LOGIC IS ONE THING AND COMMONSENSE ANOTHER. ~ Froi Santi

“treatise on matters pertaining to thought.”

“spoken word, in-depth study, discourse, or simply reasoning”

- One of the great TRIUMVIRATEGreek Philosophers

- Founder of Logic

- Analysis of propositions and syllogism

- How these are exemplified in inferences

GREEK LOGIC Zeno (336 – 264

B.C.), the founder of the Stoic School, penned this science, Logic.

CHINESE LOGIC

Mozi (Mo Tzu ca. 470 – 391 B.C.) a contemporary of Confucius.

HINDU LOGIC Nyaya is one of the six

Orthodox or Astikaschools in Hindu Philosophy which subscribed to the authority of the Vedas.

ISLAMIC LOGIC Avicenna (Ibn Sina

980 – 1037 A.D.) wrote to the hypothetical syllogism.

MEDIEVAL (Scholastic) Logic

Severinus Boethius (ca. 470-524 A.D.) stipulated commentaries on the Categories and translation on the Isagoge of Phorphyrius.

Peter Abelard (1079-1142 A.D.) improved treatise in logic with the inclusion of the valid rules of argument.

William of Ockham (1288- 1348 A.D.) developed theory of consequences in his work Summa Logicae.

MODERN LOGIC Francis Bacon (1561 –

1626 A.D.) wrote the Novum Organon, The “new instrument”. He introduced the method known as inductive reasoning.

Correct thinkingDetermination and certainty

about goals in lifeDevelop correct reasoningTransformation of inner self

To be critical and rational To improve the natural aptitude of students To detect and avoid errors in arguments To avoid dogmatism and incorrigible bigotry To argue from knowledge, not ignorance Improved planning Enhanced creativity Refrain from jumping to conclusion Tool for social transformation

Logic only applies to statements, not to the real world.

It deals only with the validity of arguments. Not with the truth value of the premises of

those arguments.

Penguin Soup Conclusion: A middle aged man walks into a

restaurant which offers authentic penguin soup. He orders a bowl of sou. He takes one spoonful, pays and exits the restaurant. He went straight home, he took his gun and shoots himself dead.

What goes on four legs in the morning, on two legs at noon, and on three legs in the evening?

The Liar: A man stands up and says “I am a liar.” is he a

liar or is he telling the truth? Explain your answer…

Did you know that the word ‘trivia’ , etymologically speaking, came from the word “tri” – which means three (3), and “via” – which means way? Literally it would mean the ‘three ways’, but originally it was referred to the trivium, the three fundamental fields of education or curriculae: Grammar, Rhetorics, and Logic. Isidore de Seville, in his Etymologiae, characterized these as the sciences of liberal arts. The mastery of these three is considered essential before on could continue to study higher learning. Logic is one of the few courses.

Mark, Sophia, Ryan, and Grace are sitting around the dining table discussing their favorite sports. Discover each person’s sport by using the clues below.

Clues: a. Mark sits directly across the tennis player. b. Sophia sits to the right of the badminton player. c. Grace sits across from Ryan d. The swimmer sits to the left of the chess player. e. A man sits on Ryan’s right.

Mark - ________________? Sophia - ______________? Ryan - ________________? Grace - ________________?

Simple Apprehension – is the first mental phase or act of the mind.

The human intellect with regard to the first mental phase generally operates in the following sequence:

Sensation Imagination Abstraction Verbalization

Sensation

Sense Image

Imagination

Phantasm

Abstraction

Idea

Verbalization

Term

Abstraction is the mental process of the obtention and formation of idea or concepts. To abstract, means to pick up from, or to draw out from. It is the grasping of what is essential to an object separating it from what is accidental.

Idea – is the mental product of abstraction. It is came from the Greek word eidos, which means image.

Collective term –represents a number of objects constituting a unit-group or whole.

Example:

Pride of lions. Troop of monkeys.

Different term – it is non-identical and with no relation at all.

Example:

Angel and ice cream

Contrary term –extreme opposites of a certain feature or subject which several intermediates exists between them.

Contradictory term –mutually exclusive and pertains to the extreme opposites with no option available option between them.

Classification of Terms Univocal – a term that expresses the same

meaning.Equivocal – a term that expresses different conventional meanings.

Analogous – a term that expresses semblances of meaning in its several uses the same spelling and same pronunciation.

Metaphorical – a term that is not used in its proper or conventional meaning and applied to something else.

