critical thinking wk 13

13IntroCausalArgumentsSpring2026.pptx

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Module 13 Introduction: Evaluating Arguments: Causal (not “casual”) Arguments – Spring 2026 Warning: A lengthy introduction.

Critical Thinking Online

Fayetteville State University

Dr. Jon Young, Instructor

Learning Outcomes: In this module, you will:

Define causal arguments as arguments whose conclusion is a causal claim, that is, one which states x (causes) y.

Note different ways in which causal claims are expressed.

Identify four patterns of causal reasoning: method of difference; method of agreement; method of agreement and difference; method of correlation.

Explain common confusions of cause and effect, including misidentifying relevant factors; confusing coincidence with causation; confusing temporal order with causation (post hoc ergo propter hoc), and confusing causes and effects.

Explain how causal claims often describe necessary and sufficient conditions.

Learning Activities and Assessments

Complete the Required Readings

PowerPoint Introduction

Chapter 10.3 in your electronic textbook .

Earn at least 6 of 10 points on the Quiz..

Submit a writing assignment.

Contribute to the Discussion.

Causal (not “casual”) arguments

This week’s lesson turns to the third inductive argument type that we will examine: causal arguments (arguments about cause and effects) or arguments whose conclusion is a causal claim.

A causal claim asserts a relationship between two events such that one causes the other.

Reasoning about causes and effects is so common that you may not be aware that you are doing it. At the same time, we often fall into common errors about cause and effect reasoning.

Discovering the relationship between causes and effects is one of the most important ways in which we as humans use our capacity to reason. Knowing about causes and effects enables us not only to survive but to improve our lives. As a child we learn very early that fire causes heat and if we get too close to it we will be burned.

Knowing the causes and effects of energy in nature enables us to harness electricity to make electric lights, heating, air conditioning, computer technology, and all the other devices we encounter in our daily lives..

Any time doctors offer diagnoses or treatments, they are relying on many conclusions about the relationships of causes and effects.

As these few examples indicate –you can probably think of many, many more examples -- discovering cause-effect relationships and using this knowledge to improve our lives has been essential to the growth of civilization.

Why it’s important:

Observing causes?

The first point, which may seem shocking at first, is that we never observe causes directly.

Rather, we observe two events, occurrences (sometimes more) that we infer are related in such a way that one causes the other.

Causal arguments draw a conclusion (make an inference) about cause and effect relationships.

Since cause and effect relationship are the result of inferences, we need to be careful about how we test them and the potential errors we can make.

Many ways to express cause-effect relationships

An argument about causes and effects (causal arguments) offers evidence to support the conclusion: x causes y.

But the conclusion of a causal argument may take many different forms, such as:

A person with x is more likely to have y than a person without x.

X is linked to y

Y is the result of X

X led to Y

X prevents Y (X cause Y not to happen)

X contributed to Y

Causal arguments are inductive

In an inductive argument, if the premises are true, the conclusion is probably true, or true within some range of probability from more likely true than to nearly certain.

Because cause and effect relationships are learned from experience, we can never be 100% certain that the future will be like the past, but we have much higher confidence in some cause-and-effect relationships than others. If I stick my hand in the fire, I have a very, very high degree of confidence that the fire (cause) will burn my hand and cause pain (effect). This confidence, however, is based on the assumption that the future will be like the past. How can I be certain about something in the future, which by definition, is beyond experience. (I will still keep my hands out of fires.)

A college degree (cause) will make me wealthy (effect). Perhaps the degree makes it more likely that you will be wealthy, but it is by no means certain.

The drugs doctors prescribe never have 100% certainty that they will cause one to get better, but in trials these drugs have been shown to be effective in a high percentage of cases and so it is more likely to help than not.

Remember:

When your physician or public health official recommends that you take a specific medicine to get a specific vaccine, they are NOT saying there are no risks. It is certainly possible that the medicine or vaccine will have an adverse effect.

Physicians and public health officials ARE saying that the potential benefits of the medicine or vaccine are greater than the risks.

This assessment is based on clinical studies that are discussed below.

When we say X causes Y we typically mean one of four possible patterns. (Based on 19th century philosopher John Stuart Mill)

Method of Agreement – X is the only relevant common factor in multiple occurrences of Y

Method of Difference - X is the only relevant difference between occurrences and non-occurrences of Y.

Method of Agreement and Difference – X is both the only relevant common factor in multiple occurrences of Y and the only relevant difference in occurrences and non-occurrences of Y.

