Introduction to logical reasoning

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DEPARTMENT OF BUSINESS AND
MANAGEMENT STUDIES
CHAPTER ONE: INTRODUCTION TO LOGICAL
REASONING
PROGRAMME: ALL BSc
COURSE TITLE: Logical Reasoning, Conceptualization and
Critical Thinking
COURSE CODE: PAID311
TOTAL CREDITS: 3
BY
NGANG PEREZ (MAJOR 1)
PAN AFRICAN INSTITUTE FOR DEVELOPMENT
-WEST AFRICA (PAID-WA) BUEA
LECTURE NOTES FOR Logical
reasoning, conceptualization and
critical thinking

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COURSE OUTLINE FOR LOGICAL REASONING, CONCEPTUALIZATION AND CRITICAL
THINKING
PROGRAMME: ALL BSc
COURSE TITLE: Logical reasoning, conceptualization and critical thinking
COURSE CODE: PAID311
TOTAL CREDIT: 3
TOTAL LECTURE HOURS: 15
LECTURER: NGANG Perez (Major 1)
A. COURSE OVERVIEW AND OUTLINE
1. Course Description:
This course provides students with a general overview on the concept of critical thinking and
logical reasoning. It emphasizes the importance of attitudes and practice for good thinking in
today’s society. It establishes a balance approach to think more and think better be it politically,
culturally, economically and socially. Critical thinking is thinking clearly and rationally. It
involves thinking precisely and systematically, and following the rules of logic and scientific
reasoning, among other things. As such the study, equips students with the technical skills to a
tremendous force of constructive argument. Thus the topics understudy will include focal areas
such as; logic and reasoning, structure and parts of argument, the concept of critical thinking
amongst others.
2. COURSE OBJECTIVES: By the end of this course, student should be able to:
• Learning Objectives: By the end of this course, students should be able to:
➢ Lay down the foundational principles of logical reasoning and its relevance
➢ Develop their capacity to think logically and critically about any given situation
within their environment
PAN AFRICAN INSTITUTE FOR DEVELOPMENT-
WEST AFRICA (PAID-WA) BUEA

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➢ Bring out clearly the differences between logical reasoning and balanced
argument
➢ Understand how to identify cause-and-effect relationships
➢ Outline the Different Types of Values
➢ Understand Moral Values and Normativity
3. COURSE SCHEDULE AND TOPICS
This course will cover the following topics in 5 learning sessions with one session per week as
follows:
Week 1: Session 1/Chapter 1: Introduction to Logical Reasoning
Date:
Topics
• Basic Concepts in Logical Reasoning
o Logic
• Reasoning
o Scientific Reasoning
• Operation of the mind
• Laws of thought
• Conclusion and Summary
• Review Questions
4. GENERAL COURSE REVIEW AND FINAL EXAM PREPARATION
Date:
Topics
• Chapter 1: Introduction to Logical Reasoning
5. OTHER REQUIREMENTS
➢ Required Text Books or Articles
❖ Leo A. Groarke and Cristopher W, Tindale 2004. Good reasoning matters: A constructive
approach to critical thinking. (3rd Edition). New York, Oxford University Press
❖ Barbara Minto, 2008. The pyramid principle: Logic in writing and thinking (3rd edition).
Prentice Hall.
❖ Nemeth, C. and Ormiston, M. (2006). Creative idea generation: Harmony versus
stimulation. European Journal of Social Psychology, 37(3):524-535.
❖ Fang, X., Singh, S., and Ahluwalia, R. (2007). An examination of different explanations
for the mere exposure effect. Journal of Consumer Research, 34(1):97-103.
❖ Epstein, R. (1999). Critical thinking. Wadsworth, Belmont, MA

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➢ Important weblinks
1) https://www.skillsyouneed.com/learn/critical-thinking.html [accessed 25th
July 2019]
2) https://philosophy.hku.hk/think/critical/ct.php [accessed 25th July 2019]
3) https://thinkeracademy.com/critical-thinking-skills/[accessed 25th July 2019]
B. COURSE EVALUATION
• Written Assignment 15%
• Graded Quiz 10%
• Discussion Assignment 5%
• Final Exams taken on Campus 70% total 100%
C. LECTURE NOTES AND PRESENTATION (Next Page)

