Inductive Arguments Slide 2 Inductive vs. Deductive Arguments
The difference between a deductive and an inductive argument lies
in what it is attempting to show. A deductive argument is trying to
show that its conclusion must follow from its premises. An argument
that successfully does this is deductively valid. Slide 3
Counterexamples If a deductive argument is a good one, you wont be
able to think of any counterexamples to it. Counterexample = a
possible situation where the premises of the argument are true but
the conclusion is false. A valid argument will not have any
counterexamples. Slide 4 Inductive Arguments An inductive argument
has a different aim. It is only trying to show that its conclusion
is supported by its premises. In other words, its trying to show
that the truth of its premises makes it more likely that its
conclusion will be true. Slide 5 Inductive Strength The quality of
an inductive argument is measured by its strength the degree to
which its premises raise the probability of its conclusion. If they
dont raise the probability very much, the argument is not very
strong. If they do, the argument is strong. Slide 6 Inductive
Strength For inductive arguments, counterexamples dont show that
the argument is bad. This is because an inductive argument is only
saying that its conclusion is very likely, not that other
possibilities do not exist. Validity isnt a feature we look for in
good inductive arguments just strength. Slide 7 Additional Evidence
Since inductive arguments dont prove their conclusion, even a
strong argument with true premises can be defeated by additional
evidence. Slide 8 Example For example: Most cats like to play.
Fluffy is a cat. Therefore Fluffy probably likes to play. This
argument is strong, but future evidence might show that its
conclusion is still false, even if its premises are true! (Fluffy
might be too old to play) Slide 9 Vs. Valid Argument Notice how
this is different from valid arguments. In a valid argument, so
long as the premises are true, no future evidence can show that the
conclusion is false. Of course, future evidence might show that the
premises are wrong! Slide 10 Induction Today, we will discuss two
different types of inductive arguments: inductive syllogism
inductive generalization Slide 11 Inductive Syllogism An inductive
syllogism is a method for arguing from a general statement to a
more specific one. A general statement is a statement about a group
of people: most teachers are smart athletes are strong in general,
dogs like to play fetch many students dont get enough sleep bankers
are usually rich Slide 12 Inductive Syllogism A general statement
about a certain group can help us make a good guess about a
particular member of that group. For instance, if we know that most
bankers are rich, we can make a good guess that Bill the banker is
rich, too. Slide 13 Inductive Syllogism In standard form: 1) Most
bankers are rich. 2) Bill is a banker. 3) Bill is rich. The general
form of the argument I just gave is: 1) Most Xs are Y. 2) A is an
X. C) A is Y. This type of argument is called an inductive
syllogism. Slide 14 Inductive Syllogism In standard form: 1) Most
bankers are rich. 2) Bill is a banker. 3) Bill is rich. Notice that
this is NOT a valid argument. The premises do not guarantee the
conclusion Bill could be a poor banker. (A counterexample!) But
since this is an inductive argument, it doesnt matter that the
argument is not valid. Slide 15 Inductive Syllogism In standard
form: 1) Most bankers are rich. 2) Bill is a banker. 3) Bill is
rich. The argument does raise the probability that its conclusion
is true. If it turns out that most bankers are rich, this makes it
more likely that Bill the banker is rich. So this is a strong
inductive argument. Slide 16 More Examples Most basketball players
are tall. Jane is a basketball player. Therefore Jane is probably
tall. Most university students are smart. Alice is a university
student. Therefore Alice is probably smart. Most Saturdays, the bus
runs late. Today is a Saturday. Therefore, the bus will probably
run late. Slide 17 Hidden Premises An inductive syllogism can have
hidden premises. Often, the second premise will be left out if it
is common knowledge (i.e., it will become a hidden premise). 1)
Most Presidents are very powerful. 2) Barack Obama is very
powerful. Similarly, the first premise may be left out if the
generalization is common knowledge. 1) Bill is a banker. C) Bill is
probably rich. Slide 18 Different Orders The premises in an
inductive syllogism dont have to come in the same order, either.
The following two arguments are the same: Most winter days are
cold. Tomorrow is the first day of winter. Therefore, tomorrow will
probably be cold. Tomorrow is the first day of winter. Most winter
days are cold. Therefore, tomorrow will probably be cold. Slide 19
Hidden Conclusion Even the conclusion of an inductive syllogism can
be hidden particularly if the conclusion is used as a
sub-conclusion in a larger argument. If Bill is rich, then he will
buy us lunch. Bills a banker, and most bankers are rich so well
probably get a free lunch today! Slide 20 Strength of
Generalization The strength of an inductive syllogism depends
primarily on the strength of the generalization. If 90% of cats
like milk, then most cats like milk, Fifi is a cat, therefore Fifi
likes milk is a pretty strong argument. If only 70% of cats like
milk, then the argument is much weaker. Slide 21 Other Evidence But
our assessment of the argument also has to do with the amount of
available evidence that has been taken into account. Consider the
example most bankers are rich, Bill is a banker, therefore Bill is
probably rich. Even though this argument is strong, our assessment
of the likelihood of its conclusion may be affected by other
available information about Bill. Slide 22 Other Evidence For
instance, if we find out that Bill invested heavily in the stock
market right before it crashed, then we might no longer accept the
conclusion that Bill is probably rich. Or, if we know that Bill is
a chronic gambler, we might use this to infer that Bill is bad at
managing his money and that hes therefore less likely to be rich,
even though he is a banker. Slide 23 Obvious Available Evidence Its
the neglect of obvious available evidence that makes the following
inductive syllogisms not very convincing: Most Americans dont speak
Chinese. The new professor of Chinese literature is American.
