Inductive Reasoning Concepts and Principles ofConstruction

Basic Categories

n Target - the category we are interested in understanding better

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

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

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

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

Basic Categories n Target - the category we are interested in understanding better n Sample - the individual or group we already know about or understand n 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? n Target - the governor’s agenda (needs to be an identifiable thing)

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

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

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

Concerns About Samples n Is the sample representative?

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

Concerns About Samples n 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 n 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 n Is the sample large enough?

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

Concerns About Samples n 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

n The sample is small, typically a single story

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

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

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

Confidence and Caution

n As sample size grows: either confidence increases or margin of error decreases

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

Confidence and Caution n As sample size grows: either confidence increases or margin of error decreases n Inductions never attain 100% confidence or 0% margin of error n 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 will bring alternatives closer to predictable ratios.