Meaning of Philosophy

- derived from the two Greek, “philos” to love, and

“sophia”, wisdom. It is literally means “love of wisdom”.
It was coined by Pythagoras c. 580-497 B.C) who
formulated a practical, ethical, and religious philosophy
which placed supreme value on intellectual activity. In
one of his travels to the ancient Greek city-states, he was
asked by one of the kings: “Are you a wise man?” To that
question, he humbly answered: “No, I am not a wise man;
I am only a lover of wisdom”.
PHILOSOPHY defines as: THE SCIENCE OF
THINGS BY THEIR ULTIMATE PRINCIPLES AND
CAUSES, AS KNOWN BY NATURAL REASON
ALONE.

*Philosophy is a science. It is not a set of opinions and

theories. It is certain knowledge of things based on
evidence and demonstration, and reduced to a
comprehensive rational system.

* Of Things. Philosophy discusses about the things that are

found in the existential world. Aside from material beings,
it also discusses, in its different branches, about non-
material beings and principles,
e.g. *about the specific and the existential
principles of things.
* about the soul
* the intellect and the free will.
*By their Ultimate Principles and Causes. By this
qualification, Philosophy is differentiated from the physical
sciences as Biology, Chemistry, etc. These special sciences
study the proximate constituent principles and explanations
(Causes) of their subject matter.
+Biology- studies the nature of the cell, protoplasm,
tissues, the activities of anabolism and catabolism While
Philosophy- studies the nature of the living being as
such, of life and its principle.

+Chemistry- studies the different elements of material

substances. While Philosophy studies the ultimate principle of the
differences of material things.

+Positive Psychology studies human behavior, its

differences and proximate causes. While Philosophical
Psychology studies the ultimate principles of human behavior,
reason and will.
*As Known by Natural Reason Alone.
Philosophy attains knowledge, not by making use of the
Principles or Articles of Faith, but by the use of the
Principles of natural cognition, which may be obtained
from the investigation of Nature and the natural study of
things.
The Philosopher, however, does not hesitate to render value
judgments for he would appraise and either approve or
condemn the individual’s behavior and the government’s
policies. This is the reason why philosophy is considered
the QUEEN OF THE SCIENCES.
The earliest philosophers in ancient times sought rational
solutions to certain genuine philosophical questions
concerning the nature of the universe and the meaning of
human experience. They were concerned with specific
problems:
With what stuff is the world made?
Is there soul or a God?
How can things change and yet remain the same?
What is the highest good for man to pursue?
 BRANCHES OF PHILOSOPHY

Philosophy has several branches which resulted

from man’s philosophical speculations.
1. Ethics or Moral Philosophy
2. Metaphysics or Ontology
3. Theology
4. Philosophy of Man
5. Cosmology
6. Political Philosophy
7. Aesthetics
8. Epistemology
9. Logic
1. Ethics or Moral Philosophy- is the philosophical
study of the morality of human acts, the search
for an understanding of the good life and the
ultimate basis of what is good or bad.
2. Metaphysics or Oncology- is the philosophical
quest for what reality is in the final analysis. It
is the study of beings, in general.
3. Theology/Theodicy or Special Metaphysics- is
the philosophical inquiry into the existence of
God. His nature, and His relations to man and
the rest of creation.
4. Philosophy of Man- is the philosophical search
for a deeper understanding of what is and what
it means to be fully human.
5. Cosmology & Philosophy of Nature- is the
philosophical search for deeper understanding of
the material universe.
6. Political Philosophy- is the philosophical search
knowledge of the ultimate foundation of the
state, its ideal form and its basic power.
7. Aesthetics- is the search for a deeper
understanding and knowledge of beauty.
8. Epistemology- is the philosophical search for
answer to the fundamental questions concerning
the conditions of knowledge, its extent and
limitations.
9. Logic- is the philosophical science and art of
correct inferential thinking and setting forth its
conditions.
 LOGIC

- is the integral part of Philosophy. The actual name of

LOGIC was introduced by Zeno the Stoic. Coming from the
Greek word “Logike”, it would etymologically means a
treatise on matter pertaining to thought.

- defines as the Philosophical science of correct reasoning or

inferential thinking.

- the science of correct and certain inference.

*Reasoning and thinking in the common definition do not

refer to the act of the mind proper, but to the mental
product thereof, namely, the syllogistic argument.
 THE NATURE OF LOGIC

1. Material Object:
The Material Object of Logic is concepts and conceptual
structures like propositions and syllogisms, taken as products of
the mind, not as psychical affections or accidental modifications
of the mind.

