Lesson 09 - Causal Reasoning

Remember
Inductive = maybe/likely/probably true [cogent]
deductive = 100% true [valid] (if premises are true)

Agenda

• Arguments and Deductive and Inductive Reasoning
• The 3rd Type of Inductive Reasoning: Causal Argument
• Necessary and Sufficient Conditions
• Misuse of Inductive Reasoning

1. Review: Deductive and Inductive Reasoning

How do the two types of reasoning fit into our concept of an argument?

Example Arguments Comparison

Argument A (Deductive):

• Mr. Chad receives a 70,000.00 per month salary from Alpha Corp
• His wife, who also works at Alpha Corp, has a monthly salary of 50,000.00
• Conclusion: It follows that the couple's monthly income from Alpha Corp is 120,000.00

Argument B (Inductive):

• Mr. Chad receives a 70,000.00 per month salary from Alpha Corp
• His wife, who also works at Alpha Corp, has a monthly salary of 50,000.00
• Conclusion: We can, therefore, assume that Mr. Chad has a higher position than his wife at Alpha Corp
• Hidden Premise: Employees in higher positions usually have higher salaries

Key Differences

Deductive Argument (A):

• ✓ The conclusion cannot be false if the premises are true
• ✓ The conclusion necessarily follows the premises
• ✓ The conclusion only spells out a fact that is implicit in the premises
• ✓ This is not new information - we also know who contributes more to the combined salary

Inductive Argument (B):

• ✓ The conclusion only probably follows the premises
• ✓ The conclusion still has room to be false, even when its premises are true
• ✓ The conclusion introduces information not directly stated by the premises
• ✓ The conclusion gives us new information

Summary Quote

"The difference between the two arguments is that a deductive argument's conclusion necessarily follows its premise(s), while an inductive argument only probably follows. A valid deductive conclusion cannot be false if its premises are true."

• He is like lion (analogy)
• He is lion (metaphor)

2. Causal Arguments & Conditions

What is a Cause?

Definition: An event that brings about a change or produces an effect

Causal Arguments Explained

• In causal arguments, it is claimed that something is (or is not) the cause of something else

Example:

• P1: You're eating too many French fries and
• P2: You don't exercise
• P3: You're going to gain weight if you don't change your ways
  • มันก็ไม่ได้ Guarantee ซะหน่อย มันไม่เหมือน 1+1=2 ซะหน่อย

Analysis:

• The speaker asserts that consuming excessive French fries and failing to exercise will lead to weight gain
• Like other inductive arguments, the conclusion is never 100% certain
• You may not gain weight due to factors like a metabolic disorder or a tapeworm

Ambiguity in the Word "Cause"

When the word "cause" is used, it is seriously affected by ambiguity.

• Conveys something that must be present for an effect (necessary)
• Is something that guarantees an effect (sufficient)
• Is both necessary and sufficient.

Example 1: Necessary Condition

Statement: "Sprinkling water on flowers will cause them to grow"

• We mean that water is required for growth
• We do NOT mean that water alone can do the job

Example 2: Sufficient Condition

Statement: "Going for a swim will cause us to cool off"

• We mean that the swim itself will do the job
• But we also understand that taking a cold shower or staying in an air-conditioned room would work as well

Solution

Using the terms 'necessary' and 'sufficient' conditions will be useful in clarifying this ambiguity.

Necessary Condition

A condition that must be present for an effect to occur (although it may not be enough to cause the effect on its own.)
เช่นพวกแบบ Oxygen is needed to cause a fire.

Definition

• It is what the name suggests
• It is a causal factor in which the effect cannot happen without it

Formula

"Without this, then not that..."

