Last time we talked about test for sufficient conditions and necessary
conditions. And those times will work fine in a lot
of cases, but they're not going to work in all cases because remember we were
looking at what caused death. Death well you're either dead or you're
not dead. When you're talking about whether the
person had fish or not, we didn't look at cases for people who had just a little
bit of fish. They either ate fish or they didn't eat
fish. But there are a lot of causal relations
that hold, not between absolute or dichotomous properties.
You're either dead or not dead. You ate fish or you didn't eat fish.
Instead, some causal relations hold between, properties that come in degrees.
For example. Carbon dioxide and global warming.
Well, there's always carbon dioxide. The atmosphere always has some of it.
So you can't say that carbon dioxide is sufficient for causing heating in the
world, since sometimes the world cools down, and there's still carbon dioxide
then. So, what we need to think about is the
degree of carbon dioxide. And sure enough that's what the
intergovernmental panel on climate change, the IPCC used to reach its
conclusion, that increasing levels of carbon dioxide were causing increasing
global temperatures. We can't use the sufficient condition
test or the necessary condition test. But we can still reach a conclusion about
causation and we can even know the mechanism for the causation.
The carbon monoxide reflects the heat from the sun back to the earth, and traps
it in like a greenhouse effect as it's called.
So the question for this lecture is, how we going to use arguments to justify
those kinds of causal claims? So, let's look at another example.
Suppose a runner runs a mile and take him ten minutes, why were they so slow?
Well, maybe because they were really heavy.
Now, weight can't be sufficient for running slow, because everybody's got a
certain weight. So it's not an on-off property, it's a
property that comes in degrees. And again, the heavier, the harder it's
going to be to run. We know the mechanism, because it takes
more energy to move a heavy body. So, we've got a pretty good causal story,
and a pretty good causal hypothesis. But you can't use the necessary and
sufficient condition test because we're dealing with properties that come in
degrees. A third example, suppose the wages go
down, well that's because the unemployment was high.
There's always some unemployment, wages are never as high as you'd like 'em to
be. So, how do you get a causal claim.
Well, it's because the more unemployment there is, the lower the wages are.
Cause if a lot of people are unemployed their willing to take jobs for a lot less
wage. So we've got a causal story, we've got a
causal claim. They seem to be justified, but you can't
use the necessary and sufficient condition test.
You need a different test. And the test you need has to deal with
properties that come in degrees. And the test that does that is called the
method of concomitant variation. It was developed by John Stuart Mill in
the nineteenth century, brilliant philosopher.
He also developed tests that basically what we've been calling the necessary
condition test and the sufficient condition test, parallel.
He gave them different names but it's the same basic idea.
This lecture's on the method of concomitant or concomitant variation,
also developed by John Stuart Mill in the nineteenth century.
And in order to apply the method of concomitant or concomitant variation, the
first thing we've got to get straight is the idea of what concomitant or
concomitant variation is. Well to avoid that word people these days
call them correlations. The first kind of correlation we've got
to understand is a positive correlation. X and Y are positively correlated when an
increase in X is associated with an increase in Y.
A decease in X is associated with a decrease in Y.
That's what a positive correlation is. Contrast a negative correlation is when
an increase in x is associated with a decrease in y, and a decrease in x is
associated with an increase in y. That's further negatively correlated
cause increases associated with decrease with the possible correlated with the
increase and increase is associated with decrease and decrease is associated.
So let's see some examples. First of all.
Calorie intake is associated with weight. The more calories you take in, the more
weight you're going to gain. So they're positively correlated.
Whereas weight and exercise are negatively correlated.
The more exercise, the less weight because it burns off those calories you
took in. So you get a negative correlation between
weight and exercise and a positive correlation between weight and calorie
intake. Another example.
Height and age are positively correlated before the age of twenty, cause people
tend to get taller as they grow older. The height and age are negatively
correlated after the age of 60, because the space between people's vertebrae tend
to decrease after a certain age. So this shows that two things can be
positively correlated in some circumstances and negatively correlated
in others. Which correlation holds is going to
depend on the circumstances, that is how old the person is.
And now the next question is how can we get from these correlations to causal
relations. But two features are correlated,
positively or negatively, then there's four possible causal relations between
them. First A might cause B.