2. Formal Object:
By the formal Object of a science we understand the primary
object of its study or consideration, by reason of which, the
science discusses the different items that fall under its study,
e.g. the four operations or functions of numbers, in the case of
Arithmetic. In the case of Logic, the Formal Object is the
inferential functions of concepts and propositions.
 DIVISION OF LOGIC
Logic is commonly divided according to the
three acts of the mind, which provide the different
elements of its subject-matter and the different bases
of the different inferential functions.

I. Apprehension, Idea, Predicability of Ideas

II. Judgment, Enunciation, Predication of Ideas
III. Reasoning, Argument, Inference of New
Predication
 Schematic Diagram
Mental Act Mental External Logical
Product Sign Issue
Apprehension Idea Term Predicability
Judgment Enunciation Proposition Predication
Reasoning Argument Syllogism Inference

Remarks:
The Mental Product or Expression which falls in between the Mental Act and the
External Sign is often designated with the name of the one of the other:
e.g. the enunciation is also commonly designated as Judgment, or as
proposition
 HISTORY OF LOGIC
ARISTOTLE (384-322 B.C) is considered as the
FOUNDER OF LOGIC. He wrote six treatises on
logical matters, the collection of which was called the
“ORGANON”.

ZENO the STOIC (336-264 B.C) introduced its actual

name. The STOIC LOGIC was mainly the Prior and
Posterior Analytics of Aristotle’s logical works,
expanded with a longer treatise on the Hypothetical
Syllogism, and with a treatise on the criterion of
truth.
 Other successors of Aristotle:
PORPHYRIUS (232-304 A.D) a neo-platonist, who
wrote a small introduction to the Categories of
Aristotle, called the “Isagoge”, the Greek word
meaning INTRODUCTION.

SEVERINUS BOETHIUS (470-524 A.D) translated

Aristotle’s Organon and wrote commentaries on the
Categories and on the Isagoge of Porphyrius.

AVICENA (Ibn-Sina, 980-1037 A.D.) and AVERROES

(Ibn-Rosh, 1126-1198 A.D.) the Arabian Philosophers
who wrote commentaries on Aristotle’s Organon
ST. THOMAS AQUINAS one of the scholars of the Middle Ages,
wrote extensive commentaries on the logical works of Aristotle.
From then we received our comprehensive science of Logic.

FRANCIS BACON (1561-1626 A.D) wrote the “NOVUM

ORGANON” with the aim of improving on the Organon of
Aristotle. He introduced the theory of Induction.

JOHN STUART MILL (1806-1873 A.D) developed the theory of

Induction into a general theory for scientific investigation.

GEORGE BOOLE was considered as the FOUNDER OF

SYMBOLIC LOGIC that gained popularity in the recent years.
It covers the same subject matter as our standard logic, but
differs as to the mathematical symbols and language that it
uses.
 EXERCISES
1. Explain why Logic may also be defined as: the
science of correct and valid rational demonstration.
2. Why is Logic necessary for the study of
Philosophy?
3. What kind of thinking are the following:
a. Pedro is not as bright as his elder brother.
b. You do not care to study your lessons; therefore you are a bad
student.
4. How can Mr. Santos be an honest and fruitful man,
when he has not paid his taxes.
 IDEA, ABSTRACTION AND
PROPERTIES OF IDEAS
IDEA- is the intellectual “image” or
representation of a thing. It is the same as the
concept in the mind. The term ideas comes from
the original Greek which means IMAGE. As applied
to the idea, the term image must be taken only
metaphorically, in an analogous sense.
The idea is an abstract representation of
things, and may be expressed or defined by
meaningful terms. Thus, e.g., an Igorot may
intellectually identify and distinguish a watch from
other objects; but if he does not know what it is for,
or does not know that it is a mechanical device for
telling time, he has no idea of it.
 IDEA AND PHANTASM
The Idea must be carefully distinguished from
the PHANTASM. The latter is a sensible image
existing in the imagination, which is one of the
internal sense-faculties located in the brain. The
Phantasm is a sensible representation of the
material features of a thing, usually a kind of
pictoral image, bearing a shape or figure. We
generally have recourse to the phantasm of things,
by way of substitute, when we are thinking of
physical objects that are not present.
The idea is the meaning of phantasm. In our
present condition a phantasm usually accompanies
the idea. It helps to fixate our thoughts.
CHIEF DIFFERENCES BETWEEN IDEA AND
PHANTASM

