Introduction to Critical Thinking

Think SlowlyAsk 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

• 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

As you can see, there are a number of possible antecedents that “make sense” out of the consequent.

Hypotheses

If ________________________________ , then he will be late for class

There are any number of possible hypotheses that can explain the consequent.

An unknown antecedent is a “hypothesis” (a conjecture)

Inference

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

Mean Principal

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_embedded&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 BiasConsider 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)

12345678910

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 BiasWe 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. ___ AIDS2. ___ Motor vehicle accidents3. ___ Breast Cancer4. ___ Medical mistakes5. ___ Aviation6. ___ 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. Chocolate barsb. Potato chipsc. Popcornd. 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

But, because of that correlation, we are quick to assume that eating sweets is the cause of the acne.

Cause

Effect

Unknown cause (possible hypothesis)

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.

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 MuslimsAbdul 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: 9,9002,000,000,000

It is highly improbable that Abdul is a terrorist.

Or, 0.000495%

Explanation of #287% 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?

1001000,000,000,000

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 TrialIf 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 NarrativesFacts 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 political-ideological 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

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.

Human beings find uncertainty very uncomfortable.

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.