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INTRODUCTION
The Study of Logic
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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
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- 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
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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
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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
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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
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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
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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
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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
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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
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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
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Kinds of concept 4.Positive Concepts: signifies the
existence or possession of somethingEx. happy
Negative Concepts: signifies the absence of something
Ex. sad
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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.
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Concept I or II C or A A or C P or N
1.
2.
3.
4.
5.
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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.
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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
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The termEXAMPLE:
Hilda is a (nun).
subject
predicate
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Ex.
Bats are flying creature.
Logic is a science that deals with the study of correct reasoning.
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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
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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
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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
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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.
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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
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Seatwork#3 Arrange the ff. from greater
comprehensiont o lesser extension1. Pedro, Filipino, Man, Asian, Brown
Race2. Square, Plane, Figure, Rectangle,
Polygon, Parallelogram, shape
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Answer to sw#3 1. Man 2. Plane Asian Figure Brown Race Shape Filipino Polygon Pedro Parallelogram
Rectangle Square
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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
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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
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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.
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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.
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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
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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
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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.
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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.
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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.
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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.
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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
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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
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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
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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
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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.
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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
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The proposition- A special type of sentence- An enunciation of truth or falsity- Verbal expression of mental judgment
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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
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exampleAll boys (are) future men.
Quantifier subject[S] copula[C] predicate[P]
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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.
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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
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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
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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
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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
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examplesA - Every monkey is an animal.E - No monkey is a human.I - Some monkeys are brown.O - Some monkeys are not brown.
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Logical diagramA PROPOSITION
PREDICATE
SUBJECT
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E PROPOSITION
SUBJECT
PREDICATE
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I PROPOSITION
SUBJECT
PREDICATE
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O PROPOSITION
SUBJECT
PREDICATE
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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.
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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.
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SQUARE OF OPPOSITIONCONTRARY
SUBCONTRARY
SUBALTERN
SUBALTERN
CONTRADIC
TO
RIES
A E
I
O
CONTRADICTO
RIES
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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.
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Examples:A - All men are rational, therefore
O - some men are not rational.
I – Some students are girls, therefore
E – No students are girls.
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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
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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.
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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 [ ? ]
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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.
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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 [ ? ].
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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.
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exampleA- All triangles are planes with three sides, therefore
I- Some triangles are planes with three sides.
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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 ].
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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 [?]