Sometimes when A and B are correlated, that means that A is causing some kind of
change in B. Second possibility, is that B causes A.
because the correlation's symmetrical. If A is correlated with B, B's correlated
with A. And then we don't know whether A causes B
or B causes A. But those are two different
possibilities, and we will have to see how to distinguish them, in a minute.
But the third possibility is that some third thing, C, causes both A and B.
If C causes B, and C also causes A, then A and B are going to be correlated.'Cause
whenever C is there, you get both of'em. And when C is not there, unless something
[INAUDIBLE] causes them. Then they're not going to be there, So A
and B will be correlated, simply because, a third thing, C, is causing them both.
And the fourth possibility is that the correlation is purely accidental.
A and B just happened to change together. Okay, so here's some examples.
First of all let's do an example of A causing B, okay?
The speed of driving is positively correlated with automobile accidents and
deaths from automobile accidents because when you're going very quickly in your
car and have an accident, you're more likely to die.
Okay, which causes which? It's the speed that causes the accidents
and the deaths. The death didn't cause you to drive
faster before you died, that seems pretty clear.
Okay, now what about the second possibility, B causes A?
Well it's just the reverse, you can use the same examples.
You can say automobile accidents and deaths are correlated with fast driving,
with speed. And in that case it's not that the thing
we mentioned first causes the thing we mention second, it's the other way
around. Because as we've said before, the speed
that causes the automobile accidents and the deaths, not the deaths and the
accidents that cause the speed. 'Kay?
What about the third possibility, that some third thing causes them both?
Well, here's an example. Having yellow teeth is correlated with
having lung cancer, well why is that? Cause there's some third thing that
causes people's teeth to become yellow and also causes lung cancer, namely
smoking. So people who smoke tend to have yellower
teeth and they also tend to have more lung cancer.
So those are correlated because smoking causes both of them.
'Kay. Another example, in young children, shoe
size is correlated, with the quality of handwriting.
As people's shoes get bigger their handwriting gets better.
Now why is that? It's because they're maturing and as
their bodies mature, their feet get bigger and also their handwriting gets
better. Well, so now we have an example of each
of the first three types of cases that we talked about.
What about the fourth? Correlation is accidental.
Well, here's an example. The height of my son and the height of
the tree outside the window, well their correlated.
The taller my son gets, the taller the tree gets.
And the taller the tree gets, the taller my son gets.
Their symmetrical, their correlated together.
Does that mean that something about the height of my son causes the height of the
tree? No.
Or visa versa. No.
Well you might say there's some third cause namely naturation.
But unlike the case of handwriting and size of feet where it was the naturation
of the same person. The same body.
Here my son's body maturing and the tree's body maturing are just unrelated.
You might say that time is the third cause that makes my son grow and also
makes the tree grow. But notice that time is an abstract thing
that's always there and always moves at the same rate.
So it can't really cause, my son to grow at this particular moment or the tree to
grow at this particular moment. It's a background condition, rather than
a cause in and of itself. So now we've got four possibilities and
we've got examples of each. The question that we have to face is,
fine, all four are possible. How do you tell which of these
possibilities is the one the applies in a particular case?
That's going to be tricky. So the problem is, how can we tell which
of the four possibilities applies in a particular case?
And one simple rule is that, when A causes B, A has to come before B.
So if the first possibility is instantiated, then you have to have A
coming before B. But if the second possibility is
instantiated, then you have to have B coming before A.
Now, in the last two, you can have them on any temporal relation you want.
But if a comes before b, then you know that b doesn't cause a and if b comes
before a, then you know that a doesn't cause b.
So, for example, exercise is correlated with weight loss.
Could it be that the weight loss causes the exercise?
Well, it's possible I suppose, but if the exercise occurs before the weight loss,
then we know it's the exercise that causes the weight loss, because the
exercise occurs before the weight loss occurs.
We can use that temporal relation to decide what causes what.
At least in some cases, because sometimes when you're dealing with a constant
factor, like CO2 variations or pollution variations over a long period of time.
If pollution causes acid rain you don't know exactly which part of the pollution
is causing which part of the acid rain. And the parts are occurring over a long
period of time so you can't tell which comes first.
But at least in cases where you can, like the exercise and the weight loss, then
you can say which causes which. Now when they're not in temporal order
like that, you have to use a different method.
