hypothetical proposition (1)
TRANSCRIPT
-
8/3/2019 Hypothetical Proposition (1)
1/31
THE HYPOTHETICALTHE HYPOTHETICAL
PROPOSITIONSPROPOSITIONS(Aristotelian Classification)(Aristotelian Classification)
-
8/3/2019 Hypothetical Proposition (1)
2/31
Conditional PropositionConditional Proposition
The conditional is the if - then proposition.
It expresses a relation in virtue of which one
judgment or proposition necessarily flows from the
other. Example.
If you are a Catholic, then you are a Christian.
Parts:
Antecedent
If it rains
Consequent
then the ground is wet.
-
8/3/2019 Hypothetical Proposition (1)
3/31
Antecedent: condition, cause, reason
Consequent: conditioned, effect, result
If then, unless when
Not all if then statements are conditional, example:
If you need money then go to the bank.
Both antecedent and consequent must be statements
There is a necessary or logical connection
between the antecedent and consequent.
Terms of conditional:
-
8/3/2019 Hypothetical Proposition (1)
4/31
Disjunctive PropositionDisjunctive Proposition
The disjunctive is the either - or statement
It expresses that two things cannot be false at the
same time; one at least must be true.
Example:
A person is either a male or female.
You are either for or against Christ.
Parts are called disjuncts
-
8/3/2019 Hypothetical Proposition (1)
5/31
Proper Disjunctive - when the component parts
are mutually exclusive or contradictories, they
cannot be both true.Pass or fail Dead or alive
Today is either Monday or Tuesday.
A parent is either a father or a mother.
ImproperDisjunctive - when the component parts
are not mutually exclusive.
Doctor or engineer Red or blue
I will visit my friend either on Monday or Tuesday.
The parent who will attend the meeting is
either the father or the mother.
-
8/3/2019 Hypothetical Proposition (1)
6/31
Conjunctive PropositionConjunctive Proposition
The conjunctive proposition expresses that two
alternatives cannot be true simultaneously.
Example: One cannot be in Davao and in Cebu at the same
time.
You cannot inhale and exhale at the same time.
Parts are called conjuncts
-
8/3/2019 Hypothetical Proposition (1)
7/31
Two-part conjunctive the conjuncts are limited to
two alternatives only.
More than two-part conjunctive the conjuncts are
not limited to two alternatives.
The suspect cannot be guilty and not guilty.
A parent cannot be a father and a mother at the
same time.
One cannot study and play at the same time.
One cannot study and play at the same timeThe president cannot be a conservative and
liberal at the same time.
-
8/3/2019 Hypothetical Proposition (1)
8/31
-
8/3/2019 Hypothetical Proposition (1)
9/31
COMPLEX AND HYPOTHETICALCOMPLEX AND HYPOTHETICAL
PROPOSITIONSPROPOSITIONS
(Modern Logic Classification(Modern Logic Classification))
-
8/3/2019 Hypothetical Proposition (1)
10/31
Simple and Complex StatementsSimple and Complex Statements
Simple statement - does not contain any otherstatement as its component.
Examples:
John is a student. Manila is a city.
Complex or compound statement contains logical
components.
(hypothetical and negative propositions in the Aristotelianlogic are considered complex.)
-
8/3/2019 Hypothetical Proposition (1)
11/31
John is a student and John is honest.
It is not the case that Marie is the best student in the
class.
Either the rebels surrender or they die in battle.
If there is a weather disturbance, then classes will besuspended.
For statements to be compound, it is necessary that the
components are statements in themselves and that they are
sensical on their own.
The man who killed Ninoy was a murderer. Not a complexstatement
Additional examples::
-
8/3/2019 Hypothetical Proposition (1)
12/31
The truth-value of a complex/compound statement
depends of the truth-value of its components.
The truth value of the statement:
Manila is a city and AMV is a college.
depends on the truth value of the components:
.
A compound statement is a truth-functional
statement.
A truth-function is an expression whose truth-value
(truth or falsity) is completely determined by the truth
values of its component statements.
Manila is a city AMV is a college.
-
8/3/2019 Hypothetical Proposition (1)
13/31
Additional Examples:
"The sun is shining" "the boys are playing."
* It is not the case that
Marie is the most beautiful girl in the world.
The truth value of this proposition is determined by the
truth-value of the logical component:
*The sun is shining and the boys are playing.
is a function of its component simple propositions:
Marie is the most beautiful girl in the world.
-
8/3/2019 Hypothetical Proposition (1)
14/31
NegationNegation
The negation of a statement is formed by using"not in the original statement or by prefixing the
phrases
"it is false that.." "it is not the case that.."
Examples:
John is notthe president of the class.
It is not the case thatthe Philippines is the
poorest country in Asia.
It is false that life is tragic.
-
8/3/2019 Hypothetical Proposition (1)
15/31
The symbol for negation is the curl .
Examples:
Students are responsible.
- ~ S
- S
It is not the case that students are
responsible.
The definition of negation may be presented in this
truth table: p ~p---------
T F
F T
The curl denies or contradicts the statement it
preceeds.
