Logic

West Visayas State UniversityService, Harmony Excellence

Hum 107 – Logic and Critical Thinking

Stephen Rey P. Ligasan, Ph. D.

I. INTRODUCTION

PHILOSOPHY

Etymological

Φίλείν Philein – love

Σοφίά Sophia – wisdom

Real

Search for meaning of life – its importance, significance, value, relevance

Elements of Philosophical search:

1. The object of the search is of real value to the subject.

2. It consumes the whole person – attention, concentration, interest, effort.

3. It is continued without let-up until (a) the answer is found, or (b) the answer is not yet found.

The Nature of Philosophy

- Man wondered, questioned, and sought for answers, a total world picture – Birth of Philosophy

- Ionians and Early Greek Philosophers

a. scientific

b. ethical

c. religious

d. aesthetic

Branches of Philosophy

Theoretical – “knowledge for the sake of knowledge itself”

1. Epistemology - knowledge

2. Metaphysics – things beyond nature

3. Cosmology – world or universe

4. Rational Psychology - soul

5. Theodicy - God

Branches of Philosophy

Practical – Material or useful end 1. Logic – reason, thought, discourse2. Ethics - morality3. Aesthetics – art and beauty4. Axiology - values5. Semantics - language6. Social Philosophy - society7. Philosophy of Man – man’s existence

Short Historical Outline

A. Pre-Socratics

B. Greeks

C. The Romans

D. The Middle Ages

E. Early Modern Period

F. The 19th Century Thinkers

G. The Contemporary Period and Post Modern Period

Why Philosophy?

1. Philosophy shows no sign of coming to an end.

2. There is no such thing in Philosophy, once it has gotten off the ground, as a completely new idea.

“If we live as we ought, we shall know things as they are, and that if we see things as they are, our vision will help us live as we ought.” -- Joad

Beginnings of Logic

Aristotle (384-322 BCE) – Father of Logic, Formal study in schools of Ancient Greece as a system of analyzing and evaluating correctness of arguments through terms

Chrysippus (279-206 B.C.) – fundamental element of logic is truth and falsity of propositions

Abelard (1079-1142) – Theory of Universals as concepts of the mind

Beginnings of Logic

Leibnitz (1646-1716) – Father of Symbolic Logic

Mill (1806-1873) – Inductive Logic

Whitehead (1861-1947) and Russel (1872-1970) – Reduction of the whole of mathematics to logic

Logic Defined

Zeno (336-264 B.C.) – coined the word logic Λογίκε – logike (systematized and intelligible) Λόγος – logos (thought, reason, discourse)

Etymological Definition – systematic study of matters pertaining to thought and discourse

Real Definition – science and art of correct thinking

Values of Studying Logic

1. Reason out clearly, spontaneously and correctly

2. Recognize good from bad reasoning

3. Use of supporting evidence or reason in arguments

4. Develop critical attitude towards assumptions and presuppositions

5. Grasp logical terminologies

Values of Studying Logic

6. Awareness of ambiguity of words and various functions of language

7. Motivation to value systematic and objective approach in analyzing issues and in doing things

Classification of Logic

1. Based on Validity of Reasoning

Formal Logic – conformity with structure of correct argument (Formal Validity – All nurses are caring.)

Material Logic – based on truth content or meaning of statement involved in reasoning (Material Validity - Some nurses are caring.)

Exercise I

Identify whether the following sentences are formally valid and/or materially valid.

1.All Germans are good singers.

2.Some students are nosy.

3.All of you will pass Logic.

4.Every soldier is courageous.

5.Water is a liquid substance.

6.Roses are animals.

7.All cats are corporeal.

8.Ilonggos are sweet.

9.All lawyers are not liars.

10.Some mothers love their children.

Classification of Logic

2. Based on Approach in Arriving at Knowledge

Deductive Logic – Universal/General to specific

Inductive Logic – Specific to universal/general

Exercise II

Identify whether the following arguments are Deductive or Inductive Logic. Give 5 examples for each type of Logic and have them compared with your seatmate.

1.All men are bodily; But John is a man; Ergo, John is Bodily.

2.America is a capitalist; But Illinois is in America; Ergo, Illinois is a capitalist.

3.Socrates is a philosopher; But Socrates is a man; Ergo, Some men are Philosophers.

4.A pencil is material; But pencils are hard; Ergo, All hard objects are material.

5.Every dog is an animal; But Rudolph is a dog; Ergo, Rudolph is an animal.

