LOGIC - Judgments and Propositions

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Page 1 “Teach a child WHAT to THINK and you make him a slave of knowledge; But, teach a child HOW to THINK and you make knowledge his slave.”

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LOGIC - Judgments and Propositionstest

Transcript of LOGIC - Judgments and Propositions

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“Teach a child WHAT to THINK and you make him

a slave of knowledge;

But, teach a child HOW to THINK and you make

knowledge his slave.”

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Module 2: JUDGMENTS AND PROPOSITIONS

Prepared by Mr. Roland Lorenzo M. Ruben

Philosophy section, SSD

De La Salle University - Dasmariñas

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OVERVIEW1. General notions

2. Divisions of Propositions

3. Categorical Propositions

4. Kinds of Categorical Propositions

5. Basic Standard Forms of Categorical Propositions

6. Reduction of Proposition to Logical form

7. Quantity of the Predicate

8. Hypothetical Propositions

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1. GENERAL NOTIONS

• That actual process that transpires in the mind to form a

judgment and a proposition may be outlined as follows:

– 1st, the mind has ideas or concepts of things;

– 2nd, these ideas are verbally expressed through the use

of terms;

– 3rd, the mind sees certain relationships existing

between these ideas or terms;

– 4th, the mind asserts the relation of affirming, or

denying of these ideas or terms;

– 5th, we communicate the assertions by means of

language, hence by means of propositions.

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Buddhist…

Monks…

Those monks are Buddhists.

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• A proposition, being a declarative sentence,

expresses either truth or falsity.

• Truth is independent of the mind. Truth lies in the conformity of the judgment to reality.

• Thus, a proposition is true if our assertion coincides with reality and false, if it does not coincide with reality.

Judgment – a mental operation by which the mind affirms or

denies anything whatsoever.Proposition – a declarative sentence which expresses a

relation of affirmation or denial between terms.

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Page 8Trillanes: Scam in Makati bigger than pork theft

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2. DIVISIONS OF PROPOSITIONS

• That which is affirmed or denied in a proposition refers to a relation between two terms. This relation is of 2 kinds:

– 1st, a relationship of affirming or denying something;

– 2nd, a relation of dependence, opposition or similarity.

• These give rise to 2 fundamental divisions of a proposition:

1. Categorical propositions

2. Hypothetical propositions

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3. CATEGORICAL PROPOSITIONS

• A kind of proposition in which the predicate is either affirmed or denied of a subject.

• It consists of 4 component parts: Quantifier [Q], Subject [S], Copula [C], Predicate [P].

– Quantifier = indicates the degree of universality (quantity) of the subject. [Universal and Particular]

– Subject = the term about which something is either affirmed or denied.

– Copula = that which expresses an affirmation or denial; linking verb [affirmative or negative].

– Predicate = that term which is either affirmed or denied of the subject.

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SUBJECT COPULA PREDICATE

That about

which

am, are, is,

am not, are

not, is not

That which is

QUANTIFIER

All, every, any, no

one, some, few,

most, many, not

all, the, a or an

etc.

The City of Makati is the model for world-class

governance under the Binays.

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4. KINDS OF CATEGORICAL

PROPOSITIONS

• Every categorical proposition has the following properties:

– Quantity = expresses the number of objects or individuals to which the proposition is applied. It refers to the extension of the subject term, its whole extension or only a part of it. Thus, the quantity or extension of the subject term determines the quantity of the proposition. [Universal & Particular]

– Quality = establishes the kind of relation asserted between the predicate and the subject of a proposition. This relation is either affirmative or negative. It is the copula who determines whether the predicate is affirmed or denied of the subject. [Affirmative & Negative]

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a. Quantity

1) Universal proposition – one whose subject is universal. If the subject term is singular, the proposition is universal. Indicators: All, every, no one, and the definite article: the.

Examples:

1. Every good deed is to be rewarded.2. No educated persons are jobless.3. All martyrs are not cowards.4. PNoy is the president of the Philippines.5. The student-leader of DLSU-D is very

scholarly.

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a. Quantity

2) Particular proposition – one whose

subject is particular. Indicators: some,

many, not all, most, etc., and the

indefinite article: a or an.