How Necessary Statements Are Expressed

• "If this doesn't happen, then that won't occur"
• "If this isn't true, then that isn't true either"
• "If this isn't present, then that won't be present"
• "If it doesn't have (A), then it can't be (B)"
• "If it doesn't do (A), then (B) won't be the result"

Example

"If you did not book your Grab ride, then it won't show up at your door"

More Examples of Necessary Conditions

1. "If the SARS-CoV-2 virus hasn't infected you, then you are not sick with COVID-19"
   • The virus infection is necessary for COVID-19
2. "If the polio vaccine does not prevent polio, then the near-zero cases of polio after vaccination are a coincidence"
   • The vaccine's effectiveness is necessary for the reduction in cases
3. "If it doesn't have wings, it cannot be a bird"
   • Wings are necessary for being a bird
4. "If your only CPU won't turn on, you cannot finish your coding task"
   • A functioning CPU is necessary for completing the task

Sufficient Condition

A condition that, if present, guarantees the effect — it’s enough to cause the effect.
Example: Striking a match in the presence of oxygen and fuel is a sufficient condition for starting a fire, assuming normal/typical conditions.

Definition

• Necessary and sufficient conditions are different
• Even if the necessary condition is met, this might not be enough to ensure that the effect will happen
• Sufficient conditions are the total conditions that must be met to ensure that the effect happens

Formula

"If this, then that..."

How Sufficient Statements Are Expressed

• "If this is true, then that will always be true"
• "If A is present, then that proves B"
• "If this is true, then that will always follow"
• "If A is present, then B must be true"

Key Point

Having the lottery ticket doesn't mean you will win the prize

Examples of Sufficient Conditions

1. "You are in Rangsit, so you are in Thailand"
   • Being in Rangsit is sufficient to prove you're in Thailand
2. "If the figure has 3 straight sides, then it is a triangle"
   • Having 3 straight sides is sufficient to identify a triangle
3. "If today is Friday, then tomorrow is Saturday"
   • Friday is sufficient to guarantee Saturday follows
4. "If the scan shows no brain activity, then the patient is clinically dead"
   • Absence of brain activity is sufficient for clinical death

Necessary vs Sufficient Conditions

Necessary

• Whenever a factor is essential, mandatory, or required for the effect to be realized

Sufficient

• Whenever an event or a factor ensures that the effect is realized

Practice: Necessary and Sufficient Conditions

Evaluate the argument. The conclusion is underlined. Identify if the premises meet the necessary or sufficient conditions.

• N = necessary
• S = sufficient
• X = neither necessary nor sufficient

Questions

1. Ben is an SIIT student. Therefore, Ben is a math expert. X
2. Ben's dorm is 10 minutes from SIIT, and he left his dorm for SIIT 15 minutes ago. Ben is at SIIT now. N
3. Ben is an SIIT student. Ben is a Thammasat University student. S
4. Ben is in the LAS101 class. Ben is an intelligent student. X
   • N คือถามว่า Ben ต้องอยู่ใน LAS101 class มั้ยเพื่อที่จะเป็น intelligent student
   • S ถามว่า Guarantee มั้ย
5. Ben started his thesis 3 semesters ago. So, Ben has been working on his thesis for 3 semesters now. N

Exercises Causal conditions, Mill’s method

0. Eating too much food will cause weight-gain. X
1. Throwing a brick through a window will cause the window to break. S
2. Releasing the shutter of a camera causes an image to appear on the film. N
3. Pulling the trigger of a gun causes it to fire. X
4. Pouring water on a wood fire will cause it to be extinguished. S
5. Eating contaminated food will cause one to become ill. X
6. Flipping the wall switch to the “up” position causes the overhead lights to go on. X
7. Getting a degree requires a minimum GPA of 2, and minimum 145 credits in a combination of major and minor subjects. N/S

If there are no oxygen, human cannot live. S

Because Chiang Mai is located in the north, there’s a lot of pollution. X

If someone coughs, they have a sore throat. X

หน้าตาดี จะต้องมีแฟนได้ X

Key Understanding

"Knowing the necessary and sufficient conditions for a claim helps us determine if there is a cause-and-effect relationship. If that factor is a necessary condition, it only allows the possibility of the effect. Factors that are sufficient conditions guarantee that the effect will happen."

