DON’T JUST THINK;
BE LOGICAL
Critical Thinking Manual for
College Students
By Lei Bao
Table of Contents
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ABOUT THE AUTHOR
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PROLOGUE
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CHAPTER 1: AN OVERVIEW OF CRITICAL THINKING
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1.1 What is critical thinking?
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1.2 Why do you need critical thinking skills?
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1.3 Higher order thinking skills
CHAPTER 2: ELEMENTS OF CLEAR THINKING
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2.1 Inquiry-based learning
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2.2 Information credibility
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2.3 Dissent and openness
CHAPTER 3: ANATOMY OF ARGUMENTS
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3.1 Objective and subjective claims
DON’T JUST THINK; BE LOGICAL
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3.2 Identifying issues
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3.3 Arguments
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3.3.1 Premises
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3.3.2 Conclusion
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3.3.3 Collaboration
CHAPTER 4: NON-ARGUMENTS
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4.1 Explanations
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4.2 Hypotheticals
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4.3 Rhetoric
CHAPTER 5: ANALYZING ARGUMENTS
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5.1 Level of reason
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5.2 Relevance
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5.3 Unstated assumptions
CHAPTER 6: TWO TYPES OF ARGUMENTS
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6.1 Deduction
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6.1.1 Validity
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6.1.2 Soundness
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6.2 Induction
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6.2.1 Strength
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6.2.2 Cogency
CHAPTER 7: BRIDGING THE GAP BETWEEN STEM AND THE HUMANITIES
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7.1 Mathematical induction
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7.2 Statistics
CHAPTER 8: INFORMAL FALLACIES
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8.1 Abusing the man
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8.2 Appeal to authority
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8.3 Circular reasoning
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8.4 Appeal to emotion
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8.5 Appeal to force
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8.6 Appeal to ignorance
DON’T JUST THINK; BE LOGICAL
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8.7 Straw man
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8.8 Red herring
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8.9 False cause
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8.10 False dilemma
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8.11 Hasty generalization
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8.12 Slippery slope
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8.13 False analogy
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8.14 Complex question
ABOUT THE AUTHOR
Mr. Lei Bao grew up in China and has been living in Guam for almost 10 years. He holds two
bachelor's degrees in English and Surveying Engineering Technology, a master's degree in Logic.
He has 13 years of teaching experience across different countries and regions. Throughout his
career in education, he always values his students' success as the measurement for his performance.
PROLOGUE
Take a moment and visualize. We are living in a world surrounded by billions of people. Each of
them has their views and perspectives. Each of them has their own beliefs and understanding of
this world. Therefore, how do you know what information is true and factual versus bias and
prejudice? This is where critical thinking comes into play.
Critical thinking is a very essential skill to acquire. As humans, we have an innate ability to think,
but at times, the thinking occurring inside our head is twisted because of our personal preference
or misleading information, which in turn changes how we think of something or the decisions we
make. What we see and hear is not always true or even based on facts. Sometimes, it is just a point
of view or conclusion based on personal judgment. It is our individual’s responsibility to be able to
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critically analyze and make sense of the information to ensure that the information we absorb or
understand is accurate. Only critical thinking can help us decipher the thinking process and
explore the truth.
CHAPTER 1: AN OVERVIEW OF
CRITICAL THINKING
Critical thinking skills become more and more important in the modern world — a world full of
redundant information. These skills gradually evolve into a vital component for achieving
academic success. You probably do not recognize that you are using critical thinking skills almost
every day, from comparing and choosing Netflix subscriptions or evaluating and assessing how to
proceed in a group project. Now it is time to systematically anatomize them and spontaneously
apply them to other scenarios.
1.1 What is critical thinking?
To think critically, we examine credibility, evaluate reasoning, and eventually make decisions. The
objective of critical thinking is to avoid prejudice and maintain a rational position. To think
critically, you contract two sides of a debate and analyze its strength and weakness. Generally
speaking, critical thinking skills include:
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Actively seeking two sides of a debate
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Examining the credibility of a claim
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Testing the relevance of the evidence used to support the claim
You need to always keep an open mind and have the courage to challenge any authority’s claim
since your goal is to interpret rationally about what we are reading, hearing, and thinking through.
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1.2 Why do you need critical thinking skills?
No matter what your major is, the process of academic life is a path to pursue rationality. This
path is not a broad road but covered by various obstacles such as bias, emotion, and misjudgment.
Critical thinking enables you to analyze, evaluate, compare, and contrast the surrounding
unstructured information, and synthesis your rational thought which reflects the merit of theories,
methods, concepts, and debates in your academic life.
Developing critical thinking skills will enable you to construct stronger arguments for your
assignments, projects, or exam questions. You will be equipped with the ability to research and
select relevant evidence to support your arguments and ideas.
1.3 Higher order thinking skills
Benjamin Bloom discovered a series of essential learning and thinking skills for college students,
which is called the “Bloom’s Taxonomy”. This method is used to categorize the levels of reasoning
skills that students use for effective learning. There are six levels of Bloom's Taxonomy:
remembering, understanding, applying, analyzing, evaluating, and creating (Figure 1).
