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From Stephen's Guide (7)
Inductive Fallacies
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Inductive reasoning consists of inferring from the properties of a sample to the
properties of a population as a whole.
For example, suppose we have a barrel containing of 1,000 beans. Some of the
beans are black and some of the beans are white. Suppose now we take a sample
of 100 beans from the barrel and that 50 of them are white and 50 of them are
black. Then we could infer inductively that half the beans in the barrel (that is,
500 of them) are black and half are white.
All inductive reasoning depends on the similarity of the sample and the
population. The more similar the same is to the population as a whole, the more
reliable will be the inductive inference. On the other hand, if the sample is
relevantly dissimilar to the population, then the inductive inference will be
unreliable.
No inductive inference is perfect. That means that any inductive inference can
sometimes fail. Even though the premises are true, the conclusion might be false.
Nonetheless, a good inductive inference gives us a reason to believe that the
conclusion is probably true.
The following inductive fallacies are described in this section
1.Hasty Generalization
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Definition:
The size of the sample is too small to support the conclusion.
Examples:
(i) Fred, the Australian, stole my wallet. Thus, all Australians
are thieves. (Of course, we shouldn't judge all Australians on
the basis of one example.)
(ii) I asked six of my friends what they thought of the new
spending restraints and they agreed it is a good idea. The
new restraints are therefore generally popular.
Proof:
Identify the size of the sample and the size of the population,
then show that the sample size is too small. Note: a formal
proof would require a mathematical calculation. This is the
subject of probability theory. For now, you must rely on
common sense
2. Unrepresentative Sample
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Definition:
The sample used in an inductive inference is relevantly
different from the population as a whole.
Examples:
(i) To see how Canadians will vote in the next election we
polled a hundred people in Calgary. This shows conclusively
that the Reform Party will sweep the polls. (People in
Calgary tend to be more conservative, and hence more likely
to vote Reform, than people in the rest of the country.)
(ii) The apples on the top of the box look good. The entire
box of apples must be good. (Of course, the rotten apples are
hidden beneath the surface.)
Proof:
Show how the sample is relevantly different from the
population as a whole, then show that because the sample is
different, the conclusion is probably different
3. False Analogy
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Definition:
In an analogy, two objects (or events), A and B are shown to
be similar. Then it is argued that since A has property P, so
also B must have property P. An analogy fails when the two
objects, A and B, are different in a way which affects whether
they both have property P.
Examples:
(i) Employees are like nails. Just as nails must be hit in the
head in order to make them work, so must employees.
(ii) Government is like business, so just as business must be
sensitive primarily to the bottom line, so also must
government. (But the objectives of government and business
are completely different, so probably they will have to meet
different criteria.)
Proof:
Identify the two objects or events being compared and the
property which both are said to possess. Show that the two
objects are different in a way which will affect whether they
both have that property.
4. Slothful Induction
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Definition:
The proper conclusion of an inductive argument is denied
despite the evidence to the contrary.
Examples:
(i) Hugo has had twelve accidents n the last six months, yet
he insists that it is just a coincidence and not his fault.
(Inductively, the evidence is overwhelming that it is his fault.
This example borrowed from Barker, p. 189)
(ii) Poll after poll shows that the N.D.P will win fewer than
ten seats in Parliament. Yet the party leader insists that the
party is doing much better than the polls suggest. (The N.D.P.
in fact got nine seats.)
Proof:
About all you can do in such a case is to point to the strength
of the inference.
5. Slothful Induction
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Definition:
The proper conclusion of an inductive argument is denied
despite the evidence to the contrary.
Examples:
(i) Hugo has had twelve accidents n the last six months, yet
he insists that it is just a coincidence and not his fault.
(Inductively, the evidence is overwhelming that it is his fault.
This example borrowed from Barker, p. 189)
(ii) Poll after poll shows that the N.D.P will win fewer than
ten seats in Parliament. Yet the party leader insists that the
party is doing much better than the polls suggest. (The N.D.P.
in fact got nine seats.)
Proof:
About all you can do in such a case is to point to the strength
of the inference.
6. Fallacy of Exclusion
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Definition:
Important evidence which would undermine an inductive
argument is excluded from consideration. The requirement
that all relevant information be included is called the
"principle of total evidence".
Examples:
(i) Jones is Albertan, and most Albertans vote Tory, so Jones
will probably vote Tory. (The information left out is that
Jones lives in Edmonton, and that most people in Edmonton
vote Liberal or N.D.P.)
(ii) The Leafs will probably win this game because they've
won nine out of their last ten. (Eight of the Leafs' wins came
over last place teams, and today they are playing the first
place team.)
Proof:
Give the missing evidence and show that it changes the
outcome of the inductive argument. Note that it is not
sufficient simply to show that not all of the evidence was
included; it must be shown that the missing evidence will
change the conclusion.
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发表于 2003-6-26 15:27:00
