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Can all "Group 1" logical indicators be negated to "some not"

cardi teacardi tea Live Member
edited January 2023 in General 39 karma

Hello everyone! I'm still going through the CC and reached the section about "Some and Most Relationships." I understand that the negation of "all" is "some not."

"All A's are B's."
Group 1 translation: A→B
Negation: A←some→/B

This might be a silly question, but does this mean that all the logical indicators in group 1 should be negated this way? For example:

"As long as there are A's, there are B's."
Group 1 translation: A→B
Negation: A←some→/B

And does this also apply to groups 2, 3, and 4? Does "all" basically represent all the universal quantifiers we learned in "Intro to Logic"?

Thank you!

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Comments

  • The2ndSageThe2ndSage Member
    64 karma

    Wow, this is a really good question and I hope someone smarter than me answers it because it has been throwing me for a loop while thinking about it. When searching on the forums, I found a related explanation to your question (here's the link: https://7sage.com/discussion/#/discussion/27407) and basically it was saying that some and most statements are not the same as conditional statements. So there is a distinction to be made, however, when it comes to negating we still have to negate sentences like the one that is in the link and it has a combination of a some statement and a conditional statement.

  • WinningHereWinningHere Member
    417 karma

    I am thinking this lesson may be referring to negating or denying a conditional. Whereby the sufficient exists AND one instance of the necessary does not.

  • Jonathan WangJonathan Wang Yearly Sage ⭐
    6866 karma

    All terms that mean the exact same thing negate the exact same way. Which makes sense, doesn't it? After all, how could two things mean the exact same thing if you're supposed to treat them differently in certain circumstances?

    So to answer your question directly, yes - "if" and all of its brethren in group 1 all negate to "some not", and the world would be totally insane if that weren't true.

  • cardi teacardi tea Live Member
    39 karma

    Thank you, everyone!

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