The second method of determining what causes what, is manipulation.
This method is used in a lot of scientific experiments where they
manipulate one factor to see whether that factor causes something else.
When you do those types of experiments you have to make a lot of assumptions or
test a lot of background conditions to make sure that there's no independent
factor that's causing the effect. But.
In the right circumstances it can work. If you want more detail about which
circumstances need to be met, then they're books by Woodward and by Pearl
that spell this out in great detail. But here we're not going to go in any
great detail. We're just going to give you the basic
idea. And the basic idea is that you manipulate
A and then look to see whether B changes, according to the change in A.
And you manipulate B and then look to see whether A changes, in accordance with the
change in B. And that's going to help you determine
what causes what. Because if when you manipulate A, B
changes, then that's an indication that A causes B.
Because if B caused A, then manipulating A wouldn't have an effect on B.
Think about it this way. You put the wood into, the engine, of a
steam train. And the wood affects the motion of the
train because it affects the way the engine works.
And then the train produces steam, but the steam doesn't cause the train to
move, it's caused by the train. So if you manipulate the steam, like with
wind blowing the steam around, that's not going to change the train.
So similarly, if you change A, and B changes, but you change B and A doesn't
change, then that's a pretty good indication that A causes B.
And that's going to rule out, the second one.
Right? That can't be true if a causes b.
The third one. That says that c causes them both, so
it's going to rule that out. And the fourth one.
It's not just an accidental correlation if a causes b.
So if you do that manipulation, you can find out that it really is the first case
that holds. At least, if all the other conditions are
met. Now, you can also do it the other way
around. If you manipulate b, and a changes.
But you manipulate A and B doesn't change, then you know that B causes A.
But. You also know.
That a does not cause b. Because if it did, the new manipulated AB
would change. And you know that, it's not just some
third cause, and you know that it's not just accidental.
So now you've isolated the second. Condition, as the one that holds, if when
you manipulate B, A changes, but when you manipulate A, B doesn't change.
Again this only holds when certain circumstances are in place.
and I'm not going to go into detail and spell out what those are, but this is the
basic idea behind a lot of experiments in science.
Here's an example. Long time ago they discovered that
smoking correlated with lung cancer. And that lead a lot of people to say that
smoking causes lung cancer. But just imagine that you're a
manufacturer of cigarettes. What are you going to do?
Well they were pretty inventive. They said, it's not the smoking that
causes the lung cancer. It's the lung cancer that causes the
smoking. Because when people have certain types of
incipient lung cancer, that is lung cancer that's about to develop into full
blown lung cancer, it makes them want to smoke.
It creates a discomfort in their lungs that's relieved by the smoking.
And that explains why people who smoke more have more lung cancer.
So, we think that A causes B, the smoking causes the lung cancer.
Their claiming that B causes A, the lung cancer causes the smoking.
How do you tell. Well you can't look at the temporal
relation, because the smoking is going on at the same time when the lung cancers
developing. So you got to do a manipulation.
You set it up in a lab. You take a bunch of animals, in this case
it was monkeys. Who don't have lung cancer.
You check 'em first, and then you force them to smoke.
You put a cigarette in their mouth so that when they're breathing they're
smoking. And sure enough they developed a lot of
lung cancer, no surprise there, poor animals.
And that showed that it was lung cancer that was caused by smoking instead of
causing smoking. Why?
Because we didn't manipulate the lung cancer.
It didn't affect the smoking but we manipulated the smoking and that affected
the lung cancer and that shows that it was the smoking that caused the lung
cancer. Here's another example, which is kind of
a mystery for awhile, an economist friend of mine told me about this.
Turns out back in the 1960's there was a positive correlation between having a
television in the home and performance in school.
Students were more successful in school if they had a television in their house.
Some people actually claimed that television was making them better
students. But in the 90's it was the other way
around. In the 90's kids who had televisions in
their home did not do as well on average as kids who had no televisions in their
home. So, there was a negative correlation.
So how could there be a positive correlation between television and school
success in the 1960's and a negative correlation between television and school
sucess in the 1990's? In order to decide between those
hypotheses, you can't manipulate it. You can't go back and change the rate at
which they're watching television and change their school performance and so
on. You need to have some background
information about the societies of the time and the kind of people who had
televisions. Well back in the 1960's it was largely
the more affluent, higher socioeconomic status people who had televisions because
they were quite expensive and not that common.