IDEA PHANTASM
1. Found in the intellect Found in the imagination
2. Universal Individual
3. Constant Changeable
4. Possible of complex Not possible of complex
and immaterial things and immaterial things
The most important difference between the IDEA and the PHANTASM
is that Idea is a UNIVERSAL REPRESENTATION, whereas the PHANTASM is
INDIVIDUAL.

eg. The Idea of a tree is equally applicable to all trees; the phantasm is not.
 ABSTRACTION
The mental process involved in the obtention of
the idea is called Abstraction.

According to its Latin original, Abstraction means

the drawing of something from some source.
Eg. Of water from a well.
 APPREHENSION

Is the act of the mind by which it “grasps” or knows the

nature or essence of a thing, without affirming or
denying about it. It is an act that is associated with
conceptual abstraction and presupposes it.
 PROPERTIES OF THE IDEA
The Idea has two important logical properties:
1. COMPREHENSION – is the set of thought
elements or conceptual feature contained in an idea.
e.g. The comprehension of the concept MAN is: Being that is
substantial, bodily, living, sentient and rational. ANIMAL is a being that
is substantial, bodily, living, and sentient.

2. EXTENSION- is the range or scope of individuals

and classes to which an idea may be applied.
e.g. The idea of a “rational animal” is applicable to individual man;
the idea of “living organism” is applicable to plants, animals, and men.
 GENERAL LAWS ON COMPREHENSION
AND EXTENSION OF IDEAS

The comprehension and Extension of one and the same

concept vary inversely, that is: The Greater the
Comprehension, the Less the extension; and vise versa.

COMPREHENSION EXTENSION
Substance Spirits Minerals Plants Brutes Men

Material Substance Minerals Plants Brutes Men

Living Material Substance Plants Brutes Men

Sentient Living Material Substance Brutes Men

Rational Sentient Living Material Substance Men

 CLASSIFICATION OF IDEAS
1. ACCORDING TO COMPREHENSION:
A. Simple - idea that expresses only one
conceptual feature, or formal reason.
e.g. beauty, being

Compound – idea that expresses several

constituent conceptual elements, or
integral features.
e.g. Man- rational animal or the
human being
B. One – idea that expresses only one thing,
nature, or formal feature, although the idea may
comprise several constituent conceptual
elements, or integral formal feature.
e.g. Man, rational animal, house, airplane

Multiple- idea that expresses in an explicit

manner a thing, nature, or formal feature as
modified by another thing, nature or formal
feature, in an accessionary manner.
e.g. a poor philosopher, a tall girl a furnish
room
C. Concrete- idea that expresses a subject that is
qualified by a nature or formal feature.
e.g. student, beautiful dress, activist, etc.

Abstract- idea that expresses only a nature, or

formal feature without a subject.
e.g. religiosity, justice, reasonableness

D. Absolute- idea that expresses a thing, nature or

formal feature, without any relation to some other
thing.
e.g. minerals, living beings, modesty, etc.

Relative- idea that expresses a thing, nature or

formal bearing a relation to something else; or
expressing explicitly a relation.
e.g. creatures, husband, motherhood
E. Complete - idea that expresses all the
conceptual reasons or formal features that
correspond to the comprehension or to the nature
of an object.
e.g. Man is a rational animal.
A car is a self-propelling vehicle adapted to
transport persons.

Incomplete - idea that expresses only some

of the conceptual reasons or formal features that
correspond to the comprehension or to the nature
of an object.
e.g. Man is a rational being; the animal nature of
man has been left out.
II. ACCORDING TO EXTENSION
A. Singular- Idea that expresses a concept,
or a set of conceptual features, that is
applicable only to one individual.
e.g. the President of the Philippines; the
actual Pope; the Prophet of Islam.

B. Universal- Idea that expresses a

concept, a nature, or a formal feature that is
applicable individually or distributively to the
individuals of a kind, or class.
e.g. boy, student, Filipino, animal
C. Transcendental- Idea that expresses a
nature, or a formal reason that is applicable
distributively to individuals of different kinds
or classes.
e.g. nature, formal feature, object,
goodness, duality, one, two, three, etc.
Numerals are applicable to different
objects:
e.g. two hailmaries, two sacks of rice,
two degrees, two concepts
D. Particular- Idea that expresses only a part of the
extension of a universal (or transcendental)
concept, whether in an indefinite, or in a definite
manner.
e.g. most women, some men, a few students,
or five students passed in the test.

