Now that we understand the distinction 
between sufficient conditions and 
necessary conditions, we need to ask how 
we can tell which conditions are 
necessary, and which conditions are 
sufficient. 
So we're going to have one pair of test 
for sufficient conditions, one pairs of 
tests for necessary conditions. 
For each of these we're going to have a 
positive test and a negative test. 
So for example, the negative test for 
sufficient conditions is going to tell 
you what's not a sufficient condition. 
And the positive test for sufficient 
conditions will tell you what is a 
sufficient conditions. 
One of these is going to be deductive and 
the other's going to be inductive. 
So let's go through these various tests 
one by one. 
First of all, you get the negative 
version of a sufficient condition test, 
which basically says. 
That something x is not a sufficient 
condition of something else. 
Why? 
If there is any case where x is present 
and y is absent. 
There don't have to be a lot of cases, 
just one. 
If there's any one case where x is 
present and y is absent. 
Then that shows you that x is not 
sufficient for y. 
This test is negative because it tells 
you what is not a sufficient condition 
for y. 
It does not tell you what is a sufficient 
condition for y. 
Basically it says if there's one case 
where X is present and Y is absent then 
that's a counter example of the 
generalization that whenever X is present 
Y is always present, because if Y is 
absent it's not present. 
So, we've now got basically an deductive 
arguement against the generalization that 
whenever X is present Y is present as 
well. 
And because it's deducted that means it's 
not defeasible. 
If you add other cases it doesn't matter. 
More information in the premises, the 
argument is still going to be valid. 
Because as long as you have one 
counterexample that shows that x is not 
sufficient for y because it's not the 
case that whenever x is present y is 
present. 
To see how this negative sufficient 
condition works, let's go through an 
example. 
Now the example we're going to talk 
about. 
Derives from the great comedy classic, 
airplane, with Lesly Neilson. 
So we have a link, that you can check 
out, if you want, and I warn you, there's 
some offensive parts of this comedy, and 
you all be ready for that. 
Partly, to avoid those essential parts, 
it also say that we can really get all 
the cases, straight, and specify them in 
the way we need to. 
We are going to use our own example. 
We are going to call it the banquet. 
So what happens, is that there are group 
of people who are eating together, and 
they eat a full meal. 
They have a soup course. 
They have a main course. 
They have some wine. 
Then they have dessert. 
And the meal goes pretty well until the 
end. 
Oh, that was great. 
I love the tomato soup. 
Yeah. 
This fish is to die for. 
Yeah and this wine, oh my gosh it's so 
good. 
I love the combination of both the fish 
and the red wine together. 
Yeah, it's so sad that the dinner is 
over. 
[SOUND] Oh man when I stood up, my 
stomach started hurting. 
Mine did too. 
Ohhhh, oh man. 
[SOUND] Oh, really? 
Yeah I think I'm dying. 
[COUGH] Ohhh, [COUGH] What's happening? 
You okay? 
Oh man what's making them all feel this 
way? 
The question is, what caused them to die? 
So we checked a number of different 
things, they weren't shot, they weren't 
stabbed. 
They were poisoned. 
Where was the poison? 
We checked their water glasses, and we 
checked for injection points, if somebody 
shot the poison through a seringe. 
None of that. 
So we figured the poison must have gotten 
to them through the food. 
And now, we need to look at all the 
different people who were at the banquet, 
and what each particular person ate at 
the banquet, in order to figure out which 
of these different food items was the one 
that killed them. 
So we have a little chart. 
Ann went to the banquet, Barney went to 
the banquet, and Cathy went to the 
banquet. 
So each of the rows on this chart 
indicates a different diner, a different 
person who ate at the banquet. 
And each of the columns indicates what 
they ate or drank. 
So one column is for the soup course. 
One column's for the main course. 
One column's for the wine, one's for the 
dessert. 
And then, of course, the last column to 
the right tells you whether they lived or 
died. 
And what we need to figure out is which 
of those food items or drinks is what 
caused their death. 
We're going to use the letter, y, to 
refer to the target feature, or the 
effect, the thing that is caused. 
And we're going to use the letter X to 
refer to the different candidates for the 
cause. 
And our question is, which candidate X is 
sufficient. 
For, the target Y. 
And the table with all the diners and all 
the courses, represents all of the data 
that we have available to us, to answer 
that question. 
So let's look first, at the very first 
course. 
The soup course. 
What does the soup course show us? 
Does it show us that anything is not 
sufficient for death? 
Yes. 
Shows tomato soup is not sufficient for 
death. 
Why? 
Because Anne had tomato soup and she 
didn't die. 
So it's not true that whenever you have 
tomato soup you die, since Anne had 
tomato soup and did not die. 
So that candidate X, tomato soup, is not 
sufficient for the target Y, death. 
Cathy shows the same thing, she shows the 
tomato soup is not sufficient for death. 
No. 
What do we learn from the main course? 
