Philos 118- Logic and Critical Thinking

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 resultedfrom man’s philosophical speculations.

1. Ethics or Moral Philosophy2. Metaphysics or Ontology3. Theology4. Philosophy of Man5. Cosmology6. Political Philosophy7. Aesthetics8. Epistemology9. 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 LOGICLogic 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 IdeasII. Judgment, Enunciation, Predication of IdeasIII. Reasoning, Argument, Inference of New Predication

Schematic Diagram

Mental Act

Mental Product

External Sign

Logical Issue

Apprehension

Idea Term Predicability

Judgment Enunciation

Proposition Predication

Reasoning Argument Syllogism InferenceRemarks: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 LOGICARISTOTLE (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.

EXERCISES1. 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 PHANTASMThe 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 and immaterial things

Not possible of complex 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.

ABSTRACTIONThe 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 IDEAThe 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.

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

COMPREHENSION EXTENSION

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 EXTENSIONA. 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 homeb. a teenagerc. feard. Lord

2. Which one of the following has a greater extension (Choose only one and explain why)

a. European, or Americanb. 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 factExample: 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 Proposition2. 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 subjectsubject, the predicatepredicate, and the copulacopula.

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

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.

ShakespeareShakespeare is England’s greatest dramatist.

Particular- if the subject designates an indefinite part of its total extension.

Some prima ballerinasprima 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 A and II are taken from the two vowels of AAffIIrmo (Affirm) and EE and OO from the two vowels of nEEgOO (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.

Ostands for particular and negative statements.

Universal/SingularA E

Affirmative Negative

I O Particular

Model Statements of these symbols are the following:

AA 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.

EE1. 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 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.

OO1. Some dogs are not black.2. Not all women are fickle.3. A few Filipina are not literate.4. Many American are not rich.5. Most Russians are not Communist Party members.

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 PI – Some men are wise O – Some men are not

wise

KINDS OF OPPOSITION

1. Contradictory2. Contrary3. Sub- Contrary4. 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 Ptherefore some S is not P. therefore some S is P.Truth Table is:

A , E O , I T F

F TRule: 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 E E AT F T FF ? 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 IT ? 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-TTherefore some doctors are not negligent.

O-?

B. Some S is P.therefore some S is not P.

Some Kittens will be dogs; I - FTherefore 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. subcontrariesb. 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.


3. No good short story is rambling; therefore every good short story is rambling.


4. Not every drama has dialogue; therefore every drama has dialogue.


5. Quite a number of novelist are Filipinos; therefore no novelist are Filipinos


6. No Greek tragedy has a fanciful theme; therefore some Greek tragedy has a fanciful themes.


7. Some existentialist are dramatist; therefore All existentialist are dramatist.


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


9. All works of Nick Joaquin are held in high esteem; therefore no works of Nick Joaquin are held in high esteem.


10. One of my friends is a short story writer;therefore none of my friends is a short story writer.

a. contradictories c. contrariesb. 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 fact3. 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.

e.g.

“Cat” rimes with “fat”,but You are a member of the club “Cat”,Therefore, you are fat.

S- Minor TermP- Major TermM- Middle Term

The violation of this rule is called the fallacyOf the four or five term or six terms.

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 MU

SU MP SU MU MP SP MU SP

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 Mp Mu

Mu Mu

Mp

The Violation of this rule is known as the fallacy of the undistributed middle.

e.g. All whales are sea creatures;But some sea creatures are sharks;Therefore some sharks are whales.

A

E

I

O

RULE # 5: IF THE TWO PREMISE ARE AFFIRMATIVE, THE CONCLUSION MUST BE AFFIRMATIVE. E g.

1. A- Operas are cultural presentations, I- But Carmen is an opera; O- Therefore, Carmen is not a cultural presentation.

Note: This syllogism is invalid because it violates rules numbers 3 and 5.

2. E- Machines differ from animals; I- But IBM computers are machines, 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.

Pu

PpMu

Sp

Sp Mp

Unequal DistributionRule N0. 3

Mu Pu

Sp Mp

Sp Pu

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 NTherefore 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; ABut Elena is not a scholar; N Elena is ineligible for club membership.

A=NNote: This is valid since the conclusion is affirmative (“is”) but equivalently negative (“ineligible” means not eligible”)

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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. NNote: 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=NNote: 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:

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ua

e e

e e

a

a a

i/o

i/o

u p

u p u

i/o

i/o

p

p

i/o

i/o

i/o

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These diagrams show when the premises do not violate the rule.

These diagrams show the rules violation.

Eg.1. Some policemen are crooks.

Ibut some policemen are honest;I some honest policemen are crooks.INote: This is an Invalid syllogism for it violates Rule # 8 and Rule # 4.

2 All babies are human beings;Abut Michael is a baby; ITherefore Michael is a human beings.I

؞Mp

Mp

Note: This is an Valid syllogism.

RULE # 9: IF ONE PREMISE IS PARTICULAR, THE CONCLUSION MUST BE PARTICULAR.

Eg.1. Some figures are parallelograms; I

but electricity is not a figure; ETherefore electricity is not a parallelogram. ENote: Invalid Rules violated: Rule # 9 & Rule # 3

2. Maoists are communists; Abut some communists live in China; ITherefore all who live in China are maoists.A

Pp

Pu

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.

Documents

Philos 118- Logic and Critical Thinking