Transcript for:
Exploring Necessary and Sufficient Conditions

when we consider arguments in the bigger picture good reasons for our beliefs sort of the core of critical thinking we should understand when conditions are necessary or sufficient and how necessary and sufficient conditions might differ let's start with necessary conditions think of it this way if a is necessary for B then B cannot be true unless a is true in other words B is true only if a is true a necessary condition for streaming a YouTube video is having an internet connection you can only stream a YouTube video if you have an internet connection a necessary condition for becoming president in the United States is being at least 35 years of age you can only become president if you are at least 35 years old the conclusion is only true if the necessary condition is true you cannot have be without a but sometimes a condition automatically establishes a certain conclusion which is actually a different concept that we call a sufficient condition if a is sufficient for B then a being true by itself is enough to make be true or to put it another way if a is true then B is true if a then B if you have access to YouTube you can watch the David Pakman show if a US presidential candidate wins 270 electoral votes he or she has enough electoral votes to become President a necessary condition for a conclusion is not always sufficient for that same conclusion and vice-versa a sufficient condition for a conclusion is not always necessary here's an example of a condition and that is necessary but not sufficient by itself for someone to become a United States Supreme Court justice it is necessary for them to be appointed by the president but that's not sufficient they must also be confirmed by the US Senate here is a condition that is sufficient but not necessary being born on US soil is sufficient for status as a US citizen but it is not necessary many people like me are born in other countries and become naturalized US citizens later in life some conditions are both necessary and sufficient for a conclusion this would mean that the conclusion statement is true if and only if the condition is true being an unmarried male is both a necessary and sufficient condition for being a bachelor for example you can't visit the capital of California unless you go to Sacramento you can't win a US presidential election with 538 electoral votes unless you win all of every state's electoral votes having 538 votes requires winning all electoral votes in every state so winning all of every state is a necessary condition and winning all the electoral votes in every state automatically establishes that you have won 538 electoral votes so it's also a sufficient condition there's nothing else you must do in order to win 538 electoral votes in science a necessary and sufficient event is considered a cause and the resulting event is considered the effect some conditions are neither necessary nor sufficient for the conclusion being a lawyer is neither necessary nor sufficient for being a politician many politicians are not lawyers and being a lawyer does not ensure that you will be a politician so it's important to be able to discern when these are being misused when a sufficient condition is being mistaken for a necessary condition or vice-versa understanding the difference between these types of conditions and their applications to arguments is another fundamental skill in recognizing good and bad arguments in yourself and in others this miniseries has been made possible in part by brilliant you're watching this video so chances are you have genuine interest in logic philosophy and problem-solving want to further your mastery you should check out this fascinating online learning service with brilliant you can solve hands-on puzzles and problems developed by professors and expert professionals from all over the world brush up on your skills when it comes to logical fallacies syllogisms deductive reasoning game theory and other domains of philosophy math and science quickly become and all-around better thinker sign up for free by going to brilliant org slash critical thinking I've put a link in the description under this video and the first 200 people who visit brilliant org slash critical thinking will get 20% off an annual Premium Membership visit brilliant org slash critical thinking