Hypothetical%20proposition classpresentation[1]

THE HYPOTHETICAL PROPOSITIONS (Aristotelian Classification)

Conditional Proposition ,[object Object],[object Object],[object Object],[object Object],[object Object],Antecedent If it rains Consequent then the ground is wet.

[object Object],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:

Disjunctive Proposition ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],Pass or fail Dead or alive Today is either Monday or Tuesday. A parent is either a father or a mother. Improper Disjunctive - 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.

Conjunctive Proposition ,[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],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 time The president cannot be a conservative and liberal at the same time.

COMPLEX AND HYPOTHETICAL PROPOSITIONS (Modern Logic Classification )

Simple and Complex Statements ,[object Object],[object Object],John is a student . Manila is a city. Complex or compound statement contains logical components. ( hypothetical and negative propositions in the Aristotelian logic are considered complex.)

[object Object],[object Object],[object Object],[object Object],[object Object],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 complex statement Additional examples: :

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Manila is a city AMV is a college.

[object Object],"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 .

Negation ,[object Object],"it is false that.." "it is not the case that.." Examples: John is not the president of the class. It is not the case that the Philippines is the poorest country in Asia. It is false that life is tragic.

[object Object],[object Object],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

Material Implication ,[object Object],If the Philippines is a democratic country, then Vatican is a state. Antecedent Consequent Parts: Example: - If.. - then..

Material Implication ,[object Object],If man could be have wings, then our ancestors are pigs. symbol of material implication - the horse shoe - ﬤ Material implication is an emphatic way of denying the antecedent . Example:

[object Object],[object Object],If Manila is a city then UST is a university. M ﬤ U Philosophy is not myth then science is empirical . ~ P ﬤ S The horse shoe is a truth functional connective

[object Object],p q p ﬤ q T T T T F F F T T F F T _____________ Five is an odd number ﬤ one is an even number . This is true (T) This is false (F) T F thus the material implication is false (F) Application:

Disjunction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],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

[object Object],p q p v q T T T T F T F 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:

Conjunction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],The dot is a truth-functional connective. It connotes that a conjunctive statement is true if both components 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 . ~q Snakes are reptiles and birds are not wild.

[object Object],p q p . q T T T T F F F 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:

Material Equivalence ,[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],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 ≡ q Metal is not air if and only if lightning is electrical.

[object Object],p q p ≡ q T T T T F F F 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:

[object Object],[object Object],T T ﬤ v T . T ( T ﬤ T ) v ( T . T) ~ ~ (T) v T F v T T Application

Hypothetical%20proposition classpresentation[1]

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