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Date: Fri, 8 Mar 2002 16:21:52 EST
Subject: Re: [lojban] Re: [jboske] Quantifiers, Existential Import, and all that stuff
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In a message dated 3/8/2002 2:47:30 PM Central Standard Time, 
jjllambias@hotmail.com writes:


> So {lo broda na zasti} is meaningless in real Lojban when {lo'i broda}
> is empty. In my version of non-Lojban it is not meaningless, it is
> actually true. In my version, the different gadri are just
> different ways to refer to the same things.

Yeah, that is a paradox in many languages: how do you say that things that 
don't exist don't exist.  Happily, in a logical language it is pretty easy: 
{noda broda} (shorter too).  But in your language, {su'o lo broda na zasti} 
seems to be true when lo'i broda is empty.  But then, all these things 
probably mean something else in your language, so this may not be a paradox 
-- just hard to be sure what they mean.

<But then in the alternate world {lo'i broda} is not empty.
In that official line then {lo'i broda} cannot refer to the
empty set.>

{lo'i broda} is not a problem, {lo broda} is -- they aren't the same, you 
know.

<I apologize for the annoyance. I always try to point out
where I deviate from the official doctrine though, so as to
minimize any misleadership.>

Sorry if I missed it (and keep missing it) in your disquisitions on 
quantifiers.

<I read that paragraph a few times and I don't understand how
it invalidates anything of my system. So, between my flawed system
in which I can't see what the flaw is, and a flawless Lojban
system which is hard to work with, I will have to go with
my flawed system.>

Insofar as I can make coherent sense of your system, it seems that every 
quantifier is attached to a {(lo) broda}, thus specifying that the range of 
the quantifier is simply that set (which, however, you allow to be empty).  
Historically, universals true about empty sets have been pulled off by 
quantifying over another set (everything) and introducing the empty set 
conditionally.  The truth then comes from the conditional reference, not from 
the quantifier.  In Llamban, the idea is to use quantifiers directly on the 
{lo broda} with the understanding that, if the set is empty, {ro lo broda cu 
brode} is true (because there are no counterexamples? -- calling it false 
makes at least as much sense).  Does this carry over to {ro da}?  I suppose 
that this could be worked into a system, and the one you present may even be 
such a system.  The only complaint against it (unless I find some actual 
inconsistency in it -- which surely could be cured easily) is that it is not 
how Lojban does it.  Lojban follows the historical precedent of logic (what 
would expect?). To be sure, the details of how this all works out have not be 
thought through very well yet, but, for a variety of reasons, this has not 
been much of a problem (we don't talk a lot about non-existents for one 
thing).  The basics are in place, it is just vocabulary that needs some 
honing.



           
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<HTML><FONT FACE=arial,helvetica><BODY BGCOLOR="#ffffff"><FONT  style="BACKGROUND-COLOR: #ffffff" SIZE=2>In a message dated 3/8/2002 2:47:30 PM Central Standard Time, jjllambias@hotmail.com writes:<BR>
<BR>
<BR>
<BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">So {lo broda na zasti} is meaningless in real Lojban when {lo'i broda}<BR>
is empty. In my version of non-Lojban it is not meaningless, it is<BR>
actually true. In my version, the different gadri are just<BR>
different ways to refer to the same things.</BLOCKQUOTE><BR>
<BR>
Yeah, that is a paradox in many languages: how do you say that things that don't exist don't exist.&nbsp; Happily, in a logical language it is pretty easy: {noda broda} (shorter too).&nbsp; But in your language, {su'o lo broda na zasti} seems to be true when lo'i broda is empty.&nbsp; But then, all these things probably mean something else in your language, so this may not be a paradox -- just hard to be sure what they mean.<BR>
<BR>
&lt;But then in the alternate world {lo'i broda} is not empty.<BR>
In that official line then {lo'i broda} cannot refer to the<BR>
empty set.&gt;<BR>
<BR>
{lo'i broda} is not a problem, {lo broda} is -- they aren't the same, you know.<BR>
<BR>
&lt;I apologize for the annoyance. I always try to point out<BR>
where I deviate from the official doctrine though, so as to<BR>
minimize any misleadership.&gt;<BR>
<BR>
Sorry if I missed it (and keep missing it) in your disquisitions on quantifiers.<BR>
<BR>
&lt;I read that paragraph a few times and I don't understand how<BR>
it invalidates anything of my system. So, between my flawed system<BR>
in which I can't see what the flaw is, and a flawless Lojban<BR>
system which is hard to work with, I will have to go with<BR>
my flawed system.&gt;<BR>
<BR>
Insofar as I can make coherent sense of your system, it seems that every quantifier is attached to a {(lo) broda}, thus specifying that the range of the quantifier is simply that set (which, however, you allow to be empty).&nbsp; Historically, universals true about empty sets have been pulled off by quantifying over another set (everything) and introducing the empty set conditionally.&nbsp; The truth then comes from the conditional reference, not from the quantifier.&nbsp; In Llamban, the idea is to use quantifiers directly on the {lo broda} with the understanding that, if the set is empty, {ro lo broda cu brode} is true (because there are no counterexamples? -- calling it false makes at least as much sense).&nbsp; Does this carry over to {ro da}?&nbsp; I suppose that this could be worked into a system, and the one you present may even be such a system.&nbsp; The only complaint against it (unless I find some actual inconsistency in it -- which surely could be cured easily) is that it is not how Lojban does it.&nbsp; Lojban follows the historical precedent of logic (what would expect?). To be sure, the details of how this all works out have not be thought through very well yet, but, for a variety of reasons, this has not been much of a problem (we don't talk a lot about non-existents for one thing).&nbsp; The basics are in place, it is just vocabulary that needs some honing.<BR>
<BR>
<BR>
<BR>
</FONT></HTML>           
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