same
subject at the same time
• denies the simultaneous possibility of two alternatives
• Conjuncts – parts of a conjunctive proposition
Examples: You cannot stand and sit at the same time.
You cannot be in Quiapo and in Makati at the same time.

12. Exercise: Conditional, Disjunctive, Conjunctive?
1. Unless a man be born again, he cannot enter into the
kingdom of heaven.
2. You cannot eat your cake and have it too.
3. If you do not study, you fail.
4. You cannot talk and sneeze at the same time.
5. Either you study your lesson or you go to the movies.
6. It is either night or day.
Conditional
Conjunctive
Conditional
Conjunctive
Disjunctive
Disjunctive

13. 3 General Types of Propositions
1. Categorical Proposition
2. Hypothetical Proposition
3. Modal Proposition
• Expresses the nature of relationship between the subject & predicate
• Does not only affirm or deny the predicate of the subject, but also states the
manner or mode in which the predicate is identified with, or denied, of the
subject

14. 4 Modes of a Modal Proposition
1. Necessary Modal Proposition
2. Contingent Modal Proposition
3. Possible Modal Proposition
4. Impossible Modal Proposition

15. 1. Necessary Modal Proposition
• a.k.a. Apodictic Proposition or Analytic Proposition
• indicative expressions: must be, is necessarily, has to be, cannot be not
• mode where one which cannot be otherwise (it must be so)
• states that the predicate belongs to the subject, and must belong to it
• expresses necessity (necessarily relationship between subject & predicate)
Examples: A triangle has three sides.
A circle must be round.
Justice must be rendered to our fellowmen.

16. 2. Contingent Modal Proposition
• indicative expressions: need not be, is not necessarily, does not have to be, cannot be
• mode where one can be otherwise (need not be so)
• declares that predicate actually belongs to subject, but not necessarily so
• expresses contingent truth (i.e., something that is, but need not be)
• relationship between the subject & predicate is uncertain
Examples: These boys need not be lazy.
The bird is flying.
Honesty need not be difficult.

17. 3. Possible Modal Proposition
• indicative expressions: can be, is possibly, is able to be, need not be
• expresses possibility (i.e., possible identity between the subject & predicate)
• predicate is not actually found in the subject, but it might be
Examples: This sick man can die at any time.
It is possible that men are living on Mars.
Truth can be attained by the intellect.

18. 4. Impossible Modal Proposition
• Indicative expressions: cannot be, is not possible, is not able to be, must not be
• Expresses an impossibility
• Predicate is not actually found in the subject & it can never be found in it
• Relationship between the subject & predicate is an impossible one.
Examples: You cannot fly to the moon.
A circle cannot be a square.
Happiness cannot be purchased.

19. Exercise: Necessary, Contingent, Possible, Impossible?
1. Every man, irrespective of creed & color, must be respected. (N)
2. Not every criminal is punished for his crime. (C)
3. Horses gallop. (C)
4. Women can fly to a honeymoon. (P)
5. God must be just. (N)
6. Men cannot fly to the moon. (I)
7. I might pass the exam. (P)
8. You cannot read his mind. (I)
N
C
C
P
N
I
P
I

20. -end-