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Figure 1 Bloom’s Taxonomy
You, as a college student, are required to develop these higher-order thinking skills for academic
success. You will find that they enhance your capability in both reading and writing, which will
eventually enable you to work effectively and efficiently as an independent learner and to
cooperate with your peers more constructively.
Source: Anderson, Lorin W., and David R. Krathwohl, eds. 2001. A Taxonomy for Learning, Teaching, and
Assessing: A Revision of Bloom's Taxonomy of Educational Objectives. New York: Addison Wesley Longman, Inc.
“No, no, you’re not thinking; you’re just being logical.” (Niels Bohr)
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DON’T JUST THINK; BE LOGICAL
CHAPTER 2: ELEMENTS OF
CLEAR THINKING
Like other skills, such as swimming, a foreign language, and math, etc., it needs repetitive practice
to adapt and be comfortable with thinking critically. In this chapter, you will learn how to think
about thinking with the elements of clear thinking.
2.1 Inquiry-based learning
Inquiry-based learning has existed for thousands of years. Both Socrates and Confucius used
variations on their inquiry-based format. It is a critical component of the scientific method of the
early enlightenment.
As an independent learner, you must adapt inquiry-based learning on every subject you are doing
or progressing. In this learning environment, your instructor is mostly a resource provider and
guide on the side empowering you to ask questions and explore the answers by yourself. You and
your classmates rely on each other and on various resources to solve problems and answer the
questions. It is a space of experimentation. While the process might seem messy compared to the
textbook-based learning approach, you can learn at a rapid pace because you are not wasting time
repeating what you have already known. There are four cycling steps for a deeper understanding
of inquiry-based learning:
1.
Asking appropriate questions of the materials
2.
Investigating answers to these questions
3.
Creating new understanding as a result
4.
Demonstrating what you have gained
This working process encourages you to engage actively and creatively with questions and
problems in collaboration with your classmates or your group. On the other hand, the research
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tasks enable the exploration and investigation of issues and are open-ended so that different
responses and solutions are possible.
2.2 Information credibility
Whenever you open an app or a website, you see information and content that was made
somewhere by someone. Before putting your trust in a source, you need to explore two more
things:
1.
The authority of the person or organization presenting the information
2.
Their perspective
When I say “authority”, I mean the person’s recognized knowledge or expertise on a topic. If you
want to tell if a source is an authority on a topic, you need to leave the source. Nobody is going to
say he or she is not an authority on this topic.
Vertically reading a website or article only gives you the information that the source wants you to
see. It’s really easy to make a website or social media account look authoritative. While using
critical thinking techniques in reading requires you to investigate a source’s authority, you want to
consider these factors:
1.
The author or authors’ professional background
2.
The process they used to produce that information
3.
The systems that are in place to catch mistakes and correct them
An author’s professional or educational background can indicate whether they are qualified to
speak knowledgeably about a topic. Generally speaking, those who work professionally in a field or
have done lots of work within it, are better equipped than random people off the street. That
doesn’t mean that experts are always right of course but they are more likely to be right than the
random people off the street. So, a scientist who has published studies on climate change in
prominent journals is a much more reliable source on climate change than a blogger with no
formal science training. Failure to believe in and trust expertise is a big problem on the internet.
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Another good indicator of whether a source is reputable is the process used to produce or gather
information. The process a source used to gather information is often right there in their work. A
reporter might attend a protest and talk to some protesters, and then describe those conversations
in a story. A professor might explain in their new study that they asked 5,000 people in a survey.
Some news organizations even publish their journalistic ethics, philosophies, and methodologies
for the public.
Lastly, the system in place to catch mistakes is just as important as the process a source uses to
collect information. News publications often employ fact-checkers and professional journalists.
Editors also take part in fact-checking efforts during the process of writing articles. Sometimes
another force steps in to help point out mistakes — the public. They might write a letter to the
editor or leave a comment. When very serious corrections are made, sometimes a publication’s
editor in chief, public editor, or ombudsman will step in to explain what went wrong.
In addition to varying backgrounds and processes for gathering information, every source also has
its perspective or point of view. You’ll notice I am not using the word “bias” because “bias” means
unfairly favoring something. However, we tend to associate bias with anyone we disagree with even
though I don’t think everyone unfairly preferences some things over others. Nevertheless, everyone
does wake up each morning with a particular perspective on the world due to their lived
experiences.
Rather than dismiss a source because their background might make them supposedly biased, use
the knowledge you learn about them to understand their perspective. Consider their reason for
sharing that information. How might their perspective influence what they’re sharing?
When reading an opinion, we should carefully consider the author’s perspective while examining
their arguments. We will talk more about opinions and arguments in the next chapter.
There is so much information online, both good and bad, that to sort through it all we need to
stop, think, and look around. We read critically to find out who is behind the information. And
then, we seek out specific information about those sources, their authority, and their perspective.
Each bit of information we get about a source is like a piece of stained glass. Once it’s all put
together, it becomes a lens through which we view their claims and argument. That makes us
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better at understanding what information is reliable and what information in turn we should pass
on. It also makes your life more colorful.
