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Negation Question

k.karmazynk.karmazyn Alum Member
edited December 2017 in Logical Reasoning 23 karma

Hello,

I have a general question about negating statements that is bothering me as I'm working through necessary assumption questions! My question is, do we negate BOTH "not" elements in a statement in order to properly negate it, or just one? For example:

"Lawrence did not get the idea in the passages in questions or did not get their formulations originally from Hartley"
To negate, do we take away both of the "nots" or just one?

Another example:

"Those who do not know a language cannot hear the way speech in that language actually sounds"
To negate, do we say "Those who do know a language cannot hear the way speech in that language actually sounds" or do we say "Those who do know a language can hear the way speech in that language actually sounds"?

Thanks and I hope this makes sense!

Comments

  • LSATcantwinLSATcantwin Alum Member Sage
    edited December 2017 13286 karma

    You have to negate it so that it says the opposite of what was originally stated.

    Example 1:

    • Lawrence did not get the idea in the passages in questions or did not get their formulations originally from Hartley

    Negation:

    • Lawrence got the idea in the passages in questions or got their formulations originally from Hartley.

    Example 2:

    • Those who do not know a language cannot hear the way speech in that language actually sounds.

    Negation:

    • (both not and cannot) Those who DO know a language CAN hear the way speech in that language actually sounds. (This does not go against what was said, we don't care about people who know a language we care about those that don't)

    • (only the not) Those who DO know a language cannot hear the way a speech in that language actually sounds. (again, we don't care about people who know a language. We care about those who don't)

    • (only the cannot) Those who do not know a language CAN hear the way a speech in that language actually sounds. (this does go against what was said)

    The word "not" or the negative does not always get negated. We are looking for the opposite of what was said. In the second example you gave, if I changed the first "not" it wouldn't be the opposite because it changes who we are talking about. Use your gut for negations, pretend like you want to disagree with everything being said. I bet most of the time you spit out a natural negation without having to over think it.

    Edit: Or if you've ever seen a child argue with their parent just to argue, that is the state of mind you want.

    • Parent: You need to eat your veggies so you can be big and strong.

    • Kid: I do not have to eat my veggies so I can be big and strong.

    • Parent: You cannot watch T.V. until you brush your teeth.

    • Kid: I CAN watch T.V. if I do not brush my teeth.

    • Parent: Your friends that do not do their home work cannot get good grades.

    • Kid: My friends that do not do their homework CAN get good grades!

  • goingfor99thgoingfor99th Free Trial Member
    3072 karma

    I love your geometric shape there.

  • SamiSami Live Member Sage 7Sage Tutor
    edited December 2017 10774 karma

    For negation, I like to think of each statement as a universe that I am dividing into halves. For example, the negation of I cannot eat an apple would be just one instance of me eating an apple.

    So for me I like to think of it more conceptually than a negation.

    For your sentence,

    "Lawrence did not get the idea in the passages in questions or did not get their formulations originally from Hartley"

    If we only say Lawrence did get the idea in the passage in questions, we could still be in this universe of our original sentence because it is still possible as he could not have just gotten their formulation originally from Hartley. Thus just having one part of sentence wouldn't allow us to step out of this universe written in the sentence.

    If we only say Lawrence did get their formulation originally from Hartley, we are still in this sentence universe because it's possible he did not get the idea in the passages in questions.

    The only way to neatly divide this sentence into two halves is to say "Lawrence did get the idea in the passages in questions and did get their formulations originally from Hartley".

    This sentence is positive not just because of the two negatives but also because of the word "or".

    In contrast if the statement instead of "or" had "and" instead, "Lawrence did not get the idea in the passages in questions and did not get their formulations originally from Hartley". We could simply negate it by saying either Lawrence did get the idea... or did get their formulations. It's possible for one of them to be negative and it still be the negation of the sentence. But both being positives are also negation of the sentence, as all these worlds are not allowed by this sentence.

    For your other statement,

    "Those who do not know a language cannot hear the way speech in that language actually sounds"

    Instead of just seeing the two negatives think of the world we are in. We are in a world where we are just talking about people who do not know a language...and all that we know about these people is that they cannot hear the way speech in that language actually sounds. To divide the world into two universe we just have to find someone who does not know a language but could hear the way speech in that language actually sounds.

    We know nothing about people who do know languages, so writing something about them would not be negating anything about people "who do not know a language".

    Let me know if this helped.

  • k.karmazynk.karmazyn Alum Member
    23 karma

    Thank you both this helped me tremendously!!!

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