## Thursday, May 28, 2015

### Statistical Syllogism

A statistical syllogism is an inductive argument in which a statistical generalization is applied to a particular case. For example:

Most surgeons carry malpractice insurance.
Dr. Jones is a surgeon.
Therefore, Dr. Jones likely carries malpractice insurance.

This sort of argument can be written in the general form:

P1. Most A's are B
P2. x is an A
C. Therefore, probably x is a B

When the proportions are known the form can be written as:

P1. Z percent of A's are B
P2. x is an A
C. Therefore, it is probable to the .Z degree that x is B

In the general forms presented above, A is called the reference class,  B the attribute class and x is the individual object.

We often use informal versions of the statistical syllogism in everyday reasoning. For instance, if you read in the New York times that the President is visiting China and you believe it to be true, on what basis do you justify this belief? Most people understand that you can't believe everything you read in a newspaper but recognize that certain kinds of reports published in certain newspapers tend to be true. This is one of those kind of reports so it is likely true.

Strength/Weakness of a Statistical Syllogism
There are two primary standards which determine the strength of a statistical syllogism. First is the strength condition which is, the closer to 100% the reference class is to the attribute class the greater the confidence in the truth of the conclusion. Conversely, the closer to 0% the weaker the argument.

Second is the available evidence condition (also called the rule of total evidence) which requires using all available evidence in constructing or assessing such arguments. With statistical syllogisms this essentially means questioning if there is additional relevant information available concerning the individual object (x) that has not been included in the premises? Another way of saying this is that the individual object must be included in the reference class most specifically relevant to the conclusion. Failure to use all available evidence is commonly referred to as the Fallacy of Incomeplete Evidence.

For example:

P1. Sixty percent of students at the University believe in God.
P2. Fred is a student at the University.
C.  It is sixty percent probable Fred believes in God.

But if we also know that Fred is a history major and that only forty percent of history majors believe in God then it would not be appropriate to use the reference class in the example since it excludes this relevant information.

Due care must be taken when judging individuals using statistical syllogisms as their misuse can contribute to stereotyping and prejudice.

A Practical Study of Argument

Critical Thinking: An Introduction to Basic Skills

Critical Reasoning and Philosophy: A Concise Guide to Reading, Evaluating and Writing Philosophical Works