Introduction to Critical Thinking
Think Slowly
Ask Questions
Cultivate a Healthy Skepticism
Making Sense
• Students often say things like “that makes
sense”, and they conclude that what makes
sense is thus true.
Truth and Making Sense
• It is important to understand that:
All that is true makes sense.
but it does not follow that:
All that makes sense is true
Critical Thinking
All giraffes are animals.
but it does not follow that:
All animals are giraffes.
Some animals are cats, dogs, humans, squirrels,
etc.
The Dangers of Inferencing
Would you agree with the following premise?
If a student is lazy and does not care about
school, then he will often be late for class?
Inferencing
It’s actually true: If a student is lazy and cares
little about school, we can reasonably expect
that he will often be late for class.
But does it follow that
“if he is often late for class, then he is lazy and
cares little about school”?
Inferencing
No, it does not. Students typically understand
that. Consider the following:
The dangers of inferencing
• If a student is lazy and does not care
about school,
• If a student is feeling very sick and
missed the bus as a result,
• If a student’s bus was late,
• If a student’s parents are always
fighting and he’s feeling rather
depressed and can’t get himself
motivated,
• If there was an accident on the road
and roads were closed,
then he will be late
for class
Inference
The “if” clause is called the antecedent, the
“then” clause is called the consequent:
If you eat cake every day, then you will get fat.
antecedent
consequent
The dangers of inferencing
As you can see, there are a number of possible antecedents that “make
sense” out of the consequent.
• If a student is lazy and does not care
about school,
• If a student is feeling very sick and
missed the bus as a result,
• If a student’s bus was late,
• If a student’s parents are always
fighting and he’s feeling rather
depressed and can’t get himself
motivated,
• If there was an accident on the road
and roads were closed,
then he will be late
for class
Hypotheses
If ________________________________ , then he will be late for class
An unknown antecedent is a “hypothesis” (a conjecture)
There are any number of possible hypotheses that can explain the consequent.
Inference
Mean
Principal
If the principal is a mean and vindictive man,
If the principal just received news that his
wife is in the hospital,
If the principal has been fasting for 24 hours
and is very hungry,
If the principal just had to suspend someone
he didn’t want to suspend,
If the principal hates young people,
then he will have a very serious
demeanor
The dangers of inferencing
Notice how often we make inferences
about people, like the school principal,
a teacher, a person living on the street,
etc. We settle upon the first hypothesis
that “makes sense” (or the one that
makes us feel better).
We forget that it is not necessarily the case that if
it makes sense, it is true.
Induction
The process of going from the evidence (the
consequent) to the hypothesis (antecedent) is
called induction. The scientific method is inductive:
If _______________ , then he will have a fever and
be vomiting.
The evidence or symptoms are in the ‘consequent’.
The antecedent is any number of possible
hypotheses (flu, another virus, food poisoning,
poison, etc.).
Testing
• That is why testing is so important in the sciences.
• A hypothesis has to be tested and tested again, etc.,
before we assume it is true.
• Keep in mind, however, that confirmation does not
prove the hypothesis. We want to test in order to
disconfirm the hypothesis:
Try to figure out this rule: Click YouTube Video:
https://www.youtube.com/watch?feature=player_embed
ded&v=vKA4w2O61Xo
Induction Biases and Fallacies
• Confirmation bias
• Availability Bias (WYSIATI)
• Post hoc ergo propter hoc (confusing
correlation with causation)
• Round Trip Fallacy
• Fallacy of Misplaced Authority
• Ad Hominem
• Narrative Fallacy and Selection Bias
Confirmation Bias
Consider that if John killed his mother, then there will be evidence of a motive (i.e.,
life insurance policy).
It was discovered that:
•
•
•
•
•
John was in debt and needed money to pay those debts.
his mother recently took out an accidental death insurance policy and named John as the
beneficiary
John does not have an alibi for the time of the murder.
John owns a hunting knife (and his mother was stabbed to death).
Neighbors said that John and his mother were arguing on the day of her murder.
All these facts “confirm” the hypothesis (conjecture) that he killed his mother. But this does not
prove he did so. Investigators know this. So often it has happened that a prime suspect like John,
who had all kinds of evidence against him, turned out to be innocent (DNA).
What is needed at this point is more attention to possible evidence that disconfirms or refutes
the original hypothesis (conjecture). What often occurs, however, is that such evidence is
overlooked, because it does not confirm our original hypothesis, and that can be a tiring thought
(we’re back to the drawing board). Lazy investigators are dangerous!
