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11EnumerativeInductionSpring2026-1.pptxModule 11 Introduction: Evaluating Arguments -Enumerative Induction – Spring 2026
Critical Thinking Online
Fayetteville State University
Dr. Jon Young, Instructor
Module 10: In this lesson, you will
Recall the distinction between deductive and inductive arguments.
State the enumerative induction argument pattern.
Define and identify in specific examples key terms related to enumerative induction: target group, sample, property in question, random sample, hasty generalization, biased sample, margin of error, and confidence level.
Explain that polls and surveys use the pattern of enumerative induction.
Evaluate specific enumerative inductive arguments, including polls and surveys.
Module 11: In this lesson, you will
Complete the Required Readings
PowerPoint Introduction
Section 10.1 in your electronic textbook .
Earn at least 6 of 10 points on the quiz.
Submit a writing assignment.
Contribute to the Discussion.
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Remember:
In the past two modules, we studied deductive argument patterns; With this lesson we turn to inductive argument patterns. The premises of an Inductive argument are intended to establish the truth of the conclusion with some degree of probability. A strong inductive argument is one in which if the premises are true, then the conclusion is probably true.
(Remember to determine whether an inductive argument is strong, we assume the premises are true. IF the premises are true, the conclusion is probably true. If we establish the actual truth of the premises of a strong argument, then the argument is cogent. Strong argument + true premises = Cogent argument.
When you make an inductive argument, you are not claiming to provide conclusions that are certain, but conclusions that are true with some degree or probability, ranging from more likely true than not to nearly certain.
If you encounter an inductive argument in everyday life, bear in mind that to reject it because the conclusion is not certain misses the point. The question for an inductive argument is how probable is the conclusion?
Consider
If your physician prescribes a specific treatment for a sickness, if you expect her to guarantee that the treatment will work and have no adverse side effects, then she will not be able to do so. She can say that in clinical trials the treatment was effective 95 times out of a hundred and she can tell you the side effects that occurred in the clinical trials. In prescribing the treatment, the physician is claiming – based on the evidence – the potential benefits of the treatment outweigh the potential harm. But she cannot be certain of it, and cannot guarantee the results.
Medical diagnoses and treatment for the most part reside in the domain of inductive reasoning.
Key Terms – This Week - Memorize
Pattern of Enumerative Induction: X percent of observed members of group A have property P. Therefore, X percent of all members of group A probably have property P. (Note: I prefer “approximately X percent of all members of group A have property P. So, if you see such language in this PowerPoint, the two phrases are equivalent.)
Note: the conclusion of enumerative induction is a generalization, that is you move from evidence about some members of a group to all members of the group.
Sample – the observed members of a target group.
Target group – the group of individuals (people or things) about which an inductive generalization is made.
Relevant property (or property in question) – the property (or attribute) under study in the target population.
Key Terms – This Week - Memorize
Simple random sampling – The selecting of a sample to ensure that each member of the target group has an equal chance of being chosen.
Hasty generalization - A conclusion about a target group based on a sample that is too small to be representative.
Biased generalization – A conclusion target group that is based on a sample that, even though large, is not representative of the target group.
Margin of error – in a survey or poll the variation between the values derived from a sample and the true values of the whole target group.
Confidence level – The probability that the sample will accurately represent a target group within the margin of error.
Enumerative Induction - A Visualization
1. Suppose I want to know what the U.S. population thinks about the quality of health care in the U.S. Each icon represents 1,000,000 people.
2. Instead of trying to ask each person, I select a sample, a subgroup, and ask their opinion. If I find that X percent of the sample have this opinion, then I can conclude that X percent of all Americans probably have this opinion. My conclusion is probably true if the sample is large enough and representative.
Enumerative Induction
Target group: People or things
If the sample reflects the variety of the target population in significant ways then we can be reasonably confident about the conclusion.
Most of the informal generalizations we make are based on samples that are too small (stereotypes) or are not representative.
Enumerative Induction – A Visualization
Population: People or things
Hasty generalization: Sample too small to draw conclusions about the whole population.
Biased sample includes only one portion of the population.
The strength of the arguments is dependent on whether the sample provides a reliable basis for the conclusion.
Enumerative Induction Identify Sample, Target Group & Conclusion
An inspector at a bag manufacturer randomly picks ten bags outs of 1000 and finds that all ten hold up to 20 pounds without bursting; so he concludes that all 1000 bags will hold up to 20 pounds. It would be very difficult and time consuming to check every bag. But it is important to make sure the bags are selected randomly.
