LOGIC AND CRITICAL

THINKING

By: SIR UMAIR NAZIR

Email: umairnazir552@gmail.com
Logic & Critical Thinking
SIR UMAIR NAZIR

Course Outline

Logical Reasoning

INTRODUCTION

This course is an introduction to the problems and techniques of

traditional and modern logic comprising both deductive and inductive
inference. The student will learn to distinguish arguments from non-
arguments, to identify and avoid common fallacies in reasoning, to test
for validity both truth functional arguments and categorical syllogisms,
to construct simple formal proofs of validity in truth-functional logic,
and to understand the nature of inductive reasoning and its
relationship to the sciences.

OBJECTIVES

The student will be able to:

1. Employ the basic vocabulary and methodologies of logic.

2. Define and identify arguments and distinguish deductive from
inductive arguments.
3. Understand the relation of the concepts of truth, validity and
soundness.
4. Understand the concept of logical form and be able to use specific
logical forms such as conditionals to test arguments for validity.
5. Identify fallacious reasoning: psychological, material and formal in
everyday conversation and popular media forms.
6. Use the concepts of theory construction and evaluation to both
construct and evaluate hypotheses reliability relative to assigned
problems.

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1. BASIC CONCEPTS.

Proposition, Arguments, Premises, and Conclusions. Recognizing

Arguments. Deduction and Induction. Validity, Truth

Recommended Text:

Irving M. Copi - Introduction to logic - Chapter: 1

2. CATEGORICAL PROPOSITIONS.

The Components of Categorical Propositions. Quality, Quantity, and

Distribution. Venn Diagrams Conversion, Obversion, and
Contraposition. The Traditional Square of Opposition.

Recommended Text:

Irving M. Copi - Introduction to logic - Chapter : 5

3. CATEGORICAL SYLLOGISMS.

Standard Form, Mood, and Figure. Venn Diagrams. Rules and

Fallacies. Venn Diagrams and the Traditional Standpoint. Translating
Ordinary Language Statements into Categorical Form.

Recommended Text:

Irving M. Copi - Introduction to logic - Chapter : 6

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4. SYMBOLIC LOGIC.

Symbols and Translation. Truth Functions. Truth Tables for

Propositions. Truth Tables for Arguments.

Recommended Text:

Irving M. Copi - Introduction to logic - Chapter : 8

5. LOGIC AND CRITICAL THINKING

What is Controversy, Aims of Critical Thinking, Definitions and

Disputes, Uses of Language

Recommended Text:

Stanley, F. Maurice - Logic and Controversy - Chapter: 2

6. INFORMAL FALLACIES.

Fallacies in General. Fallacies of irrelevance. Fallacies of

Presumption, Ambiguity, and Grammatical Analogy.

Recommended Text:

Stanley, F. Maurice - Logic and Controversy - Chapter: 3

Irving M. Copi - Introduction to logic - Chapter: 4

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Definition of Logic

▪ The term “logic” came from the Greek word logos, which is
sometimes translated as “sentence”, “discourse”, “reason”
“rule”, and “ratio”.
▪ The science of reasoning.
▪ A study of the principles and methods used to distinguish good
from bad reasoning.
▪ The study of the principles of correct reasoning.

Sentences

▪ Sentences are the arranged strings of words.

▪ Sentences are either meaningful or meaningless.

Examples:

a) A cat is sitting on the mat. (meaningful)

b) A tac is sitting on the mat. (meaningless)

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Proposition
▪ Some sentences can be verified by sense experience
▪ A statement that expresses a concept that can be true of false.

Examples:

a) It is raining outside.
b) Today is Sunday
c) Mamnoon Hussain is the President of Pakistan.
d) 2 + 2 = 4
e) Human beings are mortal.

Premise / Premises

▪ A sentence or sentences use to serve as the base or ground to

find out the conclusion.
▪ A statement by which we draw conclusion.

Examples:

a) All men are mortal. (Premise)

b) Ali is a man. ( Premise)
_____________________________________
Therefore, Ali is mortal. (Conclusion)

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Some Premise Indicators

▪ Since
▪ Because
▪ Although
▪ And
▪ But
▪ For
▪ Follows from
▪ As shown by
▪ In as much as

Conclusion

A sentence drawn by premise or premises.

Examples:

a) All men are mortal. (Premise)

b) Ali is a man. (Premise)
---------------------------------------------------
Therefore, Ali is mortal. (Conclusion)

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Some Conclusion Indicators

▪ Therefore
▪ Whence
▪ Hence
▪ So
▪ Consequently
▪ As a result
▪ It can be concluded.
▪ Proves that
▪ Thus

ARGUMENT

An argument is a combination of premise / premises and

conclusion.
Examples:
2 (Premise)
+2 (Premise)
--------------
4 (Conclusion)

▪ No mango is sweet
Therefore, no sweet is mango.

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REASONING

▪ The use of logical thinking in order to find results or draw

conclusions.
▪ The act of process of drawing conclusions from facts, evidence,
etc.
▪ The process of drawing conclusion from data.