Relative Term – terms that are opposites but bear mutual relation or dependence to one another.

Privative Term – one of the term contains the perfection from which the other term lacks.

Associable Term – terms that has relationship with each other, connected with each other.

Relative Term – terms that are opposites but bear mutual relation or dependence to one another.

Privative Term – one of the term contains the perfection from which the other term lacks.

Associable Term –terms that has relationship with each other, connected with each other.

Paradoxical Term – a term that two opposed terms combined together to form a new meaning.

Solve the following: 26 L of A 7 W of the W 24 H in a D 9 P of the SS 56 W in a Y 101 D 7 C of the R 10 L I 4 S of the S 29 D of F (LY)? 52 C in a D 3 BM (SHTR)? 5 F in a H 12 S of the Z 8 T of the O

Conclusion:

A half naked man found dead on top of a mountain with a toothpick in his right hand.

Allan, Jasmine, Roger and Cedrick are four creative artistswith their own respective professions. One is a dancer,another is a painter, the other one is a singer, and the lastone is a writer. What is each person’s artistic hold?

Clues: A. Allan and Roger were in the audience the night the singer

made his debut on the concert stage. B. Both Jasmine and the writer have had their portraits

painted from life by the painter. C. The writer, whose biography of Cedrick was a best seller, is

planning to write a biography of Allan. D. Allan has never heard of Roger.

Grumpy was in front of Dopey. Stumpy was behind Sneezy and Doc. Doc was in front of Droopy and Happy. Sleepy was behind Stumpy, Smelly and Happy. Happy was in front of Sleepy, Smelly and Bashful. Bashful was behind Smelly, Droopy and Sleepy. Sneezy was in front of Dopey. Smelly was in front of Grumpy, Stumpy and Sneezy. Dopey was in front of Droopy. Sleepy was in front of Grumpy and bashful. Dopey was behind Sneezy, Doc and Sleepy. Stumpy was in front of Dopey. Smelly was behind Doc.

Arrange the dwarves in order of succession.

1st 8th

2nd 9th 3rd 10th

4th

5th

6th

7th

Indefinite pronouns and adjectives Example: a lot of, almost all, some

▪Universal: refers to all definite members of a group. Ex. All, any, no, one, whatever, each

Immediate – a term that is directly form from the perception of objects.

Example: whistle, ringing phone, boiling water

Mediate – a term is formed through further deliberation, evaluation or scrutiny of the object.

Example: Higgs Boson particle, Metaphysics, GMA-ABSCBN rift, Pheochrocytoma

According to Quality A. positive

i. Form and Meaning

Ex. Life, justice, wisdom, power, freedom

Example: death, ignorant, evil, hate, jealousy Negative – negation of the original term with

the use of prefixes or suffixes, viz., un-,il-,im-,dis-,dys-,mis-, non- and less

Form and Meaning, e.g., unwise, illegal, invalid, dishonest, misbehave, impolite, lifeless

Form and not in Meaning, e.g., infinite, undivided, independent, impartial

Definition of terms Definiendum – term to be defined\ man Definiens – defining term\ a rational animal Denontata – extension of the term\ Juan Types of Definition 1. nominal – expresses what the name means Ex. Euthanasia – derived from the Greek

words eu ‘good, happy, or well” + thanatos‘death” w/c means “ a happy death”

Benevolent came from the Latin words bene“good” + volens (voluntas) “will”, which means “goodwill”

Real definitions – refers to a definition of a term in the way it is standardly used in language. It is also to state the conventional, dictionary meaning.

Ex. Pastel – means a color having a soft, subdued shade. / netizen – refers to a user of the internet, esp., a habitual or avid one.

Process in Judgment Apprehension of concepts – ideas and terms are

placed in the first stage. Mental comparison of concepts – ideas and

terms are compared to each other whether it is identical or different from each other.

Mental predication – pronouncement of identity or non-identity.

Written predication – stage of expressing an enunciation in a form of verbal statement. We call it a “proposition”

Diagram example: Ideas of “apple” and “fruit” – apprehension “apple” vs “fruit” – comparison/identification “apple” = “fruit” – identical predication/

agreement Apple is a fruit – written predication/assertion

It gives a direct and unconditional assertion of the affirmation or denial of something.

A declarative sentence Basic Elements of Categorical Proposition Subject term – part of proposition about which

something is affirmed or denied. Predicate term is the part of the proposition

which signifies what is affirmed or denied of the subject.