2.3 Dissent and openness
Many social manners are about creating consistency. It is easy to overlook the vital importance of
dissent in an effective community. Communities rely on shared values and common purpose.
Critical thinkers try to build alignment around their decisions working to eradicate passive or
aggressive behavior. Common values and customs are there to streamline the conduct of
stakeholders and remove unwanted individualists.
You can imagine that a functioning community is like a school of fish that all swim in the same
direction. However, the community cannot work without pockets of dissent. We need the obstinate
fish that has his or her own view and tries to swim in a different direction. We need dissent and
divergence in order to reach the right conclusions and decisions at the end. If no one challenges
the beliefs in the community, there will be no beliefs but only thoughtless unchanging doctrine. Full
consensus leads to full mediocrity.
As a critical thinker, you make decisions and you stand for them, but you must also leave room for
those who disagree with you and listen to them. Listen to the dissenters and understand why they
are having a different opinion. You do this not only for them but for anyone in the community who
may become a dissenter once in the future.
From time to time, you will make changes to your decisions and beliefs based on the input from the
dissenters. As you do that, it is important that you make it known to everybody that you did listen
to them and you did take their view into account. That statement alone will reassure everybody
that it is perfectly a right to speak your mind to say what you think and make proposals that
diverge from the current plan. When that happens, your organization’s strengths become much
more agile, productive, and innovative because people know they won’t be judged by their
opinions.
Once the dissenting views have been heard and fully considered, it’s time for alignment again.
After divergence comes convergence, decisions are made and communicated. Now it is time for the
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community to agree and commit or to disagree and commit. Commitment from everyone is the
key.
For long-term success, the team of critical thinkers must learn to appreciate dissent and to create
unity around the joint commitment. When that happens, the fish will again all swim in the same
direction. But the direction may have been influenced by the obstinate few who had valuable input
on the direction and where the community is going.
CHAPTER 3: ANATOMY OF
ARGUMENTS
As you know, critical thinking allows you to apply reason or logic to evaluate something you read,
hear, or see. In most of the case, people use critical thinking to evaluate argument someone has
made. In this chapter, we will step back and carefully examine claims, issues and arguments
logically and anatomize arguments to see what they really are.
3.1 Objective and subjective claims
Arguments are made up of claims. Logic texts are more commonly used interchangeable terms
such as statement and proposition. These are all intended to mean the same thing.
Claim = Statement = Proposition
An objective claim is a statement about a factual matter that can be scientifically measured and
proven to be either true or false. For these factual matters, there are recognized criteria and
methodologies to determine whether they are true or false.
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A subjective claim, on the other hand, is not a factual matter. It is an expression of opinion, belief,
or personal preference. A subjective claim cannot be proved right or wrong by any generally
accepted criteria while an objective claim can be.
The distinction between subjective and objective claims is a subtle one. You should be careful not
to simplify it into assumptions about truth values or to end up in a position of relativism or
objectivism.
Claims scatter on a spectrum from being objective to being subjective depending on the degree. At
the objective end of the spectrum are facts. They can be deemed to exist as being true or false
independent of the individuals making the claim.
At the other subjective end of the spectrum are opinions. They are only held to be relevant to the
subject making that claim. Therefore, only the subject can truly validate the claim. For example,
the claim — I like math — is a subjective claim. The validity of this statement is fully dependent
on the subject making the statements.
Most claims might be somewhere in between pure objective facts and pure subjective opinions. To
determine whether a claim is objective or subjective, one can ask if it meets several criteria to be
deemed an objective claim.
1.
An objective claim can be proven to be true or false.
2.
An objective claim has a consensual method for determining whether they are true or
false.
3.
In the event of a disagreement about whether the claim is true or false, at least one
person will be correct.
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Thus, a question of fact has a either correct or incorrect answer while a preference has as many
better or worse answers. These different types of claims create different dynamics to issues.
My dear students:
If you step back and think about the fears and worries you are having, you might
find out that most of them are derived from other people’s judgments. We are
allowing other people’s opinions to influence our life. You know that letting
somebody else dictate your life leads to unhappiness, but you cannot control it.
You care about the comments from your parents, friends, or anyone related to
you if you do this or that. Many life gurus persuade us not to do that, but they
can never explain the methodology about how-to.
This section helps you realize that a subjective claim is an expression of opinion,
belief, or personal preference. It cannot be proved right or wrong by any
generally accepted criteria. In that case, wasting your attention on those
unprovable claims is an inefficient lifestyle. If your goal is to live a healthier,
happier, and successful life, apply critical thinking to distinguish subjective claims
and objective claims first and spend most of your energy on the objective ones.
Lei Bao
3.2 Identifying issues
Now we’re moving to the core of the matter. Issues are the motivation of applying critical thinking
and the central focus which critical thinking addresses. Whenever we are questioning the truth or
falsity of a claim, we raise an issue.
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Example 1
Claim: I need a pair of new glasses.
Issue: Do I need a pair of new glasses?
Example 2
Claim: Tom’s laptop was stolen yesterday.
Issue: Was Tom’s laptop stolen yesterday?