E. Collective- Idea that expresses a group of

individuals as a set, not as individuals.
e.g. family, army, nation.
A collective concept may be singular,
universal, or particular.
e.g. RP Armed Forces: army, in general; some
armies
 THE TERM, SIGN OF THE
CONCEPT
The TERM, from the Latin TERMINUS would literally
mean the last element into which a proposition may
be resolved, namely, the SPOKEN or the
WRITTEN WORD.

Since TERM express CONCEPTS, they are essentially

SIGNS.

TERM- is a sensible conventional sign

expressive of a concept or idea.
- may also be defined as a SPOKEN or
WRITTEN WORD EXPRESSIVE OF A CONCEPT.
1. Express what are the following are through
clear conceptual features:
a. a home
b. a teenager
c. fear
d. Lord
2. Which one of the following has a greater
extension (Choose only one and explain
why)
a. European, or American
b. Woman, or Lady
JUDGMENT, THE SECOND
ACT OF THE MIND
 Is the mental act which affirms or denies something.
The product of judgment is called a Proposition.
Therefore a Proposition is a sentence which affirms
(asserts) or denies (negates) something.
 In English grammar we speak of a sentence as a group
of words that expresses a complete thought, and we
consider four kinds of sentences.
 1. Declarative: one which states a fact
Example: My house is a red-roofed bungalow in Greenhills.
 2. Interrogative: one which asks a question.
Example: How are you this beautiful morning?
 3. Imperative: one which makes a request or gives a command.
Example: Please send me some sampaguita plants
“Build thee more stately mansions, O my soul.”
 4. Exclamatory: one which expresses a strong feeling.
Example: What a lovely thing to say!
 Aristotle defines the proposition as “a
sentence that could either be true or false.”
One can hardly ask if “ How are you this
beautiful morning?” and “What a lovely thing
to say!” are true or false. But “ My house is a
red-roofed bungalow in Greenhills” is either
true or false.
 KINDS OF PROPOSITIONS
 In Logic there are many kinds of
propositions:
1. Categorical Proposition
2. Hypothetical Proposition

BASIC ELEMENTS OF THE CATEGORICAL PROPOSITION

 The categorical or Attributed Proposition has a
subject-predicate relationship: its subject is affirmed
or denied by the predicate. Its basic elements, are:
the subject,
subject the predicate,
predicate and the copula.
copula
 In the statement, “The story he told you is
apocryphal,”
 The Subject is __________.
 The Predicate is ____________.
 The copula is __________.

The SUBJECT is the one spoken of, the one

about whom or of which something is
affirmed or denied.
The PREDICATE is what is affirmed or denied
of the subject.
The COPULA links the subject with the
predicate.
 Quality of the Proposition
1. The copula is the qualifier of the proposition.
Because of it, the proposition is either
AFFIRMATIVE or NEGATIVE.

The following are considered affirmative but

equivalently negative statements.
1. He who is not a college graduate is ineligible.
2. Some animals are non-mammals
 Quantity or Extension of the
Proposition
The quality of the proposition is equivalent to the
quality of its subject.
 Singular- if the subject stands for a single definite
individual or group.
 Shakespeare is England’s greatest dramatist.
 Particular- if the subject designates an indefinite part
of its total extension.
 Some prima ballerinas are Margot Fonteyn and Natalia Makarova.
 Universal- if the subject can apply to every portion
signified by the term.
 Love is a many-splendored thing.
  The quantifiers- every, each, all, some,
several, many, etc. play a significant role.
Quantity of the Predicate
1. Find out first if the predicate is singular. It is singular
if it refers to a single definite individual or group.
Example: Dr. Cris Bautista is the most outstanding heart
transplant surgeon.
2. If the predicate is not singular, and if the proposition
is affirmative, then the predicate is particular.
Example: Gabriel Marcel is a French philosopher.