Confirmation Bias
The confirmation bias is the tendency to favor evidence
that confirms our hypothesis. Those pieces of evidence
stand out for us (they seem right), precisely because they
confirm our original hypothesis.
But, confirmation does not prove a hypothesis. What a
good scientist or investigator will do is seek out evidence
that “disconfirms” a hypothesis, proving it is false.
I.e., If the principal above has 6 kids at home, that is
strong evidence that the hypothesis “he hates kids” is
wrong.
Confirmation Bias
• I formulate a hypothesis that “Chinese women
are bad drivers”.
This year I saw three accidents involving Chinese
women. Thus, I conclude that the evidence proves
my point.
(However, throughout the year, I saw many more
accidents. The only ones that stand out in my mind
are those involving Chinese women, because these
confirm my hypothesis)
The Murder of Dorothy Donovan
A 70-year-old woman, Dorothy May Donovan, was found murdered in her home. She
was stabbed to death. Nothing was missing from the home, and she had not been
sexually assaulted. She has one son, Charles Holden, for whom she took out an
insurance policy. He is the sole beneficiary. What can we infer from these facts?
•
•
•
•
She was killed by her son Charles (a factory worker), who had debts and needed
the insurance money.
She was killed by someone hired by her son, Charles, who had debts and needed
the insurance money.
She was killed by a perfect stranger (to both of them), an ex-con, who broke into
the house because he needed a place to sleep, but when she confronted him, he
killed her for fear that she could identify him, and he would be sent back to jail.
She was killed by someone about to rob the house, but when she woke up and
came down and saw the man, she screamed and threatened to call the police, he
panicked, stabbed her, and fled the scene without achieving his goal, which was to
rob the house.
Donovan murder continued
The police take Charles in for questioning. Here is his
story:
• At around midnight on June 22, 1991, he was leaving a
Hardee’s restaurant when a man came to his truck,
asking for a ride. The man said that his sister was
having a baby and that he needed to get to the
hospital. Charles told the police that at first, he told
the black man that he could not give him a lift, because
he wasn’t going very far—he only lived a few blocks
away. But after some pressure, he changed his mind
and gave the man a lift.
Donovan murder
Shortly thereafter, Charles stopped at an
intersection (in Delaware, just outside of
Harrington). The hitchhiker got angry and started
attacking him. Charles said he opened the door, got
out and ran. The hitchhiker grabbed a screwdriver
from the floor of the truck and ran after Charles,
and the fight continued. So Charles stopped and
agreed to take the man to where he wanted to go.
But as the hitchhiker went around to the passenger
side, Charles jumped in, locked the door, and drove
off. The hitchhiker tried to run after him, but soon
gave up.
Donovan murder
Charles did not want to turn and proceed to his home, which
was half a mile from where he left the man, in case the
hitchhiker would see him and take revenge, so he continued
to drive around. Finally, he returned to his trailer, but he
noticed someone lurking around it; he looked like the
hitchhiker. So he did not pull into the driveway. Instead, he
called the police from a local pay phone. An officer came and
went with him to his trailer and then his mother’s house,
Dorothy Donovan, who lived in the house next to the trailer.
They saw that the back door window had been broken and
there was blood inside the house. They proceeded up the
stairs to Dorothy's bedroom and found her lying dead; she’d
been stabbed to death.
Facts in evidence:
Nothing was stolen from the house, so this was not a robbery. It was
not a sexual assault. Charles refused to take a polygraph. So what
motive could anyone other than Charlie have for killing this woman?
What is the likelihood that a hitchhiker would eventually turn down a
street and find Charles’ mother’s house and kill her? Why would he do
so? In revenge for not getting a lift farther up the road? And how
would he know that this was Charles’ mother? The likelihood that he
would find Charles’ house is very low; the probability that he would
know that his mother lived in the house behind him is even lower.
Moreover, Dorothy Donavan recently took out an accidental death
insurance policy and Charles was the sole beneficiary, and he needed
money to pay back certain debts that he had. And who likes living in a
trailer when you can inherit a beautiful house upon the death of the
owner?
As you can see, there is a great deal that confirms the hypothesis that he is the
killer.
How would you rate the likelihood that this story is
the truth?
On a scale of 1 – 10 (1 = highly unlikely; 10 = almost certainly true)
1
2
3
4
5
6
7
8
9
10
Donovan murder
The police thought his story was ludicrous.
Conclusion
• The forensic team found a bloody palm print on
the stair railing. It did not match Charlie’s palm
print. Witnesses at the Hardee’s confirmed that
the hitchhiker did exist. The DNA evidence did
not match Charles.
