Negations - Every/IF

A Daring Doughnut

Hello everyone! I was curious about using IF/Every with negations. I understand that you essentially negate the necessary variable in the sentence and move on ward (These are the quiz's im talking about https://7sage.com/lesson/quiz-negation-4-answers/ Q.2). My question is that when we look at every as a sufficient in group one, we never had a negation attached to it. When do I know to negate the premise after every and when do I know to take it face value as in previous lessons? Unless I missed it, we were never taught why we are suddenly not taking every at face value as the sufficient and leaving it at that?

KevinLuminateLSAT

Consider the statement "Every banana is yellow". This means, "If banana -> yellow". What if you wanted to say that this statement was not true, or in other words, that "It is not true that every banana is yellow"? In that case, you are saying that "Some bananas are NOT yellow", or that "Even if something is a banana, it might NOT be yellow." This is an example of negating the original conditional statement. To negate it, we say that the sufficient condition CAN be true even when the necessary condition is NOT true.

Please note that if there is nothing that requires you to think about the negation of a conditional relationship, then you don't need to do the process that I described above. So that may be the source of your confusion. When you were first learning about "every" you didn't negate the statement because you were learning what "every" means. Now, you're learning about what "NOT every" means.

Jerry

You negate by adding a "not."

I find it most useful to just recite out loud a comeback in a sassy manner. You'll probably intuitively be able to figure out where to place the negation. It's a relatively natural process. At least for me...

So, the statement is "Every snowman is white." The negation would be. "Um, no, that's not true. Not every snowman is white. Some of them are yellow."

And it works for everything else, too.

"If you teach a man to fish, you will feed him for a lifetime."

"Girl, no, stop playing with me. Tina taught my uncle how to fish, and she stopped feeding him as soon as they got divorced. So, if you teach a man to fish, he still might not be getting any dinner."

Jonathan Wang

I don't think he's asking how to negate a statement. I think he's asking why, after being told we have to take statements at face value, we are suddenly trying to negate them or otherwise manipulate them.

The answer is that you're mixing concepts. It is true that we need to take whatever we've given as a true undeniable fact. That will never change. However, in order to evaluate an argument, you often need to understand the negation of a concept as well so you can figure out how things interact.

Simple example: All apples are fruits. What happens when I hand you a wrench?

Well, you know a wrench is not an apple, so you know you can't satisfy the sufficient condition. You also know that a wrench is not a fruit, so you can take the contrapositive (Not a fruit -> Not an apple) and arrive at the conclusion that the wrench is not an apple. Fine.

But how did you know that a wrench is not a fruit? Knowing that your "not a fruit" category includes wrenches was the key to putting all this information together. So you see, you're still taking all the information at face value factually - all apples are delicious, and I have a wrench - but in order for me to understand the execution of the argument, I had to understand what the negation of a fruit was ("not a fruit"), then realize that a wrench falls into that category, and then execute the logic from there.

Another example for you to consider on your own. If you're a good person, you'll never cheat. Good Person -> Never Cheat. Contrapositive, NOT Never Cheat -> NOT good person. How many different ways can you think of to satisfy the "NOT never cheat" condition, and do any of them require you to deny the fundamental truth of the relationship that was initially given to you? This should show you the delineation between accepting the factual truth of a statement vs executing those statements in a method of reasoning.