Do we learn that anything is not 
sufficient for death? 
Yes. 
We learned that chicken is not sufficient 
for death. 
Because Ann has chicken and doesn't die. 
And what does Cathy tell us is not 
sufficient for death? 
The case of Cathy tells us that beef is 
not sufficient for death. 
So, now we have a whole list of things 
that have been ruled out as sufficient 
conditions. 
Tomato soup, chicken and beef. 
And what about the wine course? 
What does Ann tell us in the wine course? 
Tells us that white wine is not 
sufficient for death. 
And what does Kathy tell us in the wine 
course? 
Red wine is not sufficient for death. 
And notice that it's Ann and Kathy that 
are giving us all this information about 
what's not sufficient, and that's because 
they didn't die, so anything that they 
ate or drank cannot be sufficient for 
death. 
But Barney did die. 
So, the things that he ate and drank 
still might be sufficient for death. 
They're not ruled out by the negative 
sufficient condition test. 
Of course, tomato soup was ruled out by 
the other cases. 
And red wine was ruled out by Kathy. 
But still, what about fish? 
Could fish be sufficient for death? 
It's not ruled out, right? 
It's not ruled out by the negative 
sufficient condition test because there's 
no case in this data, where somebody eats 
fish and doesn't die. 
But does that mean that eating fish is 
sufficient for death? 
No, cause this is just the negative 
sufficient condition test. 
It tells you whats not sufficient, it 
doesn't tell you what is sufficient, 
okay. 
But still, you want to look at the rest 
of the chart and figure, is there 
anything else is not ruled out sufficient 
condition. 
Well pie is ruled out as a sufficient 
condition because Anne had pie, is still 
alive. 
Kathy shows that ice cream is not a 
sufficient condition for death. 
But cake still might be a sufficient 
condition for death, for all we've read. 
So now we've got two candidates, fish and 
cake still might be sufficient conditions 
for death. 
They're not ruled out by the negative 
sufficient condition test but that 
doesn't mean they are sufficient for 
death. 
In order to conclude that they are 
sufficient conditions for death, we need 
to apply not the negative sufficient 
conditions but instead the positive 
sufficient condition test. 
The positive sufficient condition test 
tells us when we have a good reason to 
believe that X is a sufficient condition. 
What makes its positive is it tells you 
that you have a reason to believe that X 
positively is a sufficient condition, 
unlike the negative test. 
It says that you have a good reason to 
believe that X is a sufficient condition 
of Y, if all of the following conditions 
are met. 
Now I want to warn you, there are going 
to be four conditions and they have to 
all be met in order for you to reach a 
positive conclusion, or be justified in 
reaching a positive conclusion that X is 
a sufficient condition of Y. 
Now, the first condition is pretty 
simple. 
It simply says, we have not found any 
case where x is present, and y is absent. 
Basically, it says, you've already passed 
the negative part of the sufficient 
condition test. 
You can't rule out x as a sufficient 
condition on the basis of any cases. 
The second part says that we've tested a 
wide variety of cases. 
Including cases where x is present, and y 
is absent. 
And the reason that we have to have this 
condition, is that, without it, we could 
reach really silly conclusions much too 
easily. 
For example, on the basis of the data 
that we looked at before. 
We could reach the conclusion that pea 
soup is sufficient. 
Because there wasn't a single person who 
had pea soup and didn't die. 
There can't be a case where somebody had 
pea soup and didn't die, if there isn't a 
case where somebody had pea soup. 
That's why we have to check cases where X 
is present. 
Similarly, imagine that the only case 
that we knew was Barney. 
Right? 
And that means that nobody lived. 
Everybody died. 
Well, if everybody dies then we don't 
have any cases where somebody had tomato 
soup and didn't die, or where somebody 
had fish and didn't die or where somebody 
had beef and didn't die or where somebody 
had cake and didn't die. 
Whatever they had they died because 
everybody died. 
So if everybody dies, it's really hard to 
tell which of the different candidates is 
the one that's really causing the death. 
So that's why we have to have some cases 
where X is present, that is where the 
candidate that we're testing is present. 
And other cases where the target feature, 
Y, is absent. 
And that's what the second part of the 
positive sufficient condition test tells 
you that you need. 
Those two clauses are pretty tricky, but 
the next ones more important and its also 
a little bit trickier. 
What it says is that, if there are any 
other features that are never present or 
y as absent, then we've tested cases 
where those other features are absent but 
x is present. 
this can be confusing but the basic idea 
is that if there are two competing 
hypothesis, two competing candidates for 
sufficient condition, and neither one is 
ruled out by the negative sufficient 
condition test, then need to look at 
cases that will decide between those 
hypothesis. 
Now in our example we saw that neither 
fish nor cake is ruled out as the 
sufficient condition. 
And if we want to decide whether it's 
fish or cake, this really is a sufficient 
condition. 