Examples:

1. An educator is an advocate of radical change.

2. Many politicians are not honest.

3. Not every activist is a communist.

4. Some independent nations are

underdeveloped.

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b. Quality

Examples:

1. All politicians are rich people.2. Drug addiction is a vice.3. Mr. Ruben is our teacher in logic.4. I am the greatest!

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b. Quality

Examples:

1. True laws are not unjust.2. Some students are not active.3. Andres Bonifacio is not a Caviteño.

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• It is the copula that determines the quality of a

proposition. While there are propositions whose

subject or predicate, or both are negative, their

quality will still be determined by their copula.

• Example:

1. The love of the Lord is unconditional.

2. An unfaithful wife is scorned.

3. That she is not the murderer is uncertain.

NOTE:

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5. BASIC STANDARD FORMS OF CATEGORICAL PROPOSITIONS

UNIVERSAL

AFFIRMATIVE

PARTICULAR

NEGATIVE

QUANTITY(extension of the subject)

QUALITY(copula)

Combining these 2 properties of quantity and

quality, the categorical propositions are designated as

follows:

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QUANTITY QUALITY

AFFIRMATIVE

(+)

NEGATIVE

(-)

Universal/

Singular A(All S are P)

E(No S are P)

Particular

I(Some S are P)

O(Some S are not P)

BASIC STANDARD FORMS or BASIC TYPES

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examples

1. All political candidates are people who wants to serve the country.

2. Some jeepney drivers are not honest.

3. Few teachers are chosen as outstanding.

4. No citizen is above the law.

5. The Catholic Church is an institution that is against artificial methods of contraception.

6. Manny Pacquiao is the new WBC champion.

7. Not all citizens are registered voters. (Some citizens are not registered voters)

8. Most Filipinos are great singers.

9. I am a Filipino.

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6. Reduction of Proposition to Logical form

The reduction of a proposition into its logical form

consists of rewording or changing a proposition not in

its logical form into a proposition which clearly

contains the four elements; namely, the quantifier (Q),

the subject term (S), the copula (C), and the predicate

term (Pr).

Mothers generally love their children.

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Pointers on how to reduce propositions to

logical form

1. Once given a proposition, determine mentally whether a

proposition is either A, E, I, or O.

2. The logical subject is that about which something is either

affirmed or denied. One must ask oneself, what is that about

which something is either affirmed or denied?

3. The copula serves to connect the subject and the predicate.

It is always the present tense indicative mood of “to be” with

or without a negative modifier and it must always follow the

subject term in number and in person.

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Pointers on how to reduce propositions to

logical form

4. The logical predicate is that which is either affirmed or

denied of a subject. Bear in mind that anything that comes

after the subject is the predicate. 1) When the main verb implies an act performed habitually, the main

verb may be used as a predicate noun.

2) The main verb may also be used as a predicate adjective which

modifies the immediate class to which the subject belongs.

3) Sometimes the complete predicate term may be expressed as a

relative clause by using some conjunctive words ‘the one,’ or ‘that

who,’ or any appropriate word and its plural form.

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Mothers generally love their children.

1. I-proposition = some S are P

2. Some mothers (S) ……………

3. Some mothers (S) are (C) ………….

4. 1) Some mothers (S) are (C) lovers of their children (Pr). [predicate noun]

2) Some mothers are loving parents of their children. [predicate adjective]

3) Some mothers are the ones who love their children. [relative clause]

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Non-logical form Categorical propositions

1. Birds fly.

2. Indonesians like spicy foods.

3. Scorpions have poison.

4. If you work, then you’ll eat.

5. Black ants do not bite.

6. Only non-students are allowed to join the contest.

7. Whosoever gives food to the hungry will enter the Kingdom of God.

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Logical form categorical propositions

1. All birds are creatures that fly.

2. All Indonesians are people who like spicy foods.

3. All scorpions are creatures that have poison.

4. All those persons who work are those persons who will eat.

5. All black ants are insects that do not bite.

6. All persons who are allowed to join the contest are the non-students.

7. All people who give food for the hungry are persons who will enter the kingdom of God.

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7. Quantity of the Predicate

• A & I propositions, both affirmative, have particular predicate terms.

