Hypothetical Proposition (1)

8/3/2019 Hypothetical Proposition (1)

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THE HYPOTHETICALTHE HYPOTHETICAL

PROPOSITIONSPROPOSITIONS(Aristotelian Classification)(Aristotelian Classification)


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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.


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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:


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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


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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.


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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


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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.


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COMPLEX AND HYPOTHETICALCOMPLEX AND HYPOTHETICAL

PROPOSITIONSPROPOSITIONS

(Modern Logic Classification(Modern Logic Classification))


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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.)


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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::


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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.


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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.


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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.


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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


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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..


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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:


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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


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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:


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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.


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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


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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:


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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.


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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.


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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.


T F thus the conjunction is false (F)

Application:


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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.


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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


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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.


T F thus the material equivalence is false (F)

Application:


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~

(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


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[(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


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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

Hypothetical Proposition (1)

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