Re: `at least one ' vrs `one or more'

[Thanatos <thanatos@DIMENSIONAL.COM>]

I'm a newbie here, but I think I can help confuse matters.

Introducing "dislike" may also help.  If you are negating "like," change
it to "dislike."  If you are negating the entire sentence, don't read
"don't like" as "dislike."

The correct negations are made clearer that way:

"Do you like all cats?"            "No, I dislike some cats."
                                   [not "I don't like (dislike) all"]

"Do you dislike all cats?"         "No, I like some cats."

"Do you like one or more cats?"    "No, I dislike all cats."
                                   [not "I don't like (dislike) some"]

"Do you dislike one or more cats?" "No, I like all cats."



From: And Rosta <a.rosta@UCLAN.AC.UK>
Date: Friday, 14 November, 1997 12:49


>Can I suggest that discussions about scope of negation,
>etc., use some sort of logical notation instead of
>ordinary English?

I've recently been doing logic in class.  Unfortunately, the characters
aren't available on the keyboard.  With the nearest I can make do with:

Ax  = all x
Ex  = there exists a, one or more, at least one, some
Lx  = I like x
~   = negation
~Lx = I dislike x

~Ax(Lx)      [ liking all cats is false ]
 <-> Ex(~Lx) [ there exists one or more cats I don't like ]

~Ax(~Lx)     [ disliking all cats is false ]
 <-> Ex(Lx)  [ there exists one or more cats I do like ]

~Ex(Lx)      [ there does not exist a cat I like ]
 <-> Ax(~Lx) [ I dislike all cats ]

~Ex(~Lx)     [ there does not exist a cat I dislike ]
 <-> Ax(Lx ) [ I like all cats ]

"I like one or more cats" <-> Ex(Lx)
"I [false] like one or more cats" <-> ~Ex(Lx)  [negating the entire
sentence]
 <-> Ax(~Lx)
 <-> "I dislike all cats."  [or, "I don't like any cats."]


>... I haven't a clue what he means. The English is too
>ambiguous.

It's resolved in spoken English by emphasis:

"I *don't* like one or more cats" <-> "I dislike all"
"I *don't like* one or more cats" <-> "I dislike one or more"

{mi na nelci lo mlatu} would be the negation of {mi nelci lo mlatu}, or
~Ex(Lx), and therefore be Ax(~Lx), or "I dislike all cats."

--
Erik W. Cornilsen