Inductive Reasoning

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Inductive Reasoning

• Concepts and Principles
• of
• Construction

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Basic Categories
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Basic Categories

• Target - the category we are interested in
  understanding better

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Basic Categories

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

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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.
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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.
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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.
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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

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Using the basic categories...Will I have a good
future if I stay with Y?

• Target - my future with Y (needs to be an
  identifiable thing)

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Using the basic categories...Will I have a good
future if I stay with Y?

• Target - my future with Y (needs to be an
  identifiable thing)
• Sample - whatever we already know about Y
  (favorable and unfavorable)

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Using the basic categories...Will I have a good
future if I stay with Y?

• Target - my future with Y (needs to be an
  identifiable thing)
• Sample - whatever we already know about Y
  (favorable and unfavorable)
• Feature in question - the goodness of my future
  (notice that the sample's features may not
  correspond perfectly to those of the target)

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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

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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.
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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 Let's say that almost all individuals
who have worked out as managers over the past
five years belonged to the same religion. Is the
best conclusion that people who belong to this
religion are good managers?
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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

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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 been able to trust my previous
assistants with doing the banking. So I expect I
will be able to trust my next assistant the same
way.
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Concerns About Samples

• Is the sample representative?

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Concerns About Samples

• Is the sample representative?

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

• Is the sample large enough?

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Concerns About Samples

• Is the sample large enough?

In general, the larger the sample, the better.
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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.
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Focus Point Fallacy of Anecdotal Evidence
My roommate told me she went to a festival a few
weeks ago and got dosed with some drug that
totally knocked her out. She woke up on the way
to the hospital. Obviously, that festival is
something to avoid next year.
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Focus Point Fallacy of Anecdotal Evidence

• The sample is small, typically a single story

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Focus Point Fallacy of Anecdotal Evidence

• The sample is small, typically a single story
• The story may be striking

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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

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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)

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Confidence and Caution
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Confidence and Caution

• As sample size grows confidence increases or
  margin of error decreases

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Confidence and Caution

• As sample size grows confidence increases or
  margin of error decreases
• Inductions never attain 100 confidence or 0
  margin of error

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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

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Mathematical NoteLaw 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.
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Analogical ReasoningThe Argument from Design
Suppose you had never seen a clock and you find
one lying on a beach. Youd 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.
Is it?