And those people typically are correlated with high school success anyway.
High socioeconomic status and high school success had been correlated.
And so, it's that correlation that's explaining why in the 1960s students who
had televisions in their homes did better in school.
But in the 1990s things have turned around.
Parents were worried about their children watching too much television.
And some parents. Actually kept televisions out of the home
so we the kids would read more. They read more books and less television.
And those kids were doing better in school, no surprise there.
So in the 1990's there were a lot of people who kept televisions out, that
produced greater school performance. And so you've got different correlations
in different times and the only way to tell what was causing what was by looking
at the background circumstances and knowing something about the societies in
which these effects are occurring. There's a lot more to say about causation
and we can't say it all here. You really ought to take a whole course
about causation and it's many different forms.
But we can help you avoid some of the most common fallacies.
Here we'll look at two common fallacies. The first one is simply confusing an
accidental correlation with a causa relation.
Sometimes this is called post hoc ergo propter hoc, or some people pronounce it
post hoc ergo propter hoc. And what it means in Latin is after this
therefore because of this. And the idea is that they're correlated,
one occurs after the other, and you conclude the second one must occur
because of the first one. It's really just an accidental
correlation, and it's a fallacy to conclude that it's a causal relation.
And of course the classic example occurred.
One time in a hotel with my son, we got onto the elevator and I reached for the
button. I wanted to push for the button for the
floor that we wanted to go to, but my son said, no daddy, no don't do it.
I said okay, and then he reached up. And pushed the button and just as he
pushed the button, the fire alarm went off.
And he started crying because he had made the fire alarm go off.
But of course, he was just committing the fallacy of post hoc ergo propter hoc.
The fire alarm didn't go off because he pushed the elevator button.
It just happened to go off after he pushed it, the elevator button.
Now that might seem like a silly mistake that only a child would make but you'll
be surprised how many times you can find this mistake being made, in serious
discussions in newspapers. Just take a look for yourself.
Now the second common fallacy that I want to describe is confusing a cause with an
effect. Here's some example.
I'm a golfer. And sometimes, I go out and play golf and
my back is just killing me. And I'm thinking, it must be why I'm
playing so bad. I can't hit the ball.
I keep knocking it off to the side. And I blame it on my back.
So I think it's the pain in my back that's causing my bad swing.
And actually, it's my bad swing that's causing the pain in my back.
I'm like twisting around the wrong way and that's causing a backache.
So I think that it's the pain in my back that's making me swing badly, it's
actually the bad swing that's causing the pain in the back.
So that's just an everyday example. Here's an example in football, American
football we're talking about here. It was noticed that there was a
coloration between the number of forward passes, and how often the team was
losing. Teams that had a lot of forward passes
were losing more often. So some coaches concluded, well we ought
not to pass the ball so much because passing the ball causes you to lose.
That's not what was going on. What was going on, is that, in the last
quarter of the game, the team that was behind would get desperate.
They needed to score a lot of points quickly, and running the ball wasn't
going to do that. So they tried passing the ball.
And they would pass more and more and more, in order to catch up.
And that meant was the fact they were losing the game that caused them to pass
the ball so often. It wasn't passing the ball often that was
causing them to lose the game. So again, they were confusing cause with
effect. Here's a third example.
It turns out that many schizophrenics smoke and take drugs and alcohol.
And so, there's a correlation between schizophrenia and drug and alcohol use
including nicotine from smoking. Some people concluded, it must be the
drugs and nicotine cause schizophrenia. No, that's not what's going on.
That's the fallacy of confusing cause and effect.
What's really going on is that their schizophrenia is causing them to smoke
and drink more. And to take drugs.
So again, what people get confused about, is they think that one thing causes
another, when it's really the other thing that causes the first thing.
Their getting the relation backwards and confused.
And that's something that you need to really be on the lookout for as you try
to figure out what causes what in your everyday life.
Because if you make that mistake you're going to get confused.
You're not going to know what manipulations will change what features
in your life. And that's why causal relations report to
figure out how to get around in the world and bring about the changes that you
want. So, watch out for these fallacies and do
the best you can to figure out how the world works.