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.