Introduction to Logic 4.

Aesthetics: Beauty and taste, and nature of art

Philosophy: The Root of Logic 5. Philosophy of the Human Person: Human

person as an individual, its nature, existence,
What was your “WHY” question when you were a kid?
and essence
What is your ultimate “WHY” question
6. Philosophy of Religion: Religious beliefs,
Definition of Philosophy doctrines, arguments, and history

Pythagoras: 7. Social, Political, and Legal Philosophy: Social

behavior, politics, government, laws, rights,
Philosophy = philos + sophia justice, and other related concepts
(love) (wisdom) Practical Fields
=“love of wisdom” 1. Ethics: Moral philosophy; moral standards and
Aquinas: conduct

“Knowledge of all things through their ultimate 2. Logic: Reasoning and critical thinking
causes acquired through the light of reason” Special Branches
Greek: Conscious desire and will to pursue wisdom and 1. Philosophy of Education
to discover the truth
2. Philosophy of Mind
Hindu: Objective and practical realization of truth
3. Philosophy of History
Chinese: Application of wisdom to attain the truth
4. Philosophy of Science
Islam: Knowledge leads to the understanding of God
(and his works), the creator of all things. 5. Philosophy of Law

Pythagoras: Three types of man: 6. Philosophy of Language

 Lover of pleasure

 Lover of success

 Lover of wisdom Mental Exercise:

A man carries his son into the hospital because his son
has a nail in his foot. The surgeon then walks in and
Among those types, which is the superior? says, “I cannot operate on this boy as he is my son”.
Why lover of wisdom, instead of being wise? What is the relation of the surgeon to the boy?
Can’t we be wise? Mental Exercise:

1. A basket contains 5 apples. How would you

Process of Philosophy divide them among 5 kids so that each one has
an apple and one apple stays in the basket?
Fields of Philosophy
Mental Exercise:
Speculative Fields
1. A basket contains 5 apples. How would you
1. Metaphysics: Fundamental nature of all reality divide them among 5 kids so that each one has
2. Epistemology: Nature and scope of knowledge an apple and one apple stays in the basket?

3. Cosmology: Inanimate beings in the universe

Logic: The Art and Science of Reasoning

As an art: It requires the performance of correct

reasoning and critical thinking
Brief History of Logic
As a science: It seeks causal knowledge to distinguish
 Greek Logic: Aristotle, founder of Logic; Zeno,
what is true from false based on scientific rules.
coined the term “logic”; Porphyrius
As reasoning: It guides humans to arrive at sound
 Hindu Logic
(valid and true) and cogent (convincing, clear, and
conclusive)reasoning.  Chinese Logic
 Formal logic- focuses on form of the details or  Islamic Logic
sequence of the logical process to achieve
validity (correctness)of an argument  Medieval Logic

 Material logic- truth content of an argument that Modern Logic:

corresponds to what is in reality  Francis Bacon: Inductive reasoning
Formal Logic  Gottfried Wilhelm Leibniz: Principle of Identity
 Ex. 1: All men are mortal. and Principle of Sufficient Reason

But Socrates is a man.  George Boole: Symbolic logic

Therefore, Socrates is mortal.  Friedrich Ludwig Gottlob Frege: Foundation of

 Ex. 2: All kids are rich. Mathematics
But Socrates is a kid.  Alfred North Whitehead and Bertrand Russell:
Therefore, Socrates is rich. Mathematical truths
 Ex. 3: All men are mortal.

But Socrates is a man.

Significance of Logic
Therefore, Aristotle is mortal.
• To be critical and rational
Formal Logic: Valid or Invalid?
• To improve reasoning based on correct
Ex. 1: A ruler is 12-inch long. inferences
But Gloria is a ruler. • To detect and avoid errors in arguments
Therefore, Gloria is 12-inch long. • To develop open-mindedness and cautiousness
Ex. 2: Carabaos have no teeth. • To argue from knowledge, not ignorance
But my grandfather has no teeth. • To improve planning
Therefore, my grandfather is a carabao. • To enhance creativity
Material Logic • To refrain from jumping to conclusions
Ex. 1: All humans are mortal. • To lead us in our search for meaning and truth
But you are a human being. • To serve as a tool for social transformation
Therefore, you are mortal.

