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 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 reality Ex. 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 concepts Ex. 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 something Ex. 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:
Justice is a prerequisite of love.
Men are creatures of God.
“Freedom” is the name of our park.
Honesty is still the best policy.
Joy is Zeny’s friend.

Assignment #2
Underline 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).
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

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
Pedro, Filipino, Man, Asian, Brown Race
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 terms
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
PARTICULAR - it stands for an indefinite subject - Indefinite pronouns and adjectives ex. 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 time ex. Filipinos are hospitable Quantities of terms
3. 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
I am a violinist’s daughter.
All the children are musicians.
Six of them are a string ensemble.
A brother is a trombone player.
Some bands are their competitors during the town fiesta.
A square is a geometric figure with four equal sides.
Two parallel lines will not meet.
You should practice what you preach.
That girl beside me is wearing a red dress.
The weather is warm.

Kinds of terms
UNIVOCAL – if they mean exactly the same thing in the last two occurrences Ex. Man is rational. Get that man!
EQUIVOCAL – if they have different meanings in at least two occurrences Ex. 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 occurrences KINDS: 1. Intrinsic analogy: used in technical terms and as definitions 2. 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 #5
Classify 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.
I am reading Rizal.
Gold is a precious metal. Lydia de Vega received a gold for 100m. Dash.
Politicians speaks of leveling the Smokey Mountain. Geneva Cruz is a member of the Smokey Mountain.
Gonzaga is a tenor. Cabahug is a tenor.
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 Road
10. Hitler is a man. Marcos is a man.

SUPPOSITION OF TERMS
It is functional – the way it is meant in the proposition
Examples:
A square is a rectangle with four equal sides.
Square has six letters
Square is the subject the sentence
A black-rimmed square clock is classy in my living room.
KINDS OF SUPPOSITION
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 3
FORMAL SUPPOSITION: is that which uses a word for its real meaning
Example: #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: #4
B] REAL SUPPOSITION: is that which uses a word in its first intention
Example: #1 uNDER real supposition:
1] Absolute Supposition: is that which uses a word for essence, but without excluding existing reality
Example: Proposition #1 Personal Supposition: is that which uses a word for the subject containing the essence signified by the word
Example: Proposition #4

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#6
Give the specific kind of supposition illustrated by the words “carabao” and “pag-asa” in each proposition below.
“Tamarao” belongs to the endangered species.
“Tamarao” is a word with three syllables.
“Pag-asa” is the name of the eaglet.
“Pag-asa” is the subject of the sentence.
“Pag-asa” means hope in English.
“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 speech
Ex. 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] 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

E PROPOSITION

I PROPOSITION

O PROPOSITION

LOGICAL FORM
WAYS OF REWRITING PROPOSITION TO ITS LOGICAL FORM
Change the verb to its present tense progressive.
Change the verb to a noun.
Change verb to a relative clause.
Change verb to a noun clause. example ALL CROCODILES CANNOT FLY.

SQUARE OF OPPOSITION
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. contrary
1 pair:
A – E: Every S is P, therefore, no S is P. or
E – A: No S is P, therefore, every S is P.

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

Rules:
If one is true, the other is false.
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 pair
I – O: Some S is P, therefore some S is not P. or
O – 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:
If one is true, the other is doubtful.
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 pairs
1. 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

If the particular is true, the universal is doubtful; but if the particular is false, the universal is false.
I- Some triangles are planes with three sides is true [ T ] therefore A- All triangles are planes with three sides is
Doubtful [?]