Method of Correlation (Concomitant Variation) – X causes Y if a change in X is associated with a change in y. (Caution: correlation may suggest causal relationships, but does not by itself prove causation. It must be established that the correlated items are the only relevant common factors and differences. Remember this rule forever: “Correlation does not prove causation.”)

Patterns of the four methods

Method of Agreement: C is the only relevant common factor among multiple occurrences of E.

Instance 1: Factors a, b, and c are followed by E.

Instance 2: Factors a, c, and d are followed by E.

Instance 3: Factors b and c are followed by E.

Instance 4: Factors c and d are followed by E.

Therefore, factor c is probably the cause of E.

Method of Difference: C is the only relevant difference between occurrence and non-occurrences of E.

Instance 1: Factors a, b, and c are followed by E.

Instance 2: Factors a and b are not followed by E.

Therefore, factor c is probably the cause of E.

Patterns of the Four Methods

Method of Agreement and Difference: suspected cause is both the only relevant common factor in multiple occurrences of E and the only relevant difference in occurrences and non-occurrences of E

Instance 1: Factors a, b, and c are followed by E.

Instance 2: Factors a, b, and d are followed by E.

Instance 3: Factors b and c are not followed by E.

Instance 4: Factors b and d are not followed by E.

Therefore, factor a is probably the cause of E.

Patterns of Four Methods

Method of Correlation (Concomitant Variation): Changes in C are associated with changes in E, so C and E are causally connected.

Instance 1: Factors a, b, and c are correlated with E.

Instance 2: Factors a, b, and increased-c are correlated with increased E.

Instance 3: Factors a, b, and decreased-c are correlated with decreased E.

Therefore, factor c is causally connected with E. (Remember that correlation alone does not prove causation. Further research is needed to establish causal relationship.)

Patterns – “Common Sense” – You use them regularly without having a name for them.

Consider this example - A group of 8 friends go to the Flying Tortilla Restaurant (one of my favorites in Santa Fe) for dinner. The group has a wonderful time, but unfortunately, 4 of the 8 become very sick later that evening. Within 24 hours they are feeling better and they try to determine why some got sick and others did not. They recall what they ate. Of the 4 who got sick, 2 ate the Chalupa Supreme, but one who did not get sick also ate this dish. One of the four who got sick ate Fajitas with chicken and beef, but so did two of the people who did not get sick. One of the group remembered that they ordered green chili salsa for their chips. The 4 who got sick all ate the green chili salsa while the 4 who ate the regular salsa did not get sick. Moreover, the person who ate more chips and green chili salsa was sick for the longest time. The group concludes that the green chili salsa was the cause (x) of the sickness (y) and report it to the restaurant

The reasoning process used to identify the cause in the previous example – which everyone of us would use -- reflects all four of Mill’s patterns of reasoning.

The four who were sick had all eaten the green chili salsa (method of agreement: green chili salsa was the only relevant common factor among multiple occurrences of the sickness)

The four who did not become sick had not eaten the green chili salsa (method of difference: eating the green chili salsa was the only relevant difference between occurrence and non-occurrence of the effect).

Green chili salsa is both the only relevant common factor in multiple occurrences of sickness and the only relevant difference in occurrence and non-occurrences of sickness. The fact that both the method of agreement and difference are evident here gives us greater confidence in the conclusion that the green chili salsa was the cause of the sickness.

The fact that the sickness was worse with the one who ate the most of it makes it more likely the cause. (Method of correlation - as consumption increased so did severity of sickness.)

Example: Method of difference

You have used your mother’s famous recipe for chocolate brownies at least a dozen times and they always turned out perfect until this last time. They did not rise up as usual and they were very gooey and stuck to the pan.

You look at the package of flour and realize what happened. You thought the flour was self-rising (as required by the recipe), but it was not.

What is the reasoning pattern?

Use of regular flour instead of self-rising caused the brownies to fail.

The flour was the only relevant difference between the times when your brownies turned out good with the recipie and this time wheny they turned out bad.

Example: Method of Agreement

One afternoon last fall, seven different cars broke down at various places in Santa Fe within an hour of each other, causing chaotic traffic jams throughout the city. Poilice investigators wondered if these breakdowns were just coincidence or if there was some underlying cause. The cars were all different makes and models so type and age of car could not be the underlying cause. In their interviews with each of the dirvers, they discovered that each had bought gasoline at the same gas stations within the previous several hours. Upon further review, the Policed discovered that all had dispensed gasoline from the same gas dispenser. They immediately contacted the station owner to try to figure out what was wrong with the gas in that specific tank.