As critical thinking: It allows to think through meeting

the intellectual standards, overcoming barriers,
avoiding fallacies, and developing sound arguments.
Course Material in GEED 20143 - Business Logic  According to Extension
1. Singular – refers to a single term or definite
Mental Phases/Acts of the Mind individuals or things (proper nouns, demonstrative
pronouns/adjectives, superlative adjectives, personal
First Phase: Simple Apprehension pronouns, articles, collective terms, articles with
singular idea)
First mental act or process in which the mind e.g. Polytechnic University of the Philippines
perceives or grasps the essence or nature of my teacher
something without affirming or denying anything This laptop
about it most diligent
It answers the question, “What is it?” 2. Particular – indefinite part of a whole; does not
Apprehension operates in the following sequence: directly specify the number of individuals or groups that
1. sensation – making use of one’s senses in is referring to (indefinite pronouns/adjectives, general
perceiving external reality to produce a sense image propositions, numbers)
2. imagination – transforming sense image into e.g. some friends 52 cards
phantasm or the sensible and concrete image of an 3. Universal – represents the entire whole or can be
object applied to each member of a class (universal quantifiers,
3. abstraction/ intellection - extracting or putting a universal idea, articles with universal idea)
meaning to the imagined phantasm to produce an e.g. all Education majors each
idea candidate
4. verbalization/external manifestation – expressing
an idea into a verbal sign whether written or oral by  According to Intension/Comprehension
which the product is a term 1. Univocal – expresses the same meaning when applied
in different contexts; possesses the same spelling and
 Idea – mental sign that the mind perceives or notices same pronunciation
e.g. Animal (Dogs are animals. Pigs are animals.)
 Term – a conventional sign or verbal 2. Equivocal – terms with two or more meanings
manifestation/external representation that expresses a. partial equivocal – a term that expresses different
an idea or concept conventional meanings that are same in pronunciation
but not in meaning
Two Groups of Signs i. homogram – different meaning, same
1. natural signs – natural entities that signify something spelling, different pronunciation
with the pattern of the natural universe; meanings not e.g. bow (inclination of the head and arrow-
created by man launcher)
2. conventional signs – man-made physical entities ii. homophone – different meaning, different
spelling, same pronunciation
Two Properties of a Term e.g. right, rite, write sweet and suite
1. intension or comprehension – totality of the qualities b. complete equivocal – a term that expresses
that constitute the meaning of a term; expresses the different conventional meanings with same spelling and
essence of the object; also known as connotation pronunciation
e.g. Science is a systematized body of e.g. ruler (leader and measuring device)
knowledge. ring (jewelry or a phone noise or a boxing
2. extension – the totality of all the individuals or arena)
objects to which comprehension of a term is applied; 3. Analogous – meaning of a term can be partly the
also referred to as denotation same and partly different in at least two occurrences
e.g. Science is extended to Physics, e.g. good meal good
Mathematics, Sociology, Psychology, etc. grades
good mother good
 The greater the intension of a term, the lesser book
its extension; the lesser the intension of a term, good luck canned goods
the greater its extension.
 According to Components
Kinds of Terms 1. Simple – a term consisting of a single word only
 e.g. cat, house, computer e.g. cause and effect teacher and student
2. Complex – a term that is made up of several
component words or compound term  According to Quality
e.g. burning sensation, word of the day, blue-eyed 1. Positive
a. form and meaning
 According to Nature or Actuality e.g. wisdom, wealth, fame
1. Concrete – pertains to tangible things in reality b. form and not in meaning
e.g. umbrella, laptop, magazine e.g. ignorance, scarcity, sin
2. Abstract – pertains to non-material things 2. Negative (indicators are negation of the original term
e.g. empathy, patience, innocence using the prefixes or suffixes such as un-, il-, im-, dis-,
dys-, mis-, non-, and -less
a. form and meaning
 According to Formation or Origin e.g. non-sense, mistrust, unkind, illiterate, immature,
1. Immediate – a term that is directly formed from the dissatisfied, dysfunction, hopeless
perception of objects; also referred to as intuitive ideas b. form and not in meaning
e.g. crying baby, roaring tiger, table e.g. independent, flawless, unleash,
2. Mediate – a term that is formed through further
deliberation, mediation, analysis, evaluation and  According to Categories (Predicaments)
scrutiny of the object with its related concepts 1. Substance (essence)- has its existence in itself and
e.g. Philosophy, Reproductive Health Law, issue on for itself; can stand on its own
abortion e.g. plant, man
2. accidents – dependent on another substance for its
 According to Relation existence
