INTRODUCTION

The Study of Logic

DEFINITION

Derived from the Greek word ”logos” which means - study, reason or discourse

LOGIC is the science and art of correct thinking

- it is a SCIENCE because it is a systematized body of logical truths

and principles governing correct thinking

- as an ART, logic is a “techne” and it teaches how to make a good argument

- often called the arts of arts because it develops and perfects the intellect which all artists need in their work

LOGIC AND CORRECT THINKING It is “correct” when it conforms to a

pattern or to rules Example: A ruler is 12-inch long

Pres. GMA is a ruler Therefore, Pres. GMA is 12-

inch long-THINKING is a mental process – involves

analysis, definition, classification, comparison and contrasts, etc.

- It guides or directs man to form correct ideas

BRANCHES OF LOGIC

FORMAL LOGIC-concerned with the aspect of form

which has something to do with the correctness or sequence or the following of rules

Ex. All men are mortal but Pedro is a man therefore Pedro is mortal

BRANCHES OF LOGIC

MATERIAL LOGIC-concerned with the aspect of subject matter

or content or truth of the argument Example: A ruler is 12-inch long

Pres. GMA is a ruler Therefore, Pres. GMA is 12-inch long

KINDS Deductive Logic: from more to less Inductive Logic: implies a sense of

probability

CONCEPTS AND TERMS The three essential operations of the

intellectMental Operations

Products External Signs

1. SIMPLE APPREHENSION

CONCEPT ORAL AND WRITTEN TERMS

2.JUDGMENT MENTAL PROPOSITION

ORAL AND WRITTEN PROPOSITIONS

3. REASONING MENTAL AGREEMENT OR DISAGREEMENT

ORAL AND WRITTEN ARGUMENTS

CONCEPT

The representation of an object by the intellect through which man understands or comprehends a thing

It is an “idea”- starts with an outside reality and apprehended by the senses

KINDS OF CONCEPT

1.First Intention: we understand what the thing is according to what it is in realityEx. A dog is an animal.

Second Intention: we understand not only what the thing is according to what it is in reality but also how it is in the mind

Ex. “Monte Vista” (Mountain View) is the name of my subdivision

KINDS OF CONCEPT

2.Concrete Concepts: expresses a “form” and a “subject”Ex. The flower rose

Abstract Concepts: has a “form” only , has intangible quality, that which cannot be perceived by the senses

Ex. Beauty in a woman

KINDS OF CONCEPT

3.Absolute Concepts: signifies the meaning of a concept, all definitions are absolute conceptsEx. A triangle is a three-sided figure.

Connotative Concepts: signifies a characteristic existing in the concept, all modifiers are connotative concepts

Ex. Drummer boy

KINDS OF CONCEPT

4.Positive Concepts: signifies the existence or possession of somethingEx. happy

Negative Concepts: signifies the absence of something

Ex. sad

SEATWORK #2

Underline the simple subject of each proposition then classify according to the four kinds of concepts in the column below:

1. Justice is a prerequisite of love.2. Men are creatures of God.3. “Freedom” is the name of our

park.4. Honesty is still the best policy.5. Joy is Zeny’s friend.

Concept I or II C or A A or C P or N

1.

2.

3.

4.

5.

ASSIGNMENT #2Underline the simple subject of each

proposition then classify according to the four kinds of concepts in the column below:

1. Love is a many-splendored thing.2. “Love” is the theme of the

homily.3. The loving couple is a model to

their children.4. Hope is the opposite of despair.5. “Hope” is the street where I live. 6. The urban poor are people in

need of hope.

THE TERM

The external representation of a concept and the ultimate structural element of a proposition.

- external representation means it is always a sign of a concept or an idea - ultimate structural element means it could either be the subject or predicate of a proposition

THE TERM

EXAMPLE:

Hilda is a (nun).

subject

predicate

PROPERTIES OF A TERM

EXTENSION OF A TERM the sum total of the particulars to

which the comprehension of a concept can be applied

The denotation of a term The terms that are members of the

domain of the concept

PROPERTIES OF A TERM

COMPREHENSION OF A TERM - the sum total of all notes which

constitute the meaning of a concept

- set of traits or characteristics that differentiates the term in a group

- the connotation of a term

PROPERTIES OF A TERM Example is the term BAT-for its extension it will include all

animals, regardless of size, shape, colour, or breeding

-further analysis (comprehension), know the nature of bats – how?

- You must try to state the trait or set of traits and characteristics that differentiates bats from the rest of the animal kingdom

PROPERTIES OF A TERM Example is the term BAT-the important common trait of bats

is: they are the only mammals capable of sustained flight like a bird

- Unlike birds, bats are able to fly at low speed with extreme maneuverability.