3. Causal Arguments & Mill's Methods

Are there other ways to prove cause and effect relationships?
Can we use observation and experience to prove causality?

John Stuart Mill's Methods

Introduction

• John Stuart Mill proposed a useful way for scientists to show that one thing causes another
• In his book A System of Logic, Mill suggested several methods for asking questions in experiments

Examples of Mill's Method of Experimental Inquiry

1. Method of Agreement

   • What things were the same when the effect happened?

2. Method of Difference

   • What things were missing when the effect did not happen?

3. Joint Method of Agreement & Difference

   • What things were the same when the effect happened?
   • What things were the same when the effect did NOT happen?

Method of Agreement

Definition

The method of agreement looks at two or more instances of an event to see what they have in common.

Example: Restaurant Food Poisoning

Scenario:

• Four people eat at a restaurant
• Only three get food poisoning
• The method of agreement tells us to investigate what the three instances have in common

Analysis Table:

Result:

• In all three instances of the effect, the appetizer was the one thing in common
• Therefore, the appetizer is the cause

Method of Difference

Definition

We look at two cases—one where the event happens and one where it doesn't. If everything is the same except for one difference, that difference is probably the cause.

Example: Different Meal Analysis

Scenario:

• Examine the same diners at a different meal
• Look for the difference between the three who got food poisoning and the one who did not

Analysis Table:

Result:

• Kristin is different from the three - she didn't get food poisoning
• We see that Kristin didn't eat fries
• Therefore, the fries are the cause

Joint Method of Agreement and Difference

Definition

The joint method of agreement and difference combines the first two approaches. Adding the results of the two methods into one analysis strengthens our claim.

Analysis

Combined Table:

• The 3 white rows show the results of agreement
• The shaded row shows the result of the method of disagreement

Key Rules

• The effect must always be present when the cause is present
• The effect must always be absent when the cause is absent

Conclusion

The joint method allows us to assert that the appetizer is a sufficient condition for their food poisoning.

Applying Mill’s Methods

“Why did some students fail in the midterm exams?”

• Create a joint method chart with:
  • At least 4 instances of the effect
  • At least 3 possible causes

Construct a table that supports this conclusion. 
Which one of Mill’s methods did the doctor use?
A man developed an allergic reaction to an unknown food. His doctor asked him
about foods that often cause allergic reactions, and the man replied that he had
eaten coconut, chocolate, nuts, milk products, shellfish, peppers, eggs, and wheat
products prior to suffering the reaction. The doctor told him to eliminate all of these
foods from his diet; when he had done so, the reaction disappeared. The doctor then
told him to introduce each of these foods back into his diet, one at a time. The man
did so, and the reaction reappeared only when he ate milk products. The doctor
concluded that milk products caused the allergic reaction.

Construct a table that supports this conclusion. 
Which one of Mill’s methods did Mrs Wilkins use?
Mrs. Wilkins sometimes has trouble sleeping. In order to determine the cause, she
decided to take note of her pre-bedtime behavior over the course of a week. On
Monday she drank camomile tea, had a late dinner, took a hot bath, read from a
book, took a walk, and slept well. On Tuesday she had a late dinner, read from a
book, and slept poorly. On Wednesday she drank a glass of wine, got a massage,
took a walk, and slept poorly. On Thursday she had a late dinner, drank a glass of
wine, read from a book, took a hot bath, got a massage, and slept well. On Friday
she read from a book, drank camomile tea, got a massage, had a late dinner, took a
walk, and slept well. On Saturday she drank a glass of wine, got a massage, took a
walk, drank camomile tea, took a hot bath, and slept well. On Sunday she read from
a book, took a hot bath, drank camomile tea, and slept poorly. What can Mrs. Wilkins
conclude is the cause of sleeping well?

4. Misuse of Inductive Reasoning

How do people misuse inductive argument?

