Judgment and

Proposition or

Logical Statement

JUDGMENT and PROPOSITION

Judgment

- is the mental act which affirms or denies something.

Proposition

- the product of judgment.

- a statement that affirms (asserts) or denies (negates) something.

• Proposition is in a form of a sentence as a group of words that expresses a complete thought.

4 Kinds of Sentences1.) Declarative : states a fact

Ex. My house is a red-roofed bungalow in Greenhills.

2.) Interrogative : asks a questionEx. How are you today?

3.) Imperative : makes a request or gives a commandEx. (a.) Please send me some sampaguita plants.

(b.) "Build more stately mansions, O my soul."

4.) Exclamatory : expresses a strong feelingEx. What a lovely thing to say!

PROPOSITION

To the Logicians:

a.) according to Bachhuber:proposition is being expressed by a declarative sentence, for

both assert or deny something.Ex. "Cainta is a town in Rizal province." (asserting)

" Manuel L. Quezon was not the first Vice-President of the Philippines" (denying)

b.) according to Copiinsisted that there must be a distinction between form (kinds

of sentences) and function (informative, expressive, directive)-not every declarative sentence seeks to inform. Quite a

number of declarative sentences are ceremonial and expressive, as with gratitude and appreciation.

PROPOSITION

To the Logicians:

c.) according to Aristotle:-defines proposition as "a sentence that could either be true

or false."-this does not mean, however, that the proposition is in fact

true or false. What matters is that this is a proposition, a logical statement, where something is asserted, and which could either be true or false.

PROPOSITION

Kinds of Propositions

a. categoral or attributedb. hypotheticalc. existentiald. non-existentiale. simplef. compound

Basic Elements of the Categorical Proposition

a. it has a subject- predicate relationship

b. its subject is affirmed or denied by the predicatetherefore, its basic elements are:

1.) the subject2.) the predicate3.) the copula

PROPOSITION

SUBJECT

- the one spoken of: the one about whom or of which something is affirmed or denied.PREDICATE

- is what is affirmed or denied of the subject.COPULA

- links the subject with the predicate; a verb to be: is, am, are (affirmative) and is, am, are not (negative)

PROPOSITION

"The story he told you is apocryphal."story : subject

apocryphal (fictitious) : predicateis : copula

NOTE: for the purpose of Logic, tenses are irrelevant. The copula "is" should be taken a tenseless sense; its pasta and future forms are usually considered part of the predicate.

In this connection, it is important to note that number, in the grammatical sense, is irrelevant also to logic.

PROPOSITION

Quality of the Proposition

-Copula is the qualifier of the Proposition. Because of it, the proposition is either affirmative or negative.

Example:1. He who is not a college graduate is ineligible.2. Some animals are non-mammals.

PROPOSITION

Quantity of Extension of the Proposition-quantity of the proposition is equivalent to quantity of its subject.

It is:

Singular if subject stands for a single definite individual or group.

Particular if the subject designates an indefinite part of its total extension.

Universal if the subject can apply to every portion signified by the term.

Quantity or Extension of the Proposition

Example:

1.) Singular: Shakespeare is England’s greatest dramatist.

2.) Particular: Some prima ballerinas are Margot Fonteyn and Natalia Makarova.

3.) Universal: Love is many-splendor things.

Quantity of the Predicate

Three Points in Determining the Quantity of the Predicate

1. Find out if the predicate is singular.

Ex. Dr. Christian Barnard is the most outstanding heart transplant surgeon.

2. If the predicate is not singular, and if the proposition is affirmative, then the predicate is particular.

Ex. Gabriel Marcel is a French philosopher.

3. If the predicate is not singular, and if the proposition is negative, then the predicate is universal.

Ex. Some men are not artists.

Symbols and Categorical Statements

• Attempts to make Logic a science of symbols to achieve shortcuts to correct reasoning.

Symbols for the Four Categorical Statements

(A,E,I,O)

A and I are taken from the two vowels ofAffIrmo (affirm) and E & O from the two vowelsof nEgO (negate or deny)

Symbols and Categorical Statements

A- stands for universal or singular andaffirmative statements.

E- stands for universal or singular and negativestatements.

I- stands for particular and affirmativestatements.

O- stands for particular and negativestatements.

Symbols and Categorical Statements

universal/singular

A

I

E

O

affirmative negative

particular

Symbols and Categorical Statements

A:1. All roses are flowers.2. Every cloud has its silver lining.3. Man is a being-for-death.4. Whoever wins will be awarded a trip to Hongkong.5. Wherever you go, I go.6. Whatever will be, will be.7. All of us in this room are Filipinos.8. Everything is in a flux.9. Francis is a scholarly Jesuit.10. His lecture on Philosophy and art is a brilliant piece of

work.

E:1. No atheist is a believer in God.2. No bird has four legs.3. Love of country is not a commodity for sale.4. None of the invited top brass showed up.5. Love means not having to say you are sorry.6. I never said he was a crook.7. He loves me not.8. Not any of the men to be arrested could be located.9. No pill box is a safe weapon.10. A squash is not an eggplant.