• E & O propositions, both negative, have universal predicate terms.

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proposition Subject Predicate

A = All S are p U P

E = No S are P U U

I = Some s are p P P

O = Some s are not P P U

Rule No. 1: If the proposition is affirmative, the quantity of the

predicate is particular (except, if the predicate singular,

essential definition and characteristic property).

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Rule No. 2: If the proposition is negative, the quantity of the

predicate is universal.

proposition Subject Predicate

A = All S are p U P

E = No S are P U U

I = Some s are p P P

O = Some s are not P P U

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8. Hypothetical Propositions

Hypothetical proposition – a compound or

complex proposition between the parts of which there exists a relation of dependence, opposition or

similarity.

• The categorical proposition uses a copula to signify the

union of predicate and subject.

• The hypothetical proposition uses a non-verbal copula.

Other examples are “if – then”, “either – or”, “cannot be – and – at the same time”, etc.

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Examples:

1. “If the light is green, then you may cross the intersection.”

2. “Either you sink or you swim.”

3. “A person cannot sneeze and breathe at the same time.”

Three kinds:

1. Conditional

2. Disjunctive

3. Conjunctive

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1. Conditional• It is a compound proposition in which one

member asserts something as true on condition that the other member is true.

• In a conditional, the component proposition which follows after the “if” clause is called the antecedent and the component proposition which follows the “then” clauseis the consequent.

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1. Conditional• A conditional proposition asserts that its

antecedent implies its consequent, so that if the antecedent is true , then the consequent is true. In similar manner, if the consequent is false, then the antecedent must be false.

• The truth of conditional hypothetical propositions does not depend on the truth of the statements taken by themselves or individually. The truth depends on the relation between the statements.

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1. Conditional

1. If an animal is incapable of thinking, then an animal is

not a man.2. If he has cancer, then he is seriously ill.

3. If over-dosage of medicine is dangerous, then it must be

avoided.

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2. Disjunctive• It is a compound or complex proposition which does not

categorically affirm either one of its members, but asserts that at least one of them is true, allowing for the

possibility that others may be true.

• Unlike a conjunctive, a disjunctive proposition contains two or more members (disjuncts) which are joined together by

“either…. or…..”• For a proposition to be a proper disjunction, all

the possible alternatives must be present or

expressed; then the truth of one is established by eliminating all the others.

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2. Disjunctive

Logical form: Either ………………..., or …………………(disjunct) (disjunct)

1. Either he committed suicide or he was killed by

somebody.2. Either the patient is operated on or he will die.

3. I will go to Ozamiz either by plane, by boat or by land

travel.

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3. Conjunctive• It is a compound proposition which expresses that two

alternative assumptions are not or cannot be true simultaneously.

• The two elements exclude one another, so that they cannot be true together and they cannot be false together.

• The component parts (conjuncts) are joined by the conjunctive particle “cannot be both…. and ….”

• For a proposition to be a valid conjunctive, it is necessary that the elements are really irreconcilable at the same time.

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3. Conjunctive

Logical form: “…cannot be….. and ….. at the same time.”(conjunct) (conjunct)

1. A student cannot be diligent and non-diligent at the same time.

2. You cannot be a loyal soldier and seditious at the same time.

3. It is obvious that a person cannot be a Negro and a

Caucasian at the same time.

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• My parents sought for nothing less, died for nothing less, than democracy and peace.

• Our foremost duty is to lift the nation from poverty through honest and effective governance.

• There can be no reconciliation without justice.

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1. Through association of ideas, our mind asserts whether one idea is affirmed or denied of another. This process is called judgment.

2. When we try to communicate this to others, we express it by means of a proposition.

3. 2 kinds: Categorical and Hypothetical4. Categorical = quantifier, subject, copula and

predicate

5. 2 properties: Quantity and Quality

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6. The combination of quantity and quality of proposition gives rise to 4 types of propositions: A, E, I, O

7. Quantity of predicate: – affirmative propositions – particular

– negative propositions – universal

8. Hypothetical = conditional, disjunctive and conjunctive

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Module 2: JUDGMENTS AND PROPOSITIONS

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