Sequential Logic Building Blocks – Flip-flops (Week 9 – Lecture 1 of 1)
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