Symbols and Categorical Statements

Symbols and Categorical Statements

I:1. Some philosophers are essentialists.2. Several philosophers are existentialists.3. Many movies are, in whole or in part pornographic.4. A few heart transplant patients are still alive.5. Most cultures are deeply religious.6. Filipinos are music lovers.7. The Japanese soldiers in World War II were barbarians.8. Pampanguenas are good cooks.9. Almost all people condemned the Plaza Miranda carnage.10. Quite a few tourists are knowledgeable of our scenic

spots.

Symbols and Categorical Statements

O: 1. Some dogs are not black.2. Not all women are fickle.3. A few Filipinos are not literate.4. Many Americans are not rich.5. Most Russians are not Communist Party members.6. Some things in life are not edible.7. All that shines is not gold.8. From the economic standpoint , not all men are equal.9. Not everyone who wears glasses is smart.10. All parrots cannot talk.

THE LOGICAL FORM

Most of the propositions taken up follow a consistent pattern: S is P (subject-copula-predicate). Those already adept in logic can easily translate, mentally, any proposition into a standard-form categorical statement.The following illustrate the logical form:

A propositions:

1. Mario sells newspapers.Mario is a [newsboy]

2. Shakespeare wrote a drama Macbeth.Shakespeare is the [dramatist] of Macbeth.Shakespeare is the [author] of the drama Macbeth.

THE LOGICAL FORM

3. Whatever is material will decay.

All things which are material are [substances] which will decay.

E propositions:

1. No crocodiles fly.

No crocodiles are [flyers].

2. None of the guests came.

No guests are [guests] who came. or

No guests are [people] who came.

THE LOGICAL FORM

I propositions:1. Some broken hearts can be mended.

Some broken hearts are mendable [things].2. A dog barked furiously last night.

Some dog is an [animal] which barked furiously last night.

O Proposition:1. Several student radicals have not traveled to Red China.

several student radicals are not [travelers] to Red China.2. We saw the zarzuela and did not enjoy it.

Some times that we saw the zarzuela are not [times] that we enjoyed.

The Hypothetical Proposition

Hypothetical Proposition

-is a compound proposition which contains a proposed or tentative explanation.

Compound Proposition

- consists of at least two clauses connected by conjunctions, adverbs, etc. which expresses the relationship between the clauses as well as our assent to it.

• The clauses are simple propositions of the

A-E-I-O variety.

3 Kinds of Hypothetical Proposition

1. Conditional Proposition

2. Disjunctive Proposition

3. Conjunctive Proposition

The Hypothetical Proposition

1. Conditional Proposition- a compound proposition in which one clause

asserts something as true provided that the other clause is true.

- the first clause= “if” clause or termed as the ‘antecedent’.

- the second clause = “then” clause or called as the ‘consequent’.Example:

If strong typhoons come, then crops will be destroyed.

(1.) The Hypothetical Proposition

(1.) Conditional Proposition

Antecedent: If strong typhoon comesConsequent: then crops will be destroyed.

NOTE: the “if…then” are the connectives and indicate that if the antecedent is true, then, the consequent must be true.

IMORTANT: -sequence between the two. -antecedent must flow with logical necessity into the

consequent-it does not matter whether individually the

antecedent or the consequence is true or false; what mattersis the relationship between them.

(2.) The Hypothetical Proposition

2. Disjunctive Proposition

- “alternative proposition”

- It is the one which presents two or more alternatives, one of which may be true.

- Its members are linked by the conjunctions “either…or.”

- It may either be strict disjunctive or broad disjunctive.

(2.) Disjunctive Proposition

Strict Disjunctive

- Only one member is true and the others are false.

Ex. “Either he is an angel or a devil.”

- A proposition and its contradictory may be asserted.

- Ex. Either a triangle is a three-sided figure or it is a non-three-sided figure.”

(2.) Disjunctive Proposition

Broad Disjunctive

- one member or more than one member may be true.

Example:

“Either Luciano or Edgardo are TOYM candidates.”

- The distinction between the strict and the broad disjunctive is based on the analysis of the subject matter and context.

(3.) The Hypothetical Proposition

3. Conjunctive Proposition- one which asserts that two alternatives

cannot be true at the same time. In fact, bothalternatives may be false.Example: 1. You cannot be in the faculty room and in theauditorium at the same time.

2. A thing cannot exist and not exist at the sametime.

Reported by GROUP #3

“JUDGEMENT and PROPOSITION or LOGICAL STATEMENT”

Arlene Abonales

Maria Joyce Lim

Renzie Relota

Kersha Sheene Martos

Art Marie Getonzo

Kimberly Havoc

The Venn Diagrams

- A clearer presentation of categorical statement.

- Called after the English mathematician and logician John Venn who first introduced it during the nineteenth century.

- If we represent the subject as S and the predicate as P, then anything that is not the subject is S’ and anything that is not the predicate is P’.

The Venn Diagrams

Figure 2

Figure 2 represents classS- a class of persons orobjects. It does notrepresent a proposition,i.e., it does not assertanything.

S

Sˡ

Figure 3

Figure 3 is a shaded circle.It represents anullification of class S. Itmeans that class S has nomembers.

S

x

Figure 4

Figure 4 has an x in itscenter. It represents thefact that there are S’s, i.e.,that there is at least onemember of S, that class Sis not empty.