1. Identical –terms that refer to the same intension or a. quantity (how much)
extension e.g. P50.00 24 hours
e.g. Jose Rizal and Philippine National Hero two meters
2. Different – terms that are non-identical and with no 3. quality (of what kind)
relation at all e.g. white or black hot, cold
e.g. shoe and cup loud,soft
4. relation (toward something)
3. Compatible – terms that can co-exist in the same e.g. creator adviser employer
object or they are associable terms friend
e.g. rich and famous hot and spicy 5. action (to make or do)
4. Incompatible – terms that cannot co-exist in the e.g. flying walking talking
same subject or they are opposed terms 6. passion (affection, to undergo)
e.g. being saved being held
 According to Incompatibility 7. when (time)
1. Contrary – opposite terms with several e.g. yesterday July 28,2017 at
intermediaries between them 4:00pm
e.g. high and low rich and poor 8. where (place)
2. Contradictory – opposite or mutually exclusive terms, e.g. in school at SM Alfonso
one of which affirms what other denies; there is no 9. posture (being-in-a-position)
middle ground e.g. lying sitting standing
e.g. life and death truth and falsity 10. habit (to have or be)
3. Privative – opposite terms, one of which signifies e.g. covered in blood in silky dress
perfection but the other denies such perfection armed with a gun
e.g. full and empty perfection and
imperfection  According to Predication (predicables)- logical
4. Correlative – terms that have a material/given classifications of universal terms that can be
relation to each other or one cannot be understood used as predicated to disclose the different
without the other; but incompatible or opposed to each features of things.
other to the point of excluding each other in the same 1.Genus – expresses a part of the essence of a thing
relation referring to a common feature of a class of species.
 e.g. Man is an animal. 1. subject term (S)- the one which is affirmed or denied
2. Specific difference – part of the essence which 2. Predicate term (P) – the action that affirms or denies
distinguishes one species form another the subject
e.g. Man is rational. 3. copula (C) – links the subject to the verb; linking verb
3. Species- expresses the complete essence of the ( in grammar); determines the quality of the proposition
subject. e.g. Logic (S) is (C) a science (P)
e.g. Man is a rational animal.
4. Property – species’ exclusive and necessary attribute Two Properties:
e.g. Man is capable of morality, religion, language 1. quality – relationship between the subject and the
and grammar. predicate terms, their agreement or disagreement as
5. Accident – attribute term which may or may not expressed by the copula verb be; can be affirmative or
belong to the subject negative proposition
e.g. Man is tall, brown and intelligent. Affirmative: Philosophy is the study of ultimate
causes.
Negative: The idea is not an external being.
Second Phase: Judgment 2. quantity – extension or the quantity of the subject
term of which the predicate term is affirmed or denied
Judgment – process of affirming or denying Singular proposition: Lorenzo Ruiz is the first
something about another thing by which the Filipino saint.
immediate product is called mental sentence of such Particular proposition: Several martyrs are
affirmation or denial Catholic saints.
Proposition – written or spoken statement that Universal proposition: All good men are just
expresses the mental sentence men.
 Categorical proposition – expresses assertion
that two ideas are in agreement or Quantity Quality
disagreement Symbols
 Hypothetical proposition – expresses a Universal Affirmative A
relationship between two or more judgments All teachers are degree holders.
Particular Affirmative I
Processes in Judgment Some Filipinos are inhospitable.
 Apprehension of concepts- ideas in the mind Universal Negative E
are placed side by side to each other No dog is a biped.
 Mental comparison of concepts – comparing Particular Nagative O
the ideas whether they are identical or different Many businessmen are not profiteers.
from each other
 Mental predication – pronouncement of the  The symbols A, I, E, O were derived from the Latin
identity or non-identity of the concepts being words AffIrmo and nEgO which mean “I affirm” and
compared; the mental product is enunciation “I deny”, respectively. Note that the first vowel of
 Written predication – expressing an each word signifies the universal propositions while
enunciation in a form of verbal statement or the second signifies the particular propositions.
manifestation, which produces a proposition  In determining the quantity of the predicate term,
rules are the following:
Prerequisites in Making Judgments 1. If the categorical proposition is affirmative, such as
1. There must be at least two or more concepts that A and I, the predicate is a particular term, provided
exist. that it is not singular.
2. In the act of comparing, the mind must examine the 2. If the categorical proposition is negative, such as E
similarities and differences to verify the truth or falsity and O, predicate is a universal term, provided that it
of the concept. is not singular.
3. The mind must lay down its acceptance and rejection