The concept of an issue is not difficult to understand. An issue is nothing more than a Yes/No
question. It is a question asking whether a given claim is true or not. However, exploring valuable
issues from various contexts is a difficult skill. The quality of the issues you discover determines the
quality of the insight of the event and breeds the quality of the decision or action making. So it
stands to reason, that if you can get better at identifying issues, you can get better answers leading
to a whole host of benefits.
3.3 Arguments
It is essential to recognize that an argument is composed to address a specific issue by offering a
position on the issue and providing reasons for that position. An argument consists of two parts:
1.
Premise(s)
2.
Conclusion
3.3.1 Premises
When someone makes an argument, they’re defending their position or stance on some issue at
hand. To analyze an argument, one thing you must do is to identify the premises. Ask yourself,
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“what reasons or evidence did the author give for their conclusion?” Or, “Why does the author
think that this is the answer?”
Sometimes the person making the argument will make it easier on you by using keywords or
phrases that indicator reason:”because”, “due to”, “as shown by”, “given that”, and so on. Be
aware of such words, but don’t rely on them. They won’t always appear in an argument.
Besides, there are sometimes unstated or implied premises. The person making the argument
maybe leave out a fact or reason, assuming that you already know that fact or that it’ll be taken for
granted. Once you’ve identified the premises, you will then need to evaluate their truth or
authenticity.
3.3.2 Conclusion
When we talk about the conclusion of an argument, we do not mean a summary or overall review
of what’s been said (as might be met when your professor asks that your paper include a conclusion
paragraph.) Rather the conclusion of an argument is what follows from the claims being made. It
is the final statement of the position someone is taking on an issue.
3.3.3 Collaboration
These two parts must work together to offer a particular stance or position on an issue. In an
argument, the premise(s) supposedly provide the reasons for thinking the conclusion is true.
For example, a student tells her instructor,
“My grandmother died, and I had to miss class to go to a funeral.”
The issue at hand is whether the student should be excused from class. Now the student believes
the conclusion is YES, and offers a reason — attending her grandmother’s funeral — to defend
that conclusion. That reason is the premise of the argument. The instructor can then evaluate
whether she has offered a good argument or not. To “evaluate” means to do two things:
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1.
Decide whether the premise or premises are true or accurate
2.
Determine whether the premises are logically related to the conclusion
In future sections, you learn more about this evaluation process. We are going to break down the
definition of an argument by focusing on four key points:
1.
Premise(s)
2.
Conclusion
3.
The application of reason or logic
4.
Relevance of premise(s) and conclusions.
Chapter 4: NON-ARGUMENTS
As we discussed in the preview module, an argument is a set of premises when combined imply a
conclusion. However, we often make a common mistake by providing information to express our
view without actually making an argument. This can be misleading at such statements often lack
rigorous evidence and a clear conclusion. We call this a non-argument. In this chapter, we will
discuss three types of non-arguments.
4.1 Explanations
For example, your parent might give an explanation that attempts to shed light on a phenomenon
about going to college.
“Everyone with a college degree learns valuable skills, such as learning to meet
deadlines and making social connections. ”
This is an attempt to explain why or how going to college will result in a positive experience.
However, she is not trying to convince you that going to college will be worth the investment.
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If we want to build up an argument based on this idea, here is the development:
Premise 1: In college, you will learn how to meet deadlines and make social
connections.
Premise 2: A college is a unique place where a person can learn skills.
Conclusion: In order to learn these skills, you should go to college.
This is an argument because provides premises that infers a conclusion. She makes a claim about
the skills that you can learn and then connects her next premise that college is the right
environment to learn these skills rather than giving you explanations without connecting them to
the conclusion. This argument is clear.
4.2 Hypotheticals
Imagine you continue to discuss the worth of a college education with your parent. She might say
“If you don’t go to college then you might not get a job.”
This is a hypothetical scenario that does not exhibit the qualities of an argument hypotheticals
may be a useful tool to support an argument but it makes no attempt to justify a clear conclusion
and thus this is not an argument.
Here is a better way to frame this argument:
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Premise 1: A college education provides you with a credential that many
employers will require.
Premise 2: If you do not have a college degree then you will be limited to specific
jobs or you may have difficulty finding a job at all.
Conclusion: In order to have a better chance at finding a job you should go to
college and earn the credential.
Rather than making a hasty conclusion, the degreeless young person will not find a job. This
argument is backed up with evidence.
4.3 Rhetoric
Plenty of politicians give speeches promising to bring change. Sometimes their words might evoke
strong feelings, but other times they might be dismissed as “just empty rhetoric.” They decorate
what they say with rhetoric which is the expression containing emotional force but carrying no
reasoning.
For example, John Kennedy says in his famous speech that
“Ask not what your country can do for you, ask rather what you can do for your
country.”
It is just to incite people to do volunteer work in a delicate rhetorical package. This use of the word
rhetoric suggests that a speech is just an empty talk, with no valuable evidence to fill it.
However, rhetoric shouldn’t be demonized as underhanded or negative. It’s a tool that can be used
for good. Rhetoric helps us develop the skill of persuasion. So practicing and understanding
rhetoric can help us in all kinds of contexts, from term papers and courtrooms to daily
conversations and advocacy, and that is why we also bring this up in our critical thinking course.
