1. Chapter 11 Inductive Reasoning Arguments from Analogy
Part 1
Arguments from Analogy
Generalizing from Samples
Statistical Syllogisms
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2. Arguments from Analogy
Something has an attribute;
:. A similar thing has that attribute.
Examples:
Bill likes hunting; therefore his brother Sam does too.
Darby is an excellent dog-sitter. Therefore she would be an excellent baby-sitter.
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Bill likes hunting; therefore his brother Sam does too.
Premise-analogue: Bill
Conclusion-analogue: Sam
Attribute of interest: liking hunting
Darby is an excellent dog-sitter. Therefore she would be an excellent baby-sitter.
Premise-analogue: Darby’s performance as a dog sitter
Conclusion-analogue: Darby’s performance as a baby-sitter
Attribute of interest: being excellent at the task
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The more numerous and diversified the similarities are between the premise-analogue and the conclusion-analogue the stronger the argument.
I. Bill likes hunting; therefore his brother Sam does too.
2. Bill and his brother Sam both like fishing, playing poker, and going to football games.
Bill also likes hunting.
:. Therefore Sam does too.
2 is stronger!
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The more numerous and diversified the differences are between the premise-analogue and the conclusion-analogue the weaker the argument.
Bill likes hunting; therefore his brother Sam does too.
If Bill and Sam are different ages, live in different parts of the country, have different professions, have different marital status, that weakens the argument.
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Given more than one premise-analogue, the more numerous and diversified the premise analogues, the stronger the argument.
1. Bill likes hunting; therefore his brother Sam does too.
2. Bill, his father, his uncle, and his sister like hunting; therefore his brother Sam does too.
2 is stronger!
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Given more than one premise-analogue, the fewer the contrary premise-analogues the stronger the argument, and the more the contrary premise-analogues, the weaker the argument.
1. Bill, his father, his uncle, and his sister like hunting; therefore his brother Sam does too.
2. Bill, his father, his uncle, and his sister like hunting, but despite the fact that there are others in the family who don’t like hunting, it is likely Sam likes hunting too.
2 is weaker!
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8. © 2015 McGraw-Hill Higher Education. All rights reserved.
ARGUMENTS FROM ANALOGY are especially important in three areas:
In medical research
Research involving animals is applied analogically to humans
In historical reasoning
Our understanding of current events is enhanced by comparing them to past events
In the law
Jurists search for legal precedents (analogous cases) to guide current decisions. Stare decisis.
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9. Generalizing from a Sample
An argument that all, or most, or some percentage of a sample have an attribute; therefore all, or most, or that percentage of a population have that attribute.
Examples:
So far I’ve like all of Professor Stooler’s lectures; therefore I will like all of his lectures.
Most Pit Bulls I know are sweet dogs; therefore most Pit Bulls are sweet dogs.
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So far I’ve like all of Professor Stooler’s lectures; therefore I will like all of his lectures.
Sample: Stooler lectures I’ve heard so far
Population: All Stooler lectures I will hear
Attribute of interest: Being liked by me
Most Pit Bulls I know are sweet dogs; therefore most Pit Bulls are sweet dogs.
Sample: Pit Bulls I know
Population: Pit Bulls
Attribute of interest: being sweet dogs
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11. The more atypical the sample, the weaker the generalization
Most Pit Bulls I know are sweet dogs; therefore most Pit Bulls are sweet dogs.
If the Pit Bulls I know were all trained to be show dogs, the argument is weaker.
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12. The less diversified the sample, the weaker the generalization
I know three Pit Bulls from the same litter. They are sweet dogs. Therefore most Pit Bulls are sweet dogs.
I know three Pit Bulls from different litters. They are sweet dogs. Therefore most Pit Bulls are sweet dogs.
First argument is weaker!
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13. “Hasty generalization!”
Generalizations based on samples too small to accurately mirror the population are inherently weak.
I know three Pit Bulls from the same litter. They are sweet dogs. Therefore most Pit Bulls are sweet dogs.
This sample is too small to accurately mirror the entire Pit Bull Population
“Hasty generalization!”