RELATIONSHIP Comprehension and Extension are

related to each other inversely Meaning: the greater the

comprehension of a term, the lesser its extension and vice versa

- the arrangement of the characteristics from general to specific

Ex. city, barangay, province, municipality, region, country , sitio

SEATWORK#3

Arrange the ff. from greater comprehensiont o lesser extension

1. Pedro, Filipino, Man, Asian, Brown Race

2. Square, Plane, Figure, Rectangle, Polygon, Parallelogram, shape

ANSWER TO SW#3

1. Man 2. Plane Asian Figure Brown Race Shape Filipino Polygon Pedro Parallelogram

Rectangle Square

QUANTITIES OF TERMS1. SINGULAR – it stands for a single definite

individual or group- Proper nouns ex. Raul, La Union, DMMMSU- Nouns modified by adjective to the superlative degree ex. most charming- Demonstratives ex. this book, that door - Collective nouns ex. flock, class- The article the ex. The man in blue shorts- Personal pronouns – I, you, he, she, we, they, my, your, our

QUANTITIES OF TERMS

2. PARTICULAR - it stands for an indefinite subject- Indefinite pronouns and adjectivesex. Some, several, many, few- Use of numbers ex. Seven tickets- Use of article “a” and “an”- General propositions: which are true most of the time but not all the timeex. Filipinos are hospitable

QUANTITIES OF TERMS3. UNIVERSAL – it stands for every

subject signified- Universal expressions ex. All, every, each, whatever, whoever, whichever, without exception, everything- Universal ideas Ex. Men are mortal- The use of articles “the”, “a”, “an” if the idea is universal Ex. The snake is a dangerous creature.

SEATWORK #4 Underline each simple subject and classify its

quantity: S for singular, P for particular, and U for universal

1. I am a violinist’s daughter.2. All the children are musicians.3. Six of them are a string ensemble.4. A brother is a trombone player.5. Some bands are their competitors during the

town fiesta.6. A square is a geometric figure with four equal

sides. 7. Two parallel lines will not meet.8. You should practice what you preach.9. That girl beside me is wearing a red dress.10. The weather is warm.

KINDS OF TERMS

1. UNIVOCAL – if they mean exactly the same thing in the last two occurrencesEx. Man is rational. Get that man!

2. EQUIVOCAL – if they have different meanings in at least two occurrencesEx. Man the lifeboat!

The son of man

KINDS OF TERMS

3. ANALOGOUS – if they have partly the same and partly different meanings in at least two occurrencesKINDS:1. Intrinsic analogy: used in technical terms and as definitions2. Extrinsic analogy: used as a metaphor

Ex. The heart of the forest

KINDS OF TERMS

KINDS:3. Analogy of Proportionality: when the terms use are similar Ex. The stepmother is cruel.

The sea is cruel. 4.Analogy of Attribution: attribute the term to its denotation

Ex. I am drinking Coke.

SEATWORK #5Classify the underlined terms- write U for

Univocal, E for Equivocal, IA for Intrinsic Analogy, EA for Extrinsic analogy, AP for for Analogy of Proportionality, AA for Analogy of Attribution.

1. I am reading Rizal.2. Gold is a precious metal. Lydia de Vega

received a gold for 100m. Dash.3. Politicians speaks of leveling the

Smokey Mountain. Geneva Cruz is a member of the Smokey Mountain.

4. Gonzaga is a tenor. Cabahug is a tenor.5. I am using Colgate.

SEATWORK #5

Classify the underlined terms- write U for Univocal, E for Equivocal, IA for Intrinsic Analogy, EA for Extrinsic analogy, AP for Analogy of Proportionality, AA for Analogy of Attribution.

6. Father Sales and my father are friends.7. The smiling sun is so brilliant.8. The mouth of the river is clean.9. We pass by Bridal’s Veil along Kennon

Road10. Hitler is a man.

Marcos is a man.

SUPPOSITION OF TERMS

It is functional – the way it is meant in the proposition

Examples:1. A square is a rectangle with four equal

sides.2. Square has six letters3. Square is the subject the sentence4. A black-rimmed square clock is classy

in my living room.

KINDS OF SUPPOSITION

1. MATERIAL SUPPOSITION: is that which uses a word for itself alone, for its spoken or written sign, not for its real meaning

Examples: #2 and 32. FORMAL SUPPOSITION: is that which

uses a word for its real meaningExample: #1

OTHER KINDS

A] LOGICAL SUPPOSITION: is that which uses a word for its second intention; that is the way the mind thinks it to be

Example: #4B] REAL SUPPOSITION: is that which

uses a word in its first intentionExample: #1

UNDER REAL SUPPOSITION:

1] Absolute Supposition: is that which uses a word for essence, but without excluding existing reality

Example: Proposition #1Personal Supposition: is that which uses a word for the subject containing the essence signified by the word

Example: Proposition #4

2. Essential Supposition: is that which uses a word for qualities necessary to the subject

Example: #1

Accidental Supposition: is that which uses a word for qualities not actually necessary to the subject

Example: #4

SEATWORK#6Give the specific kind of supposition illustrated

bythe words “carabao” and “pag-asa” in eachproposition below.1. “Tamarao” belongs to the endangered

species.2. “Tamarao” is a word with three syllables.3. “Pag-asa” is the name of the eaglet.4. “Pag-asa” is the subject of the sentence.5. “Pag-asa” means hope in English.6. “Pag-asa” is now the adopted child of bird

lovers.

