Transcript Critical Thinking: Chapter 10

Critical Thinking: Chapter 10
Inductive Arguments
Arguments
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Before we can evaluate an argument,
we need to analyze it. We need to be
clear what the argument is trying to
prove, what evidence it uses, and
how it relates this evidence to its
conclusion.
Inductive Arguments
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When we extend what we have already
observed to things or situations we have
not observed, we are reasoning
inductively; we are producing inductive
arguments.
Inductive Arguments
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Example: The dog has barked at me for
the last three mornings, so I think he will
bark at me this morning.
Inductive Arguments
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Remember: An inductive argument is an
argument the premises of which are
intended to provide some degree of
probability for the truth of the
conclusion.
Therefore it is not sound or valid, but
weak or strong.
Deductive Arguments
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Remember: A deductive argument sets
out to guarantee the truth of its
conclusion based on the truth of its
premises.
Inductive Arguments
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Remember:an inductive argument
attempts to offer a probability that its
conclusion is true based on the truth of
its premises.
Inductive Arguments
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Inductive arguments give us a way of
extending our belief from things we
know about to things unknown.
Important Definitions
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Sample: The term sample refers to an
item or items we believe something
about.
Important Definitions
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Target: The term target refers to an item
or group of items to which we wish to
extend our belief.
Important Definitions
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Feature: The item we know about in the
sample and we extend to the target
object is the feature (or property) in
question.
Example
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Premise: X has properties a, b, c.
Premise: Y has properties a, b, c.
Premise: X has further property p.
Conclusion: Y also has property p.
X is our sample, Y is our target, an p is our
feature (or property) in question.
Analogical Arguments and
Generalizations
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Inductive arguments can be divided into
two categories: Analogical arguments
(or argument by analogy) and inductive
generalizations.
Arguments by Analogy
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Ordinarily, arguments by analogy have
one thing or event for a target.
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In an analogical argument, the sample
and target are distinct-one is not a part
of the other.
Analogies
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Analogies are arguments that deal with
comparing two similar things, one which
is familiar and one which is unfamiliar.
The key to analyzing analogies, is to
determine what these two things are and
how they are similar.
Analyzing Analogies
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So, analyzing an analogy means
translating it into standard form.
Example: “Three of my friends bought
their computers on the internet and they
were all unhappy with them. I was
thinking about ordering my new
computer online but now I think that if I
do, I’ll be unhappy with it.”
Analyzing Analogies
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Such translations are made easier since
you know from the standard form what
parts you need to look for: The sample
and the target, the similarities that are
known, and the property in question “X.”
Remember, the conclusion is always
about the target and always asserts that
the target has the property in question
“X.”
Analyzing Analogies
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p1: Friends’ computers were: (1) bought
online
p2: My computer will be: (1) bought
online
p3: Friends’ computers: (2) made them
unhappy
c: My computer will: (2) make me
unhappy
Evaluating Analogies
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There are several things to consider when
evaluating an analogy, but they all boil
down to this basic rule, “the more similar
the sample and the population, the higher
the probability that the conclusion is
true.” Each of the individual things to
consider in your evaluation is concerned
in some way with measuring this
similarity.
Evaluating Analogies
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1. The larger the sample, the stronger the
argument.
If our computer buyer had 10 friends
who were unhappy with the computers
they purchased on the internet, the
argument would be stronger.
Evaluating Analogies
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2. The greater the percentage of the sample
that has the property in question, the greater
the chance that the target has the additional
attribute.
Consider an analogy with a sample of 10 people
who bought computers online. Suppose 3 of
the 10 were unhappy. Now suppose that 8 of
the 10 were unhappy. Which would make our
analogy stronger?
Evaluating Analogies
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1. The greater the number of relevant
similarities between the sample and the target,
the stronger the conclusion.
If all of our friends’ computers were the same
brand as the one we are buying, the analogy
gets stronger. If they all ordered from the same
company that we are going to use, the analogy
gets stronger.
Evaluating Analogies
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2. The fewer know dissimilarities between the
sample and the target, the stronger the
argument.
If all the friends bought one type of computer
and you are considering a different type, the
analogy gets weaker. If theirs were refurbished
and yours will be new, the analogy gets weaker.
