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批判性思维基础:必要条件与充分条件(补充)

CRITICAL THINKING - Fundamentals: More About Necessary and Sufficient Conditions [HD]

(片头音乐)
(intro music)
大家好 我是凯利·希夫曼
Hi, my name is Kelley Schiffman.
现在在耶鲁大学读研
I’m a graduate student at Yale University,
今天我要再讲一点
and today I’d like to talk a bit more
必要和充分条件的知识
about necessary and sufficient conditions.
我们以前已经讨论过
Now, this video builds somewhat on the
必要条件和充分条件
discussion of necessary and sufficient
今天接着讲
conditions in my previous video on the topic.
所以 我们先快速复习一下
That said, let’s review quickly.
如果说p是q的必要条件
To say that p is a necessary condition for q
就是说只有p成立 q才成立
is to say that q is true only if p is true.
我们也可以说得通俗点
We can put this in more ordinary terms,
就像很多观众经常会说
as one of our viewers did, by saying that
p是q必需的 因为
p is necessary for q because
要想让q成立需要p先成立
p being true is needed for q to be true.
如果说r是s的充分条件
To say that r is a sufficient condition for s
就是说如果r是正确的 s也正确
is to say that if r is true, then s is true.
换句话说 r是s的充分条件
In other words, r is sufficient for s
因为只要有了r就能实现s
because r is all you need to get s.
r足够让你获得s
r is enough to get s.
必要条件和充分条件有四种组合方式
Now, there are four possible combinations of necessity and sufficiency.
有充分必要条件
We can have necessity and sufficiency together.
必要不充分条件
We can have necessity but not sufficiency.
充分不必要条件
We can have sufficiency but not necessity.
还有一种可能性
And we can have a case where we have
既不充分也不必要条件
neither necessity nor sufficiency.
我们来分别看下例子
Let’s look at an example of each.
下面这个例子
Here’s an example where we have a
我们用到了
necessary and sufficient condition
充分必要条件
for some outcome.
我走进一家快餐店
I walk into a fast food restaurant.
点了一份薯条
I place an order for some french fries,
并付了钱
and pay for those fries.
此时 点餐和付款
Now, my placing that order and paying for
就是我得到薯条的
the fries is both necessary and sufficient
充分必要条件
for receiving them.
必要性表现在如果我不点餐或者不付款
Necessary, because they’re not going to
他们就不会给我
give me the french fries unless I order
这些薯条
them and pay for them.
充分性表现在我只需要做这些
And sufficient, because that’s all I have to do.
只需要点餐并付款
I just have to order them and pay for them,
就能得到薯条
and I’ll get them.
当然 我得提醒一下
Of course, there’s a caveat here.
当我说点餐和付款
In saying that ordering and paying for the
是得到薯条的充分必要条件时
fries is both necessary and sufficient,
实际上有一个前提假设
I’m making certain background assumptions.
前提是 比如说
I’m assuming, for example, that there’s
没有流星会在接下来的几秒
not going to be a meteor hitting the
撞击这家餐馆
restaurant in two seconds, because if that
如果真发生了 点餐和付款
were the case, then my ordering the french
就不再是得到薯条的
fries and paying for them would not be
充分必要条件了
sufficient for my receiving them, since
因为餐馆几秒内就会被撞飞 我是等不到薯条了
the restaurant will be destroyed in two seconds, before I can ever receive them.
同样的 还得假设
Similarly, I’m assuming that the
今天餐馆的薯条不是免费的
restaurant isn’t giving away free fries today.
如果免费 付款实际上
If they were, then my paying for the fries
就不是得到薯条的必要条件了
would not, in fact, be necessary for receiving them.
记住关键的一点
Now, there’s an important lesson here,
无论何时 当我们
which is that any time we assess the
判定充分必要条件时
necessary and sufficient conditions for an
都要做类似的前提假设
outcome, we make these sorts of background assumptions.
一些约定俗成的前提
We take certain things for granted.
现在 再考虑一下
Consider, now, a condition that’s
必要不充分条件
necessary, but not sufficient.
举这样的例子要相对简单一点
It’s relatively easy to come up with these sorts of examples.
我们可以想一些这样的事情
All we have to do is come up with
它们为另一些事情所需
something that’s needed for something
但又不够
else, but not enough for it.
例如 适度的锻炼
A moderate degree of exercise,
对保持健康来说是必须的
for example, is necessary for staying healthy.
但是还不够 因为还需要
It’s not sufficient, because some other
一些别的事 比如健康饮食
things are necessary – a good diet, for example.
现在 再来说说充分不必要条件
What, now, about sufficient, but not necessary, conditions?
我的小狗泰迪特别容易被逗乐
Consider my dog Teddy, who’s really easy to make happy.
给它一点吃的就够它开心了
Giving him a treat is sufficient to make him happy.
但这不是充要条件
It’s not necessary, though, since there’s
因为让它开心的方法有很多
lots of other ways to make him happy.
扔给它一个球也能让它开心
Throwing a ball for him is also enough to make him happy.
还可以挠它的肚子
Or I could scratch his belly.
所有的这些事情都是
All of these activities are sufficient for
让泰迪开心的充分条件 因为
Teddy’s happiness, since each of them is
每一件事都足以让它开心
enough to make him happy.
但没有一件是必须的
But none is necessary, since there are so
因为有很多不同的方法让它开心
many different ways to make him happy.
最后 我们再来看下
Finally, let’s consider conditions that
既不必要也不充分条件
are neither necessary nor sufficient.
比如说
Here’s an example.
我想要一块蛋糕
I want a piece of cake.