Paradigm of Logic

“Terms compose a proposition, while propositions form an inference.”

INFERENCE

PROPOSITIONS

TERMS

Elements of Logic and Its Thinking Equivalent

1. TERMS - CONCEPTS

2. PROPOSITIONS - JUDGEMENT

3. INFERENCE - REASONING

II. CONCEPTS AND TERMS

Terms A.As a sign of a concept, oral terms are articulate sounds that serve as a conventional or arbitrary sign of a concept.

B.From the point of view of the term’s being the ultimate structural element to which a proposition or argumentation can be resolved, a term is a word or group of words that can serve as the subject or predicate of a proposition.

Comprehension, Extension and their Inverse Relationship

1. Comprehension of a term – sum of understandable aspects or elements of the quiddity signified by the term.

e.g. Man = rational, sentient, animate or living, corporeal substance

2. Extension of a term – includes subjects signified by the term.

e.g. Man = Filipinos, doctors, nurses, etc.

Exercise IIIState if the following pairs of terms have greater or identical comprehension.

1.Triangle and figure

2.Triangle and plane figure bounded by three straight lines

3.Triangle and isosceles triangle

4.Dog and animal

5.Animals and substance, material, living and sentient

6.WVSU and College of Medicine

7.Zenith and peak

8.Man and doctor

9.Man and substance, material, living, sentient and rational

10.God and Supreme Being

Extension of Terms

2 Kinds of Extension of Terms

1. Absolute Extension of Terms – includes

everything that has the comprehension of the term

e.g. man – includes all races of men

2. Functional Extension of Terms – includes subjects that it actually sets before the mind when it is used in discourse

Functional Extension

3 Kinds of Functional Extension of Terms

1. Singular – one definitely designated

individual or group

e.g. this man, that boy, the prettiest girl

2. Particular – indeterminately designated portion

e.g. some boys, a few girls, most students

3. Universal – sets before the mind each of the subjects whose nature it signifies

e.g. Every nurse, everybody, each individual

Exercise IVIdentify whether the following underlined terms are singular, particular or universal functional extension.

1.Charisse is a good singer.

2.Several students are nosy.

3.Few of you will pass Logic.

4.Every soldier is courageous.

5.Pocahontas is a princess.

6.All dogs are animals.

7.These cats are corporeal.

8.Many Ilonggos are sweet.

9.All lawyers are not liars.

10.Some mothers love their children.

Inverse Relations of Comprehension and Extension

“As the person’s comprehension of the term (and concept) increases, its extension decreases, and vise versa.”

ELEMENTS COMPREHENSION EXTENSION

Man Substance, material, living, sentient, rational

All actual or possible men

Animal Substance, material, living, sentient

All actual or possible men plus all actual and possible other animals

Organism Substance, material, living

All actual or possible men plus all actual and possible other animals, plus all actual and possible plants

Body Substance, material All actual or possible men plus all actual and possible other animals, plus all actual and possible plants, plus all possible non-living bodies

Exercise VArrange the terms from greater comprehension to lesser extension.

1.Table, plastic table, matter, solid object

2.Three-sided figure, figure, right triangle, triangle

3.Dog, organism, mammal, Labrador, animal

4.Water, body, substance, material, non-living body

5.Rational, man, rational animal, doctor, Ben

6.Animal, winged creature, raptors, bird, Philippine eagle

7.Red rose, plants, material, substance, rose, living

8.Institution, college, educational institution, student

9.Book, knowledge, fictitious books, If Tomorrow Comes

10.Angel, Being, Spiritual Being, Archangels, Michael

Distributive or Divisive, and Collective Terms

Distributive or Divisive Terms (and Concepts) – signifies the essence or quiddity of individuals taken singly

e.g. soldier, player, duck

Collective Terms (and Concepts) – signifies the essence or quiddity of a group of individuals but not of those individuals taken singly, as a unit.

e.g. children, team, committee, jury, flock, herd

N.B. Collective terms can be universal (All team), particular (Some team), and singular (This team)

Universal, Particular and Singular Terms

Singular – stands for one individual or group and designates them definitely. Determinants - Proper names, superlatives, demonstrative pronouns, common nouns, collective nouns

Particular – stands for an indeterminately designated portion of its absolute extension. Determinants – Some, three, several, a few, most

Universal – stands for each of the subjects to which it can be applied. Determinants – Every, each, without exemption, whatever

Exercise VIIndicate the quantity or extension of the terms as singular, particular or universal.