Although the evidence is looking better for
Charles, the narrative is still rather unbelievable
(improbable). And so authorities began to
speculate that perhaps Charles hired someone to
kill his mother.
Solved
• 15 years later, a DNA match surfaced. The killer was
Gilbert Cannon of Delmar, MD. He was high on cocaine
at the time, and he said that he went to that particular
house because it was the first one he could find in
which there appeared to be no one home. He was
surprised to learn that this was the mother of the man
who gave him a lift (Charles).
• As you can see, what appears to be highly improbable
(his story) may still turn out to be true. A theory with
lots of evidence that confirms a hypothesis (that he is
the killer is highly probable) may be false.
Availability Bias
We have a tendency to make decisions and/or judgments on the basis of
information that is readily available, all the while believing that this is all that
is available (There is a bias in favor of readily available information). For
example:
Circle the number for that which you think (based on what you know) is the
number one cause of death annually in the United States.
1.
2.
3.
4.
5.
6.
___ AIDS
___ Motor vehicle accidents
___ Breast Cancer
___ Medical mistakes
___ Aviation
___ Weapons related violence
Availability bias
The answer is “medical mistakes”.
• Most people would not put medical mistakes,
because that information is not made available to
us. What is made available is AIDS deaths, motor
vehicle accidents, plane crashes, etc.
• Bias in the media contributes to availability bias.
There is so much that is not covered in the media
for one reason or another that is far more
important than what is typically covered.
WYSIATI
WYSIATI is the acronym for What You See Is All There Is
(Daniel Kahneman, Thinking Fast and Slow)
Mr. Alphonso once told me that when he first came to
Canada from India, he was expecting students to stand up
as he entered the classroom; for teachers are highly
esteemed in India. He was rather taken aback when he
first walked in to a classroom here; students would be
talking to one another and they would pay not the
slightest attention to him. Like the rest of us, he was
subject to an availability bias (What You See Is All There
Is)
Availability bias
What is the most popular snack in the world
among teenagers?
a.
b.
c.
d.
Chocolate bars
Potato chips
Popcorn
Other
Availability Bias
Ans: Other: rice.
For the answer, we tend to look to what is immediately available to us, forgetting
that there is so much we do not see (so much that is not available).
Availability Bias
If you were to go to a movie depicting inner-city
drug gangs and gang wars, violence, etc., and
then were asked upon leaving the theatre
whether gangs are becoming a serious problem
in Toronto, you would probably answer ‘yes’,
relying on the most available information,
without making the effort to think through the
question.
Fallacy of post hoc ergo propter hoc
Assuming that when one event
precedes another, it is the cause of
the succeeding event.
I was doing poorly in school, but
then my grandmother gave me this
pagan amulet to wear around my
neck, and then my marks started to
improve. I am convinced it works.
I wear it all the time now.
Post hoc…
John purchases a new laptop and it works fine
for months. He then buys and installs new
software. The next time he starts up his new
laptop, it freezes. He concludes that the
software is the cause of the malfunction.
Confusing correlation and causation
“Every time my older brother eats sweets, it
gives him acne. Thus, sweets cause acne”
There might indeed be a correlation between
those who have acne and those who eat sweets.
But correlation is not necessarily causation.
Sweets and Acne
Cause
Effect
But, because of that correlation, we are quick to assume that eating sweets is the
cause of the acne.
However, it is
possible that both
are caused by
some other factor,
i.e., anxiety, stress.
The stress at exam
time causes a
person to eat more
sweets, and at the
same time, the
anxiety causes his
or her acne to
break out. The
sweets are not
necessarily the
cause of the acne,
although sweets
and acne are
correlated.
Unknown cause (possible
hypothesis)
Correlation and causation
“The majority of prison inmates come from poor
backgrounds. Therefore, poverty is the cause of
crime”
Causation…
This is a popular confusion of correlation and causation.
Forensic psychologist Stanton Samenow points out that we must not
overlook the very real possibility that those kids with anti-social
personality are the cause of instability in their families and their
parents’ marriages, which in turn can lead to divorce, then poverty,
etc.
Also, the correlation can easily be explained by reversing the terms:
those who have a criminal personality do not want to work hard, are
not responsible enough to hold down a steady job, they are unreliable,
thus most often unemployed, thus living below the poverty line.
There is no simple explanation
Round trip fallacy
A common statistical error:
#1:
99% of all terrorists are Muslims
Abdul is a Muslim.
Therefore, Abdul is a terrorist.
Or
#2:
87% of oranges in this box are grade A.
This orange is grade A.