The gas dispenser turnd out to be the only reelevant common factor in multiple occurrences of the effect.

Example: Method of Agreement and Difference

Jall, Jame, Jerd, Jaste, and Jeld earned an A for midterm in Critical Thinking

Rilke, Rette, Rart, Rad, and Reeze earned a D at midterm.

When the five R students compared themselves to the J students, they discovered that the J students never missed class and completed all the work on Canvas. All of the R students missed at least three classes and only occasionally completed the work in Canvas.

Rart concludes that class attendance and completing Canvas work are causes of good grades. He suggests that his classmates should vow to never miss class and to complete all work in Canvas.

(Rad disagrees. Noting that all the A students have names that begin with J, he proposes that they change their names to ones that begin with J).

Example: Analysis

Rart is smart!

Method of agreement: Regular class attendance and completion of Canvas assignments are the relevant common factors in the J students’ success, just as the failure of the R group to attend class and complete Canvas assignments is the common factor leading to their bad grades.

Method of difference: Class attendance and Canvas completion are the relevant differences between groups that were successful versus those who were not successful.

Rad commits a common causal confusion, which we will discuss below, of misidentifying common factors as relevant that are not.

Example

The examples so far are very simple – possibly you would call them “common sense,” but consider the next example, which is typical of scientific and medical research.

Note: while much more complex in content, the pattern of reasoning is the same as in these previous simple examples.

Medical research

A company works feverishly to develop a drug for treating COVID 19. The company has tested it sufficiently on animals to believe that it is safe for humans.

They assemble 200 patients of all ages who have COVID-19. They randomly give 100 participants the new treatment and 100 are randomly selected to receive a placebo.

We call these the experimental group (or “treatment” group since they receive the treatment) and the control group (does not receive the treatment).

The researchers track how many days it takes for each person to get better. If they find that the experiment group requires fewer days to get better than the control group, they will conclude that the treatment works. (Please note that statistics will be used to make sure the difference is not by chance; when the difference is determined to be too great to be chance, we say the difference is “statistically significant.) Any difference that is not statistically significant will be rejected as inconclusive.)

“Controlled” cause to effect experiment

This experiment is designed to ensure that receiving the new drug (cause) is the only relevant difference between the two groups. So any difference in time required to get better (effect) is due to this difference.

At the same time, the relevant common factor in each group is receiving or not receiving the proposed drug.

Effect to cause study (Method of difference and agreement)

The movie, “Dark Waters,” recounted the story of people in West Virginia town who won a major lawsuit against a chemical company because the company was putting chemicals into the water supply, which led to elevated numbers of certain types of cance

To win the lawsuit the plaintiffs could not offer mere speculation; they had to offer strong evidence that the contaminated water was the cause of the cancer. How did they establish the link between the drinking water and the cancers?

(The movie is now available on several platforms. If you get a chance to see it, please do so since it illustrates effect to cause study very well.)

Effect to cause study (Method of difference and agreement)

First they discovered that the incidence of cancer in the town was so high when compared to other places that it could not be by chance. The drinking water is the only relevant difference between those places with abnormally high rates of cancer and those with normal rates..

Second, the drinking water was the only relevant common factor among those with the high rates of cancer.

The essential point here is that scientific and medical research utilize the same patterns of reasoning about causes and effects that we use in our daily lives.

Common Confusions – Causal Reasoning Note: Similarities and differences between this list and the textbook are noted below.

Just as our reasoning about causes and effects take on one or more of these patterns, so too do common confusions:

Misidentifying or overlooking relevant factors (Textbook speaks of two different confusions)

Confusing coincidence with cause

Confusing cause with temporal order (post hoc ergo propter hoc)

Confusing cause and effect

Accepting anecdotal evidence as proof of cause-effect relationship (Textbook does not discuss, but it’s important.)

Misidentifying or overlooking relevant factors

Four people of a group of eight get sick after going to a restaurant together. If I notice that all to have a last name that starts with M and suggest that is the cause then I am misidentifying the first letter of their last name as relevant and overlooking a more relevant factor, namely, what common dish did the four eat. (Not all common factors are relevant to cause and effect.)

