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Re: [lojban-beginners] Just to double check, about {da} and quantifiers
2011/6/2 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.
I think either you or I must have skipped a groove here (to use old
vinyl metaphors). How can you say in one breath both that it
translats as "each of the members of the set" and "it is certainly not
each of the members of the set"? Which is it???
>
>>> 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".)
>
But that is PRECISELY my "unless". If you have an empty universe,
(="unless there are no things") We have been talking all along about
the odd case of an empty universe. (or the slightly less bizarre case
of a particular subset being empty, i.e.m, catdogs)
>>>> 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?
Okay. I've thought about it, and yes, that's a correct
reformulation. (I think the va'o clause in the middle was confusing
me)
So let's go back to the part you wrote before, but elided this time 'round...
> "Now, for each value of "da", "da gerku je mlatu" is false, and "da
> nomei" is also false.
Here's the part right here... How do you know/assert "da gerku je
mlatu" is false for evey da? In fact, there might be a universe of
discourse where it is not. (For example, if we are talking about the
characters on Nickolodeon cartoons.) So, "va'o lo nu da nomei" adds
that fact in. That there are no da that fit that mold. (the answer to
your next question -->)
> So ganai ... gi ... is true because the first part is false. What did
> the never satisfied "va'o lo du'u da nomei" term add?
>
>> "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.
>
Right, we agree about this being our disagreement.
>> 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.
That was the ONLY thing I was qualifying with my va'o -- "...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.
But that's analagous, and is also true for every value of broda.
However, it's another step removed from the original "lo no..."
question.
--gejyspa
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- References:
- [lojban-beginners] Just to double check, about {da} and quantifiers
- From: ".arpis." <rpglover64+jbobau@gmail.com>
- Re: [lojban-beginners] Just to double check, about {da} and quantifiers
- From: Jorge Llambías <jjllambias@gmail.com>
- Re: [lojban-beginners] Just to double check, about {da} and quantifiers
- From: ".arpis." <rpglover64+jbobau@gmail.com>
- Re: [lojban-beginners] Just to double check, about {da} and quantifiers
- From: Jorge Llambías <jjllambias@gmail.com>
- Re: [lojban-beginners] Just to double check, about {da} and quantifiers
- From: Michael Turniansky <mturniansky@gmail.com>
- Re: [lojban-beginners] Just to double check, about {da} and quantifiers
- From: Jorge Llambías <jjllambias@gmail.com>
- Re: [lojban-beginners] Just to double check, about {da} and quantifiers
- From: Michael Turniansky <mturniansky@gmail.com>
- Re: [lojban-beginners] Just to double check, about {da} and quantifiers
- From: Jorge Llambías <jjllambias@gmail.com>
- Re: [lojban-beginners] Just to double check, about {da} and quantifiers
- From: Michael Turniansky <mturniansky@gmail.com>
- Re: [lojban-beginners] Just to double check, about {da} and quantifiers
- From: Jorge Llambías <jjllambias@gmail.com>
- Re: [lojban-beginners] Just to double check, about {da} and quantifiers
- From: Michael Turniansky <mturniansky@gmail.com>
- Re: [lojban-beginners] Just to double check, about {da} and quantifiers
- From: Jorge Llambías <jjllambias@gmail.com>