Therefore, this orange came from this box.
Explanation of #1
There are about 2 billion Muslims in a world of
about 7 billion. Thus, about 30% of the world’s
population are Muslims. There are about 10,000
terrorists in the world, 99% of whom—let’s
assume—are Muslims. That gives us 9,900
terrorists who are Muslim, out of the 2 billion
Muslims in the world. That’s:
9,900
Or, 0.000495%
2,000,000,000
It is highly improbable that Abdul is a terrorist.
Explanation of #2
87% of oranges in this box are grade A. (There are 100 oranges in this
box)
But this orange in my hand is grade A. Can we conclude that it is from
this box? There are billions and billions of grade A oranges in the
world. What are the chances that this grade A orange is from this box
of 100 oranges?
100
1000,000,000,000
Highly improbable.
However
We can indeed argue the following statistical argument:
87% of oranges in this box are grade A.
This orange is from this box.
Therefore, this orange is grade A.
(87% probability = high)
Or,
95% of all Italians are Catholic.
Luigi is Italian.
Therefore, Luigi is Catholic
(95% probability = high)
Catholic or Protestant
World renowned golfer Rory McIlroy (winner of
the 2014 British Open) is from Northern Ireland.
Catholics make up a 40% minority in Northern
Ireland.
60% of Northern Irish are non Catholic.
McIlroy is Northern Irish.
Therefore, McIlroy is non Catholic
(60% probability that conclusion is true)
From a statistical point of view, the conclusion “he is Catholic” is unwarranted.
Rory McIlroy, it turns out, is Catholic
Probable arguments are always uncertain
Fallacy of Misplaced Authority
Consists of appealing to the testimony of an authority on an
issue that is outside his or her proper field of competence
(expertise).
"My doctor assured me that Fords are the best cars.
Therefore, I'm going to buy a Ford. After all, he is a doctor."
Having a symposium with this year’s Nobel Prize winners in
Chemistry, Physics, and Medicine in order that they may
shed light on world issues and offer political solutions to the
world's problems.
The Fallacy of ad hominem
(to the man)
This involves the criticism of some person's position or
belief by criticizing the person rather than the position
itself. I.e.,
• That man couldn’t be a good priest, just look at his
belly.
• He doesn’t know what he’s talking about. Just listen to
his stuttering.
• I’m not going to vote for him; I can’t stand the way he
looks.
Ad Hominem
How can this man possibly
be right about the Theory
of Relativity? Look at the
way he combs his hair!
Ad Hominem
Oh my G _ _ ! Look at his eyes! I’d
vote for him over Harper any day!
The Narrative Fallacy
• “The narrative fallacy addresses our limited ability to
look at sequences of facts without weaving an
explanation into them, or, equivalently, forcing a logical
link, an arrow of relationship upon them. Explanations
bind facts together. They make them all the more easily
remembered; they help them make more sense.
Where this propensity can go wrong is when it
increases our impression of understanding.”
• —Nassim Nicholas Taleb, The Black Swan (see our
Library for this great book)
The Narrative Fallacy
• A narrative is a coherent ‘story’.
• Life is very complex, and it is very difficult to make sense out of it.
• What people often do is they construct a narrative that “makes sense” out
of complex phenomena.
I.e.,
• It’s hard to make sense out of violence and tragedy. So, we often hear
the saying: "What goes around comes around".
• Everyone gets what he or she deserves. If a person is bullied, or is a
victim of some terrible injustice, there is a tendency to construct a
narrative, which is a large hypothesis, and then look for evidence that
bolsters the narrative: I.e., he or she must have done something to
deserve it.
• The narrative has to be tested, because it is a hypothesis.
Narrative and the Zimmerman Trial
If you recall the George Zimmerman Trial in the U.S., you’ll see an example of competing
narratives.
Prosecution Narrative:
The prosecution’s narrative was something like the following:
•
•
•
•
George Zimmerman was a wannabe cop
He saw a kid wearing a hoodie on a dark and rainy night in a neighborhood.
Although he was told by dispatch to stay in his car, he left his car, wanted to be a
hero.
He was racist, engaged in racial profiling, so he pursued this person who was
treated as a suspect and shot him (Trevon Martin).
The defense had a different narrative.
•
•
•
George Zimmerman was hired to patrol this housing area where there were recent
break-ins by black kids wearing hoodies.
When he went to follow the suspect, he was confronted, punched, knocked down
and Trevon Martin began banging his head on the cement.
George Zimmerman shot him in self-defense.
Of course, both cannot be true. It is up to the
prosecution to prove their case (burden of proof
is on prosecution).