Evaluating Analogies
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1. When considering a feature of the sample
that we are unsure of in the target, the greater
the diversity in the sample, the better the
argument.
Consider processor speed. If we don’t know
the speed of the processor in the target, we
want a large diversity of processors in our
sample. This gives a greater likelihood that the
sample will be similar to our target population.
Evaluating Analogies
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2. The more guarded the conclusion is, the
stronger the argument is. (Consider the burden
of proof!)
Consider these two conclusions: (1) I will be
terribly unhappy with my computer, (2) I will
be less than perfectly pleased with my
computer.
Evaluating Analogies
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Conclusion 2 is more guarded, it is much
more likely that you’ll be less than
pleased than it is that you’ll be terribly
unhappy, thus 2 is easier to prove.
Evaluating Analogies
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Unlike determining the validity or
invalidity of a deductive argument,
evaluating an inductive argument like an
analogy is somewhat subjective. The
strength or weakness of an analogy will
depend, in part, to how relevant and
similar the two analogues seem to the
reader.
Evaluating Analogies
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Instead of immediately trying to determine in
some objective way an analogy’s absolute
strength, it is prudent to evaluate it by
determining what would make it stronger or by
comparing it to other analogies. By comparing
the relative strength of an analogy with actual
or potential rivals you can get a good sense of
its absolute strength.
Arguments by Analogy
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Example: I am scared to let Susan see
me in this sweater. A couple of my other
friends told me it makes me look like a
child, and she’s at least as critical as
they are.
A weak or strong analogy? Strong.
Arguments by Analogy
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Example: A watch could not assemble
itself, because it’s too complex. The
universe is at least as complex as a
watch. So the universe could not have
assembled itself either.
A weak or strong analogy? Weak.
Inductive Generalization
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Generalizations always have a class of
things or events as a target (rather than
one thing or event for a target as in
analogies).
In all cases, generalizations have their
samples drawn from the target class
(while this is never true of arguments by
analogy).
Inductive Generalization
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Example: How can you say that people
act out of self-interest? Didn’t you read
the story about the airplane that skidded
off the runway into the ocean? One man
kept passing the life preservers to other
people so they would live instead of
him.
Analogical Arguments and
Generalizations
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In other words: In an inductive
generalization, we generalize from a
sample of a class or population to the
entire class or population, while in an
analogy we generalize from a sample of
a class or population to another
member of the class or population.
Fallacies
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What is a biased example? It is a
sample that does not accurately
represent its class.
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A biased generalization is a fallacy
because its sample is not representative
of the target population.
Fallacies
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A hasty generalization is a
generalization which is made with a
sample that is too small.
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An appeal to anecdotal evidence is a
form of the hasty generalization.
Fallacies
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We generally reject anecdotal evidence
because, while credible, an anecdote is
only one experience and as such is
statistically irrelevant.
When should a random
sample be used?
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A random sample should be used in an
inductive generalization whenever the
target class is heterogeneous (unrelated
to or unlike each other), otherwise you
would have an analogy.
When should a random
sample be used?
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For example, if you want to know how
Republicans are going to vote, then you
have to have a large sample size
because people are so different from
each other.
Margin of Error
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The larger the sample size size the
smaller the margin of error.
True or False?
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It is fair to say the same criteria used to
evaluate inductive generalizations can
also be used to evaluate analogies.
True or False?
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True! This is because while they differ in
how they are set up, the two kinds of
arguments both follow the same
principles.
True or False?
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An inductive generalization moves from
something we know about the target
class to a claim about a sample.
True or False?
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An inductive generalization moves from
something we know about the target
class to a claim about a sample.
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False! It goes the other way, from a
sample to a target.
Review
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When we make an analogical argument
or a generalization, we draw a
conclusion about a target based on a
sample.
Review
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The goal of randomness is to achieve
representativeness.
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A sample is random if every member of the
target population has an equal chance at
being selected for the sample.
Review
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True or False? No generalization based
on an unrepresentative sample is
trustworthy.
Review
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True! The sample must be
representative to be used appropriately.
Review
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True or False? An inductive
generalization cannot establish that
some precise percentage of a target
population has a given characteristic.
Review
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True! Remember, with inductive
arguments we are talking about
probabilities rather than certainties.