OTHER TYPES

- IMAGINARY SUPPOSITION: exists as a product of imagination

Ex. Fictional character METAPHORICAL SUPPOSITION: term is

used as a figure of speechEx. The smiling sun SYMBOLIC SUPPOSITION: signifies a

group of men Ex. L.A. Lakers

THE PROPOSITION

- A special type of sentence- An enunciation of truth or falsity- Verbal expression of mental

judgment

STRUCTURAL ELEMENT

S – C – P

[subject]- [copula]- [predicate] Subject stands for the thing signified, the

one spoken of Predicate stands for what is affirmed or

denied of the subject copula- links the subject and the predicate

- * acceptable only is the present tense is or is not

EXAMPLE

All boys (are) future men.

Quantifier subject[S] copula[C] predicate[P]

LOGICAL SYMBOL[FOUR STANDARD PROPOSITIONS]

QUANTITY

QUALITYAFFIRMATIVE NEGATIVE

UNIVERSAL, SINGULAR

AEvery S is P.

ENo S is P.

PARTICULAR

ISome S is P.

OSome S is

not P.

EXAMPLES

A - Every monkey is an animal. E - No monkey is a human. I - Some monkeys are brown. O - Some monkeys are not

brown.

LOGICAL DIAGRAM

A PROPOSITION

PREDICATE

SUBJECT

E PROPOSITION

SUBJECT

PREDICATE

I PROPOSITION

SUBJECT

PREDICATE

O PROPOSITION

SUBJECT

PREDICATE

LOGICAL FORMWAYS OF REWRITING PROPOSITION

TO ITS LOGICAL FORM1. Change the verb to its present

tense progressive.2. Change the verb to a noun.3. Change verb to a relative clause.4. Change verb to a noun clause.

EXAMPLE

ALL CROCODILES CANNOT FLY.

1.NO CROCODILES ARE FLYING.

2.NO CROCODILES ARE FLYERS.

3.NO CROCODILES ARE REPTILES THAT CAN FLY.

4.NO CROCODILES ARE FLYING REPTILES.

SQUARE OF OPPOSITION

CONTRARY

SUBCONTRARY

SUBALTERN

SUBALTERN

CONTRADIC

TO

RIES

A E

I

O

CONTRADICTO

RIES

CONTRADICTORIES

- 2 pairs: 1] A – O: Every S is P, therefore, some S

is not P. O – A: Some S is not P, therefore,

every S is P.

2]E – I: No S is P, therefore, some S is P. I– E: Some S is P, therefore, no S is P.

EXAMPLES:

A - All men are rational, therefore

O - some men are not rational.

I – Some students are girls, therefore

E – No students are girls.

RULES:

1. If one is true, the other is false.

2. If one is false, the other is true.

A - All men are rational is true [ T ], therefore O - some men are not rational. False or F

CONTRARY- 1 pair:A – E: Every S is P, therefore, no S is P. orE – A: No S is P, therefore, every S is P.

Example:E- No students are girls, therefore, A - every students are girls.

RULES:

1. If one is true, the other is false.

2. If one is false, the other is doubtful.

Example:E- No students are girls is false [

F ], therefore, A - every students are girls is

doubtful [ ? ]

SUBCONTRARY- 1 pairI – O: Some S is P, therefore

some S is not P. orO – I: Some S is not P, therefore

some S is P.EXAMPLE:I - Some students are girls,

therefore O - some students are not girls.

RULES:

1. If one is true, the other is doubtful.2. If one is false, the other is true.

EXAMPLE:I - Some students are girls is true

[ T ], therefore O - some students are not girls is

doubtful [ ? ].

SUBALTERNS

- 2 pairs1. A – I: Every S is P, therefore

some S is P. I – A: Some S is P, therefore

every S is P.

2. E – O: No S is P, therefore some S is not P.

O – E: Some S is not P, therefore no S is P.

EXAMPLE

A- All triangles are planes with three sides, therefore

I- Some triangles are planes with three sides.

RULES:

1. If the universal is true, the particular is true; if the universal is false, the particular is doubtful

A- All triangles are planes with three sides is true [ T ], thereforeI- Some triangles are planes with three sides true [ T ].

2. If the particular is true, the universal isdoubtful; but if the particular is false, theuniversal is false.I- Some triangles are planes with threesides is true [ T ]thereforeA- All triangles are planes with three sides

isDoubtful [?]