Therefore, he doesnt speak Chinese. Most of the citizens of
Zimbabwe are poor. Therefore, the president of Zimbabwe is poor.
Slide 24 Different Argument Form Inductive syllogisms are easily
confused with a different argument form: 1) Most Xs are Y. 2) A is
a Y. C) A is an X. An example to show why this is bad: 1) Most
teachers are adults. 2) Bill is an adult. C) Bill is a teacher.
Slide 25 Inductive Generalization The other form of inductive
argument we will discuss today is inductive generalization.
Inductive generalization is a way to argue from specific to general
claims. So in a sense, its the opposite of the argument style we
just looked at. Slide 26 Inductive Generalization However, its not
exactly the opposite: 1) Bill is rich. 2) Bill is a banker. C) Most
bankers are rich. This would not be a good argument. You cant go
from an observation about one person to a claim about a whole
group. Instead, in order to justify the statement that most bankers
are rich, we need to look at lots and lots of particular bankers.
Slide 27 Samples Ideally, when we are trying to find out whether a
large percentage of a group has a certain property, we would check
every member of the group. But for a lot of groups, thats just not
possible there are too many to check. Instead, we look at a sample,
or a subset of the group. Slide 28 Inductive Generalization Say we
look at a sample of bankers and find that 90% of them are rich. We
can then use that information to support a conclusion that most
bankers are rich. So the argument form of an inductive
generalization is: 1) Most of the observed sample of Xs are Y. C)
Most Xs are Y. Slide 29 Other Examples We have given our new pet
food to 200 cats. All but one liked the food. Therefore, we believe
that most cats will love our new pet food. We polled 1000 people in
Hong Kong and asked them if they preferred coffee or tea. 886
people replied tea. Therefore, it seems likely that most Hong Kong
people prefer tea. Slide 30 Representative Samples The success of
an inductive generalization depends on how good the match is
between the sample and the entire group. If our sample of bankers
is 90% rich, but bankers on a whole are only 30% rich, our argument
will not be a good one. Slide 31 Samples Of course, we cant check
this match directly the whole point of using a sample was that we
cant check the properties of the entire group! If we knew that
bankers were 30% rich, we wouldnt need to test a sample. Slide 32
Sample Size But, there are ways to make educated guesses about how
closely the percentages match. One of the easiest is the size of
the sample if we survey 10% of the bankers, well have a better
estimate than if we survey 1% of the bankers. When all else is
equal, a larger sample is better than a smaller sample. Slide 33
Sample Size Slide 34 Size of the Group Sometimes its difficult to
tell if weve sampled a large percentage or a small percentage of
the total group because sometimes we dont know who belongs in the
group! This is particularly tricky for cases where we have to rely
on self-identification not everyone is going to admit to being a
member of the group pornography users! Slide 35 Representative
Samples Another factor is whether the sample is representative.
Slide 36 Representative Samples For instance, say we want to know
whether most bankers are rich. But say our sample only contains
bankers who went to Harvard. Our sample is BIASED not all bankers
go to prestigious schools, and whether or not one goes to a
prestigious school is likely to influence whether or not one is
rich. Slide 37 Perfectly Representative Samples A perfectly
representative sample does not contain any bias. In a perfectly
representative sample, the percentage of bankers in the sample that
went to Harvard would be the same as the percentage of total
bankers that went to Harvard. Slide 38 Relevant Factors Of course,
it is not usually possible to use a perfectly representative sample
the sample will almost always contain a greater or lesser
percentage of for example, red-headed bankers, left-handed bankers,
etc. But ideally well make sure that any relevant factors like
education match pretty well. Slide 39 Biased Samples Other examples
of (relevantly) biased samples Using a sample of Americans to make
claims about what kinds of movies people (worldwide) will like.
Using a sample of only first-years to make claims about the work
habits of university students. Slide 40 Sneaky Bias Sometimes bias
can be sneaky: Phone polls during elections often end up with a
sample containing too many old people old people are more likely to
be at home when the phone rings. Also, they are more likely to have
a land line! Slide 41 Random Samples Well also do our best to make
sure that even factors that dont appear relevant will be reasonably
represented in the sample. Often the best way to do this is to use
a random sample a sample where every member of the target group has
the same chance at being included in the sample. Slide 42 Dont
Reverse Terms Just like with inductive syllogism, its important to
be careful not to reverse terms with inductive generalization. This
is not a good argument: 1) Most of the sample of doctors we
surveyed are rich. C) Most rich people are doctors. The reason this
is a bad argument is that, while you might have tested a good
sample of doctors, you might not have tested a good sample of rich
people. Slide 43 Anecdotal Evidence Unfortunately, many people
often make inductive generalizations on very bad samples.
Sometimes, samples of only one case! This is called relying on
anecdotes, or anecdotal evidence using a single case, or just a
few, to draw conclusions. It is not a very strong form of argument.
Slide 44 Cherry Picking You often see this in advertisements rather
than giving a percentage of people who gained a benefit from the
product, advertisers will simply show a single person saying that
the product worked for them. Slide 45 Anecdotal Evidence as
Argument Sometimes people try to reject arguments on the basis of
anecdotal evidence, too!
