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Negation Help

luffyyyyluffyyyy Alum Member
in Logical Reasoning 699 karma

Hi all!

Just a question on negation. So from what I understand, there are 2 ways we can deny the relationship (i.e A some /B and A and /B). But would it be ok to write /A and B ?

For example, if the record sells well, you will be famous.
Denying this relationship we get:
1) the record sells well and you will not be famous, or
2) some records sell well and you are not famous

Would it be illegal to say "the record doesn't sell well and you will be famous" (/Sell Well and Famous) ?

Please let me know, thanks in advance !

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Comments

  • Matt SorrMatt Sorr Alum Member ⭐
    2245 karma

    If I’m understanding what you’re asking, it’s possible for the records to not sell well and you still become famous. In your scenario, the records selling well is the sufficient condition and becoming famous is the necessary condition. If you deny the sufficient (meaning the records don’t sell well), the necessary is free to act as it pleases. This is true in every situation (and JY frequently points it out in LG explanation vids). So if the records don’t sell well, you may or may not become famous. Perhaps you’ll get famous through a different avenue.

    What we can’t infer, however, is that if the records don’t sell well you will definitely become famous. As mentioned above, it’s possible you become famous, but also possible you don’t become famous.

    I hope this answers at least part of what you’re asking. If I totally missed the point, though, just say so!

  • luffyyyyluffyyyy Alum Member
    edited August 2022 699 karma

    Hi @"Matt Sorr" !

    Thank you so much for your reply. I guess my question came from watching the video on "Deny the Relationship" lesson https://7sage.com/lesson/deny-the-relationship/

    JY mentions that when we deny the relationship, we can say "it is not the case that A --> B" which means "some A are not B" or "there are A and not B" and my confusion was just that if it would be ok to say "there are B and not A".

    Perhaps you answered the question, but I am just still not too clear on it. Thank you so much!!

  • Matt SorrMatt Sorr Alum Member ⭐
    2245 karma

    @jessica8871 Okay, I think I'm grasping what you're asking now. Thanks for clarifying. I certainly didn't answer your question, but I'll give it another go. Again, please just let me know if I'm missing the point. Apologies for the hassle!

    You said that you're confused about if it's okay to infer"there are B and not A" after learning that "some A are not B."

    The answer: No, you're not able to say that "there are B and not A." All we know is that there are instances where you have an A that isn't a B. We do not know if there are instances where you have a B that isn't an A. For all we know, maybe all B's are A's. Maybe some B's are A's. Maybe no B's are A's.

    So, to give an example, if you're told that there are dogs (filling in for the "A" variable) that aren't pugs (filling in for the "B" variable), then we can conclude "some A (dogs) are not B (pugs)." Given this information, however, we cannot conclude "some B (pugs) are not A (dogs)," or, to phrase it how you did in your question, we can't conclude "there are B and not A." For all we know, maybe all pugs are dogs. Maybe only some pugs are dogs. Maybe no pugs are dogs. We just can't infer anything from the statement "some dogs aren't pugs."

    I hope this helps! Again, please just let me know if I missed the point. Trust me, I know it's no fun to ask a question just to have someone answer it incorrectly!

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