This week, we're going to be talking about refutation.
To refute an argument or to subject it to refutation, is to show that the argument
is unsuccessful. The argument is invalid, or unsound, or
commits one of the fallacies that we've described,
but in any case, to refute the argument is to show that it's unsuccessful.
Now, this week we'll be talking about four different methods of refutation,
four different ways that you can show an argument is unsuccessful.
In this lecture, we'll talk about counterexampling the argument,
counterexamples. What's a counterexample? Well, a
counterexample is an example that runs counter to some generalization.
So, if someone puts forward a generalization, you can produce a
counterexample to the generalization, an example that runs counter to the
generalization in order to show that the generalization is not true.
Now, some arguments contain generalization in their premises or
contain a generalization in their conclusion, and if you counter example
one or more of those generalization, you put forward a counterexample to one or
more of those generalization, then you've shown that the arguement is no good.
Either the conclusion, the conclusion generalization is not true
or one of the premises, one of the premise generalizations is not true.
But in any case, whether the conclusion is not true or whether one of the
premises is not true, the argument itself is going to be at the very least unsound.
Let me give you an example of an argument that contains a generalization in its
conclusion and can be successfully counter exampled and thereby refuted.
Consider the following display of information from the U.S.
government. It indicates level of income and level of
unemployment for people age 25 and over at different levels of educational
attainment. So, depending on what level of
educational attainment you have, the average income that you can expect per
week and the average unemployment rate that you the average unemployment rate
for people at that level of income is going to vary.
Now, someone looking at the data represented by this chart might say,
people with professional degrees make more money than people without a
bachelors degree. People with professional degrees make
more money than people with bachelor's degrees.
Okay, now, if that generalization is understood to mean just that, on average,
people with professional degrees make more money than people with bachelor's
degrees, then in the United States for people over 25 today,
that generalization is true. But if the generalization is understood
to mean that all people with professional degrees make more money than any person
with a bachelor's degree, then that claim can easily be
counterexampled. And it can easily be counterexampled just
by finding one person who has no higher educational attainment than a bachelor's
degree, and then another person who has a professional degree, where the first
person happens to make more money than the second person,
and there are plenty of pairs of people like that, I can assure you.
Let's consider another case in which we can refute an argument by means of
counterexample. Suppose we consider the various cases in
which we think it's wrong for someone to do something.
Now, one thing that we'll notice that a lot of those cases have in common is that
they're all cases in which it would be wrong for everyone to do that same thing.
So for instance it would be wrong for everyone to engage in murder and so we
think it's wrong for anybody to engage in murder.
It would be wrong for everyone to lie and so we think it's wrong for anybody to
lie. And it would be wrong for everyone to
steal and so we thinks it's wrong for anybody to steal.
Now, suppose that, when we survey these cases,
we arrive at the general conclusion that whenever it's wrong for everyone to do
something, it's gotta be wrong for anybody to do it.
Now, that conclusion might seem plausible to you,
especially when you keep in mind the examples that we've just considered.
But now, think about a case where six of us are sitting around a table and we
finished our dinner, and the plate of bread in the middle of the table, the
plate of bread that was there for all of us to eat from has just one piece of
bread left. Now, it would certainly be wrong for all
of us to reach over and start fighting over that piece of bread, tugging at it
from different angles, and tearing it apart selfishly?
That would be wrong, but does that mean that it's wrong for
anybody to take the bread? I don't think so.
We don't have to leave a piece of bread on the table after we're all done eating,
that would just be wasting food. It would be fine for one of us to take
the bread. What's not fine is for the six of us to
all fight over that last piece of bread. So, that example is a counterexample to
the generalization that whenever it's wrong for everyone to do something, it's
wrong for anyone to do that. So, if our survey of cases led us to
conclude the truth of that generalization, then that argument was
unsuccessful. That argument from the survey of cases that we surveyed earlier
to the general conclusion that whenever it's wrong for everyone to do something,
it's wrong for anyone to do it. That argument is unsuccessful and we can
prove that it's unsuccessful by offering this counterexample to the conclusion.