Chapter 8

Enumerative Induction Examples

'I've owned 2 dell computers and both sucked. I'm starting to think all dell computers are crap.' 'Two of my friends took philosophy classes, and said they were fun. I'm beginning to think taking a philosophy class would be a good idea.'

The statistical strength of the generalization

A premise that tells us '99% of M are P' is not as powerful as a premise that says '70% of M are P' or 'most M are P'. The stronger the generalization, the stronger the argument.

Evaluating Statistical Syllogisms

Are the premises acceptable? In a particular do we have good reason to believe the initial generalization? Is it, for example, the result of a good argument from enumerative induction? If the grounding of the generalization is weak, then the argument is weak.

Deductive Argument

Intended to provide logically conclusive proof for its conclusion.

Inductive Argument

Intended to supply only probable support for its conclusion. It's either 'strong' or 'weak'. The conclusion of a strong argument is likely true. If its premises are true, the argument is cogent. It lets us move beyond the evidence.

Statistical Syllogism Pattern

Premise 1: A proportion X of the group M have characteristic P. Premise 2: Individual S is a member of group M. Conclusion: Individual S has characteristic P.

Enumerative Induction treated Deductively

Some M are P. All S are M. So, all S are P.

Enumerative Induction

Some arguments reason from characteristics of the group to those of a member of that group. Most Philosophers I've met are nerds. MacDonald is a Philosopher. So, MacDonald is probably a nerd too! Whenever we begin with observations about some member of a group and end with a generalization about all of them, we have this type of induction.

Target population / target group.

The group as a whole, it's what we're aiming to reach a conclusion about.

Rule of Thumb

The more homogenous a target group is, the smaller the sample can be; the less homogenous, the larger the sample should be.'

Sample

The observed members of the target group.

Relevant property / property in question.

The property or characteristic we're interested in.

Sample Size

The reliability of a generalization depends on this. Basing a conclusion on inadequate ss: hasty generalization. The larger the ss, the more likely it is to reliably reflect the nature of the larger group.

Representativeness

This is required for an enumerative induction to be useful. It must represent the target group , and if it doesn't then it's a biased sample. The sample should : have all the same relevant characteristics, and have those characteristics in the same proportion that the target group does.

Inductive Reasoning

We start with premises about individual members of a group to reason to conclusions about the group as a whole. The movement is from particular to general.

Enumerative Induction form

X per cent of the observed members of group A have property P. Therefore, X per cent of all members of group A probably have property P. - Not all examples actually mention percentages, though. Usually 'most' or 'all' is implied.

Analysis

You need to be able to identify the individual being examined, the group to which that individual is said to belong, the characteristic being attributed, and the proportion of the group said to have that characteristic.

Statistical Syllogism

sometimes we have good, but incomplete knowledge of some group of people or things and based on that, we reach a conclusion about some member of that group. Example) 'Canada's Parliament is overwhelmingly white and male. So, your MP is probably a white male!' They use inductive reasoning to move from a statistical generalization to a conclusion about some member of that group. It won't necessarily cite an actual, numerical statistic. The first premise will always contain a generalization about the group.