Every morning I notice that just as the bus arrives across the street, the church bells begin to ring. If I conclude that the bus causes the bells to ring, I have overlooked an important relevant factor, namely that the bus arrives at 11 am, which is the time the church bells begin ringing every day.

When the western states of the U.S. were being settled, some observers noted that the rise in number of churches was correlated with an increase in prostitution. If I claim that the churches are the cause of the increased prostitution, then I am overlooking a very relevant common factor, namely, the increase in population is likely the cause of both phenomenon.

Confusing coincidence (correlation)with cause

Two things are events are correlated if a change is one is accompanied by a change in the other: an increase or decrease in X is related to increase or decrease in Y; the correlation could be inverse: increase in X leads to decrease in Y and vice versa. Correlation may suggest a causal relationship, but could be mere coincidence. Correlation, by itself, does not prove causation. We must show that the correlated items are the only relevant common factors or differences.

It seems that every time I forget my umbrella it rains; if I remember my umbrella, it does not rain.

I start drinking Bronco Blue Energy Drink and notice that the more I drink, the better my grades are. I conclude, “Wow, this drink makes me smarter!”

In each of the most previous years, the number of movies described as “violent” has increased. During those same year, violent crime increased. So the violence in movies caused the violence in society.

Remember: correlation (coincidence) may suggest causal relationships, but such hypotheses must be tested according to methods of agreement and difference.

Confusing temporal order with causation. (post hoc ergo propter hoc)

A cause precedes an effect in temporal order, but temporal order alone does not establish a cause-effect relationship.

The city hired a new chief of police. In the following year, the crime rate went down. Therefore the hiring of the new police chief caused the crime rate to go down. (perhaps the new chief did make changes that reduced crime, but pointing out the temporal order alone does not establish causation.)

A state establishes stricter rules for purchasing guns and over the next year the murder rate goes down. Before you conclude that the stricter rules “caused” the decline in murders, you would have to explore other potential relevant common factors or relevant differences.

Temporal order alone – that is one thing comes after another -- does not establish causation.

The Latin phrasing of this fallacy is especially accurate. “Post hoc ergo propter hoc” literally means “after this, therefore, because of this.” Sometimes I will refer to this fallacy in the Latin because it is so accurate. Sometimes, we shorten the Latin to simply post hoc fallacy. (Perhaps you can impress your family and friends by throwing around these terms.)

Confusing cause and effect (reverse causation)

We may reasonably suspect a cause-effect relationship, but it may be that the cause is actually the effect and/or the effect is the cause.

Abundant evidence shows that people with a bachelor’s degree have higher lifetime earnings than those without one. Is the bachelor’s degree the cause of higher wealth OR is it that those who are wealthy (cause) go to college at higher rates effect?

Many people have noted that an increase in violence in movies and violence in society are related. But is the violence in movies the cause of violence in society OR is the violence in society the cause of increased violence in society?

Accepting Anecdotal Evidence as Proof

“Anecdotal evidence” refers to one-time or occasional occurrences of an effect. We must be careful about accepting such anecdotal evidence of “proof” of a causal connection.

Marketers of weight-loss programs or exercise equipment frequently give a few examples of individuals whose lives were changed dramatically for the better because they used the product. Such anecdotal evidence conveniently excludes all those who used the product and had no positive results.

Anecdotal Evidence - Example

The link between smoking and lung cancer is well-established. Comparisons of people who contract lung cancer and those who do not show that there are many more smokers in the group with lung cancer than in the group without lung cancer. This does not mean that everyone who smokes will contract lung cancer, only that smokers are more likely than non-smokers to contract lung cancer. This finding has been well-established. However, if I point to my grandfather who lived to a 100 and smoked a pack a day as “proof” that the findings about smoking are wrong, I am accepting anecdotal evidence as proof.

Evaluate this example

Every morning my grandmother drinks a glass of water with a drop vinegar in it. She is 95 years old and is as alert and active as many who are twenty years younger than her.

Based on this experience, you hypothesize that a daily glass of water with a drop of vinegar causes longevity.

Which of the following would help you test your hypothesis?

You speak to some of your grandmother’s elderly friends to determine how many of them have a daily drink of water with vinegar.

You ask some of your friends with elderly, healthy grandparents if their grandparents drink water with vinegar.

Which of the following would help you test your hypothesis?

You speak to some of your grandmother’s elderly friends to determine how many of them have a daily drink of water with vinegar. No, this would be anecdotal evidence.