Copula – is the part of the nproposition which either joins or separates the verb “to be”.

Ex., Particular Quantifiers: A lot of , almost all, few, majority of, many,

most of, much, not all, not every, some Universal Quantifiers: All, any, anybody, each, every, everything,

no,none, no one, nobody, nothing, whatever QUALITY OF CATEGORICAL PROPOSITIONS Affirmative Propositions I am very ambitious individual, Few birds are

chirping, All deep thinkers are philosophers.

Negative Propositions None of them are pagans, Every library is not

a playground, not all celebrities are mesmerizing, an angel is not a devil.

COMBINATIONS AND SYMBOLS OF CATEGORICAL PROPOSITIONS

Universal ------------------- Affirmative Particular ------------------- Negative

Universal + Affirmative = A Universal + Negative = E Particular + Affirmative = I Particular + Negative = O

LETTER TYPE FORMAT

A and I Universal/Particular All S is P.

E and O Universal/Particular Propositions

Some S is not P.No S is P.

The result from the merger of these propositions are represented by the symbols A, E, I, and O. These vowels are lifted from the Latin words “AFFIRMO” – I affirm and NEGO – I deny.

Affirmative Negative

Universal A E

Particular I O

LETTER TYPE FORMAT

A Singular or Universal Affirmative

propositions

All S is P.

E Singular or Universal Negative propositions

All S is not P.No S is P.

I Particular Affirmative Propositions

Some S is P.

O Particular Negative Propositions

Some S is not P.Not all S is P.

A-form (Singular or Universal Affirmative) All S is P Ex. All voters are citizens.

▪ All governors are politicians.

E-form (Singular or Universal Negative)

All S is not P. or No S is P.

ex. No fly is bee.

I am not God.

I-form (Particular Affirmative) Some S is P. Ex. Some Filipinos are living in USA. Some universities are non-sectarian.

O-form (Particular Negative) Some S is not P. or Not all S is P. Ex. Some priests are not married. Not all habits are guilty.

Categorical propositions are in standard form only if they appear in the following way:

All S are P. All members Included e.g: All spiders have 8 legs.

No S are P All members Excluded e.g: No dogs are fish

Some S are P. Some members Included e.g: Some human beings are

astronauts

Some S are not P. Some members Excluded e.g: Some people are not

banker robbers.

Fishes swim. REDUCTION: Fishes swim

The fishes are swimming creatures(the subject) (copula) (predicate)

I bought this book.Possible Reductions:

I am the one who bought this book.

I am the person who bought this book.

Mr. Santillan will give the exam today. Mr. Santillan is the one who will give the exam today.

John sells newspaper. John is a newspaper seller.

A few students participate to UAAP. Few students are AUUP participants.

Some bitter persons can be broken hearted. Some bitter persons are broken hearted people.

Reduce the following propositions to Standard Form.

1. Finders, keepers. 2. Martha sings a song. 3. All owls do not swim. 4. The guest came. 5. Filipinos like to hug. 6. Centipedes have many legs. 7. Black ants do not bite. 8. Telephone coordinators are generally cordial. 9. If you work, then you’ll work. 10. No ID, No entry

Who Works Where? Alex, Betty, Carol, Dan, Early, Fay, George and Harry are eight employees of

an organization

They work in three departments: Personnel, administration, and Marketing with not more than three of them in any department.

Each of them has a different choice of sports from Football, Cricket, Volleyball. Badminton, Lawn Tennis, Basketball, Hockery and Table Tennis not necessarily in the same order.

Dan works in admin and does not like either Football or Cricket. Fay works in Personnel with only Alex who like table tennis. Earl and Harry do not work in the same dept. as Dan. Carol likes Hockey and does not work in Marketing. George does not work in Admin and does not like either Cricket or

Badminton. One of those who work in admin likes Football. The one who likes Volleyball works in Personnel. None of those who work in admin likes either Badminton or Lawn Tennis.

Harry does not like Cricket

Who are the employees who work in the Administration Department?

In which Department does Earl work?

Identify the truth value of the following “propositions”. Write V-valid and IN-invalid statements.

_____ 1. All birds have wings. _____ 2. All movies have directors. _____ 3. Some tragedy stories are happy ending. _____ 4. Few spiders are poisonous. _____ 5. Majority of Lyceans are Lasallians. _____ 6. Almost all band members are drug addicts.