3. If the predicate is not singular, and if the proposition

is negative, then the predicate is universal.
Example: Some men are not artists.
 SYMBOLS OF THE
CATEGORICAL STATEMENTS
 Since Aristotle’s time there have been
attempts to make logic a science of symbols
to achieve shortcuts to correct reasoning.
Among these are symbols for the four (4)
categorical statements, namely, A, E, I, O. A
and I are taken from the two vowels of
AffIrmo (Affirm) and E and O from the two
vowels of nEgO (negate or deny).
A stands for universal or singular and
affirmative statements.
E stands for universal or singular and negative
statements.
I stands for particular and affirmative
statements.
O stands for particular and negative
statements.
 Universal/Singular
A E

Affirmative Negative

I O
Particular
 Model Statements of these symbols are the following:
A
 All roses are flowers.
 Every cloud has its silver lining.
 Man is a being-for-death.
 Whoever wins will be awarded a trip to Hongkong.
 Wherever you, go, I go.
 All of us in this room are Filipinos.
 Everything is in a flux.
 Francis is a scholarly Jesuits.
 Whatever will be, will be.
 His lecture on philosophy and art is a brilliant piece of
work.
E
1. No atheist is a believer in God.
2. No bird has four legs.
3. Love of country is not a commodity for sale.
4. Love means not having to say you are sorry.
5. I never said he was a crook.

I
1. Some philosophers are essentialists.
2. Several philosophers are existentialists.
3. Many movies are, in whole or in part, pornographic.
4. A few heart transplant patients are still alive.

O
1. Some dogs are not black.
2. Not all women are fickle.
3. A few Filipina are not literate.
4. Many American are not rich.
 RULE FOR THE DISTRIBUTION OF
THE TERM IN A PROPOSITION
1. In a Universal Affirmative Proposition, only the
Subject supposes Universally, or is distributed.
(Su Pp)
2. In a Universal Negative Proposition both the
Subject and the Predicate suppose Universally, or
is distributed. (Su Pu)
3. In a Particular Affirmative Proposition neither the
Subject nor the Predicate supposes Universally,
but Particularly. (Sp Pp)
4. In a Particular Negative Proposition only the
Predicate supposes Universally. (Sp Pu)
 LOGICAL PROPERTIES OF
PROPOSITIONS
1. Opposition
2. Equivalence
- are the Two Logical Relative
Properties of Proposition.

A. OPPOSITION - is the disagreement or

difference as to Quantity, or Quality, or
both, of two propositions having the same
subject and the same predicate.
 SQUARE OF OPPOSITION
A – All men are wise E – All men are not wise
A – All S is P E – All S is not P

I – Some S is P O – Some S is not P

I – Some men are wise O – Some men are not wise
 KINDS OF OPPOSITION
1. Contradictory
2. Contrary
3. Sub- Contrary
4. Subaltern

1. Contradictory- propositions are those

having the same subject and the same
predicate, but differ in quantity and
quality.
Eg.
All men are wise. – Some men are not wise.
Some men are wise. – All men are not wise.

These are 2 pairs of Contradictories:

A – O and E – I, Universal against Particular of
opposite quality, thus:
Eg.
Every S is P; No S is P
therefore some S is not P. therefore some S is P.
Truth Table is:
A,E O,I
T F
F T
Rule: If one is True, the other is False. If one is False,
the other is True.
2. CONTRARY – are those that have the same
subject, predicate and universal extension;
but differ as to quality.
- There is only one pair of contraries. This is
A-E, both universal but one affirmative, the
other negative.
Truth Table is:
A EE A
T FT F
F ? F ?
Rule: If one is True, the other is False
If one is False, the other is doubtful.
 Eg. A. Every S is P.
therefore No S is P.
Every Catholic church has a cross.
Therefore no Catholic church has a cross in it.

B. Every S is P.
therefore ? No S is P.
All lakes are mountains.
Therefore no lakes are mountains.
C. No S is P;
Therefore every S is P.
No dictator is a secure man;
therefore every dictator is a secure man

D. No S is P;
therefore? Every S is P.
No Catholics are devotees of the Blessed
Virgin;
Therefore all or/every Catholics re devotees
of the Blessed Virgin.
3. SUBCONTRARY- are those that have the
same subject, predicate and the same particular
extension; but differ as to quality

-This is also one part of sub contraries: I-O, both

particulars but each of a different quality.

Truth Table is:

I O O I
T ? T ?
F T F T

Rule: if one is true, the other is doubtful. If one is

false, the other is true.
Eg. A. Some S is P.
therefore? Some S is not P.
Some doctors are negligent; I-
T
Therefore some doctors are not negligent. O-?

