Logic Week 2 Lecture

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    The Art of Correct Thinking

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    Simple Apprehension

    Judgment

    Reasoning

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    MentalOperations

    MentalProduct

    External Sign

    SimpleApprehension

    Concept Term

    Judgment Enunciation Proposition

    Reasoning Argument Syllogism

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    Taken from theLatin word prehenderewhich meansto siezeThe first operation

    of the human mind

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    The operation of themind by which wementally grasp a thing,making it present in & to

    our minds withoutaffirming or denyinganything about it

    the operation by whichwe grasp the essences ofthe things

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    Error in Simple ApprehensionIndistinctiveness

    Arise either due toimperfections of our faculties

    limited knowledge of objects

    which form our conceptions

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    Object of SA refers to what we grasp bysimple apprehension

    Material Object the whole thing that is known by SA the thing as itself & w/ all its attributes

    Formal Object the essences or quiddities of things what is known about M.O. through the useof some faculty

    SA grasp only what a thing is

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    Concept

    product which SAproduces within the mind

    as means of knowing theessences of things

    The mental expression ofan essence or quiddity

    pure image or sign; function asgiving knowledge of whatever it

    signifies

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    Concept

    the representation of anobject by the intellect throughwhich man understands or

    comprehends a thing

    An idea that starts with an

    object reality and apprehendedby the senses

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    Kinds of Concept First Intention

    A concept by which we understand what athing is according to what it is in reality,independent of our thinking about it

    Second Intention

    A concept by which we understand NOTonly what a thing is in reality but alsohow it is in the mind

    e.g. Man is rational being

    e.g. Man can either be male or female

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    Kinds of Concept Concrete Concept

    A concept which expresses a form and asubjectConcrete- can be perceived by the senses

    Abstract Concept

    A concept which has form ONLYForm- refers to abstract quality, intangible,can not be perceived by the senses

    e.g. intelligent student, black dress

    e.g. intelligence, blackness, loyalty

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    Kinds of Concept Absolute Concept

    Signifies the meaning of completesubstance endowed with its independentreality

    Connotative Concept

    Signifies the object as an accidentexisting in a substancePresent a form without a subject

    e.g. Man, God, Society

    e.g. kind person, beautiful dress

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    Kinds of Concept Positive Concept

    Signifies the existence or possession ofsomething

    Negative Concept

    Signifies the non-existence or non-possession of something

    e.g. Alive, rational

    e.g. Death, irrational

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    Refers to theprocess of Formation

    of ideas

    also known asIDEOGENESIS

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    Preliminaries

    Human Person a rational being who cancognize;

    Sensitively needs senses for operation senses know only the accidentalqualities come in contact only with what appearson the surface know the things as it appear BUT can

    not know what it is

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    Intellectuallyfunctions without bodily organ knows the essence of reality

    knows NOT only the accidents

    but also its substance immaterial & can not come indirect contact with material realities

    & has to make use of sensory data

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    The object of Intellect

    is the abstract anduniversal essence ofsensible realities

    The Formation of ideas

    thefundamental operation ofthe intellectrequires that sense have tofunction first

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    Thing

    Externalsenses CommonsenseProper

    CommonSensibles

    PERCEPT

    SENSIBLE ORDER

    impressedspecie in S.O

    imaginationcognitive sensesense memory

    PHANTASM

    expressedspecie in S.O

    containindividuating,concretequalities

    containindividuating, concretequalities

    individualized

    form in S.O

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    INTELLECTUAL ORDER

    discardsindividuatingcharacteristics

    both

    receptive &reactive

    abstractednature taken in bypossible intellect

    AGENTintellect POSSIBLEintellectPower to abstract Power to understand

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    gathers from objective realties proper& common sensiblescommon sense unifiedthem intoperceptual wholes

    External Senses

    Perceptthe form of the object as it exist in thesenses

    called impressed specie because it is theresult of the operation wherein qualitiesof the object are taken in by externalsenses & IMPRESSED upon the mind in the

    presence of objective reality

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    Phantasm

    the image which is an EXPRESSED speciein sensible ordercalled expressed because it is amanifestation of the representative powerof the internal senses

    to be understood by the intellectual itsindividualized form MUST be converted intosomething intelligible

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    The Human Intellect

    Agent IntellectPossible Intellect

    Power to abstract

    Power to understand

    Receives impressed specie, grasps andunderstand it

    Expresses its understanding by producingan Idea or concept

    A formal sign which represent

    the being or essence of the

    object known

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    What is truth?

