Chapter 5-Inductive Reasoning

inductive argument

intended to supply only probable support for its

conclusion.

– It is either “strong” or “weak.”

-in addition, its premises are true, or very probably true, the argument is said to be cogent.

• allows us to reason “beyond the evidence”—from bits of what is already known to conclusions about what those bits suggest is probably true

Inducitve Arguments forms

• enumerative induction

• statistical syllogisms

• analogical induction

Enumerative Induction

premises about individual members of a group to conclusions about the group as a whole

e.x

Most peace activists I know are kind-hearted. So probably all peace activists are kind-hearted.

Enumerative Induction components

• Target group (target population): The whole collection of

individuals under study

• Sample (sample member): The observed members of the

target group

• Relevant property (property in question): A property, or

characteristic, that is of interest in the target group

Enumerative Inductive arguments can fail in 2 ways

1. The sample can be too small.

2. The sample can be not representative of the target group. 

• it must resemble the target group in all the ways that matter. If it doesn’t, it’s a biased sample.

• To be truly representative, the sample must be like the target group by:

  – having all the same relevant characteristics; and

  – having them in the same proportions that the target group does.

Hasty generalization: (fallacy related to inductive arguments)

The fallacy of drawing a conclusion about a target group on the basis of a sample that is too small.

The more homogeneous a target group is in its traits relevant

to the property in question, the smaller the sample can be; the

less homogeneous, the larger the sample should be

selective attention (results in biased sampling)

the tendency to observe and remember things that reinforce our beliefs

and to gloss over and dismiss things that undercut those beliefs.

Opinion Polls in Enumerative Inductive Arguments

Opinion polls are used to arrive at generalizations about something.

As inductive arguments, opinion polls should:

– be strong; and

– have true premises

So, they should:

– use a sample that is large enough to represent the target population

accurately in all the relevant features; and

– generate accurate data.

Random sampling

can be used to ensure the sample is representative.

– In a simple random selection, every member of the target group has an equal chance of being selected for the sample.

Samples need not be enormous to be accurate reflections of the larger target population achieved through random sampling

(non-random selection, based on preconceived notions about what characteristics are representative, will likely result in a biased sample.)

Self-selecting sample

the process by which you allow survey subjects to choose themselves.

– The sample is likely to be biased in favour of subjects who, for example,

just happen to be especially opinionated or passionate on the subject in

question.

– The media sometimes acknowledge the use of self-selecting samples by

labelling the survey as “unscientific.”

Margin of error

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 the target group within the margin of error

e.x

A 95% confidence level means that there is a 95% chance that

the results will accurately reflect the frequency in the total

population.

Statistical Syllogisms

are inductive arguments that apply a statistical generalization

—a claim about what is true of most members of a group or category

—to a specific member of a group or category.

To analyze a statistical syllogism, we need to be able to identify:

– The individual being examined

– The group to which that individual is said to belong

– The characteristic being attributed

– The proportion of the group said to have that characteristic.

The first premise is a generalization—a statement about the members of a group or class. (The first premise of a statistical syllogism will be arrived by an argument using enumerative induction.)

• If the grounding of the generalization is weak, then the argument is weak.

—even good ones, with acceptable premises—cannot

guarantee their conclusions.

e.x Example:

• Premise 1: In general, the spiders that live in Canada are harmless.

• Premise 2 (unstated): That spider there is in Canada.

• Conclusion: That spider is harmless

Analogical Induction

because two or more things are similar in several respects, they must be similar in some further respect.

• Arguments by analogy can establish conclusions only with a degree of probability.

  – The greater the degree of similarity between the two things being compared, the more probable the conclusion is.

Pattern:

– Thing A has properties P1, P2, and P3 plus the property P4.

– Thing B has properties P1, P2, and P3.

– Therefore, thing B probably has property P4.

Criteria for judging the strength of arguments by analogy:

1. Relevant similarities

2. Relevant dissimilarities

3. The number of instances compared

4. Diversity among cases