Since moving to Santa Fe, NM, I have found that all the native New Mexicans I have met love green and red chilis. I suppose nearly all native New Mexicans love green and red chilis.
According to 1,500 randomly selected Americans by the Pew Research Center, on the eve of President Trump’s Inauguration, 70% percent of American are deeply concerned about the price of food and other consumer goods, while 61% are very concerned about the cost of gasoline. Approximately the same percentage of all Americans are deeply concerned about the cost of these items.
Of a sample of 25,000 patients in a clinical trial, the vaccine was 95% effective in preventing illness with no long-lasting negative side effects. The vaccine is, therefore, safe and effective for all Americans.
Generalizations Identify Sample, Target Group & Conclusion
An inspector at a bag manufacturer randomly picks ten bags out of 1000 and finds that all ten hold up to 20 pounds without bursting; so he concludes that all 1000 bags will hold up to 20 pounds. It would be very difficult and time consuming to check every bag. But it is important to make sure the bags are selected randomly. Sample: Ten bags selected randomly; Target Group: 1000 bags; Conclusion: All the bags will hold up to 20 pounds. (100 percent of observed member of group have relevant property, hold up to 20 pounds, so 100% of the target group will have the property.)
Note: the paper bags are homogenous, all are alike. When the target group is homogeneous, the sample does not have to be as large as when the target group if comprised, say of college students, who are not a homogeneous group, but display great variety.
Since moving to Santa Fe, NM, I have found that all the native New Mexicans I have met love green and red chilis. I suppose nearly all native New Mexicans love green and red chilis. Sample: native New Mexicans I have met; Target group: New Mexicans; Relevant property: loves green and red chilis. Conclusion: Nearly all New Mexicans love red and green chilis. Note the pattern: X percent, nearly all, of the observed members of target group have property A. Therefore, nearly all of the target group will have this property.
Generalizations Identify Sample, Target Group & Conclusion
According to 1,500 randomly selected Americans by the Pew Research Center, on the eve of President Biden’s 2023 State of the Union address, 70% percent of American are deeply concerned about the price of food and other consumer goods, while 61% are very concerned about the cost of gasoline. Sample: 1,500 Americans surveyed; Target Group: All Americans. Conclusion: Approximately 70% of Americans are deeply concerned about price of food and other consumer goods; approximately 61% are very concerned about the price of gasoline.
Of a sample of 25,000 patients in a clinical trial, the vaccine was 95% effective in preventing illness with no long-lasting negative side effects. The vaccine is, therefore, safe and effective for all Americans. Sample: 25,000 patients in the clinical trial; Target Group: All Americans. Conclusion: Vaccine will be effective 95% of the time.
Note that both arguments rely on the pattern: X percent of the observed members of a target group have property P. Therefore, X percent of the target group will probably have property A.
Evaluating Enumerative Inductive Arguments
Remember: The two most important questions to ask when evaluating an enumerative inductive argument are: Is the sample large enough to make a reasonable inference about the target population? Is the sample sufficiently representative of the target population to make a reasonable inference about the target population?
A generalization that fails to meet the first of these requirements (sample is large enough) is a hasty generalization.
A generalization that fails to meet the second of these requirements (sample is sufficiently representative of the target population) is a biased generalization.
Consider the following:
Nearly every person I have met from North Carolina is a fan of college basketball. It’s very likely that most people from North Carolina are fans of college basketball.
I have owned four Hondas and every one has given me good service. I am pretty sure that all Hondas are good cars.
All the FSU students I’ve talked to do not like the transition to online instruction. I bet most students in the country feel the same way.
Relph and Dunward, who are on the football team, have GPAs above 3.2. I suppose all members of the football team have high GPAs.
Highlighted words indicate that conclusion is intended to be probably true, NOT certainly true.
Premise(s) in black font; conclusion in red font:
Nearly every person I have met from North Carolina is a fan of college basketball. It is very likely that most people from North Carolina are fans of college basketball.
I have owned four Hondas and every one has given me good service. I am pretty sure that all Hondas are good cars.
All the FSU students I’ve talked to do not like the transition to online instruction. I bet most students in the country feel the same way.
Relph and Dunward, who are on the football team, have GPAs above 3.2. I suppose all members of the football team have high GPAs.