You identify a group of 50 90+ year olds who are as alert and active as your grandmother and another 50 90+ year olds who are in bad health and determine if there is a significant difference in the practice of having a daily drink of water with vinegar. Yes, this would give you a means for comparing the incidence of the suspected cause among those who have and do not have the desired effect. With such a comparison, you cannot make a reliable conclusion about cause and effect because you have not eliminated other relevant factors.

You go to a rest home and ask for volunteers who are willing to have a daily drink of water with vinegar; after six months you compare the health of the water-vinegar drinkers and the non water-vinegar drinkers. No, though you establish control-experimental groups, you have not accounted for the potential pre-existing health conditions hat could affect the outcomes.

You ask some of your friends with elderly, healthy grandparents if their grandparents drink water with vinegar. No, this is anecdotal evidence.

Example from the early days of the pandemic

Early in the pandemic, before vaccines and treatments, many drugs were considered as being effective in treating Covid 19. One such drug was hydroxychloroquine.

Many hospitals have simply been giving hydroxychloroquine to patients, reasoning that it might help and probably will not hurt, because it is relatively safe.

Early reports from France and China offered promising evidence, but these students were crbecause they did not include control groups to compare treated versus untreated patients. Researchers called the reports anecdotal, and said the lack of controls made it impossible to determine whether the drugs worked.

The new study, of 62 patients with an average age of about 45, did have a control group. It was conducted at the Renmin Hospital of Wuhan University, in Wuhan, China. The patients were carefully chosen to exclude people with medical problems that could be made worse by hydroxychloroquine, like abnormal heart rhythms, certain eye diseases, and liver or kidney problems.

Half the subjects — the controls — received just the usual care given to coronavirus patients, and half had usual care plus hydroxychloroquine. The usual care included oxygen, antiviral drugs, antibiotics and other treatments. They were treated for five days, and their fevers and coughing were monitored. They also had chest CT scans the day before the study treatment began, and the day after it ended.Coughing and fever eased a day or so earlier in the patients who received hydroxychloroquine, and pneumonia improved in 25 of 31, as opposed to 17 of 31 in the controls. With further study, this drug proved to be ineffective. Such research involves trial and error and is always self-correcting.

Answer the questions about this case on the next slide.

Which of the following is false?

The control group and experimental group were similar in age and severity of the illness.

Without a comparison of impact of drug on those who received it versus those who did not, it is impossible to know if the drug is only factor contributing to improved results.

The results prove that the drug should be widely used on all patients.

Because the study was limited to patients with mild to moderate symptoms, we cannot be sure that the drug will be effective on those with severe symptoms.

25 of 31 (81%) members of the experimental group improved more quickly compared to 17 or 31 (55%) of the control group.

Which of the following is false?

The control group and experimental group were similar in age and severity of the illness.

Without a comparison of impact of drug on those who received it versus those who did not, it is impossible to know if the drug is only factor contributing to improved results.

The results prove that the drug should be widely used on all patients. False

Because the study was limited to patients with mild to moderate symptoms, we cannot be sure that the drug will be effective on those with severe symptoms.

25 of 31 (81%) members of the experimental group improved more quickly compared to 17 or 31 (55%) of the control group.

Consider this example

In 1990, an ambitious first-grade teacher in Charlotte, introduced a new method of reading instruction for her 24 students. In 2020, she was able to contact all 24 students and found that 100% of the students had attended college and were employed in professions. This long-term success proves that her method of reading instruction contributed to their long-term success. (See next page for analysis)

Let imagine this first-grade teacher was even more ambitious: she also identified 24 similar students in another first-grade class whose teachers did NOT use this teacher’s method of reading. In 2020, whe contacted these students as well; she found that @75% of the them attended college and were employed in professions. Three of the 24 dropped out of high school. The ambitious first grade teacher claims that these results strengthen her conclusion that her reading instructor is the key to her students’ success.

Which of these is FALSE?

It is virtually impossible to identify the method of reading instruction as ONLY relevant common factor contributing to the success of the students.

It is equally impossible to identify the method of reading instruction as the ONLY relevant difference between the two the 100% success of one group and the lower success rate of the other group.

The teacher’s information is little more than anecdotal evidence that proves little.

Other teachers should try the method of instruction.

Which of these is FALSE?

It is virtually impossible to identify the method of reading instruction as ONLY relevant common factor contributing to the success of the students.