B. Some S is P.
therefore some S is not P.
Some Kittens will be dogs; I -F
Therefore some kittens will not be dogs. O - T
C. Some S is not P.
therefore? Some S is P.
Some plants are not animals; O-T
Therefore some plants are animals. I - ?

Some clever men are not cynics; O-

T
Therefore some clever men are cynics I - ?

Cynics- someone who believes that self-interest is the motive of all human
conduct.
D. Some S is not P.
therefore some S is P.
Some women are not politicians;
Therefore some women are politicians.
4. SUBALTERNS- are those having the same subject
predicate and quality; but differ as to quantity.
Like the contradictories, the subalterns come also in two
pairs: A-I and E-O, opposite in quality but the same quality.

Truth Table is:

A, E I, O I,O A,E
T T T ?
F ? F F

Rule: If the universal is true, the particular is true.

If the universal is false, the particular is doubtful.
If the particular is true, the universal is doubtful.
If the particular is false, the universal is false.
EXERCISES: Multiple Choice: Choose the correct
letters.
1. Not all novels are interesting reading; therefore
Some novels are interesting reading.
a. contradictories c. subcontraries
b. contraries d. subalterns
2. Each novelist tries to inject local color in his works;
Therefore some novelist tries to inject local color in his
works.
a. contradictories c. subcontraries
b. contraries d. subalterns
3. No good short story is rambling; therefore every
good short story is rambling.
a. contradictories c. subcontraries
b. contraries d. subalterns

4. Not every drama has dialogue; therefore every

drama has dialogue.
a. contradictories c. subcontraries
b. contraries d. subalterns

5. Quite a number of novelist are Filipinos; therefore

no novelist are Filipinos
a. contradictories c. subcontraries
b. contraries d. subalterns
6. No Greek tragedy has a fanciful theme; therefore
some Greek tragedy has a fanciful themes.
a. contradictories c. subcontraries
b. contraries d. subalterns

7. Some existentialist are dramatist; therefore All

existentialist are dramatist.
a. contradictories c. subcontraries
b. contraries d. subalterns

8. All works of Rizal are novels, therefore No works

of Rizal are novels.
a. contradictories c. subcontraries
b. contraries d. subalterns
9. All works of Nick Joaquin are held in high
esteem; therefore no works of Nick Joaquin
are held in high esteem.
a. contradictories c. subcontraries
b. contraries d. subalterns

10. One of my friends is a short story writer;

therefore none of my friends is a short
story writer.
a. contradictories c. contraries
b. subcontraries d. subaltern
B. EQUIVALENCE
- is the property of two propositions having the same
subject, the same predicate and meaning, but
differing as to expression, or in matter of one or
more negative particles.

E.g.
All men are animals – No man is not an animal.

OBVERSION
- this is one of the logical procedures for
forming equivalent propositions. The original
proposition is called the OBVERTEND, and the
resultant proposition is called the OBVERSE.
 Steps in Writing Obversion
1. Retain the subject and its quantity.
2. Change the quality.
3. Put the contradictory or contrary of the original
predicate.

Four Categorical Forms maybe Obverted in the

following Manner;

1. A to E- Every S is P;
Therefore no S is non- P.
e.g. Every man is mortal.
Therefore no man is immortal.
2. E to A – No S is P;
Therefore every S is non-P.
e.g. No man is unembodied;
Therefore every man is embodied.

3. I to O – Some S is P;
Therefore some S is not non-P.
e.g. Some geniuses are mathematicians;
Therefore some geniuses are not non-mathematicians.

4. O to I – Some S is not P;
Therefore some S is non-P.
e.g. Some drugs are not habit-farming;
Therefore some drugs are non-habit forming.
 To summarize the Schema of Obversion:
Obvertend(Original Proposition) Obverse (New Proposition)

A- Every S is P. ………… E- No S is non-P.

E- No S is P. ………… A- Every S is non-P.
I- Some S is P. ………… O- Some S is not non-
P.
O- Some S is not P. ….. I- Some S is non-P.
Exercises: Give the Obverse (and the symbol) of each
of the following.
1. Cebu is a progressive island.
2. Magellan and Lapu-lapu were not friends.
3. No Cebuano is unpatriotic.
4. The Sinakulo is a lenten drama of Christ’s
passion.
5. A happy occasion is the Sinulog Festival.
6. Tuba is not a refreshing softdrink.
7. Romblon is “Marble Country”.
8. A feature during fiestas is the Ati-atihan.
9. A source of livelihood is fishing.
10. Many of the menfolk are farmers and loggers.
 REASONING AND THE
SYLLOGISM
REASONING- means Inferential thinking, and
is classified as the Third Act of the Mind.
e.g.
Moral rights are moral means,
But, human freedom is a moral right.
Therefore, human freedom is a moral means.
 In Psychology- Reasoning is a series of mental
comparisons and judgments united together
into a single inferential process.
e.g.
All members of this class are present.
But, Tom is a member of this class;
Therefore, Tom is present.

