Inductive Reasoning Concepts and Principles ofConstruction.

Inductive ReasoningInductive Reasoning

Concepts and PrinciplesConcepts and Principles

ofof

ConstructionConstruction

Basic CategoriesBasic Categories


Target - the category we are Target - the category we are interested in understanding betterinterested in understanding better



Sample - the individual or group we Sample - the individual or group we already know about or understandalready know about or understand




What is known about the sample may be the result of polling or experimentation.




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.




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.




Feature in question - the property we Feature in question - the property we know about in the sample and know about in the sample and wonder about in the targetwonder about in the target

Using the basic categories...Using the basic categories...Will the governor cut funding for the CSU?Will the governor cut funding for the CSU?

Target - the governor’s agenda Target - the governor’s agenda (needs to be an identifiable thing)(needs to be an identifiable thing)


Target - the new governor’s agenda Target - the new governor’s agenda (needs to be an identifiable thing)(needs to be an identifiable thing)

Sample - whatever we already know Sample - whatever we already know about his ideas about educationabout his ideas about education


Target - the new governor’s agenda Target - the new governor’s agenda (needs to be an identifiable thing)(needs to be an identifiable thing)

Sample - whatever we already know Sample - whatever we already know about his ideas about educationabout his ideas about education

Feature in question - support for Feature in question - support for education (notice that the sample’s education (notice that the sample’s features may not correspond features may not correspond perfectly to those of the target)perfectly to those of the target)

Two Main Types of Two Main Types of Inductive ReasoningInductive Reasoning

Inductive generalization - intends a Inductive generalization - intends a conclusion about a class of things or conclusion about a class of things or events larger than the subset that events larger than the subset that serves as the basis for the inductionserves 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.



Analogical argument - intends a Analogical argument - intends a conclusion about a specific thing, conclusion about a specific thing, event, or class relevantly similar to event, or class relevantly similar to the samplethe sample

Concerns About SamplesConcerns About Samples

Is the sample representative? Is the sample representative?



The more like one another the sample and The more like one another the sample and target are, the stronger the argument.target are, the stronger the argument.




Paying attention to this concern helps avoid Paying attention to this concern helps avoid the biased sample fallacy, which (like all of the the biased sample fallacy, which (like all of the inductive fallacies) results in an unusably weak inductive fallacies) results in an unusably weak induction.induction.




Paying attention to this concern helps avoid Paying attention to this concern helps avoid the biased sample fallacy, which (like all of the the biased sample fallacy, which (like all of the inductive fallacies) results in an unusably weak inductive fallacies) results in an unusably weak induction. induction. Self-selected samples are known Self-selected samples are known problems in this regard.problems in this regard.


Is the sample large enough? Is the sample large enough?



In general, the larger the sample, the In general, the larger the sample, the better.better.



In general, the larger the sample, the In general, the larger the sample, the better.better.

Paying attention to this concern helps avoid Paying attention to this concern helps avoid the hasty conclusion and anecdotal evidence the hasty conclusion and anecdotal evidence fallacies. These are both very common.fallacies. These are both very common.

Focus Point: Fallacy of Focus Point: Fallacy of Anecdotal EvidenceAnecdotal Evidence


The sample is small, typically a The sample is small, typically a single story single story



The story may be striking The story may be striking



The story may be striking The story may be striking The story is treated as though it were The story is treated as though it were

representative of the targetrepresentative of the target



The story may be striking The story may be striking The story is treated as though it were The story is treated as though it were

representative of the targetrepresentative of the target Best use of the anecdote: to focus Best use of the anecdote: to focus

attention (NOT as key premise)attention (NOT as key premise)

Confidence and CautionConfidence and Caution


As sample size grows: either As sample size grows: either confidenceconfidence increases or increases or margin of margin of errorerror decreases decreases



Inductions Inductions nevernever attain 100% attain 100% confidence or 0% margin of error confidence or 0% margin of error



Inductions Inductions nevernever attain 100% attain 100% confidence or 0% margin of error confidence or 0% margin of error

In many cases, evaluation of these In many cases, evaluation of these factors can be factors can be reasonablereasonable without without being mathematically precisebeing mathematically precise

Mathematical Note:Mathematical Note:Law of Large NumbersLaw 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.

Inductive Reasoning Concepts and Principles ofConstruction.

Documents

sample slide

better n sample

samples n

target slide

basic categories n target

identifiable thing n

better slide

education n feature