    Adaequatio intellectus et rei (St.Thomas Aquinas, Summa Theologiae Iq. 21a. 2c)

    the conformity between theintellect and reality

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    Term

    the external representationof a concept and the ultimatestructural element of a

    proposition

    may be oral or written orprinted

    in logic it is always a sign of aconcept or an idea

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    Classification of TermsUnivocaltermsIf exhibit similarity in meaning

    or signification when used in at

    least two occasionse.g. Francis Bacon is a philosopher.

    Frederich Nietzsche is a philosopher.

    e.g. The Pope is a man.Mao Tse Tung is a man.

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    Classification of Terms

    e.g. Her boyfriend gave her a ring.The bells ring.

    Equivocal termsIf exhibit difference in meaning orsignification whenever they are used in

    at least two occasions

    e.g. You should see her bend over theflower at the bend of the road.

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    Classification of TermsEquivocal terms

    Can be known by considering the threeprocesses

    e.g. resume- resume; lead - lead

    Spelling aloneSame spelling, differentpronunciation, different meaning

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    Classification of TermsEquivocal terms

    e.g. made-maid; seek-sick; sale-sail

    Sound alone

    Same pronunciation, differentspelling, different meaning

    Both sound & spellingSimilar sound & spelling butdifferent meaning

    e.g. match-match; right-right; light-light

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    Classification of Terms

    e.g. Orange (a fruit) &orange (color)land (ground) &land (to set down)

    health ---with primary meaning

    health----with secondary meaning

    Analogous termsexpress partly the same & partlydifferent meanings when used in at

    least two occasionsProportionality & attribution should benoted

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    Term

    Comprehension of a Term the sum total of all the notes( theelements that comprise the

    significance of an idea) whichconstitute the meaning of a concept

    Extension of a Term the sum total of the particularsto which the comprehension of aconcept can be applied

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    JUDGMENTANDPROPOSITION

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    MentalOperations

    MentalProduct

    External Sign

    Judgment Enunciation Proposition

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    What is

    Judgmentand

    Proposition?

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    The second operation

    of the human mind

    a mental process of

    transferring from the ideal orderto the real order

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    the act whereby the

    intellect compares twoideas noting theiragreement or disagreement

    and either combines or

    separates them

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    defines as the act by which themind affirms or denies something

    about something else

    that which is deniedor affirmed by the other

    that to which it issaid to belong or not to

    belong

    known as

    Attribute

    known as

    subject

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    the act by

    which themind affirmsor denies an

    attribute ofa subject

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    express in sentence known asproposition, the product of

    judgment

    needs simple apprehensionsince without ideas to be

    compared NO judgment cantake place

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    the external sign of judgment

    Defines as a statement whichaffirms or denies somethingabout a certain reality or object.

    Often formulated in declarativeform

    A triangle is a three-sided figureSUBJECTATTRIBUTE

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    The third operation

    of the human mind

    a mental process wherein the

    intellect arrives at new judgmentor at a new truth by usingjudgment previously known

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    in this act or mental

    process, the mind or theintellect advances fromone thing understood toanother- ( engaged in

    mental discussion)

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    the reasoning from the particular to

    universal; from specific instances to theformulation of general principles; fromcause to effects

    Induction

    a.k.a.

    A POSTERIORIreasoning

    methods of reasoning employed byphysical sciences; chemistry, biology,

    medicine

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    the reasoning from the universal tothe particular; from laws to their

    operations principles; from causes toeffects

    a.k.a A PRIORIreasoning

    Deduction

    method used in mathematical &philosophical sciences

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    The Basic

    Elements ofCategoricalProposition

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    In Logic

    there are many kinds of propositions :A. categorical or attributed

    B. hypothetical

    C. existential or non-existential

    D. simple or compound

    Here we will treat first the categoricalproposition

    Introduction.

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    Categorical or attributive propositionhas basic elements:

    a.the subject

    b. the predicatec. the copula

    Ex. The story he told you is apocryphal.

    the subject the predicatethe copula

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    About the SUBJECT... it is the one spoken of

    the one about whom or which something isdenied or affirmed

    About the PREDICATE

    it is what is affirmed or denied of thesubject

    About the COPULA it links the subject with the predicateit is the verb to be: is, am, are (affirmative)

    is, am, are not (negative)

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    For purposes of Logic

    tenses are irrelevantthe copula is should be taken in a tenseless

    sense

    its past and future forms are usually considered

    part of the predicate

    ex. Magellan was the discoverer of the Phils.

    In logic Magellan is the Spaniard who

    discovered Phils.

    Red China will be the country to watch.