All men are rational animals.

But, Pedro is a man;
Therefore, Pedro is a rational animal.
 SYLLOGISM/CATEGORICAL
SYLLOGISM
 Is a Logical expression, in which one proposition is
expressly inferred from other two propositions.

 Came from the Greek SYN-LEGEIN or SYN-LOGOS,

etymologically would mean “to think in a connected
manner”, or connected thought”.

 Is the principal form of Deductive Reasoning, and its

Absolute manner of drawing the Conclusion is the
kind most suited for philosophical and scientific
knowledge.
3 PROPOSITIONS THAT MADE
UP THE SYLLOGISM
1. Major Premise- usually a principle or
general truth/fact.
2. Minor Premise- particular fact
3. Conclusion- result of two premises.

The premises are also termed

ANTECEDENT (that which comes before)
and the Conclusion is termed
CONSEQUENT (that which comes from
after).
 THE TERMS OF THE
CATEGORICAL SYLLOGISM
1. Major Term – which is the Predicate of the
Conclusion and is found in the Major
Premise.
2. Minor Term – which is the Subject of the
Conclusion and is found in the Minor
Premise.
3. Middle Term – which is found in the two
premises but not in the Conclusion.
e.g.
All men are rational beings.
But, Francis is a man,
Therefore, Francis is a rational
being.

EXERCISES: Please see Page 235-238, Intro. To Logic by C.L. Cruz

Rules with Regards to the Inference
of the Truth of the Conclusion. If the
Syllogism is Correct, Then:
1. True Premises beget a true Conclusion.
2. False Premises may have a False, or a True
Conclusion. But if the Conclusion happens to
be True, it is not due to Consequence from
the False Premises. Its Truth is accidental to
such Inferential Consequence. It merely
happens to be True on its own.
e.g. All the Apostles were traitors.
But, Judas Iscariot was an apostle;
Therefore, Judas Iscariot was a traitor.
3. Hence, If a Conclusion is True, it does
not necessarily follow that its
premises are True.
4. A False Conclusion is due to the
falsehood of one or both premises.
e.g. Every tree is a cat,
But, the oak is a tree;
Therefore, the oak is a cat.
 GENERAL RULES OF THE
CATEGORICAL SYLLOGISM
 To determine validity, Andrew Bachhuber
lists Ten General of the Categorical
Syllogism. The First Four are about the
Number, Arrangement, and Quantity of
Terms; the next Three are about the
Quantity of the Propositions, and the last is
on the Existential Subject.
RULE # 1: THERE MUST BE ONLY THREE
TERMS IN THE SYLLOGISM: THE MAJOE
TERM, THE MINOR TERM, AND THE
MIDDLE TERM. The violation of this rule is called the fallacy
e.g. Of the four or five term or six terms.

“Cat” rimes with “fat”,

but You are a member of the club “Cat”,
Therefore, you are fat.
S- Minor Term
P- Major Term
M- Middle Term
RULE # 2: THE MAJOR TERM IS THE
PREDICATE OF THE CONCLUSION AND
IS FOUND IN THE MAJOR PREMISE;
THE MINOR TERM IS THE SUBJECT OF
THE CONCLUSION AND IS FOUND IN
THE MINOR PREMISE; AND THE
MIDDLE TERM IS FOUND IN THE TWO
PREMISES BUT NOT IN THE
CONCLUSION.
e.g.
The sick man needs an operation;
but tonsillectomy is an operation;
Therefore, the sick man needs tonsillectomy.
RULE # 3: THE MAJOR AND MINOR
TERMS SHOULD ONLY BE UNIVERSAL
IN THE CONCLUSION IF THEY ARE
UNIVERSAL IN THE PREMISES:

The following schema are valid:

MU PP PU MP MU PP PU M U
SU MP S U MU MP SP MU S P
SU PP SU PU SP PP SP PU
The Violation of this rule, which is in effect the extension of a term, is
known as the illicit process of the Major Term or the illicit process of
the Minor Term.
e.g.
Every skyscraper is a building,
But no bungalow is a skyscraper;
Therefore, no bungalow is a building.

e.g.
Every circle is a sphere,
But every circle is a figure;
Therefore every figure is a sphere.
RULE # 4: THE MIDDLE TERM MUST BE
UNIVERSAL AT LEAST ONCE.

