Sufficient and Necessary Conditions

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• 1 Like

  Steven_B-1 Member

  August 2022 800 karma

  Forget about the contrapositives for a second, just remember that if you're tackling a sufficient assumption question, whichever answer choice you pick should convince you 100% that the conclusion is true.

  So if i say: X likes sweet stuff. Therefore, X likes ice cream.

  You should immediately be thinking what?? but just because they like sweet stuff doesn't mean they like ice cream. A sufficient assumption will lead you to the conclusion without a shadow of a doubt.

  The SA here could be: Anyone who likes sweet stuff likes ice cream

  Plugging that statement into our original argument will make the conclusion 100% true.

  On the other hand, A necessary assumption is anything that is needed just to keep the argument "alive." You don't have to prove that the conclusion is true and that's where you can distinguish both concepts (yes they can overlap but that's rare). A necessary assumption can be any seemingly insignificant detail that is needed to give the argument a chance just to survive. These can be very "dumb" and "obvious" things but the dumber and simpler, the better.

  So coming back to our original example above. Let's try to identify some necessary assumptions. I'll give you examples:

  --- X exists. (cause otherwise what the hell is the argument talking about? If X doesn't exist then we have to throw the whole argument out the window )
  --- Sweet stuff exists. (same as above, if sweet stuff doesn't even exist, then why are we talking about some inexistent thing?)
  --- Ice cream exists. (same as above ).

  Those may seem obvious and silly but those are all things that we are assuming and that necessarily have to be true just for the argument to have a chance.

  Let's do some others that are not so obvious.

  --- X has the ability of liking things. (because if X did not have the ability of liking things then how could the argument even have a shot of being right)

  -- It is not impossible for someone to like sweet things and ice cream at the same time. (this basically says it is possible for you to like sweet things and ice cream). That's necessary because otherwise the argument completely falls apart.

  -- It is possible to like more than one thing. (similar to the one above and also necessary because otherwise you could never reach the conclusion).

  Etc.....

  Hope this helps!
• GoTribe21 Member

  August 2022 edited August 2022 62 karma

  The sufficient assumption makes sense but still slightly confused about a necessary assumption. So in an example where " if x --> y. and the conclusion is y therefore, x. Which variable is the necessary condition? X is the SA because you need it in order to get to y but I don't understand how NA plays a role in this case.

  Disregard, I figured it out The necessary condition has to be introduced.
• Steven_B-1 Member

  August 2022 800 karma

  Okay good, you got the SA down. It's what we need to prove that the conclusion is 100% valid.

  Now, during NA questions, we are trying to identify things that are necessary to keep the argument alive and they are things that we are already assuming. Hence why it is called a necessary assumption.

  Don't confuse a necessary condition with a necessary assumption. Neither of X -> Y are necessary assumptions. Think about necessary assumptions more intuitively and think about them in the context of an argument.

  Okay so forget about conditionals and let's look at the following argument.

  I am the best employee because I work faster than everyone.

  Now let's identify things that must be true if my argument is to have a fighting chance. Remember, I am not trying to prove it 100% correct, I'm just identifying the assumptions that I necessarily made.

  It must be true that:

  • I am employed (The argument never explicitly says I am employed anywhere but we are obviously assuming that, otherwise the argument makes no sense).

  • I have the capacity of working faster than at least someone. ( This has to be assumed aka a necessary assumption, because otherwise how could I ever conclude that im the best on the basis of being faster than others?).

  -Being faster than others is relevant to being the best employee. (This has to be true otherwise the argument falls apart because my only evidence for claiming to be the best was to mention my speed relative to others).

  Both of these statements are statements that MUST be assumed for the argument to hold any water, therefore they are necessary assumptions.

  Let me give you an example of what is NOT a necessary assumption:
  I arrive at my job before every other person. (the argument says that I am the best because i am faster, therefore arriving first or last doesn't have to be true).
  I earn more money than everyone at my job. (what does money have to do with the argument?? nothing so it cannot be a necessary assumption.
  I'm so LSAT obsessed that I enjoy answering forum questions on 7sage. (completely irrelevant and therefore not necessary)

  NONE of those statements are necessary for the argument.

  LMK if this helps. I think NAs are difficult at first because we're not used to identifying the basic assumptions we all employ on a daily basis but once you practice a bit, it'll click.
• teechj117 Alum Member

  August 2022 edited August 2022 296 karma

  Synonyms can help when you're first trying to grasp these concepts. My prof in uni would refer to "sufficient" and "necessary" in terms such as "antecedent" and "consequent", respectively. Another one is "certain" and "required". If this helps, use it, if not, don't worry.

  You're also not alone in being stuck with SA and NA questions. I thought of them being the most difficult to understand when you're introduced to them. Drilling can help, but I thought of it to be extremely frustrating when these concepts weren't sticking. Highly recommend @Steven_B-1's breakdown, but also writing down sufficient and necessary assumptions following a premise or argument. You actually do necessary and sufficient assumptions all the time without thinking about it, but now it's time to draw a line in the sand of your mind and do some conscious sorting.

  It's okay to move on and not have a complete understanding of that section, because you'll actually be called to understand sufficiency and necessity in different ways with logic games. Don't let that intimidate you. It will help you. Give yourself time, and be kind to yourself. You got this