_____ 7. Some actors are engineers. _____ 8. Few gadgets are made of plastics. _____ 9. Most uncles are masculine. _____ 10. A lot of people love to drink water. _____ 11. Each child has a toy. _____ 12. Some nightmares are good dreams. _____ 13. All wives are mothers. _____ 14. Few laptops are netbooks. _____ 15. No welders are women.

_____ 16. All cell phones are phones. _____ 17. Not all hospitals are accredited by Philhealth. _____ 18. No books are notebooks. _____ 19. Every house has lights. _____ 20. Few shoes are made of rubber.

TEST II. Identify the following proposition if it is A-universal affirmative, E-universal negative, I-particular affirmative and O-particular negative

_____ 1. All vampires are blood-suckers. _____ 2. Not all blood-suckers are mosquitoes. _____ 3. Majority of vegetables are twining plants. _____ 4. A fish is not a reptile.

_____ 5. Few nurses are doctors. _____ 6. A lot of tablets are rechargeable. _____ 7. Each transformer is robot. _____ 8. No Filipinos are Polish. _____ 9. A lot of men are not emotional. _____ 10. Almost all snakes are venomous. _____ 11. Every ant has a colony. _____ 12. Robin Williams was a versatile actor. _____ 13. Some cheaters are liars. _____ 14. All womanizers are men.

_____ 15. Most animals have four legs. _____ 16. She is not a boy. _____ 17. All bags are not clothes. _____ 18. Some foods are delicious. _____ 19. Majority of voters are citizens. _____ 20. Few Filipinos love to eat raw foods.

Test III. Provide the missing term for each propositions. Consider the “truth value”

(2 points each)

1. All people have_______________. 2. Some animals are ______________. 3. Almost all birds are _____________. 4. Not all cellphones have _________. 5. A lot of insects are ______________.

6. All _________________ are poisonous. 7. Not all ______________ are expensive. 8. Majority of _______________ are dying. 9. Some _______________ are not artistic. 10. A lot of _____________ are not athletic. 11. Few ___________ are ______________. 12. All _________ are not ______________.

13. The ___________ is a _________________. 14. Few ___________ are ________________. 15. All ____________ are _________________. 16. _______ babies have _________________. 17. _______ of students are ______________. 18. _______ computers are _______________. 19. _______ animations are not ___________. 20. _______ girls do not have _____________.

Is a compound proposition which contains aproposed or tentative explanation. It doesnot affirm or negate. It comprisessuppositions or clauses which are conditionedor dependent on each other with regard totheir truth value. It uses conjunctions,connective or conditional markers (copulas)to unify its propositions, such as if-then,either-or, not both, and cannot.

If it rains, then the roof gets wet. Either she is an angel or a devil. A thing cannot exist and not exist at the same

time.

CONDITIONAL PROPOSITIONS – is a hypothetical propositions in which the assertion of the truth of the consequent is dependent upon the condition established by the truth of the antecedent. it follows then, IF the antecedent is true THEN the consequent must also be true.

Examples:If he is asleep, then his eyes are closed. (antecedent) (consequent)

If the student completes his academic course, then he will be graduated.

If we had not eaten, then we would be hungry. If you kiss me, then I will hug you.

Is a hypothetical proposition which affirms thepossibility of one or more of the alternativesor suppositions to be true. This type ofproposition expresses a disjuncts (alternant)all of which cannot be true or false togetherbut one must be true and the other (orothers) false.

DISJUNCTIVE INDICATOR:Either . . . or

A body is either in motion or at rest.Either you are alive or dead.

KINDS OF DISJUNCTIVE PROPOSITIONS

1. Perfect Disjunction – mutually exclusive to each other. The other part must be true, but both cannot be true. It must be one or the other.

a. Disjuncts are contradictoryb. One must be truec. Both cannot be true nor false together at the same

time.

Imperfect Disjunction – is a kind of disjunctivewherein the two enunciations are so related thatone must be true but both may be true. If youdeny one member, you must affirm the other.However, you can still affirm one memberwithout being forced to deny the other.

a. One must be trueb. Both may be truec. Deny one, affirm the otherd. Affirm one, not be forced to deny the other.

Examples:

John is either eating or watching. Either you are writing or listening. God is either just or merciful.

CONJUNCTIVE PROPOSITIONS – is a hypothetical proposition which asserts that the two alternatives cannot be true at the same time. It denies the possibility of the two conjuncts to exist simultaneously in the same subject at the same moments of time.

Examples:

You cannot jump and walk at the same time.