1.Captain John Smith (is a sailor).

2.A man (is running down the street).

3.Whoever is in this room (is welcome).

4.A few students (were absent from class).

5.All Filipinos (are human beings).

6.This dog (is a collie).

7.Every dog (is an animal).

8.A dog (is barking loudly).

9.Some cats (are sweet).

10.The lady (is walking).

SIMPLE APPREHENSION AND CONCEPTS

Simple Apprehension or concept – act of the mind understanding the essence or general meaning of a thing without affirming or denying anything.

e.g.

“Man,” “book,” “friend,” or “car”

Judgment – affirmation or denial of what is apprehended

e.g. “Man is a corporeal being.”

The Object of Simple Apprehension

Object – a thing becoming known

a.Material Object – whole object in itself with all its attributes and relationships

b.Formal Object – what we know about the material object through cognition

e.g. 1. An object at a great distance

2. As something

3. As an animal, as a man,

4. As John Smith

Concepts

Concepts – mental expression of an essence or quiddity, a pure image or sign, giving knowledge of what it signifies.

Kinds:

A.First and Second Intention

First Intention – concept according to its own proper being. E.g. Man is mortal.

Second intention – concept that also averts to special mode of existence that the thing has as it exists in the mind. E.g. Man is a universal concept.

Exercise VIIClassify the subject term as a first intention or a second intention. Ask yourself, does the predicate belong to the subject as it exists or can exist in the real order or only as it exists in the mind?

1.Man is a rational animal.

2.Man is an bodily.

3.Man is the middle term of an argument.

4.Man is a social being.

5.Man has an eternal destiny.

6.Man is appetitive.

7.Man has a greater comprehension than “animal.”

8.Man is the subject of the last proposition.

9.Man’s soul is just around.

10.Man is the king of all animals.

Kinds of Concepts

B. Concrete and Abstract Concepts

Concrete concepts – a form (perfection or attribute) as inherent in a subject

e.g. man, bird, flower, house, pencil, book

Abstract concepts – a form (perfection or attribute) as separated from its subject

e.g. animality, whiteness, chairness

Kinds of Concepts

C. Absolute and Connotative Concepts

Absolute concepts – presents its object to the mind as an independent reality, as a substance. It expresses subject (concrete) and form (abstract).

e.g. man, animal, humanity, animality

Connotative concepts – presents its object to the mind as an accident, implying a substance. It merely “connotes” but does not express the subject in which the form inheres.

e.g. long, acrobat, rider, weak, orator, teacher

Exercise VIIIFirst classify each of the following as concrete or abstract; then as absolute or connotative.

1.God

2.Size

3.Energy

4.Yellowish

5.Good

6.Goodness

7.Rational animal

8.Powerful

9.Orator

10.Student

Kinds of Concepts

D. Positive and Negative Concepts

Positive concepts – presents a thing in the mind according to what it is

e.g. being, man, rational, living

Negative concepts – presents a thing in the mind according to what it is not

e.g. non-being, non-man, irrational, dead

N.B. No concept is entirely negative in all respects

Oral Terms

Oral Terms

An articulate sound

A sign

A conventional or arbitrary sign

Sign of a concept

Terms based on Certain Criterion

1. Components

a. Simple terms – made up of single word only representing an idea or thing

e.g. table, chair, pencil, Ann

b. Compound – made up of arranged group of words which refers to one thing or kind of thing taken together as a unit

e.g. The Beautiful lady with a pencil sitting on a chair and writing in the table is Ann.

Terms based on Certain Criterion

2. Significance and non-significance

a.Significant terms – if it signifies or describes a thought or an idea

e.g. All men are corporeal.

b. Non-significant terms – without any meaning, it simply points out the thing.

e.g. Mr. Brown, Mr. White, this book

Terms based on Certain Criterion

3. Meaning – transmits a thought or idea, and sets a boundary to terms

a. Univocal terms – different in spelling and sound but have the same meaning

e.g. beautiful and pretty, physician and medical doctor

b. Equivocal terms – the same spelling and sound but different in meanings in at least two occurrences

e.g. bark, page, pen,

Terms based on Certain Criterion

3. Meaning – transmits a thought or idea, and sets a boundary to terms

c. Analogical terms – partly the same and partly different meanings in at least two occurrences

Intrinsic and Extrinsic

Intrinsic Analogy – realized in each of the analogues of the term. E.g. Being

Extrinsic Analogy – realized only in its primary analogues. E.g. Healthy – predicated only in living organisms

Analogous Terms

Analogy of Proportionality and Attribution

Analogy of Proportionality – similarity of two relationships

E.g. Foot of man and Foot of the mountain

Analogy of Attribution – relationship of a secondary analogue to a primary analogue

E.g. Healthy complexion - health, House of Representatives – house, Macbeth and Hamlet – Shakespeare, Permanent departure - death

Exercise IXClassify the italicized terms as (1) univocal, (2) equivocal (3) analogous by analogy of proportionality, or (4) analogous by analogy of attribution. If terms are analogous, state if the analogy is intrinsic or extrinsic.