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WEEK 1:
SESSION 1/CHAPTER 1 INTRODUCTION TO LOGICAL REASONING
1.0 Brief Introduction
Let me begin this chapter by saying that, one of the central attributes that distinguishes man from
other living organisms is the ability to think. Without this distinctive characteristic, life would be
hard to live. This course on logical reasoning is out to demonstrate the importance of logical
reasoning in your daily lives in general and in your respective professions in particular.
1.1 LEARNING OBJECTIVES
By the end of this session, students should be able to;
• Define logic and reasoning
• Explain the concept of logical reasoning
• Discuss the relevance of reasoning in a logical manner
• Reason logically
• Determine correct from incorrect reasoning
• Apply the principles of logical reasoning to practical situations
• Understand the barriers to logical reasoning.
1.2 DEFINITION OF KEY TERMS
➢ Logic: It is a branch of philosophy that is concerned with the study of the method and
principles used to distinguish correct from incorrect reasoning or valid from invalid
arguments. It is also the science of the principle of valid thinking. The four main types of
logic are formal, material, analytical and symbolic logic.
➢ Reasoning: Reasoning simply means looking for justification. There are two methods of
reasoning: inductive and deductive reasoning.
1.3 THE MAIN CONTENT
In this basic chapter of our lectures we will be considering some major concepts related to logical
reasoning and conceptualization. These concepts will include logic, reasoning, mind operation,
and laws of thought.
1.3.1: Basic Concepts in Logical Reasoning
1.3.1.1: Logic
It is a branch of philosophy that is concerned with the study of the method and principles used to
distinguish correct from incorrect reasoning or valid from invalid arguments.

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It is also the science of the principle of valid thinking. The four main types of logic are formal,
material, analytical and symbolic logic.
Many people associate logic with brain teasers and mathematical puzzles, which seem to have
little relevance to real life. The truth is that logic is of great practical significance. If your friend is
in New Zealand, you know she is not in Japan. That is logic. This piece of everyday reasoning
involves logic. The core of logic is about consistency and deduction, both of which are
indispensable for everyday thinking, not to mention scientific research and legal reasoning. Logic
also plays a special role in computer technology. Computers are good at processing information
because their processors can perform a huge number of logical operations very quickly. Obviously,
normal people are capable of logical reasoning to some extent, or else we would not be able to
survive very long! But making the effort to study some logic can improve our understanding of
what good reasoning is like so we can become even better.
In this section, we shall look at some basic concepts of logic.
a. Consistency
A set of statements is consistent when and only when it is logically possible for all of them to be
true in the same situation. Otherwise they are inconsistent. So for example, "Adrian is happy" and
"Adrian is married" are consistent with each other since there is no reason why a married person
cannot be happy. On the other hand, "Visanna is 30 years old" and "Visanna is 20 years old" are
obviously inconsistent. Here are a few more points to remember about consistency:
• Inconsistent statements are also known as contraries.
• We can also speak of a single statement as consistent or inconsistent, depending on whether it is
logically possible for it to be true. "There are round squares" is inconsistent and false. "Paris is in
France" is consistent and true. "Nobody lives in Paris" is consistent but false.
• Whether a set of statements is consistent depends on whether it is logically possible for all of
them to be true in the same situation. It is not necessary that they are actually true. "Paris is in
Italy" and "Nobody lives in Paris" are consistent with each other, even though both are actually
false.
• To show that a set of statements is consistent, we can either show that they are actually true or
describe a logically possible situation in which they are all true. Consider the two previous
statements about Paris. Imagine that Italy conquers France with chemical weapons and takes over
Paris. But Paris became contaminated and everyone leaves. This imaginary situation is farfetched
but coherent, and shows that the statements are consistent.
• Statements that are actually true are consistent with each other, but false statements might or
might not be consistent with each other. The two previous statements about Paris are false but
consistent. "Nobody lives in Paris" and "Only 10 people live in Paris" are false and inconsistent
with each other.