    In LogicRed China is the country we shall

    have to watch.

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    It is also important

    to note that in Logic:

    number is irrelevant

    like A horse is an animalit is equivalent to

    all horses are animalsno distinction is made between

    horse and horsesand between

    animal and animals

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    The quality of proposition is determinedby the quality of the copula

    Affirmative

    whenever the predicate term acceptssomething of the subject term

    Negative whenever the predicate term negates ordenies something of the subject term

    e.g. All roses are flowers.

    e.g. A squash is not an eggplant.

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    THE quantity of the proposition is equivalent to the

    quantity of its subject

    it is SINGULAR if the subject stands for a single

    definite individual or group

    it is PARTICULAR if the subject designates an

    indefinite part of its total extension

    it is UNIVERSAL if the subject can apply to every

    portion signified by the term

    Examples:

    Singular : Shakespeare is Englands greatest dramatist.

    Particular: Some prima ballerinas are not Margot Fonteyn

    Universal: Love is a many-splendored things.

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    a. Singular

    - stands for a single definiteindividual or group.

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    1. Proper Noune.g. Karl, Vladimher, DLSHSI etc

    2. Nouns modified by adjectives insuperlative degree

    e.g. first, worst, most charming etc.

    3. Demonstrativese.g. this and that

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    4. Collective Nouns

    e.g. a] flock, orchestra, audience

    b] A hundered balloons filled the ceilingc] A thousand people jampacked the gym.

    5. The article Thee.g. the gentleman in barong tagalog.

    the restaurant across the street.6. Personal Pronouns

    I, you, they, we, he, she, my etc.

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    b. Particular

    - a term is particular whenit stands for an indefinite

    part of an absoluteextension.

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    1. Indefinite pronouns and adjectives

    like Some, several, many, few, most2. Use of Numbers

    like Seven, nine, one, four

    3. Articles A and An4. General propositions

    like Filipinos are hospitable.

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    c. Universal

    - a term is universal

    when it stands for every

    subject signified.

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    1. Universal expressionslike All, ever, each, whatever, whoever, no,

    whichever, without, exception, everything.2. Universal ideas

    like Men are mortal.3. the articles the, a and an if the idea is

    universal

    note: articletheissingularif it refers to definite individual or groupit isuniversalif it refers to universal idea.

    articlea and anareparticularif they connote an indefinite part of

    absolute extension; it isuniversalif they connote universal ideas

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    Proposition[symbol]

    Quantity Quality

    A Universal orSingular

    Affirmative

    E Universal orSingular

    Negative

    I Particular Affirmative

    O Particular Negative

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    Is entirely different from the quantity ofthe proposition

    to determine the quantityof thepredicate, the point of reference will be thequality of the proposition, whether

    affirmative or negative

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    Particular

    if the quality of the proposition is affirmative,the quantity of the predicate is automaticallyparticular

    if the quality of the proposition is negative,the quantity of the predicate is automatically

    universal

    Universal

    This modern technology is the solution

    to our problem

    Most ideas are not expressed

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    Symbols and theCategoricalStatement

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    Since the time of Aristotle there have been attempts to make logic a scienceof symbols to achieve shortcuts to correct reasoning. Among these are

    symbols for the four categorical statements namely:Astands for universal or singular and affirmative statements

    E - stands for universal or singular and negative statementsIstands for particular and affirmative statements0stands for particular and negative statements

    A E

    I 0

    universal / singular

    affirmative negative

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    MODEL STATEMENTS

    A1. all roses are flowers2. every cloud has its silver lining

    3. every man is being-for-death

    4. wherever you go, I go

    5. whoever wins will be awarded

    a trip to Hongkong

    6. whatever will be, will be

    7. all of us in this room are Filipinos8. everything is in a flux

    E1. no atheist is a believer of God2. no bird has four legs

    3. love of country is not a

    commodity for sale

    4. none of the invited top brass has

    showed up

    5. I never said he was a crook

    6. he loves me not7. a squash is not an elephant

    8. no pill box is a safe weapon

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    MODEL STATEMENTS

    I1. some philosophers are essentialist2. several philosophers are

    existentialists

    3. most cultures are deeply religious

    4. Filipinos are music lovers

    5. quite a few tourists are

    knowledgeable of our scenic spots

    O1. some dogs are not black2. not all women are fickle

    3. a few Filipinos are not literate

    4. Many Americans are not rich

    5. Not all that shines are gold

    6. most Russians are not communist

    party members

    7. some things are not edible

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    o No Filipinos is unmindful for his beloveddead.