of the ideas. Particular quantifiers:
a lot of minority of not all
Categorical Proposition somebody numbers
Three Elements:
 almost all many not every Third Phase: Reasoning
someone
few most of nearly all  (as the third mental phase), the mental
something operation wherein the mind infers a new truth
majority of much some drawn out from a previous judgment or several
several judgments that possess logical relation or
connection (deductive logic) or probable
Universal quantifiers: connection (inductive logic) with each other.
all each no
whatever Methods (Types of Reasoning)
any every none 1. Deductive Reasoning – reasoning from a
whoever universal/general idea or premises to a particular or
anybody everyone no one without individual conclusion; or from a broader thought to a
anyone everything nobody simple one
exception e.g. All men are mortal.
anything everybody nothing But, Socrates is a man.
Therefore, Socrates is mortal.
Rules of Reduction to Standard Form 2. Inductive Reasoning – reasoning form known
1. The arrangement of the proposition should always particular instances to generalizations.; or from specific
be S-P-C. to general
2. The original meaning of the proposition must not e.g. Juan is an Asian.
be changed. Pedro is an Asian.
3. The copula must always be in present tense. Maria is an Asian.
Tomas is an Asian.
 Rule for affirmative propositions: If the quality of But, Juan, Pedro, Maria and Tomas are
the proposition is affirmative, the quantity of the Filipinos.
predicate is particular. Then, Filipinos are (most likely to be) Asians.
 Rule for negative propositions: If the quality of the
proposition is negative, the quantity of the  Inference – the process by which the mind gets new
predicate is universal. knowledge by drawing out the implications of what it
already knows; any series of propositions (premises)
Hypothetical Proposition so arranged that the consequent flows from the
1. Conditional Proposition – expresses a necessary antecedent through a logical sequence; proceeding
relationship between an antecedent and a consequent; from known truths (premises) to new truths
conditional indicators are If, then; In case; Provided (conclusion)
that; Only if; On condition; Unless Premises – the part of the inference from
e.g. If a person is seriously sick, then his life is which the conclusion is drawn or the
endangered. knowledge is derived
(if-antecedent) (his life Sequence – the necessary connection between
is endangered – consequent) the premises (antecedent) and the conclusion
2. Disjunctive Proposition – contains two or more (consequent)
alternatives which are so related that one of them must e.g. All students are learners; but PUPians are
be true students; thus, PUPians are learners.
e.g. A student passes or fails his course. (antecedent)
(disjuncture is expressed by “or”, or “either”, “or”) (consequent)
3. Conjunctive Proposition – contains alternatives of  Mental argument – connected series of two or more
which only one must be true; emphasized by the propositions related to each other in such a way that
expressions, “can not be..at the same time” or “cannot all but one of them (premises) are supposed to
be both” provide support for the remaining one (the
e.g. I cannot be telling the truth and telling a lie conclusion)
at the same time.  Syllogism – external representation of an argument
Two Kinds:
 1. Categorical syllogism – with categorical 2. Contrariety/Contrary Oppositions – relationship
propositions between propositions with the same subject, same
2. Hypothetical proposition – at least one predicate, same universal quantity, but different in
proposition is a hypothetical proposition quality
- relationship between A and E
Two Types of Inference - cannot be both true but can be simultaneously
1. Immediate false
2. Mediate Rules: a. If one of the contrary propositions is true, the
- the conclusion passes from one proposition other is false.
- the conclusion passes from two propositions b. If one of the contrary propositions is false, the
- without a medium other is doubtful.
- through a medium E.g. All philosophers are searchers for meaning.
- to a new proposition but not a new truth No philosophers are searchers for meaning.
- to a new proposition and a new truth 3.Subcontrary – relationship between propositions with
-e.g. No bees are flies. (no medium) the same subject, same predicate, same particular
- e.g. No bees are flies; those bees are flies quantity, but different in quality
Thus, no flies are bees. (new proposition - relationship between I and O
(medium). So, those are not flies. (new - cannot be both false but can be
but no new truth) simultaneously true.
proposition and also a new truth) Rules: a. If one of the subcontrary propositions is false,
All men are mortal beings; thus, the other is true.
All men are free; Brian is a man; b. If one of the subcontrary propositions is true,
some mortal beings are men. the other is doubtful.
Thus, Brian is free. E.g. Some cops are good traffic enforcers.
 Medium – intermediary proposition (premise) that Some cops are not good traffic enforcers.
stands between one proposition of the antecedent 4. Subalternation – relationship between propositions