'~'
This is a simple
statement
the negative
statement
If p is true then
~p is false
If p is false
then ~p is true
-
8/3/2019 Hypothetical Proposition (1)
16/31
Material ImplicationMaterial Implication
Material implication is an if then statement.
If the Philippines is a democratic country,
then Vatican is a state.
Antecedent
Consequent
Parts:
Example:
- If..
- then..
-
8/3/2019 Hypothetical Proposition (1)
17/31
Material ImplicationMaterial Implication
This is another type of implication where there isno real or causal connection between the
antecedent and the consequent.
If man could be have wings, then our ancestorsare pigs.
symbol of material
implication - the horse shoe -
Material implication is an emphatic way of
denying the antecedent.
Example:
-
8/3/2019 Hypothetical Proposition (1)
18/31
material implication is true if it is not the case that
the antecedent of the statement is true and its
consequence is false.
The only way it can be false is if the antecedent
is true and the consequent is false
If Manila is a city then UST is a university. M U
Philosophy is not myth then science is
empirical.~ P S
The horse shoe is a truth functional connective
-
8/3/2019 Hypothetical Proposition (1)
19/31
Material implication may be defined by this truth
table:
p q p q
T T TT F FF T T
F F T
_____________
Five is an odd number one is an even
number.This is true (T) This is false (F)
T F thus the material implication is false (F)
Application:
-
8/3/2019 Hypothetical Proposition (1)
20/31
DisjunctionDisjunction
The disjunctive is the either- or statement.Two things cannot be false at the same time one at
least must be true.
The disjunction of two statements is formed by
inserting the word "or" between them.
Examples:
An A proposition is affirmative or O is negative.The antecedent is condition or consequent is cause.
-
8/3/2019 Hypothetical Proposition (1)
21/31
The symbol for disjunction (inclusive) is the
wedge
The wedge is a truth-functional connective.
It connotes that a disjunctive statement is true if at
least one of the components it connects is true.
I either run or I get hit.
Examples:
p v q
Logic is not fiction or arts is not magic. ~p v ~q
v
-
8/3/2019 Hypothetical Proposition (1)
22/31
Disjunction may be defined by this truth table:
p q p v q
T T TT F TF T T
F F F
_____________
Five is an odd number v one is an even number.
This is true (T) This is false (F)
T F thus the disjunction is true (T)
Application:
-
8/3/2019 Hypothetical Proposition (1)
23/31
ConjunctionConjunction
The conjunctive is formed by placing the word andbetween two statements.
The conjunction in Aristotelian is not a conjunction in
modern logic.
Examples:
An I proposition is affirmative and E is negative.
Three is a odd number and six is divisible by two.
PNB is a bank and SM is a department.
-
8/3/2019 Hypothetical Proposition (1)
24/31
The symbol for conjunction is the dot.
The dot is a truth-functional connective.
It connotes that a conjunctive statement is true if bothcomponents it connects are true.
PNB is a bank and SM is a mall.
Examples:p . q
Politics is not showbiz and painting is an art. ~p . q
(. )
p . ~qSnakes are reptiles and birds are not wild.
-
8/3/2019 Hypothetical Proposition (1)
25/31
Conjunction may be defined by this truth table:
p q p . qT T TT F FF T F
F F F
_____________
Five is an odd number . one is an even number.
This is true (T) This is false (F)
T F thus the conjunction is false (F)
Application:
-
8/3/2019 Hypothetical Proposition (1)
26/31
Material EquivalenceMaterial Equivalence
Material equivalence is the bi-conditional statementThe phrase if and only if is placed between two
statements.
Examples:UST is a university if and only if a university is a big
school.
Ten is an even number if and only if an even number
is divisible by two.
-
8/3/2019 Hypothetical Proposition (1)
27/31
The symbol for material equivalence is
The is a truth-functional connective.It connotes that a materially equivalent statement is
true if both components are true or both are false.
PNB is a bank if and only if and SM is a mall.
Examples:p q
Politics is showbiz if and only if painting is
not an art.
p ~q
()
~p qMetal is not air if and only if lightning is
electrical
-
8/3/2019 Hypothetical Proposition (1)
28/31
Material equivalence may be defined by this truth
table:
p q p q
T T TT F FF T F
F F T
_____________
Five is an odd number one is an even number.
This is true (T) This is false (F)
T F thus the material equivalence is false (F)
Application:
-
8/3/2019 Hypothetical Proposition (1)
29/31
~
(If critical thinking is important then Logic is required in college) or
(St. Thomas is a philosopher and St. Dominic is the founder of the Order of
Preachers.)
T T v
T . T
( T T ) v ( T . T)~
~ (T) v T
F v T
T
Application
-
8/3/2019 Hypothetical Proposition (1)
30/31
[(one is less than any even number and two is
divisible by two) or (five is an odd number or six
is less than seven)] then ~(ten is equal to fivetimes two or nine is eleven minus five).
[ (T . T) v (T v T)] >~
(T v F)[ T v T] > ~T
T > F
F
-
8/3/2019 Hypothetical Proposition (1)
31/31
Determine the truth-value
A T B F C - ?
~[(A . B) > (C v A)] [ ~(B > C) v (A . B)]
~[(F) > (T)] [
~(T) v (F)]
~[T] [ F v F]
F F
T