Before the case was underway and all evidence
was in, however, it appeared that America
settled upon a narrative: the “wannabe racist
cop” narrative.
Two Narratives
Facts in evidence:
You come home:
• Door is open.
• Things from drawers strewn everywhere, lunch is on the
table, one bite out of a sandwich.
• blood drops on the floor.
• No one is home.
• Cash is missing from the money drawer where it is kept for
emergencies
Which narrative do you think is correct?
Two Narratives
Narrative 1: Your sister came home from school, made a
sandwich, someone entered the house, attempted to rob her
of money, threatened her with a knife, cut her with the knife,
she then gave up the money, kidnapped her for ransom -your father is very wealthy.
Narrative 2: Your sister came home from school, made a
sandwich, friend came over, so she made a sandwich for her
too, cut herself with the knife, told her friend to look for her
health card in a drawer, which is why stuff is strewn
everywhere, she found the health card, she grabbed some
cash that was in the drawer, they left in a hurry to the
hospital, forgot to lock the door.
Which narrative is true?
• Both make sense. Both are possible. There is
evidence that corroborates both narratives.
• We need more evidence to see which one receives
greater corroboration. If a piece of evidence arises
that disconfirms a narrative, then we know it is false.
That, however, does not necessarily make the other
remaining narrative true.
Selection bias
• This is a statistical bias: This involves a sampling
error. We look for samples to test our
hypothesis, but we select samples that are likely
to confirm our hypothesis or narrative (i.e.,
unrepresentative sample, or too small a sample).
• I.e., “Students want more Italian food in
Cafeteria”. We sampled a grade 12 physics class
in the 2nd semester, made up of 65% Italian
students.
The Fallacy of Composition
• involves attributing to the whole what belongs to
the part
Or,
• attributing to the part what belongs to the whole.
For example:
• McGivney is one of the top schools in the country.
Hence, John (who is a McGivney student) is one of
the top students in the country.
The Fallacy of Composition
• John is one of the top students in the country.
Since he goes to McGivney, it follows that
McGivney is one of the top schools in the
country.
• When I stand up at a football
game, I can see better. Thus,
when everyone stands up at the
game, everyone will see better.
Ideology and Fundamentalism
• What all fundamentalists—whether the religious fundamentalist
(i.e., Muslim, Catholic, Protestant, Hindu, etc.) or the politicalideological fundamentalist—have in common is an over-confidence
in their inferences and in the way they interpret the world (their
narratives), as well as a lack of awareness of the profound
limitations of our own intellectual frame of mind at any one time.
• Moreover, fundamentalists of whatever stripe always seek to create
an environment that excludes anyone who is not of like mind.
• The tendency is to root out “trouble makers” in order to protect the
community from challenges that make them think.
The Closed Society
Human beings find uncertainty very
uncomfortable.
But as you know, we are more often wrong than we are right. Our day
to day inferences and hypotheses are often wrong.
Thus, if we succeed in creating safe environments in which only those
who see eye to eye with us in almost every way are allowed to belong,
we’re never going to discover that we are wrong.
Learning only takes place through a “clash of cultures”, to use Karl
Popper’s expression.
The Closed Society
A closed society is characterized by a culture of fear,
one not open to healthy debate (closed to a “clash
of cultures”).
Many in Canada are afraid to express their views on
certain issues for fear of ridicule or prosecution or
of being sent to “sensitivity training classes”, etc.
“Political correctness” is a characteristic of the
closed society.
The Open Society
In an open society, we recognize that
“disconfirmation” (refutation) proves a theory
wrong, so we welcome evidence that might
refute a reigning theory.
An open society encourages healthy debate,
healthy skepticism, open criticism.
Ever Expanding Ignorance
• Physicist Richard
Feynman: “Science is
an ever expanding
frontier of ignorance”.
• The more we discover,
the more we come to
realize how little we
know.
• Each new discovery
opens up a vast realm
of which we are
ignorant.
Learning
• That is not only true for the scientist, but for
the rest of us as well.
• The more we learn and discover, the more we
realize how ignorant we are, how much more
there is to know.
• A closed society protected from criticism and
opposition is a stagnant society.
The Irony of War
• The irony is that an open society welcomes a
clash of cultures, a clash of ideas and hypotheses
in every area, even religion.
• Without that openness, the only other way to
resolve conflict is through force. War is often the
result of political or ideological fundamentalism.
• The only way to peace in the world is to welcome
the clash of ideas, encourage healthy skepticism,
the clash of “cultures”.
• The way to war is to suppress debate.