and the conclusion. with the same subject, same predicate, same quality,
but different in quantity
- relationship between A and I; E and O
Kinds of Immediate Inference Rules: a. If the universal proposition (A or E) is true, the
1. Logical Opposition – the process by which the mind particular proposition (I or O) is also true.
proceeds (directly or indirectly) from the known or b. If the universal proposition (A or E) is false, the
assumed truth or falsity of one proposition to the truth, particular proposition (I or O) is doubtful.
falsity or doubtfulness of another proposition; c. If the particular proposition (I or O) is true, the
opposition is the logical interrelations between the universal proposition (A or E) is doubtful.
truth and falsehood of propositions involving the same d. If the particular proposition (I or O) is false, the
items universal proposition (A or E) is also false.
E.g. Some terrorists are rebels.
Four Kinds of Oppositions (from Categorical All terrorists are rebels.
Propositions)
1. Contradictory – relationship between two
propositions with the same subject and predicate but 2. Logical Equivalence (Eduction)
different in both quantity and quality  Propositions are formulated differently by
- relationship between A and O; E and I interchanging the subject and the predicate or
- cannot be both true and cannot be both false; by using/omitting the negatives but their
opposite truth values meanings are retained
Rules: a. If one of the two contradictory oppositions is
true, the other is false. Four Kinds of Eduction (Formal)
b. If one of the contradictory oppositions is false, 1. Conversion – reconstructing a new proposition by
the other is true. interchanging the subject and the predicate,
E.g. All murders are crime. considering that the quality is retained and no any term
Some murders are not crimes. is extended; the original proposition is called
convertend while the new proposition is called Rules of Complete Contraposition (CC): 1. Obvert the
converse contraponend.
Rules: 1. Interchange the subject and the predicate of 2. Convert
the convertend. the obverse.
2. Retain the quality of the convertend. 3. Obvert
3. Do not extend any term. the converse.
*Partial Conversion is: I to I; E to E *CC is A to A; E to O; O to O
E.g. Some professors are researchers. (convertend) E.g. Trees are protectors of environment from land
Some researchers are professors. (converse) erosions.
*Complete Convesion is: A to I; E to O Non-protectors of the environment from land
E.g. All painters are artists. erosions are non-trees.
Some artists are painters.
4. Inversion – the subject and the predicate are
2. Obversion – formulating a new proposition by retained to their original position; while the quantity of
changing the quality, retaining the subject and quantity the given proposition is changed; only A and E can
of an original proposition, and contradicting the original undergo inversion process; the original proposition is
proposition; the original proposition is called obvertend called invertend while the new proposition is called the
while the new proposition is called obverse inverse
Rules: 1. Retain the subject and the quantity of the Rules of Partial Inversion:1. Retain the subject and the
obvertend. predicate in their original place in the inverse.
2. Change the quality. 2. Change the quality.
3. Contradict the predicate. 3. Contradict the original
*Obversion is: A to E; E to A; O to I; I to O subject.
E.g. All crimes are immoral. (obvertend) *Simple Inversion is: A to O; E to I
All crimes are not moral. (obverse) E.g. Every school is an agent of change. (invertend)
Some non-schools are not agents of change.
3. Contraposition- formulating a new proposition (inverse)
whose subject is the contradictory of the original
predicate; combination of conversion (by interchanging Rules of Complete Inversion: 1. Retain the subject and
the subject and the predicate) and obversion (by adding the predicate and its quality in the inverse.
contradictory term of the predicate term in the new 2. Change the quantity.
proposition); the original proposition is called 3. Contradict both the
contraponend while the new proposition is called the subject and the predicate.
contraposit *Complete Inversion is: A to I; E to O
Rules of Simple Contraposition (SC): 1. Obvert the E.g. All grapes are fruits.
contraponend. Some non-grapes are non-fruits.
2.
Convert the obverse. Summary of Values
*SC is A to E; E to I; O to I *S –subject P- predicate Not Legitimate –
E.g. Fishes are rich in protein. (contraponend) invalidity of O conversion
No non-rich in protein is a fish. (contraposit)

A E I O
Proposition All S are P No S are P Some S are P Some S are not P
Converse Some P are S No P are S Some P are S Not Legitimate
Obverse No S are non-P All S are non-P Some S are not non-P Some S are non-P
Simple Contraposit No non-P are S Some non-P are Not Legitimate Some non-P are not
S non-S
Complete Contraposit All non-P are Some non-P are Not Legitimate Some non-P are not
non-S not non-S non-S
Complete Inverse Some non-S are Some non-S are Not Legitimate Not Legitimate
non-P not non-P
Partial Inverse Some non-S are Some non-S are Not Legitimate Not Legitimate
not P P