所以我去厨房
So I go into the kitchen, and I mix a
把做蛋糕的配料全混合到碗里
bunch of ingredients for the cake together in a bowl.
但这并不是得到蛋糕的充分条件
Now, that alone is not sufficient for my
因为我还需要
getting a piece of cake, because I still
搅拌它们 把它们放进烤盘里
have to stir those ingredients, put them in a pan,
再放进烤箱里烘焙
put them in the oven, bake the cake.
混合这些配料也不是
Mixing those ingredients is also not
得到蛋糕的必要条件
necessary for my getting a piece of cake.
为什么?
Why not?
因为我可以很轻易地
Well, because I could just as easily walk
到街上买一块蛋糕
down the street and buy a piece of cake.
现在我们来考虑这个问题
Let’s turn, now, to consider the question
为什么必要条件 充分条件很重要?
of why necessary and sufficient conditions are important.
为什么我们要弄清它们的区别?
Why is it important that we be clear on this distinction?
原因之一是 我们总是
Well, one answer is that we tend to
混淆必要条件和充分条件
confuse necessary and sufficient
有时甚至会造成小麻烦
conditions all the time, sometimes with harmful results.
这是一个来自生活中的真实案例
Here’s an example pulled from real life.
莎拉 汤姆和博比同时出现在案发现场
Sarah, Tom, and Bobby are all found at the
现场还有一把非法枪支
scene of a crime, along with an illegal gun.
莎拉以非法持枪罪被起诉
Sarah is charged with possession of the
在法庭接受审讯
gun, and brought to trial on that charge.
莎拉的律师坚称她是无辜的
Her attorney argues that Sarah’s innocent,
因为枪其实是汤姆的
because the gun actually belongs to Tom.
在陪审团商议结果之前
Now, before the jurors deliberate,
法馆对陪审团说:
the judge tells them the following:
“如果你们判定枪是汤姆的,
“If you decide that the gun belongs to
就必须判决莎拉无罪”
“Tom, then you must judge Sarah to be innocent.”
陪审团商议之后
The jurors deliberate,
判定枪不是汤姆的
they decide that the gun does not belong to Tom,
由此 他们判定莎拉有罪
and on that basis alone, conclude that Sarah is, in fact, guilty.
判定她非法持枪
That is her illegal gun.
如果我们停下来想一想 就会发现陪审团犯了一个巨大的错误
Now, if we pause, we see the jurors made a huge mistake.
他们把必要条件当成了充分条件
They confused a sufficient condition with a necessary one.
如果枪是汤姆的
If the gun belongs to Tom, that’s a
这将是莎拉无罪的充分条件
sufficient condition for Sarah’s innocence.
但不是必要条件
It’s not necessary, though.
即使枪不是汤姆的 莎拉也可能无罪
Sarah could be innocent even if the gun does not belong to Tom.
还有一点可以证明莎拉无罪
There could be another reason for her innocence.
比如 如果枪是
For example, if the gun belongs to some
第三个人 即鲍比的
third person – Bobby, for example.
因为陪审团将必要条件
Because the jurors confused a sufficient
当成了充分条件
condition with a necessary one,
他们忽视了这种可能性
they overlook this possibility,
武断地将莎拉定罪
and so hastily convicted Sarah.
如果你对这类的故事感兴趣
If you’re interested in this sort of
我强烈推荐你去affirming the consequent上
mistake, I highly recommend that you check
观看马修·哈里斯的视频
out Matthew Harris’s video on affirming the consequent.
我们对必要条件和充分条件
Now, a very different sort of reason
这么感兴趣
that we’re interested in necessary and
还有一个原因
sufficient conditions is that they can
就是它可以帮助我们去认识事物
help us figure out what things are.
它们是怎么帮我们的 看这个例子
To see how this works, consider a simple case:
正方形是个什么东西?
what sort of thing is a square?
想要弄清这个问题
We can begin to answer this question by
我们可以列出正方形的所有必要条件
articulating all the necessary conditions for being a square.
第一个必要条件是它是个平面图形
One necessary condition is that it’s a plane figure.
另一个是它有四条边
Another is that it have four sides.
第三个必要条件是
A third necessary condition is that those
每一条边都是等长且笔直的
sides are equal and straight.
最后一个必要条件 它有四个直角
And finally, it’s necessary that it has four right angles.
当我们把所有的必要条件放在一起
When we put all these necessary conditions
就得出了正方形成立的充分条件
together, we get the sufficient condition for being a square.
实际上我们已经得出了正方形的定义:
Indeed, we get the definition of a square:
正方形就是有四个等长笔直的边
a square is a plane figure with four
四个直角的平面图形
equal, straight sides and four right angles.
当然 不是所有的概念
Now, of course, not all concepts are as
都像正方形这样容易讲清
easy to get a handle on as the concept of a square.
想想公平 平等 幸福这些概念
Consider the concepts of fairness, or equality, or happiness.
它们比正方形这样的概念
These concepts, unlike the concept of a
更模糊 起码更具争议性
square, are a lot fuzzier, or at least more controversial.
我们在关于什么是公平
We disagree over what fairness is and over
什么是幸福的问题上观点不同
what happiness is, and having a good
而且 正是由于对它们的必要条件
grasp on the difference between necessary
和充分条件的理解不同
and sufficient conditions allows us to
才让我们一直在探索它们的真谛
start making progress toward figuring out what they are.
给你们留一个任务
I’ll leave you, then, with the task of
试着提出幸福的
trying to come up with the necessary and
必要条件和充分条件
sufficient conditions for happiness.

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视频概述

介绍了必要条件和充分条件及它俩的四种组合方式。

听录译者

收集自网络

翻译译者

研究僧

审核员

NL

视频来源

https://www.youtube.com/watch?v=9uOF3AZI_Gc

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