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• If a set of statements is inconsistent, the statements will entail a contradiction of the form:
P and it is not the case that P.
• Take "Nobody lives in Paris" and "Only 10 people live in Paris." The second statement entails
"It is not the case that nobody lives in Paris," and together with the first statement they entail the
blatant contradiction:
Nobody lives in Paris and it is not the case that nobody lives in Paris.
• Many inconsistencies are easy to detect, but not always. Suppose someone says we should be
cautious in making general claims. This seems like good advice because sweeping generalizations
like "Every Italian loves pizza" and "All Belgian chocolates are good" are bound to have
exceptions. So we might be tempted to conclude that all general claims have exceptions. But the
claim "All general claims have exceptions" is actually inconsistent. It is itself a general claim, and
if it were true, it should also have an exception. But this implies that not all general claims have
exceptions. In other words, the claim cannot possibly be true and is therefore inconsistent!
If we want to speak truly, we should avoid inconsistent statements. But sometimes ordinary
speakers use sentences that seem to be inconsistent, such as "I am happy and I am not happy."
Why do people say things that cannot be true? One answer is that these sentences have incomplete
meaning. When we fully specify their meaning, they are no longer inconsistent. For example,
perhaps the speaker is happy that she is getting married, but she is also not happy that her ex-
boyfriend showed up at the wedding. She is happy about one thing and not happy about a different
thing, so there is no real inconsistency.
b. Logical Equivalence
If P entails Q and Q entails P, then P and Q are logically equivalent—for example, "Superman is
more powerful than Batman" is logically equivalent to "Batman is less powerful than Superman."
When two statements are logically equivalent, they necessarily have the same truth value—it is
not possible for one of them to be true and the other one to be false.
c. Negation
The negation of a statement P is any statement whose truth-value is the opposite of P. Given any
statement in English, we can form its negation by appending the expression "it is not the case that."
So the negation of "it is raining" is "it is not the case that it is raining," or, in other words, "it is not
raining." Here are some facts about negation:
• A statement and its negation are always inconsistent with each other.

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• A statement and its negation form a pair of exhaustive and exclusive alternatives, e.g. Santa Claus
exists; Santa Claus does not exist. They cannot both be true and they cannot both be false.
• Negation involving modal verbs in English can be tricky. "You must leave" and "you must not
leave" are inconsistent. But they are not exhaustive alternatives because it is also possible that
there is nothing you must do. Perhaps it is up to you whether you stay or leave. The negation of
"you must leave" is "it is not the case that you must leave," not "you must not leave." However,
the negation of "you may leave" is "you may not leave"!
• In formal logic, the negation of P can be symbolized as ~P, >P, or not-P
d. The conditional
A conditional statement (or a conditional) is any statement of the form "If P then Q"—for example,
"If you are a member, then you can get a discount." Conditionals are of special importance because
they can be used to formulate rules and general laws:
• Computer programs contain lots of rules about what to do in some given situation. A rule for
removing spam messages might be: "If an email contains the words Viagra and sex, put it in the
trash folder."
• A lot of legal rules are conditionals describing the legal consequences of specific situations—for
example, if you are in a moving vehicle equipped with seat-belts, then you are required to wear
one.
Given a conditional "if P then Q", P is the antecedent of the conditional, and Q the consequent. To
accept a conditional is to accept a certain logical or evidential connection between P and Q. But
you don't have to accept that P and Q are both true. For example, you might agree with this
statement:
If the sun explodes tomorrow, then we shall all die a sudden death.
But you can consistently agree that the statement is true, even if you do not believe that the sun
will explode tomorrow, and you also do not believe that we shall all die suddenly.
1.3.1.2: Reasoning
Reasoning simply means looking for justification. There are two methods of reasoning: inductive
and deductive reasoning.
a. Deductive reasoning: It is reasoning from general to particular. Look at the example
below:
All men are mortal
John is a man
Therefore, John is mortal