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CHAPTER 5: ANALYZING
ARGUMENTS
Chapter 3 was about understanding how an argument is built. The focus to analyze the argument
is to look closely at the evidence the author presents and ask if it is relevant and sufficient. We can
analyze and evaluate an argument through the four perspectives:
1.
Level of reason
2.
Relevance
3.
Unstated assumptions
5.1 Level of reason
In making an argument, an individual relied on reason or logic to defend a particular conclusion,
rather than on emotion, intuition, or instinct. For example, an employee tells his boss,
“Please give me a raise. I need to make more money so I can buy a bigger
house.”
He is trying to appeal to his boss's emotions, hoping the boss might feel bad for him. Whether he
needs a bigger house or not the employee is not offering an argument as to why he should get a
raise. He simply trying to persuade his boss to agree with his desire.
To make an argument, the employee could align his workplace accomplishments, projects he has
initiated, deadlines he’s met, and other concrete reasons that could justify a raise.
5.2 Relevance
Remember the use of the term “supposedly” in our definition: a premise supposedly provides a
reason for thinking the conclusion is true. When someone makes an argument, they believe that
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the premise(s) they offer justify or support the conclusion they’ve drawn. However, the point of
applying critical thinking to arguments is to evaluate whether that is the case. For example, when
you asked your classmate about taking a certain class? Instead of telling you what the class was like
he says,
“Oh no! Do not take that class. I hate that class. It’s so early in the morning, and
I am not a morning person.”
To support his conclusion that you should not take the class, the premises are that
Premise 1: the class meets early in the morning
Premise 2: he does not like mornings.
Now, did those promises tell you whether you should take that class? What is your classmate’s
dislike mornings have to do with you? So when you analyze an argument you must not only
evaluate the premises and conclusions separately, but you need to consider the relevance between
them.
5.3 Unstated assumptions
Sometimes, it can be difficult to tell whether someone’s making an argument or whether the
argument the making is a good one because pieces of the puzzle are missing. People do not always
explain their arguments very well. Have you ever heard the phrase “it goes without saying”? That
“it” is an unstated assumption — a premise that, for some reason, is simply assumed rather than
explicitly stated. For example, consider the following argument.
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“It’s not required for you to do an internship. You would rather spend your
summer at the beach, so don’t do an internship.”
The unstated assumption here that “goes without saying,” is that people should only do what they
want to do — you want to spend the summer at the beach, therefore you should do that instead of
getting an internship.
The problem with unstated assumptions is not that they are (or are not true). The problem is if
they remain hidden, then your analysis of an argument is incomplete. Not all unstated assumptions
will be true or accurate or reasonable. If you do not bring them out of hiding, by figuring out
when some piece of an argument is missing and filling in that gap, we may miss a weakness or
error in reasoning that can undermine the argument’s conclusion.
If you’re the one making the argument, if you leave some premise unstated, someone else may fill
in the gap for you, and they may not fill it with the same reason you would have used! In this case,
you’re allowing someone else to make your argument for you and to put words in your mouth that
might not belong there. In both assessing and making arguments, you should always be alert to
what is not being stated.
CHAPTER 6: TWO TYPES OF
ARGUMENTS
There is a great divide in the world of rational argument: deductive and inductive arguments. All
arguments fall into one camp or the other but what is the dividing line?Generally speaking,
deduction is an argument from general to specific, and induction is an argument from specific to
general.
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Deduction = "General to Specific"
Induction = "Specific to General"
However, what divides the deductive from the inductive is not only the patterns but the intent.
When you are considering an argument, it is important to know which type you are dealing with.
You can’t decide whether an argument is successful unless you know what it is trying to achieve. In
this chapter, we are going to elaborate on their differences in detail.
6.1 Deduction
Deduction aims to provide certainty. It offers a guarantee that the conclusion is true. It delivered
the proof. Here is an example.
Premise 1: All dogs are mammals.
Premise 2: Some dogs can be trained to help humans.
Conclusion: Some mammals can be trained to help humans.
A closer look at this argument will show how deduction aims for a guaranteed conclusion. So now
the conclusion is proven. You can see the intent of a deductive argument is to provide certainty.
The conclusion is inescapable if all the premises are true.
6.1.1 Validity
We hear the words valid and validity used all the time. This section will discuss what validity means
in the context of deductive arguments. The concept of validity is a tool for evaluating the internal
logic of a deductive argument. To say a deductive argument is valid is not the same as saying that
the argument is good or sound. Here is an example.
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Premise 1: All snails can speak Chinese.
Premise 2: A garden snail is a snail.
Conclusion: A garden snail can speak Chinese.
Although it seems counterintuitive, this is a valid argument. An argument is valid if the truth of
the premises would guarantee the conclusion. If it is true that all snails can speak Chinese, then it
must be true that a garden snail can speak Chinese.
6.6.2 Soundness
Let’s put the argument in the previous section under more scrutiny.
Premise 1: All snails can speak Chinese. (False)
Premise 2: A garden snail is a snail.