1. Triangles are scalene, isosceles and equilateral.

2. His taste for books is better than his taste for burgers.

3. People do too much lying – some in their beds and some in their conversation.

4. Cabbages and potatoes are vegetables.

5. A nurse must have patience with their patients.

6. Both God and creatures are beings.

7. My father fed my stomach while father fed my soul.

8. Her boyfriend passed away.

9. Reading Jason Bourne is just like reading Ludlum.

10. A pen is good in writing and an eraser is good in removing ink.

Supposition of Terms

Suppositio Terminorum – is the property (that terms acquire from their use in a proposition) by which a term stands for a definite one of the various things that it can stand for. function in discourse nature of predicate attributed to the term

E.g.

1.Man has three letters.

2.Man is mortal.

3.The man is happy.

Kinds of Supposition

1. Supposition of Subject Terms – as subjects of propositions, they are either material and formal.

a)Material supposition – use of a term for the spoken or written sign itself, not what it signifies. E.g. Man is watching a movie.

b)Formal supposition – use of a term for what it signifies. E.g. Man is a rational animal.

1-Logical formal supposition – use of a term for a second intention. E.g. Man is a species.

2-Real formal supposition – use of a term for a first intention. E.g. Man is mortal.

Kinds of Real Formal Supposition

(1) Absolute supposition – use of a term for an essence as such, separating from, but not excluding, actual existence in the real order.

E.g. Man is mortal.

(2) Personal supposition – use of a term, not for an essence as such, but for the subject in which essence signified by a term is realized.

E.g. The young man is more happy today.

Kinds of Real Formal Supposition

(1) Essential Supposition – use of a term for a subject inasmuch as this subject is the subject of necessary attributes.

E.g. Man is mortal and Every man is mortal.

(2) Accidental Supposition – use of a term for a subject in as much as this subject is the subject of unnecessary attributes.

E.g. The man has a dirty face.

Exercise IXWhat kind of supposition is treated in the following: Encircle your answer.

1.Man is a universal concept. (Logical, Real)

2.A man is walking in the mountain. (Material, Formal)

3.Man is corporeal. (Absolute, Personal)

4.The man has a funny face. (Essential, Accidental)

5.Man is a rational animal. (Logical, Real)

6.Man is a living-being. (Material, Formal)

7.The tall man is a good player. (Absolute, Personal)

8.Every man is bodily. (Essential, Accidental)

9.Man cooks food. (Material, Formal)

10.Man is the middle term in an inference. (Logical, Real)

Kinds of Supposition

2. Some other kinds of supposition

a.Proper and Improper – Supposition of “dog” is proper in “A dog is an animal,” improper in “The dog ought to be locked in jail.”

b.Determinate and Indeterminate – Supposition of “a horse” is determinate in “Lost: a horse.” Indeterminate in “Wanted: a horse.”

c.Distributive or Divisive and Collective – Supposition of “five men” is distributive or divisive in “Five men are walking,” collective in “Five men make up a basketball team.”

Exercise XClassify and compare the supposition of the italicized terms in each pair of propositions.

1. The eleven boys are running.

The eleven boys are nursing students.

2. For sale: a car.

Wanted: a wife.

3. A whale is a mammal.

Whales are swimming two mile away from the shore.

4. I am looking for a good wife to marry.

Mel Rose is a good wife to marry.

5. He roars like a lion when angry.

The lion is a brute.

Assignment1. What are predicables?

2. Identify, define and give related examples of the 5 predicables.

3. Discuss the Aristotelian Categories or Predicables.

a. The categories as Expressing Modes of Being (10)

b. The Notion of a Logical Category

4. What are definitions? Identify and give brief descriptions of the different kinds of definitions. What are the rules governing definition?

5. Answer all remaining exercises in your booklets.

6. Submit answers for items 1 to 4 at stephenligasan@yahoo.com