Inductive Reasoning

Inductive Reasoning Concepts and Principles of Construction

Basic Categories

Basic Categories • Target - the category we are interested in understanding better

Basic Categories • Target - the category we are interested in understanding better • Sample - the individual or group we already know about or understand

Basic Categories • Target - the category we are interested in understanding better • Sample - the individual or group we already know about or understand What is known about the sample may be the result of observation, polling or experimentation.

Basic Categories • Target - the category we are interested in understanding better • Sample - the individual or group we already know about or understand What is known about the sample may be the result of observation, polling or experimentation. Credibility of observation is always an issue. In polling, this makes the neutrality and focus of questions a concern.

Basic Categories • Target - the category we are interested in understanding better • Sample - the individual or group we already know about or understand What is known about the sample may be the result of observation, polling or experimentation. Credibility of observation is always an issue. In polling, this makes the neutrality and focus of questions a concern. In experimentation, the issue is experimental design.

Basic Categories • Target - the category we are interested in understanding better • Sample - the individual or group we already know about or understand • Feature in question - the property we know about in the sample and wonder about in the target

Using the basic categories...Will the governor cut funding for the CSU? • Target - the governor’s budget agenda (needs to be an identifiable thing)

Using the basic categories...Will the governor cut funding for the CSU? • Target - the governor’s budget agenda (needs to be an identifiable thing) • Sample - whatever we already know about his support for education

Using the basic categories...Will the governor cut funding for the CSU? • Target - the governor’s budget agenda (needs to be an identifiable thing) • Sample - whatever we already know about his support for education • Feature in question - funding for education (notice that the sample's features may not correspond perfectly to those of the target)

Two Main Types of Inductive Reasoning • Inductive generalization - intends a conclusion about a class of things or events larger than the subset that serves as the basis for the induction

Two Main Types of Inductive Reasoning • Inductive generalization - intends a conclusion about a class of things or events larger than the subset that serves as the basis for the induction Making this type of argument work often requires careful collection of facts, including sophisticated methods of insuring randomness of sample.

Two Main Types of Inductive Reasoning • Inductive generalization - intends a conclusion about a class of things or events larger than the subset that serves as the basis for the induction Example: We have observed that individuals who have successfully mounted surprise attacks on Americans over the past five years have belonged to the same religion. We conclude that people who belong to this religion despise Americans.

Two Main Types of Inductive Reasoning • Inductive generalization - intends a conclusion about a class of things or events larger than the subset that serves as the basis for the induction • Analogical argument - intends a conclusion about a specific thing, event, or class that is relevantly similar to the sample

Two Main Types of Inductive Reasoning • Analogical argument - intends a conclusion about a specific thing, event, or class that is relevantly similar to the sample Example: I've liked the last five issues of The Nation magazine. So I expect I will like the next issue.

Concerns About Samples • Is the sample representative?

Concerns About Samples • Is the sample representative? The more like one another the sample and target are, the stronger the argument.

Concerns About Samples • Is the sample representative? The more like one another the sample and target are, the stronger the argument. Paying attention to this concern helps avoid the biased sample fallacy, which (like all of the inductive fallacies) results in an unusably weak induction.

Concerns About Samples • Is the sample representative? The more like one another the sample and target are, the stronger the argument. Paying attention to this concern helps avoid the biased sample fallacy, which (like all of the inductive fallacies) results in an unusably weak induction. Self-selected samples are known problems in this regard.

Concerns About Samples • Is the sample large enough?

Concerns About Samples • Is the sample large enough? In general, the larger the sample, the better.

Concerns About Samples • Is the sample large enough? In general, the larger the sample, the better. Paying attention to this concern helps avoid the hasty conclusion and anecdotal evidence fallacies. These are both very common.

Focus Point: Fallacy of Anecdotal Evidence

Focus Point: Fallacy of Anecdotal Evidence • The sample is small, typically a single story

Focus Point: Fallacy of Anecdotal Evidence • The sample is small, typically a single story • The story may be striking

Focus Point: Fallacy of Anecdotal Evidence • The sample is small, typically a single story • The story may be striking • The story is treated as though it were representative of the target

Focus Point: Fallacy of Anecdotal Evidence • The sample is small, typically a single story • The story may be striking • The story is treated as though it were representative of the target • Best use of the anecdote: to focus attention (NOT as key premise)

Confidence and Caution

Confidence and Caution • As sample size grows: confidence increases or margin of error decreases

Confidence and Caution • As sample size grows: confidence increases or margin of error decreases • Inductions never attain 100% confidence or 0% margin of error

Confidence and Caution • As sample size grows: confidence increases or margin of error decreases • Inductions never attain 100% confidence or 0% margin of error • In many cases, evaluation of these factors can be reasonable without being mathematically precise

Mathematical Note:Law of Large Numbers While evaluation of factors relevant to the strength of an induction can be reasonable without being mathematically precise, in cases of chance-determined repetitions, more repetitions can be expected to bring alternatives closer to predictable ratios. It's not a sure thing, but it becomes ever more likely with more repetitions.

Analogical Reasoning:The Argument from Design Suppose you had never seen a clock and you find one lying on a beach. You’d assume it had been made by an intelligent being. Consider the Earth. It is much more complex than a clock. So it must have been created by an intelligent being. This, says the argument from design, is a good reason to think that a creator God exists.

Inductive Reasoning