Conclusion: A garden snail can speak Chinese.
This is a valid argument, but it is not a sound argument. Soundness is an evaluation of both
whether an argument is valid and whether its premises are true. A sound argument must be both
valid and have true premises. Not all snails can speak Chinese. So one of the premises is false and
our argument is not sound.
Validity and soundness are properties of an argument, while the truth is a property of a claim.
Here is an argument that is sound because it is both valid and has true premises.
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Premise 1: All legal voters in the U.S. are adults. (True)
Premise 2: John is a legal voter in the U.S. (True)
Conclusion: John is an adult. (True)
Here is an argument where the premises are true but the argument is invalid. So the argument is
not sound.
Premise 1: All legal voters in the U.S. are adults. (True)
Premise 2: John (17 -year-old) is a legal driver in the U.S. (True)
Conclusion: John is an adult. (False)
This argument is not valid because the conclusion is not guaranteed by the truth of the premises.
Therefore, it is not sound. Let’s take a look at this one.
Premise 1: All legal voters in the U.S. are adults. (True)
Premise 2: Tom (20-year-old) is a legal driver in the U.S. (True)
Conclusion: Tom is an adult. (True)
In this particular case, both the premises are true and the conclusion happens to be true. However,
the two premises don’t logically guarantee that conclusion. So the argument is invalid. Therefore, it
is not sound.
In summary, we should only adopt conclusions of arguments that are both valid and sound.
6.2 Induction
Now it is time to consider the other type of reasoning — inductive arguments. 99% of the
arguments that we encounter in the real worlds of business, medicine, law, science, education, etc.
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are inductive arguments. It is only in specialized domains such as mathematics and computer
programming that we can regularly deploy the power of deduction.
The intent of induction is to demonstrate that the conclusion is likely true. It is not asking for
certainty, but only reasonable confidence. An inductive argument makes the case that a conclusion
is probably true. Look at this example.
Premise: Tomorrow is the government's payday.
Conclusion: There is probably a lot of traffic tomorrow.
Is it for sure that there is a lot of traffic tomorrow? Who knows? Maybe a sudden bad weather
condition closes all the business activities, or a public emergency presses everyone staying at home.
However, can you be reasonably confident that there is a lot of traffic tomorrow? Sure! The past
experience has never failed to show us that there was a lot of traffic on the government’s payday.
So, the possibility is high that tomorrow will be the same.
Inductive arguments never provide absolute proof. So it would be unfair to call an inductive
argument a failure only because it does not provide absolute proof. Its goal is not for absolute
proof but only the possibility.
6.2.1 Strength
Inductive arguments whose premises give us a strong (even if potentially defensible) reason for
accepting the conclusion are called strong inductive arguments. In contrast, inductive arguments
that do not provide a credible reason for accepting the conclusion is considered weak inductive
arguments.
Since inductive arguments have a different intent comparing with those deductive arguments. It
would be unreasonable for us to apply the same standard to evaluate them. We cannot use the
terms “valid” and “sound” in reference to inductive arguments. Those two terms can be only
applied to the deduction.
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Inductive arguments’ intent is not to guarantee the conclusion. Therefore, every inductive
argument is invalid following the previous definition. However, that does not mean that they are
useless. Instead, we will say inductive arguments are relatively strong or weak depending on how
probable their conclusions are supported by their premises. That one inductive argument is
stronger than another means one’s conclusion is more probable than the other given their
respective premises. Obviously, the strength or weakness of an inductive argument admits of
degrees. The more probable the conclusion is the stronger the induction is.
6.2.2 Cogency
The concept of strength is not enough for us to accept an inductive argument. For inductive
arguments, we will need to add the concept of cogency to our evaluative criteria as we add the
concept of soundness for deductive arguments. A cogent argument is a strong inductive argument
that has all true premises.
CHAPTER 7: BRIDGING THE GAP
BETWEEN STEM AND THE
HUMANITIES
In today’s society, the popularity of humanities seems to be declining. This is partly because of the
advocacy of STEM — science, technology, engineering, and mathematics. They teach us what the
world is made up of and provide us the convenience to live in this physical world. However, STEM
can’t replace humanities to inspire us how to interpret the world, how to interact with other
people, and how to find the meaning of our lives, etc. In many careers, this is an essential skill to
have. So it is wrong to see humanities as less valuable than STEM. The controversy should not
exist at the beginning if critical thinking bridges the gap between stem and the humanities. In this
chapter, we are going to discuss two essential applications of critical thinking in the STEM
disciplines.
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7.1 Mathematical induction
Mathematical induction is a method of proof. It is a method widely used for proofs related to
discrete numbers. Here is an example using mathematical induction to prove a conjecture.
Proof.
2+4+6+ ... + 2n = n(n+1)
(n is a natural number)
We cannot check the reliability of the formula for all the terms of the expression one by one. To
prove the validity of the formula for each term, we need inductive reasoning showing that if the
formula is true for one integer then it will also be true for the next, and so on.
Premise 1 (Base case): Formula is true for n=1
Premise 2 (Inductive case): If the formula is true for n=k, then the formula is true
for n = k+1
Here is the proof.