One cannot be in EAC and DLSHSI at the same time.

Both day and night cannot happen in the campus simultaneously.

He cannot be an elementary student and a RAD college student at the same time.

One cannot be studying in the classroom and eating at the canteen at the same time.

Write Sir if the conditional is true and Me if false.

1. If you are not dead, then you are alive.2. If John is my brother, then I am his sister.3. If God created humans, then he loves humans.4. If God exists, then the world exists.5. If there is an effect, then there is a cause.6. If you sleep early, you’ll wake up early.7. If you’ll study, then you’ll pass the subject.8. If you leave home early, you won’t be late for school.9. If you tell the truth, you will not feel guilty.10. If you will allow me to kiss you, you will not regret it.

1. Either you come to school or you stay home.2. Either you are my son or I am not your father.3. You are either worried or you are not.4. The statement is either true or false.5. The dead may either be in heaven or in hell.6. The President is either be a Catholic or a

Protestant.7. The tree is either too low or too high.8. Either you say yes or you say no to the proposal.9. The bird is either a parrot or an eagle.10. Today is either your birthday or not.

1. No one can be a sinner and a saint at the same time.2. A person cannot be asleep and awake at the same time. 3. We cannot have morning and evening at the same time.4. No one can drink and eat at the same time.5. No one can laugh and cry at the same time.6. You cannot close your fist and open it at the same time.7. A man cannot walk and run at the same time.8. A teacher cannot pass or fail a student at the same time.9. You cannot be a scholar and a moron at the same time.10. Something cannot be possible and actual at the same

time.

Ambiguous words The meaning shift and change within the course of

argument.

EQUIVOCATION – fallacy of four termsEx. Love is blind.

But, God is love.Ergo, God is blind.

You’re like a denture.Because, I can’t smile without you.

Amphiboly – this fallacy is committed when an argument uses statement that are unclear because of the loose, ambiguous, obscure or awkward way in which the words are combined creating moe than one meaning.

Ex. Free children below five with coke can enter.▪ She cannot bear children.

▪ Q. How can you drop a raw egg onto a concrete floor w/o cracking it?

▪ A. Concrete floors are very hard to crack!

It lacks proper punctuation and it placed differently in different phrases.

Ex. A woman without her man is nothing.▪ Boy: a woman, without her man, is nothing.

▪ Girl: no, it should be, a woman: without her, man is nothing.

▪ Two people were arguing how to read the sign. It says

▪ The panda eats shoots and leaves.

▪ The panda eats, shoots, and leaves.

The fallacy is committed when a conclusion is drawn about a whole based on the features of its constituents when, in fact, no justification provided for the inference.

Ex. Atoms cannot be seen by the naked eye.▪ But, humans are made up of atoms.

▪ Therefore, humans cannot be seen by the naked eye.

▪ Henry Sy is a millionaire.

▪ But, Henry Sy is a Filipino.

▪ Therefore, Filipinos are millionaires.

It assumes the truth of the conclusion 1. Hasty Generalization – when one considers certain

exceptional cases and generalizing to a rule that fits them alone.

Ex. Eating dried fish is not good (because it cause allergy to some), Therefore, let us not eat anything that is dried (vegetables, tea, coffee, wheat)…

▪ Pilo is from the province of Cavite.

▪ Pilo is a topnotcher in the bar exam.

▪ Therefore, all people from Cavite are topnotchers.

Providing a premise or a statement which has the same meaning as the conclusion.

Ex. Why are you absent yesterday?

▪ Because, I was not present.

▪ Why are you late for school?

▪ Because, I was not able to come to school early.

The analogy is not strong enough to support the conclusion.

Ex. Ang LOVE… Bob Ong: parang ELEVATOR lang yan. Bakit mo

pagsisiksikan yung sarili mo kung wala ng pwestopara sayo. Meron naman HAGDAN ayaw mo langpansinin.

Some students are like nails. Just as nails must be hit in the head in order to make them work, so must students.

When an argument mistakenly attempts to establish a casual connection between events which are not really causally correlated.

Ex. My friend met an accident because it was Friday the 13th.

▪ My girlfriend broke up with me because I woke up at the wrong side of the bed this morning.

Two or more implicit assumptions are inclusive in one logical question but only one answer is allowed.

Ex. Have you stopped smoking?

▪ Were you late yesterday because you went to your girlfriend’s house before going to school?

▪ Did you commit murder using your right or left hand?