大家好 我是Kelley Schiffman
Hi, I’m Kelley Schiffman!
I’m a PhD student at Yale University.
And today I want to talk about necessary and sufficient conditions.
We hear the words “necessary” and “sufficient” all the time.
比如 “就这么参加测试 不足以通过”
“Merely taking the test isn’t sufficient for passing it.”
“The lawyer convinced the jury that there is sufficient evidence to convict the accused.”
“Pain is a necessary part of every human life.”
“Practice is really necessary for success.”
But what exactly do these words mean?
If P is necessary for Q, then Q cannot be true unless P is true.
Philosophers sometimes put this by saying that Q is true only if P is true.
Let’s consider a case to helps us get clear on this.
What’s necessary for getting accepted to a university?
Well, you might think that one necessary condition is being human.
You can only be accepted to a university if you are human.
Another necessary condition is submitting an application.
You can’t get accepted to a university unless you apply there.
Another necessary condition is perhaps having decent grades.
Okay, so what about sufficient conditions?
If P is sufficient for Q,
then P’s being true is enough to make Q true.
哲学家们通常将其称为 如果P对 则Q对
Philosophers often put this by saying that if P is true, then Q is true.
Now it’s a little harder to think of a sufficient condition
for getting accepted to a university.
But consider some seventeen year old who just won the Nobel Prize in chemistry.
Seems like that is pretty sufficient for getting accepted to university.
Now, necessary and sufficient conditions come in all combinations.
Here is an example of a necessary, but not sufficient, condition.
Steering well is a necessary condition for driving well.
除非控制好车子 否则 不可能开得好
You can’t drive well unless you steer your car well.
However, steering well is not sufficient for driving well,
since steering well is not enough to make it true that you are driving well.
你可能控制得好 但由于某些原因 仍驾驶不好
You could steer well but still drive badly for other reasons.
Here is an example of a sufficient but not necessary condition.
Boiling potatoes in water is a sufficient condition for cooking them,
since it’s true that boiling potatoes is enough to cook them.
However, boiling potatoes in water is not a necessary condition for cooking them,
since you can cook them in many other ways:
煎 炸 烘 烤
frying them, grilling them, baking them, roasting them.
And finally here is an example of a necessary and sufficient condition:
getting all of the answers correct on a test
is necessary for getting a perfect score on the test,
because you will not get a perfect score on the test
unless you get all the answers correct.
Getting all of the answers correct is also a sufficient condition
for getting a perfect score,
because getting all of the answers correct is enough to get a perfect score.
There is nothing else you must do in order to get a perfect score.
Subtitles by the Amara.org community
大家好 我是Kelley Schiffman