Fallacies of inductive arguments

Question 1

three categories

Answer 1

1. Problems with the sample that is used.
2. Problems with reasoning about probability.
3. Problems with reasoning about causality.

Question 2

1. Hasty Generalisation

Answer 2

The most basic fallacy of inductive reasoning falls into the first category.
•This fallacy is the fallacy of hasty generalisation.
•Often when people say “don’t generalise”, what they mean is do not commit a hasty generalisation.
•A hasty generalisation is an inductive argument (generalisation) that is based on an inadequate sample
•Other things being equal, as the size of the sample increases the strength of the argument also increases.
•Other things being equal, an inductive argument is stronger the more representative its sample is.

Question 3

inadequate sample

Answer 3

a. being too small, or

b. failing to be representative.

Question 4

2. Fallacies of Probability

Answer 4

•Even if an inductive argument is based on a good sample, the argument can fail to be strong if it involves flawed reasoning about probability.

1. Gambler’s fallacy
2. Ecological fallacy

Question 5

2. Fallacy of probability:

1. Gambler’s fallacy

Answer 5

The belief that statistical imbalances in random events will “correct” in the future.
–If you have rolled a die five times and each time you have gotten a six, what is the probability that on the sixth roll you will get another six?
–The probability is just one in six (as it was before you rolled the die the first time).
–The previous five rolls of the die have no causal effect whatsoever on what the die will do the sixth time that you roll it.
•If you encounter five really odd cases in a row, that does nothing at all to decrease the probability that the sixth case will also be very odd.

Question 6

2. Fallacies of Probability:

2. Ecological fallacy

Answer 6

The ecological fallacy occurs when correlations that hold for a population are assumed to hold for individuals within that population.
–In a famous example, Durkheim showed that in nineteenth century Europe there was a positive correlation between the percentage of Protestants in a population and the incidence of suicide in that population.
–From this he concluded that Protestants are more likely than Catholics to commit suicide.
–However, the data could also be explained by Catholics living in Protestant areas being more likely to commit suicide than Catholics living in Catholic areas.

Question 7

3. Causal Fallacies:

1. Correlation implies causation

Answer 7

Correlation between two factors does not entail causation between those factors.
–It is not the case that if two factors are correlated, then one causes the other.
•This does not mean that correlations are not important in discovering causal relationships.
–If one factor causes another, then the factors are generally correlated.
•So, correlation is generally a necessary but not sufficient condition for causation.

Question 8

3. Causal Fallacies:

2. The third cause fallacy

Answer 8

Occurs when a correlation is taken to show that one factor causes another factor without properly considering the possibility that the two factors are correlated because they are both caused by a third factor.
•In a well-known example, epidemiological studies showed a correlation between hormone replacement therapy and lower levels of coronary heart disease. –Some researchers and medical practitioners concluded that hormone replacement therapy reduces the risk of coronary heart disease.
–However, randomised controlled trials indicated that hormone replacement therapy actually slightly increases the risk of coronary heart disease.
–The correlation between the therapy and a lower risk of coronary heart disease was due to the fact that both of these are causally related to socio-economic conditions.

Question 9

3. Causal Fallacies

3. Regression Fallacy

Answer 9

•For many phenomena, a deviation from the mean is generally followed by a regression to the mean.
•It is fallacious to conclude that an effect of a deviation from the mean causes a regression to the mean without adequately considering whether the regression would have occurred naturally.
–It is fallacious to assume that treatment caused a patient’s return to health without adequately considering whether the return to health would have occurred naturally.

Question 10

Conclusion

Answer 10

• An inductive argument is strong just if the observed frequencies in its sample significantly increase the probability that its conclusion is true.
• While it is not always possible to precisely determine the strength of an inductive argument, one can be better or worse at judging the strength of inductive arguments.
• Whether or not an inductive argument is strong depends partly on the context in which the argument is evaluated.
• Confirmation bias and the availability heuristic are cognitive biases that often seriously skew probabilistic reasoning.
• Make sure that you can identify all of the fallacies of probabilistic reasoning that have been introduced in this lecture.