Example: 2 + 2 = 4

Kinds of Reasoning

There are two kinds of reasoning:

▪ Deductive Reasoning
▪ Inductive Reasoning

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Deductive Argument

▪ When conclusion is completely supported by its premises, it will

be deductive argument.

▪ Deductive reasoning or deduction starts with a general case and

deduces specific instances.

Example of a Valid Deductive Argument

All men are mortal. (Premise) = True

Ali is man. (Premise) = True
----------------------------------------------------------
Therefore, Ali is mortal. (Conclusion) = True

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Inductive Reasoning

▪ Inductive reasoning, or inductive, is reasoning from a specific

case or cases and deriving a general rule .It draws inferences
from observations in order to make generalizations.

▪ An Inductive is the process where a small observation is used to

infer a large theory.

EXAMPLES OF AN INDUCTIVE ARGUMENT

ALI is a man and he is a mortal.

Saif is a man and he is a mortal.
Saad is a man and he is a mortal.
Umair is a man and he is a mortal.
_______________________________
Hence, All men are mortal

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INFERENCE

▪ Inference is the process by which we move toward conclusion

from premises by applying reason.

▪ A process of reasoning …

Types of Inference

▪ Immediate inference
We draw conclusion from a single premise.

▪ Mediate Inference
Premises can be two (minimum) or more than two…

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INFERENCE CAN BE DONE IN FOUR STAGES

Observation: collect facts, without bias.
Analysis: classify the facts …..
Inference: from the patterns, infer generalizations about the
relations between the facts.
Confirmation: testing the inference through further observation.

TRUTH

A property of statements i.e. that they are the case.

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VALIDITY

A property of arguments, i.e. that they have good structure. The

premises and conclusion are so related that it is absolutely impossible
for the premises to be true unless the conclusion is true also.

SOUNDNESS

A property of both arguments and the statements in them, i.e., the

argument is valid and all the statements are true.

Terms & Classes or Categories

A term can be the name of a class or a group.
Example:
Cat is a name of a group of animals having some common features.
A class / category is a group of things, people or animals having
common features.
Examples:
Class of Cats
Class of Dogs

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Categorical Proposition

A categorical proposition joins together exactly two categorical terms

and asserts that some relationship holds between the classes they
designate.
Example: Cats are mammals
In the above statement cats are representing a class and mammals is also
a name of class.

4 Categorical Propositions

There are four types of categorical propositions

A = All men are mortal.
E = No men are mortal.
I = Some men are mortal.
O = Some men are not mortal.

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Quality

A proposition can be affirming something or denying something if it

affirms then it would be an Affirmative Proposition, If it denies then it
would be a Negative Proposition.
Examples:
All students are present. (Affirmative)
Some students are not present. (Negative)

Quantity

A Proposition can be consisting of all members of any Class (Universe)

or some members of that class (Particular).

Examples:

All students are present. (Universal)

Some students are present. (Particular)

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Distribution

When a term refers to all its members it will be a distributed term.

Examples:

A = All toys are broken.

A = All boys are intelligent.

CATEGORICAL PROPOSITIONS
A BIRD EYE VIEW

Code Quality Quantity Subject Predicate

Distribution Distribution
A Affirmative Universal Yes No
E Negative Universal Yes Yes
I Affirmative Particular No No
O Negative Particular No Yes

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The Traditional Square of Opposition

The square of opposition is a chart that was introduced within

classical (categorical) logic to represent the logical relations in virtue
of their form. The square, traditionally conceived which is shown in
below diagram:

Diagram:

Every S is P No S is P
A contraries E

Subalterns Contradictories Subalterns

I sub-contraries O
Some S is P Some S is in not P

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CONTRARIES

The relationship between A & E proposition is Contrary. They can’t

both be true at the same time. So if you know one is true, then you
also know that the other is false.

Examples:

A = All roses are red. T / F

E = No rose is red. F / T

Sub-Contraries

Sub-contraries are exactly the opposite of contraries. It is always the

case that at least one is true. If you know that once is false, then you
automatically know that other is true.
(They can however both be true simultaneously.)
Examples:
I = Some roses are red.
O = Some roses are not red.

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Sub-alternation

With sub-alternation, you should remember that you can go down with
true i.e. if A is true, then I is true as well and up with false i.e. If I is
false, then A is false as well. But not vice versa.

Contradictories

The contradictories, [(A&O)], [(E&I)] can’t both be true at the same

time and in the same sense. One true and one false, but both can’t be
true at the same time.

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Chart for Truth Values of the Propositions

A = True E = False I = True O = False

E = True A = False I = False O = True

I = True E = False A = Undetermined O = Undetermined

O = True A = False I = Undetermined E = Undetermined

Chart for False Values of the Propositions

A = False O = True I = Undetermined E = Undetermined

E = False I = True A = Undetermined O = Undetermined

I = False E = True A = False O = False

O = False A = True E = False I = True

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