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  1. #11
    jutfrank's Avatar
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    Re: No other boy in the team is a better player than Tom

    Quote Originally Posted by Glizdka View Post
    I'd expect "No other boy is as good as Tom is" to be commonly understood as "Every other boy is worse than Tom is",
    Correct. That's what it means in ordinary language.

    but in logic, only to mean "Every other boy is either better or worse than Tom, just not equally good".
    What do you mean by 'in logic'? If this were the case, a logician would write such a proposition in logical form to make the meaning unequivocal.

  2. #12
    Glizdka is offline Senior Member
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    Re: No other boy in the team is a better player than Tom

    Quote Originally Posted by jutfrank View Post
    What do you mean by 'in logic'? If this were the case, a logician would write such a proposition in logical form to make the meaning unequivocal.
    You caught me off guard. I know logic only from math.

    Can I do like a mathematician would?

  3. #13
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    Re: No other boy in the team is a better player than Tom

    What do you mean?

  4. #14
    Glizdka is offline Senior Member
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    Re: No other boy in the team is a better player than Tom

    I used the word logic a bit too carelessly. When you said about a proposition in logical form, I realized I couldn't deliver. I've never studied logic except for in math.

    Would a semanticist understand a mathematician?


    let:
    T
    - team, set of boys
    a - Tom, a boy
    x - boy other than Tom
    prowess at sport be value of variable

    T={a, x1, x2, x3, ... xn-1}
    a∈T
    x∈{T\a}


    "No other boy is a better player than Tom" means "Every other boy is worse than Tom" and "Tom is the best boy in the team".

    ∀x∈{T\a}:x≯ a ↔ x<a ↔ a>x



    "No other boy is a better player than Tom" means "Every other boy is either worse than or as good as Tom", but it doesn't imply that "Tom is the best boy in the team" because "There may be a boy in the team that is as good as Tom".

    ∀x∈{T\a}:(x≯ a ↔ x≤a ↔ x<a ∨ x=a) ↛ a>x ∵ ∃'x∈{T\a}:x=a



    "Tom is the best boy in the team" implies that "No other boy in the team is a better player than Tom".

    ∀x∈{T\a}:a>x → x≯ a
    Last edited by Glizdka; 17-Dec-2020 at 08:25. Reason: made it a bit clearer

  5. #15
    jutfrank's Avatar
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    Re: No other boy in the team is a better player than Tom

    I'm not sure what you're asking or why, Glizdka.

    What is it that you're trying to learn with all this?

  6. #16
    Glizdka is offline Senior Member
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    Re: No other boy in the team is a better player than Tom

    I've reworked post#14. It was unreadable. I hope it's clearer now.

    Quote Originally Posted by jutfrank View Post
    I'm not sure what you're asking or why, Glizdka.

    What is it that you're trying to learn with all this?
    Are these true?

    A) "No other boy is a better player than Tom" means "Every other boy is worse than Tom" and "Tom is the best boy in the team".
    B) "No other boy is a better player than Tom" means "Every other boy is either worse than or as good as Tom", but it doesn't imply that "Tom is the best boy in the team" because "There may be a boy in the team that is as good as Tom".
    C) "Tom is the best boy in the team" implies that "No other boy in the team is a better player than Tom".
    Last edited by Glizdka; 17-Dec-2020 at 08:07.

  7. #17
    Rover_KE is offline Moderator
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    Re: No other boy in the team is a better player than Tom

    Is anybody else's head spinning?

  8. #18
    Piscean is offline VIP Member
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    Re: No other boy in the team is a better player than Tom

    Quote Originally Posted by Glizdka View Post

    A) "No other boy is a better player than Tom" means "Every other boy is worse than Tom" and "Tom is the best boy in the team".
    B) "No other boy is a better player than Tom" means "Every other boy is either worse than or as good as Tom", but it doesn't imply that "Tom is the best boy in the team" because "There may be a boy in the team that is as good as Tom".
    C) "Tom is the best boy in the team" implies that "No other boy in the team is a better player than Tom".
    A) It does not necessarily mean what those two sentences say.
    B) Yes.
    C) It does
    not just imply that.
    Typoman - writer of rongs

  9. #19
    jutfrank's Avatar
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    Re: No other boy in the team is a better player than Tom

    You're not using the word imply quite right. What you mean is entail.

  10. #20
    Glizdka is offline Senior Member
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    Re: No other boy in the team is a better player than Tom

    Quote Originally Posted by Piscean View Post
    C) It does not just imply that.
    Quote Originally Posted by jutfrank View Post
    You're not using the word imply quite right. What you mean is entail.
    I've changed imply to entail. Are these true?

    C1) "Tom is the best boy in the team" entails "No other boy in the team is a better player than Tom".
    a>x → x≯ a

    C2) "No other boy in the team is a better player than Tom" doesn't entail "Tom is the best boy in the team".
    x≯ a ↛ a>x
    Last edited by Glizdka; 17-Dec-2020 at 18:36.

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