History of Philosophy
Lecture 4
Inductive arguments
By David Kelsey
Inductive arguments
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Prediction:
– Inductive arguments give us a way of extending our beliefs about things we
know of to things unknown.
– Inductive arguments make predictions about things unknown or about the
future.
– Inductive arguments assume:
– Examples:
A general formula
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A general formula: Here is a general formula which is followed by
almost all inductive arguments:
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Some thing or class of things X has properties a, b and c.
Another thing or class or things Y has properties a, b and c.
X has some further property p.
Thus, Y also has property p.
The Harley example:
– Some Harley Davidson motorcycle’s are new, are taken care of and well
maintained & are of a particular make and model…
– My Harley is like this also.
– The other Harley’s leak oil.
– Thus,
More examples
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Banging the gate:
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On Monday, Tuesday and
Wednesday I left at 9am, and
banged the gate shut loudly.
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On Thursday I will leave at 9am
and bang the gate shut loudly.
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Peaches:
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The peaches I bought at the
marked were all sitting in a particular
crate, were all about the same age
and were all about the same
ripeness.
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The entire batch of peaches at the
market are sitting in the same crate,
are of the same age and are the
same ripeness.
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The peaches I bought were all
mushy.
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Thus,
On Monday, Tuesday and
Wednesday the dog barked loudly
at me as I left.
Thus,
The sample
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The sample: the thing or group of things which we believe something about.
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The sample is just the thing or things that we know something about.
– Examples:
The Target
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The target: the thing or things that we extend our belief to.
– The target is just the thing or things about which there is something we
don’t know.
– And while we don’t know something about the target,
• We reason from other things (the sample,) that the target will have some property.
– Examples:
The Target
#2
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Single and Plural targets:
– The target can be a single thing, like
– Or it can be an entire class of things, like
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Sometimes the members from the sample are drawn from the target:
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Sometimes the members of the sample aren’t members of the target:
The property in question
• The property in question: some of its features:
– We know that the sample instantiates this property.
– We don’t know whether the target instantiates this property.
– We infer that the target instantiates this property because the sample does.
– Examples:
Arguments by analogy
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An argument by analogy:
– 1. Ordinarily has one thing or event for a target.
– 2. Never has it’s sample drawn from the target class.
– Examples of arguments by analogy:
Inductive Generalizations
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An Inductive Generalization:
– 1. Always has a class of things or events for a target.
– 2. Always has it’s sample drawn from the target class.
– For example:
4 principles about
good inductive reasoning
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Representative-ness principle:
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The more alike one another our sample and target are, the stronger our argument,
the less like one another our sample and target are, the weaker our argument.
Representative sample: A sample that is similar in relevant respects to the
target.
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The more an inductive argument’s sample is similar to its target in all relevant respects
the more representative the sample is said to be.
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Question: what’s a relevant respect?
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Biased sample: A sample that is significantly different from the target in one or
more relevant respects.
Principles two, three
& four
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2) If, in giving an analogical argument, we don’t know whether our target has
some relevant property:
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3) If we do know that our target has some relevant property P:
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4) In general, the larger the sample the stronger the argument.
Exercises
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Are the Following Inductive Generalizations or Arguments by analogy?
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1. With 7 out of the last 9 El Nino’s, we saw below-average rainfall across the northern
United States and Southern Canada. So the chances are we’ll see the same with the
next El Nino.
2. Bill Clinton lied to the American public about his relationship with Monica Lewinsky;
therefore, he probably lied to the American public about most things.
3. You’re going out with a Georgette? Well, don’t expect much because I’ve known
three and they’ve all been stuck up annoying brats. I’ll bet this one will be too.
What is the sample, target and property in question for each of the following
inductive arguments?
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4. Too much sun will make your face all wrinkly; I suppose it would have that effect on
your hands, too.
5. Most of my professors wear glasses; it’s a good bet most professors everywhere do
the same.
6. Yamaha makes great motorcycles, so I’ll bet their pianos are good, too.
Answers to the Exercises
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Answers:
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1. Argument by analogy
2. Inductive generalization
3. Argument by analogy
4. The sample: your face; The target: your hands; Property in Question: Being wrinkly
from exposure to the sun
5. The Sample: most of my professors; The Target: Most professors everywhere; The
property in question: Wearing glasses
6. The Sample: Yamaha Motorcycles; The Target: Yamaha Pianos; The Proerty in
question: Being good