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b. Inductive reasoning: It is reasoning from particular cases to make generalized conclusions.
For example:
“A dog steals. Therefore, all dogs are thieves.”
Scientific Reasoning
Science is regarded as one of the greatest achievements of human beings, alongside art, music, and
literature. Technology is a product of science, and it has a huge impact on our lives. But the core
of scientific methodology is hypothesis testing, an essential part of critical thinking.
Broadly speaking, hypothesis testing is a matter of gathering evidence to select the best hypothesis.
(In this lecture, a hypothesis is the same as a theory or a claim— a statement that can be either true
or false.) But hypothesis testing is not just for scientists. In any type of career, we have to solve
problems, and hypothesis testing helps us find the best solutions to our problems. Suppose your
mobile phone is not working. Is the battery dead or is the phone broken? You try to recharge it to
see if it works. If it does the phone wasn't broken. This is hypothesis testing. Or think about how
to improve your health. What should you eat and what exercises should you do? You need to gather
information and evaluate different theories before coming up with a plan. This also involves
hypothesis testing.
There are two noteworthy features about hypothesis testing. First, it is based on evidence, not on
gut feelings, tradition, popularity, authority, or personal preferences. Second, hypothesis testing is
fallible, and it is often difficult to prove that a theory must be correct. Our evidence might be
tainted without our knowledge, or perhaps the evidence is inconclusive. This does not mean we
should give up scientific reasoning. We do our best to identify the theory that has the highest
probability. It is too bad if we turn out to be wrong, but such is the uncertainty of life. This is like
investing in the stock market. Nobody can predict the future accurately all the time. But someone
who is correct 70% of the time will already be doing very well.
1.3.1.3: Operation of the mind
This is the process through which the mind performs certain intellectual activities. It involves three
stages:
1. Simple apprehension: At this initial stage the find forms ideas or concepts by the process
of abstraction. Some of these concepts come from sense experience.
2. Judgment: At this stage the mind affirm or negate a statement or proposition which it
comes across.
3. Reasoning (drawing inferences): It is the process from which a judgement is derived from
one or two judgements whose truth or falsity is implied in the former. For example:
No thieves are honest people
Some children are thieves
Therefore, some children are not honest people.

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1.3.2: Laws of thought
These are the basic principles that guide logical reasoning. There are four of these principles
1.3.2.1: Principle of identity: According to this principle, a thing is what it is. It cannot be
something else. This principle is relevant because it helps us to distinguish one thing from the
other. For example, a telephone is a telephone. In reasoning, it holds that the same term must have
the same meaning in the course of the same argument.
1.3.2.2: The principle of excluded middle: It simply states that a statement is either true
or false. In states that in two contradictory statements, one must be true and the other false. There
is no half way for something to exist. It is either inexistence or not.
1.3.2.3: The principle of contradiction: It denies the idea that something cannot be in
existence and non-existent at the same time. A statement cannot be true and false at the same time.
It must be either true or false.
1.3.2.4: The principle of sufficient reason: It states that everything must have a sufficient
reason why it is so and not otherwise. This principle also be likened to that of causality which
holds that everything that exist in the universe has a cause for its existence.
Proposition: It is a statement that either makes an assertion or a denial. For example. “These are
mangoes” “These are not mangoes”
1.4 Conclusion
Logical reasoning (or just “logic” for short) is one of the fundamental skills of effective thinking.
It works by raising questions like:
If this is true, what else must be true?
If this is true, what else is probably true?
If this isn’t true, what else can’t be true?
These are all inferences: they’re connections between a given sentence (the “premise”) and some
other sentence (the “conclusion”). Inferences are the basic building blocks of logical reasoning,
and there are strict rules governing what counts as a valid inference and what doesn’t — it’s a lot
like math, but applied to sentences rather than numbers
1.5 Summary
Generally we have seen what logical reasoning is all about. There are two basic types of logic,
each defined by its own type of inference. They correspond to the two categories in the example
from section 1.
Deduction is when the conclusion, based on the premises, must be true. For example, if it’s true
that the dog always barks when someone is at the door and it’s true that there’s someone at the

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door, then it must be true that the dog will bark. Of course, the real world is messy and doesn’t
always conform to the strictures of deductive reasoning (there are probably no actual dogs who
always bark when someone’s at the door), but deductive reasoning is still important in fields like
law, engineering, and science, where strict truths still hold. All math is deductive.
Induction is when the conclusion, based on the premises, is probably the answers are less definitive
than they are in deductive reasoning, but they are often more useful. Induction is our only way of
predicting what will happen in the future: we look at the way things are, and the way they have
been in the past, and we make an educated guess about what will probably happen. But all
predictions are based on probability, not certainty: for example, it’s extremely probable that the
sun will rise tomorrow morning. But it’s not certain, since there are all sorts of catastrophes that
could happen in between now and then.
1.6 Review Questions
❖ Describe the four basic principles that guide the logical reasoning
❖ Explain the concept of mind operation
❖ With the aid of examples define
o Principle of Identity
o Principle of excluded middle
o Principle of contradiction
o Principle of sufficient reasoning
1.7 References
❖ Barbara Minto, 2008. The pyramid principle: Logic in writing and thinking (3rd edition).
Prentice Hall.
❖ Mclnerny, D,Q. 2004. Being logical: A guide to good thinking. USA, Random House.
❖ Leo A. Groarke and Cristopher W, Tindale 2004. Good reasoning matters: A constructive
approach to critical thinking. (3rd Edition). New York, Oxford University Press
❖
1.8 Task
❖ Read the notes on unit 1.3.2 (Laws of thought) and make a power point presentation of not
more 10 slides
1.9: Reading Assignment/Suggested Readings:
❖ Read this article by Reichertz, Jo (2014), "Induction, deduction, abduction", in Flick, Uwe
(ed.), Qualitative Data Analysis, SAGE Publishing, Accessed from
https://en.wikipedia.org/wiki/Logical_reasoning June 30, 2019
1.10 Reading Assignment Supplementary Source
❖ You Tube Video lecture: How to Master LSAT Logical Reasoning
❖ Video Highlights: - Learn how to improve your score in the Logical Reasoning section of
the LSAT.
❖ Note: To access the video, copy and paste this Playlist