It is equally impossible to identify the method of reading instruction as the ONLY relevant difference between the two the 100% success of one group and the lower success rate of the other group.

The teacher’s information is little more than anecdotal evidence that proves little.

Other teachers should try the method of instruction. False. (Other teachers should seek more evidence before concluding this method is best.)

Let’s review

Which of the following is not a pattern of causal reasoning?

X is a cause of Y if it is the only relevant common factor in multiple occurrences of Y. (Method of difference)

X is a cause of Y if it is the only relevant difference in occurrence and non-occurrence of Y. (Method of agreement)

X is both the only relevant difference in occurrences and non-occurrences of Y and the only relevant common factor in multiple occurrences of Y. (Method of difference and agreement)

X may be causal factor of Y if change in X is associated with a change in Y.

(Method of correlation or concomitant variation)

Post hoc, ergo propter hoc (after this, therefore because of this) This is not a pattern of causal reasoning but a common confusion about causes and effects.

Analyze examples

A man is convinced that duct tape cures the measles. His conclusion is based on the following experiences: instead of giving his three children measles vaccine, he put a piece of duct tape on their forehead while they slept overnight. None contracted measles.

Which of the following is FALSE?

To prove his conclusion, he would need to compare incidence of measles among a group of children who were vaccinated and group of children receiving the duct tape.

The man is accepting anecdotal evidence as proof of a causal relationship.

Duct tape has proven to have many benefits so it is reasonable to accept the man’s conclusion.

Analyze examples

Which of the following is FALSE?

To prove his conclusion, he would need to compare incidence of measles among a group of children who were vaccinated and group of children receiving the duct tape. True

The man is accepting anecdotal evidence as proof of a causal relationship. True

Duct tape has proven to have many benefits so it is reasonable to accept the man’s conclusion. False

Example

The headline of a magazine article says that people who eat a handful of peanuts every day are less likely catch colds. Before you start eating a handful of peanuts every day, what kind of evidence would you want to see?

At least ten people who ate peanuts every day and did not catch colds.

A comparison of the incidence of colds among those who ate peanuts and those who did not.

The number of people with many colds who did or did not eat a handful peanuts every day.

Do smoking bans improve health?

How would you collect evidence to suggest that bans of smoking in public have a positive health benefit. Which of the following would be the best way to test it?

Set up two groups of people and ask one group to smoke a lot in public and other which you prevent from smoking in public. After six months you check the general health of both communities.

Identify several communities that have had such bans for a number of years and communities that do not have such bans and compare the incidence of heart disease, cancer, and other major illnesses in both.

Find some healthy communities and some unhealthy communities and compare the number of each that have a smoking ban.

Ethical Considerations in Research

Ethical considerations sometimes prevent the use of cause to effect studies. The infamous Tuskegee Syphilis Study, from 1932 – 1972, the U.S. Public Health Service monitored the effect of untreated syphilis in poor black men. The study followed 600 men of which 2/3rds had the disease at the beginning of the study. The researchers were going to compare the progression of the two groups. The men never knew that they had syphilis and thought they were just receiving free health care. Even after penicillin was proven to be an effective cure for syphilis, it was withheld from the patients. Once this study became widely known, the U.S. government established guidelines for research using human subjects – if you major in any discipline that does experimentation with human subjects, you will learn the procedures for complying with federal guidelines. One of the major components of these procedures is informed consent; that when a person agrees to participate, he/she knows fully what the experiment is designed to do.

If any of you conduct any type of research using human or animal subjects you will have to learn and apply these ethical guidelines.

Necessary and Sufficient Conditions and Claims about Causes and Effects

Recall our discussion of necessary and sufficient conditions when we discussed arguments based on conditional statements. We said that x is a sufficient condition for y if x guarantees y; x is a necessary condition for y if you cannot have y without x.

(Remember that in a true conditional statement, If x, then y, the antecedent is a sufficient condition for y; and y is necessary for x. Hence, Modus Ponens, “If a, then b. a. Therefore b,” is always valid just as Modus Tollens, “If a, then b. Not b. Therefore not a,” is always valid.)

The concept of necessary ad sufficient conditions also apply to claims about causes and effects.

Necessary and sufficient conditions and Claims about Causes and Effects

Claims about causes and effects are sometimes expressed as claims about necessary and sufficient conditions.

