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Fundamentals: Necessary and Sufficient Conditions

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(intro music) Hi, I'm Kelley Schiffman! I'm a PhD student at Yale University. And today I want to talk about necessary [br]and sufficient conditions. We hear the words "necessary" and [br]"sufficient" all the time. "Merely taking the test isn't sufficient [br]for passing it." "The lawyer convinced the jury that there is sufficient evidence to [br]convict the accused." "Pain is a necessary part of every human[br]life." "Practice is really necessary for [br]success." But what exactly do these words mean? If P is necessary for Q, then Q cannot be[br]true unless P is true. Philosophers sometimes put this by saying[br]that Q is true only if P is true. Let's consider a case to helps us get [br]clear on this. What's necessary for getting accepted to [br]a university? Well, you might think that one necessary [br]condition is being human. You can only be accepted to a university[br]if you are human. Another necessary condition is submitting[br]an application. You can't get accepted to a university [br]unless you apply there. Another necessary condition is perhaps[br]having decent grades. Okay, so what about sufficient conditions? If p is sufficient for Q, then P's being [br]true is enough to make Q true. Philosophers often put this by saying that[br]if P is true, then Q is true. Now it's a little harder to think of a [br]sufficient condition for getting accepted to a university. But consider some seventeen year old who[br]just won the Nobel Prize in chemistry. Seems like that is pretty sufficient for [br]getting accepted to university. Now, necessary and sufficient conditions [br]come in all combinations. Here is an example of a necessary, but [br]not sufficient, condition. Steering well is a necessary condition[br]for driving well. You can't drive well unless you steer [br]your car well. However, steering well is not sufficient [br]for driving well, since steering well is not enough to make[br]it true that you are driving well. You could steer well but still drive badly[br]for other reasons. Here is an example of a sufficient but [br]not necessary condition. Boiling potatoes in water is a sufficient[br]condition for cooking them, since it's true that boiling potatoes is [br]enough to cook them. However, boiling potatoes in water is not [br]a necessary condition for cooking them, since you can cook them in many other [br]ways: frying them, grilling them, baking them, [br]roasting them. And finally here is an example of a [br]necessary and sufficient condition: getting all of the answers correct on a [br]test is necessary for getting a perfect score[br]on the test, because you will not get a perfect score [br]on the test unless you get all the answers correct. Getting all of the answers correct is also[br]a sufficient condition for getting[br]a perfect score, because getting all of the answers correct[br]is enough to get a perfect score. There is nothing else you must do in order[br]to get a perfect score. Subtitles by the Amara.org community