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❖ URL: https://youtu.be/6QtoaQ1o-DI
❖ Source: https://www.youtube.com/watch?v=6QtoaQ1o-DI. Retrieved 30 June 2019.
1.11 Written Assignment
❖ Describe the four basic principles that guide the logical reasoning
1.12 Discussion Assignment
❖ Discuss, is logical reasoning necessary for everyday life?
1.13 Graded Quiz
1. One of the central attributes that distinguishes man from other living organisms is ---: Tick
the most appropriate.
a. His level of civilization
b. The capacity to grow
c. The ability to think
d. Its nature to reproduce
2. Generally, there are four main types of logic. Tick the most appropriate combination.
a. Formal, material, analytical and symbolic logic
b. Formal, material, exponential and symbolic logic
c. Discrete, material, analytical and symbolic logic
d. Evolutional, formal, exponential, Discrete
3. - - - is the study of the method and principles used to distinguish correct from incorrect
reasoning. Tick the most appropriate.
a. Argument
b. Psychology
c. Philosophy
d. Logic
4. Computers are good at processing information because. Tick the most appropriate.
a. Their processors can perform a huge number of logical operations very quickly
b. Their systems are designed to perform multitasking activities effectively
c. They are structured to reproduce complex information faster than humans
d. The machines make very little or limited error in the processing of information
5. A set of statements is consistent when and only when it is logically possible for… Tick the
most appropriate.
a. All of them to be true in the same situation.
b. Some of them to be true in different situations
c. All of them to imply the same thing in the same situation
d. Some of them to imply the same thing in different situations
6. Is it possible that sometimes ordinary speakers use sentences that seem to be inconsistent,
such as "I am happy and I am not happy?” Tick the most appropriate
a. Yes

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b. No
c. Sometimes
d. Yes, but it depends on the situation
7. There are two noteworthy features about hypothesis testing. Tick the most appropriate
combination
a. It is based on evidence and it is fallible
b. It is based on evidence and authority
c. It is based on tradition and it is fallible
d. It is based on tradition and it is evidential
8. The operation of the mind performs certain intellectual activities except one. Tick the best
exception.
a. Rational Thinking
b. Simple Apprehension
c. Judgement
d. Reasoning
9. According to the principle of - - -, a thing is what it is. It cannot be something else. Tick
the most appropriate.
a. The principle of excluded middle
b. The principle of contradiction
c. Principle of identity
d. The principle of sufficient reason
10. According to the principle of - - -, it denies the idea that something cannot be in existence
and non-existent at the same time. Tick the most appropriate.
11. Normal people are capable of logical reasoning to some extent. True or False
a. True
b. False
c. True but depends on the situation
d. None of the above
12. Inconsistent statements are also known as contraries. True or False?
a. True
b. False
c. True, but depends on the situation
d. None of the above
13. The process from which a judgement is derived from is called - - -. Tick the most
appropriate
a. Operation of the mind
b. Simple apprehension

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c. Reasoning
d. Argument
14. - - - principle is likened to that of causality which holds that everything that exist in the
universe has a cause for its existence. Tick the most appropriate.
15. - - - is a statement that either makes an assertion or a denial. For example, “These are
mangoes” “These are not mangoes”
a. Hypothesis
b. Assertion
c. Proposition
d. Statement

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