Last time we ended with a bit of mystery. We concluded that, fish might still be
necessary and not sufficient for death, and red wine might be necessary but it's
certainly not sufficient for death. And the question is well, if neither of
those is sufficient, what is sufficient. To answer that question, we've gotta look
at complex conditions. Now, complex conditions are just,
conditions or features or candidates, that are combinations of other candidates
or features or conditions. They might be, a negation, not having
fish. They might be a disjunction.
Having either fish or beef. But we're going to look at conjunctions,
that is having some combination of two or more of the food and drink at the
banquet. And we're going to understand these in
exactly the same way we understood the simple or atomic, conditions or features,
or candidates. So for example, we're going to use the
same definition of the sufficient condition.
F is a sufficient condition for G. Well what that means is that whenever F
is present so is G and then we're going to have a negative test for a
sufficient condition. This is just reminding you of couple of
lectures ago that X is not a sufficient condition of Y there is of a certain
target like death if there is any case where X is present and Y is absent.
And notice since we used X and Y as variables, you can stick anything in for
them. So, to get a conjunctive, condition,
we're going to simply substitute in the conjunction W and X.
So, W and X, that combined conjunctive candidate, is not a sufficient condition
for Y, if there's any case where both W and X are present, and Y is absent.
Just like in the other cases, but we're just using a conjunction to replace one
of the variables. And we can look at our data from before
to determine which conjunctions are and are not sufficient conditions for death.
So are there any conjunctions that still might be sufficient conditions for death.
What about tomato soup and chicken. Maybe when you have tomato soup and
chicken together that'll kill you. Nope, that can't be.
Why not? Which case rules out the conjunction of
tomato soup and chicken as a sufficient condition of death?
Anne does, because Ann had tomato soup and chicken but she didn't die.
What about. Red wine and cake.
There's red wine and cake together as a combination, as a conjunction.
Is that sufficient for causing death? Well it caused death, or it was related
to death, in the case of Barney. But is there another case where you have
red wine and cake without death? Look down the list and you'll see, it's
Doug. Doug shows us that red wine and cake are
not sufficient for death. Now, which conjunctions are not rule out
as sufficient conditions for death? Wow what about fish and red wine?
Could that be sufficient? Well Barney has fish and red wine and he
dies. And Emily has fish and red wine and she
dies. And Fred has fish and red wine and he
dies. And there's nobody else that has fish and
red wine who doesn't die.'Cause there's nobody else who has fish and red wine
other than those three. So it looks like fish and red wine might
be a sufficient condition for death. Okay what about fish and cake?
Could that be sufficient? Yeah so far that could be sufficient as
well. Fish and cake.
Barney has them and dies. Fish and cake.
Fred has them and dies. So fish and cake might be a sufficient
condition, of death, according to the data that we have so
far. So let's look next in what's necessary,
because the same points are going to apply.
We're going to take the definition of a necessary condition.
F is a necessary condition for g, if whenever, f is absent, g is absent.
We're going to use the same old negative test of a necessary condition.
X is not a necessary condition of y. If there's any case where x is absent but
y is present, because that shows that x is not necessary for y.
And all we have to do is to substitute a conjunction in for the variables X and Y,
in order to apply this test to conjunctive cases.
So, a conjunction W end X is not necessary for Y.
If there's any case, where you have that conjunction both w and x.
As being absent and yet y is present. So now we have a negative test for
conjunctive necessary conditions. Let's go back to our data.
Is leek soup and fish necessary for death?
No. Well, who shows that? Barney, because Barney dies without
having leek soup and fish. Is there any other case that shows that?
Yeah, Emily shows that, because she died without having leek soup and fish.
So that combination is not necessary for death.
Okay, so Barney and Emily, show that leek soup and fish is not necessary for death.
What about tomato soup and fish? They both had tomato soup and fish, so
maybe tomato soup and fish is necessary for death?
Because that work, no because if Fred, Fred dies without having tomato soup and
fish because he has leek soup and fish. So Fred shows up a combination tomato
soup and fish is not necessary for death. Because you can die without that
combination if you have leek soup and fish instead.
So neither of those combinations is necessary.
What might be necessary? Which combination is not ruled out as
necessary? Well, here is one.
They should red want. Fish and red wine might be necessary for
death, because everybody who died at this banquet had fish and red wine.
There was nobody who died without having fish and red wine, so fish and red wine
is not ruled out as a necessary condition of death.
The wait a minute. Fish and red wine was also not ruled out
as a sufficient condition for death, because everybody who had fish and red
wine together, died. That means that this particular
combination, fish and red wine, is both necessary and also sufficient for death,
at least given the data that we have so far.
I won't go through developing the positive tests for conjunctions because
its going to be just like the positive necessary condition test at the positive
sufficient condition test that we went through in previous lectures you just
substitute conjunctions for the very well set you get those test.
But it looks like for the data so far we've got at least some reason to believe
that fish and red wine is necessary for death and also sufficient for death.
Great, now we know which combination meets those tests, but what does that
tell us. We don't know any mechanism.
Right? Why would fish and red wine cause death.
Well obviously these people die to bet taste, the chef could put all afternoon
on the fish, kept stand effective people might eat his beautiful fish and have red
wine which is going to destroy the taste of the dish.
So anybody order the red wine with the fish poisoned him.
That would be the mechanism for why everybody who had fish with red wine
died. You know, there might be some other story
about how some chemical in the fish interacted with the red wine.
But if you can rule that out from background knowledge we've got a pretty
good reason to belief that somebody back there in the kitchen probably the chef
was the one who was mad at them, poisoned them.
They died of bad taste. Now we need more research to be sure.
We need lots more candidates. We need to test various combinations,
but that's just an inductive argument. Inductive arguments never make you
absolutely certain that the conclusion is true.
they're defeasible. They're not valid.
We know all that. But at least we have some evidence to
believe that fish and red wine is necessary and sufficient for the death.
That's what caused these people to die. And it's the chef, who ought to go to
jail. We've gone through one example in some
detail but like many other things in this course, the best way to learn this
material is to practice, practice, practice.
So let me give you a little hint. You can create all the exercises you
would ever want just by taking the chart that we've looked at in the last couple
of lectures that goes from Ann through Harold.
And change what each of them had in the soup course, or what each of them had in
the main course, or what each of them had in the line course, or what each of them
had in the dessert course. Or changed which ones lived and which
ones died. And you can create more examples to
practice the necessary condition tests and the sufficient condition test.
Hey, if you want to know whether you got it right, bring your chart and your
answer to the discussion forums, and the other students in the course can
help you out by telling you whether they agree about what's necessary and
sufficient, in the setup that you created.
So if all you students out there in coursairea land, practice, practice,
practice by changing the banquet to change your own specifications.
The you'll all learn better, how to distinguish necessary and sufficient
conditions and how to test for necessary and sufficient conditions.
So go off and have some fun with it