Then what we need to look at is a case 
where fish is present, but cake is not. 
And a case where cake is present, but 
fish is not. 
We can't be sure from the first three 
cases because we don't have that 
combination of fish and cake. 
So we have to do a little more research. 
And luckily for us, not for them of 
course because one of them dies. 
So luckily for us Doug and Emily were 
also at the banquet. 
And Doug had tomato soup, beef, red wine 
and cake and lived. 
Emily had tomato soup, fish, red wine, 
pie and poor Emily died. 
The crucial thing here is that Doug had 
cake but not fish, and Emily had fish but 
not cake. 
Now, did these cases help us determine 
whether cake is sufficient for death? 
Yes, because one of these new cases rules 
out cake as a sufficient condition of 
death. 
Which one does that? 
Well it's Doug, because by the negative 
sufficient condition test, Doug had cake 
and didn't die, so that shows you the 
cake is not sufficient for death. 
Now does Emily rule out anything as a 
sufficient condition for death? 
No. 
Why not? 
Well, because she died. 
And if somebody dies they can't rule out 
something that's sufficient condition for 
death. 
Cases of death can't rule out what's 
sufficient for death, because to rule it 
out, you need a case where the candidates 
present and the targets not present. 
Okay? 
So the cases that rule out something as a 
sufficient condition of death are going 
to be the cases without death. 
Anyway, fish still might be a sufficient 
condition for death. 
So fish seems to be the only remaining 
candidate because we ruled out cake. 
So fish is the only remaining candidate 
for a sufficient condition, at least 
among those on the list. 
Now, we can conclude fish is a sufficient 
condition for death. 
Right? 
No, because remember, I told you, I 
warned you, there could be four 
conditions. 
We need all those conditions to be met in 
order for us to be, reasonably conclude 
that something sufficient in this one 
more to come. 
But why do we need more? 
The answer really is that. 
We don't know whether all the different 
features that might of caused the death 
are on our list. 
We've only looked at the soup course, the 
main course, the wine and the dessert. 
It might be something else. 
So we need to add one more clause. 
This last positive clause to our positive 
sufficient condition test. 
Namely that we've tested enough cases of 
various kinds that are likely to include 
a case where x is present and y is absent 
if there is any such case. 
So this cause is obviously going to be 
hard to apply. 
Right, it's not mechanical. 
How do we know that whether we've tested 
enough cases of various kinds? 
We have to know what kinds of things can 
cause death, and which kinds of things 
that can't cause death. 
That's going to depend on background 
conditions, background knowledge, right? 
We need to know something about potential 
causes of death, what can and cannot 
cause death. 
And we need to take that for granted in 
applying this last cause, so it's not 
going to be simple at all. 
But if we do know that there has to be 
some sufficient condition. 
I mean after all, people just don't die 
for no reason. 
And if we know that nothing else could be 
a sufficient condition, because maybe we 
checked the water and we looked for 
syringe marks and there were no bullet 
holes and so on. 
Then we have to have at least some reason 
to believe that the sufficient condition 
must be somewhere among the features that 
we're testing. 
Some people might say it's something 
else. 
After all, could be, I've got an idea. 
It could be the fact that both Barney and 
Emily both have the letter E in their 
name. 
But, you know that's not going to cause 
their death. 
That's just common sense, background 
knowledge. 
We looked at their glasses. 
There was no poison in their glasses. 
So, we have at least some reason to 
believe that the sufficient condition 
must lie somewhere among the features 
that we're testing. 
Now, this argument is not deductive. 
If something fails in negative sufficient 
condition test, then it's valid to 
conclude that, that candidate is not a 
sufficient condition for that target. 
But if something passes the positive 
sufficient condition test, then the 
argument's not valid. 
It's possible still that this is not 
sufficient and that argument, namely an 
application of the positive sufficient 
condition test, can be undermined by 
future data. 
It's defeasible like all inductive 
arguments. 
For example, we haven't mentioned Fred, 
Gertrude and Harold yet. 
And what do they show? 
Well wait a minute, Gertrude. 
Shows that fish is not sufficient after 
all. 
Notice that all the data before Fred, 
seem to a point of conclusion, that fish, 
was sufficient for death, but it just 
take ones more case, go through, to show 
that fish is not really sufficient for 
death afterall. 
That shows that it is an inductive 
argument, and that means that its going 
to be diffusible. 
Still, of'course, the inductive argument, 
can be strong, if w have enough. 
Data, we've looked at enough cases. 
And our background knowledge really is 
reliable. 
So, we're not saying that inductive 
arguments are no good, but the point is 
that their defeasible. 
Their going to be better when we've got 
more data, when our background 
assumptions are more reliable. 
And strength then is going to be a matter 
of degree and can go from slightly strong 
to very strong. 
In this case, because of Gertrude, we 
know that fish is not sufficient. 
So I have to think more about what still 
could be sufficient. 
But first, let's ask what's necessary.