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When n=1, LHS of the equation equals 2, and RHS of the equation equals 1 x
(1+1) = 2.
Let n=k, and assume 2+4+6+ ... + 2k = k(k+1) is true.
When n = k+1,
LHS of the equation is
2+4+6+ ... + 2k +2(k+1) = k(k+1) + 2(k+1), and
k(k+1) + 2(k+1) = (k+1)(k+2).
RHS of the equation is (k+1)(k+2).
So LHS equals RHS meaning the formula is true for n = k+1.
The mathematical proof is now completed.
7.2 Statistics
Statistics is the area of mathematics that applies inductive reasoning as the foundation for
collecting and analyzing data. Some examples might be keeping track of your favorite team as they
rack up wins and losses, or perhaps using data to predict the outcome of an election. To be more
specific, statistics can be broken down into the areas of:
-
Sampling
Sampling is a method of inductive generalization. We collect the data from a selective
sample and project the property to the entire population. This is arguably the most
important area of all statistics. It’s important because it ensures that we collect our data in
just the right way. So we can make a cogent argument to draw a reliable conclusion. It
also helps us know when we have just enough information for further analysis.
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-
Descriptive statistics
Descriptive statistics is about summarizing or highlighting important aspects of our data.
The tools here are about describing the information you have collected with a graph
under the area of descriptive statistics.
-
Inferential statistics
Inferential statistics is about finding the trend and making predictions from our data.
Here the goal is to take just a small bit of information, analyze it carefully, and then see
what conclusions we can infer about the bigger picture.
Whether a solid conclusion can be drawn with a statistics method in your research relies on the
quality of the inductive argument you establish. You should always apply the knowledge you
learned from the previous chapters to secure the strength and cogency of the arguments you use to
support the research.
CHAPTER 8: INFORMAL
FALLACIES
An informal fallacy is any kind of error in reasoning that renders a weak inductive argument.
They can involve distorting relevance, manipulating conclusions, distracting you from the actual
issue, etc. It seems like they are not difficult to spot, but this is not always the case.
Sometimes informal fallacies are used intentionally to try and win a debate. In these cases, they are
often presented by the speaker with a certain level of confidence. In doing so, they are more
persuasive. If they sound like they know what they are talking about we are more likely to believe
them even if their stance doesn’t make complete logical sense.
Most informal fallacies can be spotted by thinking critically. Make sure to apply the method of
analyzing arguments from Chapter 5 when you sense an error in the reasoning process. By
applying critical thinking, you will be able to detect logical fallacies in the world around you and
prevent yourself from using them as well.
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8.1 Abusing the man
Abusing the man fallacy is when someone uses a personal attack as the refutation for an argument.
It is an attack on the author’s character or attributes to discredit their argument. Here is an
example.
Person A: For providing better education feasibility to the local college students,
we should increase the WiFi coverage on campus. In that case, students can
access the online education services for various purposes such as classroom
activities, library group discussions, or field projects.
Person B: Why should we listen to you? You did not even graduate from college.
Person A may not graduate from college, but that does not automatically undermine his or her
argument. Person B’s rebuttal is not addressing the issue of whether we should increase the WiFi
coverage on campus but attacking Person A personally. This is not a strong rebuttal to the
argument. It is a fallacy.
8.2 Appeal to authority
An appeal to authority is when someone uses an authority’s opinion as a premise to support the
conclusion. Not all appeals to authority are contributing to weak arguments. Only those appeals to
inappropriate authority are. For example,
Person A: This Facebook post says I can get Covid-19 from dogs.
Person A’s argument above is weak unless the author of the Facebook post is an expert in diseases
and shares the majority opinion of the medical community. Otherwise, there is no reason to listen
to it.
Let’s see another one.
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Person B: My doctor says I should reduce my sugar consumption for less
inflammation.
This is an appropriate appeal to authority because it fulfills two conditions.
1.
The authority being appealed to is an expert in the topic
2.
The majority of experts on that topic agree with that opinion
8.3 Circular reasoning
Circular reasoning, or begging the question, is when the argument is restarted rather than proven.
In other words, instead of explaining why the conclusion is true, you just paraphrase the original
conclusion as proof. Here is an example.
My father is always right because he has never done anything wrong.
You haven’t explained why your father is always right. You’ve just confirmed that he is always
right. A typical formula for circular reasoning is:
A is true because A is true.
8.4 Appeal to emotion
An appeal to emotion fallacy is when an author uses emotion-based language to try to persuade
the reader or listener of a certain belief or position. It follows the formula:
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Conclusion: X is true.
Premise: Think of how sad you will be if it’s not true or how happy you will be if
it is true.
Here is an example.
Conclusion: I deserve a better grade for my final exam.
Premise: This past week was a disaster for me. My grandpa passed away. My
girlfriend broke up with me. And my car got stolen.
In general, what someone perceives to be unfair, how someone is feeling, or even things that
someone might perceive to be moral or immoral do not carry much weight for making a strong
argument.