    o Dozens of flowers are gifts ofremembrance.

    o Many faith healers are fake.o Every man is a homo viator [traveller].o No man is an island.o All men are beings for death.

    o Our guardian angels are powerfulprotectors.

    o Not all spirits are good

    Identify what symbols are the ff prop. and why:

    All t ffi i l t l b iti

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    Subject term Predicate

    termQuantity of

    propositionQuality of

    the Prop.Symbol Quantity

    of the

    predicate

    Government

    officialsNatural-

    born

    citizens

    Universal Affirmative A Particular

    Involuntary act Consciousact

    Universal Negative E Universal

    Movie directors Passionate Particular Affirmative I Particular

    Commentators Objective Particular Negative O Universal

    All government officials are natural-born citizensNo involuntary act is a conscious actSeveral movie directors are passionate

    Not all commentators are objective

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    1.

    2.

    3.

    4.

    5.

    6.

    7.

    8.

    9.

    Subject

    term

    Predicate

    termQuantity of

    propositionQuality of

    the Prop.Symbol Quantity of

    the

    predicate1.

    2.

    3.

    4.

    5.

    6.

    7.

    8.

    9.

    10.

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    The Logical Form

    Most of the propositions taken upfollow a consistent pattern i.e.

    S is P (SUBJECT-COPULA-PREDICATE).Those already adept in logic can easily translate,

    mentally, any proposition into a

    standard-form categorical statement.But neophytes need more time to think and would so better if they write downthe propositions in their logical form.

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    AProposition:1. Avoid using the word one in your predicate for it is vague and

    indefinite.

    ex. Mario is the one who sells newspaper

    Mario is a newsboy

    2. Avoid using redundant terms.

    ex. Shakespeare is the writer who wrote Macbeth

    Shakespeare is the author of Macbeth

    3. whatever, whoever and only, be replaced by ALL

    ex. a. Whatever is material will decay

    all things which are material are [substances] whichwill decay

    b.whoever is hungry will be fed

    all persons who are hungry areto be fed

    c. only family members will be admitted

    all those who will be admitted arefamily members

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    EProposition:1. None, nothing, nowhere and other negative word are

    interchangeable by NO and should follow the S is/are P

    pattern.

    ex. a. No crocodiles fly

    No crocodiles are flyers

    b. none of the guests came

    no guests are [people] who came

    c. nothing that is a plant is an animal

    no plants are animals

    d. nowhere that he goes is decentno place that he goes to is decent

    e. there are no men with tails

    no men are with tails

    *sometimes linguistic distortion are unavoidable in

    reducing propositions to their logical form.

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    IProposition:1. the quantifier some is interpreted as at least one possibly more,

    hence the copula can be is or are.

    ex. some broken hearts can be mended

    some broken hearts are mendable

    2. many, several, a few, most and other indefinite quantifiers are

    interchangeable by some.

    ex. A dog barked furiously last night

    some dog is an animal who barked furiously last night

    -there are inefficient teachers

    some teachers are inefficient

    -a few students go to concerts

    some students are concert goers

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    OProposition:1. several student radicals have not traveled to Red China

    several student radicals are not travelers to Red China

    2. All glib talkers are not intelligent

    some glib talkers are not intelligent

    3. we saw the zarzuela and did not enjoy it

    some of us are not happy with what we watched, the zarzuela.

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    I and OProposition:1. a few students go to concerts

    some students are concert goers [ I ];

    the others are not concert goers [ O ]

    2. all except, all but, as well as quasi-numerical quantifiers such as

    almost all, not quite all, and almost everyone are quite vague.ex. Almost everyone is a card-carrying member

    may mean, some are card carrying members;

    it can also mean, some are not card-carrying members

    all but her friends are invited;may also mean, no enemies of her are invited.

    3.hence, for claritys sake, we shall consider such statements as

    referring to two joint categorical proposition.

    Schematic Formulations

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    Schematic Formulations[Venn Diagram]

    A Every S is P

    All S are P

    ENo S is PS is not P

    I Some S is PSome S are P

    0Some S is not P

    Some S are not P

    universal or singular and affirmative

    universal or singular and negative

    particular and affirmative

    particular and negative

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    Some Reminders:1. The E may have either is or are depending on the

    subject.

    2. The some is indefinite and, thus, may take on the is and

    are copulas again depending on the subject.

    3. In reducing proposition to logical form, keep in mind the ff:

    3.1 keep the original subject

    3.2 do not use the progressive tense for your predicate

    3.3 avoid using the word one

    3.4 avoid redundancies

    3.5 be simple and direct in your answers