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 intellect

Mental 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 #2Underline 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 termEXAMPLE:

Hilda is a (nun).

subject

predicate

Ex.

Bats are flying creature.

Logic is a science that deals with the study of correct reasoning.

Properties of a termEXTENSION 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 extension1. Pedro, Filipino, Man, Asian, Brown

Race2. 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 terms2. 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 terms1. 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 terms3. 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 termsKINDS: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 SUPPOSITION1. 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

exampleAll boys (are) future men.

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

Logical symbol[Four standard propositions]QUANTIT

YQUALITY

AFFIRMATIVE NEGATIVE

UNIVERSAL, SINGULAR

AEvery S is P.

ENo S is P.

PARTICULAR

ISome S is P.

OSome S is

not P.

Universal Affirmative Proposition All students in logic class are intelligent. Every men on the planet is a human

being. Everything in this world is temporary.

Note: Change is permanent

Universal Negative Proposition No students in logic class are intelligent. No men on the planet is a human being. Nothing in this world is temporary.

Note: No Change is permanent

Particular Affirmative Proposition Some students in logic class are

intelligent. Few men on the planet is a human

being. Something in this world is temporary.

Note: Not every Change is permanent

Particular Negative Proposition Some students in logic class are not

intelligent. Few men on the planet is not a human

being. Something in this world is not

temporary.

Note: Not every Change is permanent

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

Logical diagramA 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 OPPOSITIONCONTRARY

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.

exampleA- 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 doubtfulA- 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 [?]