8.5 Appeal to force
An appeal to force fallacy is a type of informal fallacy that arises when the argues instead of
showing the evidence appeals to intimidation or use force to gain acceptance of his or her
conclusion. In other words, the appeal of force fallacy happens when the arguer tries to persuade
the other or the listener by pointing out his or her power over the other or warning the other of
the bad consequences if he or she refuses to accept his or her argument. For example,
You better think twice before breaking up with me. Don’t forget your dad is an
employee of my family’s corporation.
If we analyze the given example, we can see that the arguer poses a threat to the listener if he or
she does not accept the conclusion. As we can see, the fact that the arguer intimidates or poses a
threat to the listener does not make the argument strong.
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8.6 Appeal to ignorance
An appeal to ignorance fallacy happens when you conclude that something is not the case because
it has not yet been proven or something is the case because it has not yet been disproven. Typical
formulas for an appeal to ignorance are:
Formula 1
Premise: Because X has not been proven.
Conclusion: X must be false.
Formula 2
Premise: Because X has not been disproven.
Conclusion: X must be true.
Let’s see some examples.
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Example 1
Premise: There is no evidence to show that ghosts do not exist.
Conclusion: Therefore, ghosts exist.
Example 2
Premise: There is no evidence to show that God exists.
Conclusion: Therefore, God doe not exist.
Both arguments appeal to ignorance because you need supporting evidence to conclude
something.
8.7 Straw man
A straw man fallacy is a technique where someone distorts the issue so that it is easier to refute, or
where someone tries to refute a point someone made by giving a rebuttal to a modified version. For
example,
Person A: We should allocate more resources to the Department of Education.
Person B: Oh, what you mean is we should starve the other departments?
Person B’s rebuttal contains a straw fallacy to undermine an honest and rational principle that
both parties’ arguments should be addressing the same issue. Obviously,
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Issue 1: Whether we should allocate more resources to the Department of
Education
Issue 2: Whether we should starve the other departments
are two different issues.
8.8 Red herring
Red herring is a fallacy that misleads or distracts a debate from the relevant issue. A red herring is
often intentionally used in politics or court debates. For example,
Reporter: Did you permit to imprison that person?
Politician: You know what? Too much fake news is around now. We should
regulate the reporters’ behavior.
The report raises an issue on whether the politician permits to imprison the person. However, the
politician intentionally distracts the relevant issue to the other one — whether we should regulate
the reporter’s behavior. This maneuver is a version of the red herring in which unnecessary issues
are introduced to confuse opponents or hide the truth in an argument.
8.9 False cause
The false cause fallacy is committed when the conclusion depends on a supposed causal
connection that probably does not exist. For example,
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Premise: I wore a green sweater in the last exam and got an A.
Conclusion: I should wear it this time to secure an A.
The author’s argument depends on the idea that wearing a green sweater causes a good grade.
This is a version of false cause. The supposed causal connection does not exist but only base on
her imagination.
8.10 False dilemma
A false dilemma occurs when an argument presents two points while disregarding or ignoring
others to narrow the argument in one person’s favor. This is also known as an “either/or” fallacy.
Here is an example.
You are either joining us or choosing to be our enemy.
There are only two options given when there are more options available. This attempts to drive the
conclusion in a direction where only one specific answer can be given to incriminate the opposing
party.
8.11 Hasty generalization
A hasty generalization is when someone generalizes without sufficient data and a credible sample
as support. For example,
Premise: My boyfriend cheated on me and broke up with me last night.
Conclusion: Men are evil and untrusted.
This argument attempts to generalize a conclusion based on limited knowledge. This fallacy is also
called “overgeneralization” which is a well-designed statistics approach trying to avoid.
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8.12 Slippery slope
A slippery slope is a conclusion based on the premise that one small step will lead to a chain of
unstoppable events and eventually resulting in some unwanted event. In other words, if we allow A
to happen, then B will happen, then C will happen, ..., then an unwanted Z will eventually
happen, which means that A should not happen. Here is an example.
Premise 1: If you don’t study hard, you won’t pass the exam.
Premise 2: If you don’t pass the exam, you will fail this course.
Premise 3: If you fail this course, you cannot graduate with a degree.
Premise 4: If you cannot graduate with a degree, you cannot find a job.
Premise 5: If you cannot find a job, you will be broke.
Premise 6: If you are broke, you don’t have money to buy food.
Premise 7: If you don’t have money to buy food, you will be starved to death in
the street.
Conclusion: Since you don’t want to be starved to death in the street, you’d
better study hard.
The problem here is that the main issue is being covered by extreme hypotheticals with no real
proof to support the relevance.
8.13 False analogy
A false analogy fallacy is when two things that are unlike are being compared based on a trivial
similarity to prove a point. For example,
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Employees are like nails. You have to hit them to make them work.
This is an absurd analogy that attempts to correlate employees and nails based on almost no
similarity.
8.14 Complex question
A complex question is a fallacy that’s often used in a courtroom. This is when the lawyer has
planted a hidden and disguised assumption in a question. No matter how you answer it, you will be
framed to accept the assumption. For example,
Lawyer: What time did you leave the crime scene?
No matter how you answer this question, you are forced to accept that you have been to the crime
scene even though you never did.
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