Last time we looked at sufficient condition tests, and they tell us what is
or is not sufficient condition. We also need to know which factors or
features or candidates are necessary conditions.
So this time we're going to look at necessary condition tests.
And as with sufficient conditions tests, there's going to be two of them.
There's a negative necessary condition test that tells you what is not a
necessary condition and then there'll be a positive necessary condition test that
tells you what is. A necessary condition.
So first, the negative necessary condition test.
It says simply that X is not a necessary condition of Y if there is any case where
X is absent and Y is present. Because to be a necessary condition, it
has to be the case that whenever X is absent,
Y is absent too. So, if there's even one case where X is
absent and Y is present, that's a counter example to the universal claim that
whenever, that is in all cases. Where X is absent, Y is absent,
okay? So let's apply this to our data so far.
Then let's look first just at the first three people and Barney and Cathy.
You remember them from last time, they were at the banquet.
Is pie a necessary condition of death? Well, is there a case where pie is absent
and death is present. Yes, that means that pie is not a
necessary condition of death. Which case shows us that,
well it's Barney. Notice that it's not Ann.
Some people get confused about this. But what Ann tells us is that pie is not
sufficient for death. It's Barney that tells us that pie is not
necessary for death because with Barney, you get death without pie.
So pie was not necessary for Barney to die.
So it's the cases of death that leave Barney out of these three, that tell us
what's not necessary for death. Now the case of Barney also tells us
there is another result its not necessary for death.
Which one is that? Ice cream.
because Barney also didn't have ice cream and he died, so he died without having
ice cream. So ice cream is not necessary for death.
So, what might be necessary for death? Tomato soup might be necessary for death,
because out of these three cases there's nobody who dies without having tomato
soup. Fish might be necessary for death,
because out of these cases there's nobody who dies without having fish.
Red wine might be necessary, and cake might be necessary.
Because Barney's the only one who dies, all of those things still might be
necessary for death. And the only way to rule out some of
those candidates so as to narrow down the field, is to get more data.
So remember Doug and Emily, our old friends from the banquet.
What do they show us? Is cake necessary for death.
No, because now we have a case of someone dying without eating cake namely Emily.
And is fish necessary for death? Whoa, well both Emily and Barney had
fish, so there's nobody who dies without having fish.
So, so far for this data, it looks like fish still might be a necessary condition
for death. So, since it survived this far, I guess
we can conclude that fish is a necessary condition for death.
No way, because remember, this is just the negative necessary condition test.
It tells us what is not a necessary condition.
We still are not in a position to conclude, that fish is a necessary
condition for death. For that, we'll need to look at the
positive necessary condition test. The positive necessary condition test is
just like positive sufficient condition test, except that you change the absent
for present in the two positions throughout the test.
So. It tells you that we have good reason to
believe that x is a necessary condition of y if all of the following conditions
are met. Now remember it's got to be all four that
are met before you can reasonably conclude that it really is a necessary
condition. And it's positive because it allows you
to conclude positively it is a necessary condition.
[SOUND] So first clause is that we've not found any case where X is absent and Y is
present. Again it's just like the sufficient
condition test except that we've changed absent for present.
And what this is saying is that this particular candidate X, has passed the
negative necessary condition test. And you got to do that, because if you're
ruled out as a necessary condition, there can't be adequate reason to conclude.
But you are a necessary condition, 'cause you've been ruled out.
Second, you've tested a wide variety of cases, including cases where X is absent,
and cases where Y is present. I mean after all, if nobody dies, you
can't test to see what's necessary for death.
You're not going to be able to have enough data.
You're going to reach silly conclusions. So, we need to make sure we have a bunch
of cases where X is absent, and a bunch of cases where Y is present or we're not
going to have any reason at all. So, remember our data,
what about tomato soup? Is tomato soup necessary for death?
Well, it might be cause we didn't have any
cases in the first three at least, where nobody drank tomato soup.
So that would be a silly conclusion to reach.
We need to look at cases where people didn't have tomato soup in order to
determine whether the tomato soup really was necessary, to cause death in that
case. Now the third, condition says that if
there are any other features, that are never absent where Y is present, then
we've tested cases where those other features are present,
but X is absent. And the idea here is that you've got
competing hypotheses. Some people might think that one
candidate is a necessary condition for death and other people might think that
another candidate is a necessary condition for death and some people might
say, well I don't know which one, because neither ones ruled out.
Well, if neither ones ruled out by the necessary test, then we need to have
cases that decide between the competing candidates, the competing hypothesis to
determine what really is necessary for death.
So that means that, in our example, at least for the first three cases, and
Barney and Cathy. Fish and red wine and tomato soup all
still might be necessary conditions of death.
And to figure out which one really is, we want to look at a case of somebody that's
fish and red wine, but not tomato soup, somebody who has fish and tomato soup,
but not red wine and somebody who has tomato soup and red wine but not fish.
So we need to do more research. Now luckily, again lucky for us but not
for them, we have additional people who came to the banquet.
It had just those combinations, namely Fred, Gertrude and Harold.
Fred had fish and red wine but not tomato soup.
Gertrude had fish and tomato soup, but not red wine.
And Harold had tomato soup and red wine, but not fish.
So, what does Fred tell us? What does this case rule out as a
necessary condition. It tells us that tomato soup is not a
necessary condition for death, because Fred died without having tomato soup.
He had leek soup instead, and no tomato soup.
What does Gertrude tell us? What does this case rule out as necessary
condition? Nothing, why? Because Gertrude didn't
die. And it's only the cases where people die
that can rule out necessary conditions. What about Harold?
What does Harold tell us? Same thing, Harold didn't die so he
doesn't rule out anything as a necessary condition,
okay. Gertrude might show us that fish is not a sufficient condition for death, we
already talked about that in the last lecture but since Gertrude and Harold are
alive and don't die, they can't rule out candidates as necessary conditions.
So, so far, it looks like fish might be necessary but not sufficient for death,
given this set of data with Ann through Harold.
It also looks like red wine. Still might be necessary but not
sufficient for death. So.
Is it reasonable to conclude that both of these features, both of these candidates
are necessary and not sufficient for death.
No, not yet. because remember there's a fourth
condition. And the fourth condition says that we've
tested enough cases of various kinds that are likely to include a case where X is
absent and Y is present, if there is any such case.
And as with the positive sufficient condition test, this is going to require
background knowledge about what kinds of things might or not be causally relevant,
might or might not be necessary in sufficient conditions for death.
It's going to be defeasible. It's not going to be valid, because it's
an inductive argument. But still, we can get pretty good reason
to believe that something's a necessary condition for death.
If we have enough cases with enough variety.
And that's what this positive necessary condition test is telling you.
What kinds of cases you need. What kind of variety you need.
Of course, the more cases and the more the variety, the stronger the reason,
because inductive arguments come in degrees but we've got at least some good
reason when these conditions are met. But if we've got both fish and red wine
as being necessary but not sufficient for death.
Well, what is sufficient for death? That's what we'll have to talk about in
the next lecture.