Sample highlighted in yellow; Target group highlighted in blue
Nearly every person I have met from North Carolina is a fan of college basketball. It is very likely that most people from North Carolina are fans of college basketball.
I have owned four Hondas and every one has given me good service. I am pretty sure that all Hondas are good cars.
All the FSU students I’ve talked to do not like the transition to online instruction. I bet most students in the country feel the same way.
Relph and Dunward, who are on the football team, have GPAs above 3.2. I suppose all members of the football team have high GPAs.
In all of these examples, the sample is either too small or are not representative. This is a typical problem with such informal generalizations.
Case Study
Attitudes about Artificial Intelligence (AI)
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In Spring 2025, the Pew Research Center conducted a survey of residents of countries throughout the world to determine their feelings about the continued use of Artificial Intelligence in daily life.
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The Pew Research Center has a strong reputation for responsible and fair survey methods so it is reasonable to assume that the samples are representative of the target populations within a margin of error of plus or minus three percentage points.
Which of the following could you reasonably infer from these data? (See next slide for options.)
Regarding their feelings about the increased use of Artificial Intelligence (AI) in our daily lives…
Approximately one in ten Americans are more excited than concerned
Americans are more concerned than most people of most other nations surveyed
Approximately half of Americans more concerned than excited about AI
Swedes among the world’s most excited
Germans and Japanese among the world’s most ambivalent.
Fewer Canadians are excited about AI than people of any other country.
Compared to the median rates of residents of all countries surveyed, more Americans are more concerned than excited and fewer Americans are more excited than concerned.
All of these can be reasonably inferred from the results.
Approximately one in ten Americans are more excited than concerned
Americans are more concerned than most people of most other nations surveyed
Approximately half of Americans more concerned than excited about AI
Swedes among the world’s most excited
Germans and Japanese among the world’s most ambivalent.
Fewer Canadians are excited about AI than people of any other country.
Compared to the median rates of residents of all countries surveyed, more Americans are more concerned than excited and fewer Americans are more excited than concerned.
What if you heard a television news reporter giving a story about these findings who says, “Most Americans distrust AI,” how would you respond?
If you already distrust AI, you will likely consider your distrust confirmed.
If you already enthusiastic about AI, you will likely just ignore the results.
Critical thinkers will review the data for themselves and note that the reporter has converted “more concerned than excited” as distrust; while this is not an unreasonable association, it is important to also note that the question was not about trust or distrust, but concern and excitement. You would also note that in view of the margin of error you, you cannot conclude that 50% is equivalent to “Most,” which could refer to a very slim or an overwhelming majority.
You should be concerned that in the rates of the median of all countries, the percentages add up to 91% 0 (34+42+16 = 91). This number cannot be explained by rounding errors. This is due to the fact that those who did not respond are not included, so approximately 9% of those surveyed did not respond.
Further analysis of the responses shows…
In most countries polled, adults ages 50 and older are more likely than those ages 18 to 34 to say they are mainly concerned about the growing use of AI in daily life. For example, 59% of older Greeks are more concerned than excited, compared with 18% of younger Greeks. (In many of these countries, older adults were less likely to provide a response.)
In the US, the gap between younger and older adults who are more concerned than excited about AI is 48% for adults younger than 50 and 55% for those 50 and older, a difference of seven points, which the smallest gap than in any other country. (the highest gaps are more than 25 points). (It is unfortunate that the age ranges are not more granular. I suspect that Americans younger than 25 would be much more excited.)
In about half of the countries polled, people with less education are more likely than those with more education to be mainly concerned about AI in daily life. (In several of these places, people with le
Opinion about increased AI use in daily life varies by internet usage. In many countries, concern about AI is more common among people who are online several times a day or less often than it is among those who are online almost constantly.ss education were less likely to provide a response.)
Are these additional findings consistent with what you would expect?
Which governments do respondents around the world trust to effectively regulate AI?
Fewer people around the world trust the US to regulate AI than trust the European Union (EU), but they trust the US more than they trust China.
Bear in mind that
These survey results provide an insightful snapshot of feeling about AI from around the world, attitudes and beliefs about technology can change very quickly, so one must be careful about assuming their continued reliability over time.
Module 11: What’s Next?
Read Section 10.1 n your electronic textbook .
Earn at least 6 of 10 points on the Quiz.
Submit a writing assignment.
Contribute to the Discussion.
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