Critical Thinking Chapter 10

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					Critical Thinking: Chapter 10

      Inductive Arguments
Arguments
   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
   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
   Example: The dog has barked at me for
    the last three mornings, so I think he will
    bark at me this morning.
Inductive Arguments
   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
   Remember: A deductive argument sets
    out to guarantee the truth of its
    conclusion based on the truth of its
    premises.
Inductive Arguments
   Remember:an inductive argument
    attempts to offer a probability that its
    conclusion is true based on the truth of
    its premises.
Inductive Arguments
   Inductive arguments give us a way of
    extending our belief from things we
    know about to things unknown.
Important Definitions
   Sample: The term sample refers to an
    item or items we believe something
    about.
Important Definitions
   Target: The term target refers to an item
    or group of items to which we wish to
    extend our belief.
Important Definitions
   Feature: The item we know about in the
    sample and we extend to the target
    object is the feature (or property) in
    question.
Example
   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
   Inductive arguments can be divided into
    two categories: Analogical arguments
    (or argument by analogy) and inductive
    generalizations.
Arguments by Analogy
   Ordinarily, arguments by analogy have
    one thing or event for a target.

   In an analogical argument, the sample
    and target are distinct-one is not a part
    of the other.
Analogies
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   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
   What is a biased example? It is a
    sample that does not accurately
    represent its class.

   A biased generalization is a fallacy
    because its sample is not representative
    of the target population.
Fallacies
   A hasty generalization is a
    generalization which is made with a
    sample that is too small.

   An appeal to anecdotal evidence is a
    form of the hasty generalization.
Fallacies
   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?
   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?
   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
   The larger the sample size size the
    smaller the margin of error.
True or False?
   It is fair to say the same criteria used to
    evaluate inductive generalizations can
    also be used to evaluate analogies.
True or False?
   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?
   An inductive generalization moves from
    something we know about the target
    class to a claim about a sample.
True or False?
   An inductive generalization moves from
    something we know about the target
    class to a claim about a sample.

   False! It goes the other way, from a
    sample to a target.
Review
   When we make an analogical argument
    or a generalization, we draw a
    conclusion about a target based on a
    sample.
Review
   The goal of randomness is to achieve
    representativeness.

   A sample is random if every member of the
    target population has an equal chance at
    being selected for the sample.
Review
   True or False? No generalization based
    on an unrepresentative sample is
    trustworthy.
Review
   True! The sample must be
    representative to be used appropriately.
Review
   True or False? An inductive
    generalization cannot establish that
    some precise percentage of a target
    population has a given characteristic.
Review
   True! Remember, with inductive
    arguments we are talking about
    probabilities rather than certainties.

				
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posted:8/15/2011
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