Re: [lojban-beginners] Just to double check, about {da} and quantifiers

[Jorge Llambías <jjllambias@gmail.com>]

On Thu, Jun 2, 2011 at 5:50 PM, Michael Turniansky
<mturniansky@gmail.com> wrote:
> 2011/6/1 Jorge Llambías <jjllambias@gmail.com>:
>> On Wed, Jun 1, 2011 at 9:24 AM, Michael Turniansky
>>
>>>  In a universe where "ro da poi gerku je mlatu" is a
>>> nomei,
>>
>> There's no such universe. "ro da poi gerku je mlatu" is a quantifier,
>> so it cannot be a nomei, whatever a nomei is (I think nothing is in
>> fact a nomei, by definition, but a quantifier is certainly not a
>> nomei).
>
>  No, "ro da..." is not a quantifier. "ro" is a quantifier. "ro da..."
> is each of the members of set (qualified by the whatever follows the
> poi)

"da" is just a place holder, it doesn't really matter if you count it
as part of the quantifier or not. The point is that the operator "ro
da poi gerku je mlatu" is something that operates on a bridi. It is
not a nomei, whatever a nomei may be.

"ro da poi ..." translates into English as "each x such that ...", or
if you wish, as "each of the members of the set ...". It is certainly
not each of the members of the set.

>> First you would have to explain how anything at all can be a nomei. My
>> understanding is that "ro da zo'u da su'o mei", "For every x, x is
>> something".  No thing is a nomei.
>
>  Unless there are in fact, no things.

No, even in that case, "ro da su'o mei" and "no da no mei" are still
true. Every thing is a su'o mei and no thing is a no mei.

Those two statements are equivalent, because "ro da" is equivalent to
"no da naku" and "su'o mei" is equivalent to "naku no mei", so:

ro da su'o mei
= no da naku naku no mei
= no da no mei

(It is also the case, in that weird special case of an empty universe,
that "ro da no mei" and "no da su'o mei". But that doesn't warrant
your "unless".)

>>> So for any broda, " ro da poi ke'a
>>> gerku je mlatu ku'o va'o lo du'u da nomei cu broda" is true.
>>
>> You are now leaving logical simplicity behind by introducing this
>> "va'o lo du'u da nomei" term.
>
>  That was the condition that you imposed -- "If there are no catdogs"
>  If there are no catdogs, then ro da is a mass composed of an empty
> set, otherwise known as a nomei.

No, "ro da" is a quantifier, an operator, whatever you want to call
it, but certainly not a mass.

>> If we try to expand your sentence to
>> logical form, we get:
>>
>> ro da zo'u ganai da gerku je mlatu gi da va'o lo nu da nomei cu broda
>
>  Stop.  Where did you get license to expand it like that?

Standard "ro da poi" expansion. How else would you propose to expand it?

>  "ro lo PA broda cu brode" expands into  "ge ro lo broda cu brode gi
> lo broda cu PAmei", I believe.

We agree about that. (Well, maybe not exactly a logical expansion,
since I think the second conjunct is a presupposition in the first
sentence, not an assertion, but they will have the same truth values.)

Our problem is that for you "lo broda cu nomei" could be true, while
for me it is false as a consequence of "no da nomei" being true and
thus there being no possible instantiation of "da" that will make it
true.

> The only reason for the existence of
> the va'o clause in the particular case we were working with was
> because you were stating that there are no catdogs.

No, we were eveluating the truth of a sentence such as "for every
catdog ..." in a universe without catdogs. We were not evaluating the
truth of a sentence such as "if there are no catdogs then ..."

If you like we can discuss that other sentence:

"ganai no da mlatu je gerku gi ro de poi mlatu je gerku cu broda", but
that's not what we were talking about.

mu'o mi'e xorxes

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