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Date: Thu, 9 Aug 2012 09:09:11 -0300
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Subject: Re: [lojban] Revising mu'ei and CAhA once again. Possible worlds.
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On Thu, Aug 9, 2012 at 7:45 AM, Gleki Arxokuna
<gleki.is.my.name@gmail.com> wrote:
> On Tuesday, August 7, 2012 2:34:44 AM UTC+4, xorxes wrote:
>>
>> In order to say that it contains both black and white balls you may
>> need something like "su'opame'iro mu'ei", "in some but not all
>> worlds". "May or may not", as opposed to just "may".
>
> Indeed. That's what I still might like.
> If {ka'e} =3D {su'opame'iro mu'ei} then the scheme will get symmetry.

I don't think that's a good idea. ka'e and bi'ai are the basic modal
operators (see http://en.wikipedia.org/wiki/Modal_logic
they even have the customary symbols =E2=96=A1 for Necessarily and =E2=97=
=87 for
Possibly). "su'opame'iro mu'ei" may facilitate your drawing, but it
has a more complex logic, for example it is no longer the dual of
bi'ai. If what you want is a simple drawing for "ka'e" in your scheme,
I suggest a bag with at least one black ball and the other balls drawn
in dotted lines, suggesting that we don't know or don't care what
color they are, as long as one of them is black.

> {su'opame'iro mu'ei} stretches across the scale not touching it's borders=
.
> If {su'opame'iro mu'ei} =3D {ka'e} then {ka'ena} and {ka'e} are the same.=
 They
> differ probably in accenting either the presense of white or black balls
> respectively. So "I could sleep"=3D"I could be awake" as we don't specify=
 what
> is more likely. We just state something in between {bi'aina} and {bi'ai}.

If you want a word for that, I suggest coining a new one ("ka'ei"?)
but leave "ka'e" for the basic modal meaning.

> In a passage to the limit {su'opame'iro mu'ei} becomes equal to either
> {bi'ai} or {bi'aina}.
>
> But if we assume that {ka'e}=3D{su'o mu'ei} then in some cases it can be =
equal
> to {bi'ai} which is nonsense.
>
> "I could swim" doesn't imply that "I necessarily swim". So stronlgy belie=
ve
> that {ka'e} must not include the case of {bi'ai} and {bi'ai na}.

"I can swim" doesn't imply "I necessarily swim", but "I necessarily
swim" does imply "I can swim". "bi'ai" does not imply "ka'ei", in fact
it implies "na ka'ei".

mu'o mi'e xorxes

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