Note: If a population is known to be homogeneous, then it is safe to generalize from a small sample.
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14. “Generalizing from Exceptional Cases”! (Biased Generalization)
Generalizations based on atypical samples are inherently weak even if they aren’t small.
I know twenty Pit Bulls, all from the same parents. They are sweet dogs. Therefore most Pit Bulls are sweet dogs.
This sample is atypical!
“Generalizing from Exceptional Cases”!
(Biased Generalization)
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15. Scientific Generalizations
Samples, populations, and attributes are clearly specified with a SAMPLING FRAME
Steps are taken to minimize bias (skew) in samples
Calculations are done using statistical mathematics
A sampling frame is a definition of a sample or population or attribute that makes clear what qualifies as membership in the group in question.
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16. Basic Concepts of Scientific Generalizing (1)
True proportion—the proportion of a population that actually has an attribute of interest
Sample proportion—the proportion of a sample that has an attribute of interest
Random Selection Process—a method for insuring that every member of a population has an equal chance of being in the sample
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17. Basic Concepts of Scientific Generalizing (2)
Error margin—the range of random variation of a sample proportion across multiple random samples
Confidence level—the probability that the random variation of a sample proportion from random sample to random sample will fall within the error margin
Statistically significant—from a statistical point of view, probably not due to chance
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Scientific Generalizations
In a large population of widgets there is a TRUE PROPORTION that are broken
A random sample of that population will yield a SAMPLE PROPORTION that approximates the true proportion
Sample proportions vary randomly from sample to sample (The “error margin”)
The larger the random sample (n), the more likely it is that the sample proportion will be close to the true proportion
This and the next two slides work together.
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19. © 2015 McGraw-Hill Higher Education. All rights reserved.
Scientific Generalizations
In a large population of widgets there is a TRUE PROPORTION that are broken
A random sample of that population will yield a SAMPLE PROPORTION that approximates the true proportion
Sample proportions vary randomly from sample to sample (The “error margin”)
The larger the random sample (n), the more likely it is that the sample proportion will be close to the true proportion
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20. © 2015 McGraw-Hill Higher Education. All rights reserved.
Scientific Generalizations
In a large population of widgets there is a TRUE PROPORTION that are broken
A random sample of that population will yield a SAMPLE PROPORTION that approximates the true proportion
Sample proportions vary randomly from sample to sample (The “error margin”)
The larger the random sample (n), the more likely it is that the sample proportion will be close to the true proportion
Higher confidence levels require wider error margins!!!
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PUBLIC OPINION POLLS involve scientific sampling
How much we can take from them depends on what two things?
How well does the sample represent the population?
2. Are questions neutral?
Mathematical calculations done by trained pollsters are uncontroversial
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Everyday generalizations are usually based on small and biased samples.
Reject error margin and confidence level indicators that exceed the strength of the supporting evidence.
“Exactly,” “around,” “about” “approximately,” etc. are “error margin indicators”
“Possibly,” “maybe,” “probably,” “almost certainly, etc. are “confidence level indicators”
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Informal confidence-level indicators:
Possibly
Quite possibly
Probably
Very probably
I’d bet the farm
Informal error-margin indicators
Exactly
Around
Approximately
About
Give or take
In the ballpark of
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24. © 2015 McGraw-Hill Higher Education. All rights reserved.
In real-life generalizations, your “confidence level” depends on your “error margin”
A safe bet matches a high confidence level with a wide error margin!
Don’t “bet the farm” a generalization holds, unless you give yourself a wide error margin.
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25. The Statistical Syllogism
An argument that applies a general statement to a specific case.
Examples:
Most teachers are Democrats.
York is a teacher.
:. York is a Democrat.
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Most teachers are Democrats; York is a teacher.
:. York is a Democrat
Premise-population: teachers
Conclusion-individual: York
Attribute of interest: being a Democrat
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The higher the proportion of the premise population that has the attribute of interest, the stronger the argument.
80% of teachers are Democrats;
York is a teacher.
:. York is a Democrat
90% of teachers are Democrats;
York is a teacher.
:. York is a Democrat
Stronger argument!
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