Humans can survive only if they have oxygen. (“only if” indicates that oxygen is a necessary condition for human life.0

The man’s death was caused by lack of oxygen. (lack of oxygen is a sufficient condition to cause death. Of course, lack of oxygen is not a necessary condition for death since death can result from many other causes.)

Water boils if and only if it is heated to at least 180 degrees Fahrenheit (“If and only if” indicates that heating the water to at least 180 degree Fahrenheit is both a necessary and suffiecient condition for achieving the effect of water boiling.

Necessary and sufficient conditions and Claims about Causes and Effects

The relationship of necessary and sufficient conditions provides the basis for actions to prevent or bring about certain specific effects.

For example, we know that pools of stagnant water are a necessary condition for mosquitos to breeds. So, removing this necessary condition is a means of reducing the number of mosquitos and prevent the spread of diseases they carry.

When we agree to get vaccinations, we do so with the hope that the vaccine will be a sufficient condition for preventing us from contracting a specific illness. (even though we know that the vaccine will proably not be 100% effective.)

Necessary and sufficient conditions and Claims about Causes and Effects

What if you purchase some new rose bushes for your yard. The instructions tell you that you to do four things for the roses to thrive:

Plant them according to the instructions;

Make sure they have eight hours of sunlight every day;

Water them at least every other day;

Fertilize them once a week for the first year.

These instructions suggest each of the four conditions are necessary for the roses to thrive; failure to do any one of them will prevent your roses from thriving. However, all four of them together are sufficient conditions. You must do them all to gurantee that the roses will thrive.

In this case, we say these conditions are individually necessary and jointly sufficient.

Necessary and sufficient conditions and Claims about Causes and Effects

Identifying necessary and sufficient conditions as causes and effects is somewhat easier regarding natural phenomena (ocygen and human life, mosquito breeding, and growing roses), but is more difficult with more complext phenomena such as human or group behavior.

You see a book that promises to give you the six keys to happiness. The writer of the book wants you to believe that the six keys are sufficient conditions for (i.e., they guarantee) happiness. In truth, even if all the key are very wise, at best they may increase the likelihood of happiness. In this case the six keys are neither necessary nor sufficient conditions fo happiness, though practicing them may increase the likelihood of happiness.

Necessary and sufficient conditions and Claims about Causes and Effects

Consider a relevant example: Is earning a college degree a necessary or sufficient condition for professional success.

It is neither; it is not the case that without a college degree, you cannot be successful; NOR is it the case that a college degree gurantees success.

It IS the case, however, that earning a college degree increases the likelihood of success; this claim can be confirmed by looking at the kinds of careers and salaries available to college graduates as compared to non-college graduates.

Determine what each of the following causal claims indicate about necessary and sufficient conditions.

Water boils if and only it is heated to 180 degrees Fahrenheit; water freezes if only if it is cooled to 32 degrees Fahrenheit.

Removal of stagnant water will eliminate the mosquito infestation.

If the U.N refuses to act, the President will deploy U.S. troops to the area

If you want your plants to thrive, be sure they have appropriate amounts of sunlight and water

Smoking during pregnancy stunts fetal growth.

Smoking can cause heart disease and strokes by clogging arteries.

Determine what each of the following causal claims indicate about necessary and sufficient conditions.

Water boils if and only it is heated to 180 degrees Fahrenheit; water freezes if only if it is cooled to 32 degrees Fahrenheit. Heating and cooling water to the specified temperatures are both necessary and sufficient conditions for the effects indicated.

Removal of stagnant water will eliminate the mosquito infestation. Stagnant water is a necessary condition for mosquito infestation, so removing it will eliminate the infestation.

If the U.N refuses to act, the President will deploy U.S. troops to the area. The U.N.’s refusal to act is a sufficient condition for the President to deploy troops.

If you want your plants to thrive, be sure they have appropriate amounts of sunlight and water. Appropriate smounts of sunlight ans water are individually necessary and jointly sufficient to cause your plants to thrives.

Smoking during pregnancy stunts fetal growth. Smoking while pregnant is a sufficient condition for stunting fetal growth.

Smoking can cause heart disease and strokes by clogging arteries. Smoking is neither necessary nor sufficient to causing heart disease and strokes, but it increases the likelihood of the effect.

What’s Next?

Read Chapter 10.3 in your electronic textbook.

Earn at least 6 of 10 points on the Quiz.

Submit a writing assignment.

Contribute to the Discussion.

Good luck!