Common Fallacies in Inductive Reasoning

Every day, we encounter arguments that misuse inductive reasoning. These may concern pregnancy, poverty, violence, or even achieving a fit and firm body. Such arguments commit mistakes through various fallacies:

1. Chicken and Egg Fallacy
2. Post hoc, ergo propter hoc (False Cause)

Chicken and Egg Fallacy

General Form

Structure:

1. A and B regularly occur together
2. Therefore, A is the cause of B

What Goes Wrong

• There is no common cause that brings about A and B
• An assumption is made that one event must cause another just because the events occur together
• The assumption is based on inadequate justification
• There is not enough evidence to draw a causal conclusion

Chicken and Egg Fallacy - Example

The Problem Illustrated

Argument A:

• The people who often have violent behaviors are the people who play violent video games
• Therefore, playing violent video games is the cause of violent behavior

Argument B:

• People who are violent play violent video games
• Therefore, violent video games are created for people with violent behaviors

Analysis

• Argument A says: A happens with B often, therefore A is the cause
• Argument B says: B happens with A often, therefore B is the cause
• Both commit the chicken and egg fallacy - we can't determine which came first or which causes which

Chicken and Egg Practice

Which is a Chicken and Egg Fallacy?

Argument A:

• Johnny Cash was famous
• He was also on television frequently
• Therefore, Johnny Cash was famous because he was on television frequently
• ❌ This IS a chicken and egg fallacy (maybe he was on TV because he was famous!)

Argument B:

• I didn't wash dishes all week
• My dirty dishes started to grow mold
• If I don't want mold growing on my dishes, I should wash them
• ✓ This is NOT a fallacy (there's a clear causal relationship)

Post Hoc, Ergo Propter Hoc

Definition

This fallacy, sometimes referred to as false cause, looks like this:

Structure:

1. Event A precedes event B
2. Therefore, Event A caused event B

Example

• Ahmed tries to open a video program on his computer, but it crashes
• He concludes that the program is causing the computer to crash

Why It's a Problem

• The fact that the opening of one program always precedes the crash is a good possibility for cause
• But it cannot be maintained as the one and only cause until a stronger link is made

Post Hoc Practice

Which is NOT an example of a post hoc fallacy?

a. I thought my team would lose the game, and they did. If I want them to win next time, I need to think more positively.

• ❌ This IS post hoc (thinking negatively doesn't cause losing)

b. Shari wanted to make a great meal for her guests, so she picked out a delicious looking recipe and followed it exactly. Her guests loved it.

• ✓ This is NOT post hoc (following a recipe has a legitimate causal relationship with the result)

c. Jason did not have time to brush his teeth before his dentist appointment. But the dentist told him he had no cavities. So, Jason has decided he does not need to brush his teeth anymore.

• ❌ This IS post hoc (one instance doesn't prove causation)

LAS101 Roadmap

Course Structure

1. Introduction
2. Definitions
3. Concepts on Proof and Belief
4. Limits of Human Thinking and Errors
5. Arguments
6. Propositions and Inductive Argument ← We are here
7. Formal Deduction ← Next target

Key Takeaways

• Deductive reasoning provides certainty (if premises are true, conclusion must be true)
• Inductive reasoning provides probability (conclusion likely but not certain)
• Causal arguments claim something causes something else
• Necessary conditions are required for an effect (without X, no Y)
• Sufficient conditions guarantee an effect (if X, then definitely Y)
• Mill's Methods help establish causation through observation
• Chicken and Egg Fallacy assumes causation from correlation
• Post Hoc Fallacy assumes causation from temporal sequence

False cause fallacies in contemporary issues

Can you analyze necessary and sufficient conditions for these causal arguments?

1. Claim: Autism rates increased after the introduction of certain vaccines, so vaccines must cause autism.
2. Claim: A government passes new economic legislation, and unemployment drops shortly after-therefore, the policy caused the drop.
3. Claim: Mental health issues among teens increased after social media became popular, so social media is the cause.
4. Claim: A company introduces Al automation, and job losses follow-therefore, automation caused unemployment.