Schema:
Mu A Mp Mu
E
I
Mu Mu
Mp
O is known as the fallacy of the undistributed
The Violation of this rule
middle.

e.g. All whales are sea creatures;

But some sea creatures are sharks;
Therefore some sharks are whales.
RULE # 5: IF THE TWO PREMISE ARE
AFFIRMATIVE, THE CONCLUSION MUST BE
AFFIRMATIVE. Unequal Distribution
E g. Mu Rule N0. 3
Pp
1. A- Operas are cultural presentations,
Sp Mp
I- But Carmen is an opera; Pu
Sp
O- Therefore, Carmen is not a cultural presentation.
Note: This syllogism is invalid because it violates rules numbers 3 and 5.

Mu Pu
2. E- Machines differ from animals;
Sp Mp
I- But IBM computers are machines,
Sp Pu
O- Therefore IBM computers are not animals
Note: The word “differ” is equivalent to “are not”; therefore the major
premise is equivalently negative, and the syllogism is VALID.
RULE # 6: IF ONE PREMISE IS AFFIRMATIVE AND
THE OTHER IS NEGATIVE, THE CONCLUSION
MUST BE NEGATIVE:
Eg.
1. Angels are spirits; A
But monuments of stones are not angels N
Therefore monuments of stones are spirits A
Note: This syllogism is invalid since the conclusion is affirmative though one of the
premises is negative. Thus it violates Rule # 6.

2. Scholars are eligible for club membership; A

But Elena is not a scholar; N

A=N
‫؞‬ Elena is ineligible for club membership.

Note: This is valid since the conclusion is affirmative (“is”) but equivalently negative
(“ineligible” means not eligible”)
RULE # 7: THE CONCLUSION IS INVALID
WHENEVER THE PREMISES ARE BOTH
NEGATIVE AND NOT EQUIVALENTLY
AFFIRMATIVE.
Eg.
1. No millionaire is a peasant; N
but no peasant is a cultured man; N
Therefore no cultured man is a peasant. N
Note: This is invalid since it violates Rules # 1 and 7. Rules # 1 because there are 4 terms in the
syllogism and Rule # 7 because all the premises and the conclusion are negative.

2. No Filipinos are not eligible; N=A

but Lim Chua is not a Filipino; N
Therefore, Lim Chua is ineligible. A=N
Note: The major premise contains double negatives- “No Filipinos” and “not”; hence it is
equivalently affirmative. The conclusion is apparently affirmative, but it is in reality negative
inasmusch as “ineligible” means “is not eligible”. Therefore this syllogism is valid.
RULE # 8: ONE PREMISE AT LEAST MUST
BE UNIVERSAL.
Schema:
a a i/o
u {e u {e p {i/o These diagrams show
when the premises do
a a
{e {i/o {e
not violate the rule.
u p i/o u

i/o
p {i/o These diagrams show
the rules violation.
i/o
p
{i/o
Eg.
Mp
1. Some policemen are crooks. I
Mp
but some policemen are honest; I
‫؞‬ some honest policemen are crooks.
Note: This is an Invalid syllogism for it violates Rule # 8 and Rule # 4.
I

2 All babies are human beings; A

but Michael is a baby; I
Therefore Michael is a human beings. I
Note: This is an Valid syllogism.
RULE # 9: IF ONE PREMISE IS PARTICULAR, THE
CONCLUSION MUST BE PARTICULAR.
Eg.
1. Some figures are parallelograms;
Pp I
but electricity is not a figure; E
Therefore electricity is not a parallelogram.PuE
Note: Invalid Rules violated: Rule # 9 & Rule # 3

2. Maoists are communists; A

but some communists live in China; I
Therefore all who live in China are maoists.A

Note: Invalid Rules violated: Rule # 9, Rule # 3 and Rule # 4

RULE # 10: THE SUBJECT OF THE
CONCLUSION MUST BE FOUND IN THE
MINOR PREMISE.