Date: Fri, 14 Feb 2014 15:36:14 -0800 (PST)
From: guskant <gusni.kantu@gmail.com>
To: lojban@googlegroups.com
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Subject: Re: [lojban] Individuals and xorlo
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Le vendredi 14 f=C3=A9vrier 2014 20:59:56 UTC+9, selpa'i a =C3=A9crit :
>
> la .guskant. cu cusku di'e=20
> > {lo sidbo} does not refer to one or more individuals, because, for ever=
y=20
> > {lo sidbo xi my}, there is another {lo sidbo xi ny} such that {lo sidbo=
=20
> > xi ny cu me lo sidbo xi my i naku lo sidbo xi my cu me lo sidbo xi ny},=
=20
> >   therefore {lo sidbo xi my} does not satisfy the condition for being a=
n=20
> > individual {RO DA poi ke'a me lo sidbo xi my zo'u lo sidbo xi my cu me=
=20
> > DA}. It means that there is no individual {lo sidbo} in this universe o=
f=20
> > discourse. Therefore {lo sidbo} is neither an individual nor=20
> individuals.=20
>
> To me it looks more like this entire process of sub-grouping is a=20
> strawman. I don't see why I should be forced to sub-divide {lo sidbo}=20
> into infinitely large {lo sidbo be ny} when I could just as well just=20
> look at each individual {sidbo} in isolation.=20
>
>

It is because the following proposition is given as an axiom in the=20
universe of discourse (UD1) on the current topic.
P1:=20
ro'oi da poi ke'a me lo sidbo ku'o su'oi de zo'u de me da ijenai da me de

In this universe of discourse, the following proposition is a theorem.
P2:
naku ro'oi da poi ke'a me lo sidbo zo'u lo sidbo cu me da

As long as talking about UD1, we are forced to think that P2, that is,=20
there is no individual {lo sidbo}, because it is a proved theorem.

On the other hand, it is also possible that we talk about such a universe=
=20
of discourse (UD2) that the following proposition is an axiom or a theorem.
P3:
ro'oi da poi ke'a me lo sidbo zo'u lo sidbo cu me da

In UD2, {lo sidbo} is an individual, and a negation of P1 is proved.

Because neither P1 nor P3 is tautology, we are not forced to think that one=
=20
of them is always true for all the universes of discourse. We have freedom=
=20
to choose non-logical axioms and a universe of discourse according to=20
context.


=20

> [ s1 , s2 , s3 , ... ]=20
>
> Why can't I just look at s1 by itself, and s2 by itself and so on? For=20
> each s_x, it holds that:=20
>
>    ro'oi da poi ke'a me s_x zo'u: s_x me da=20
>
> So each s_x is an individual.=20
>
>

That is UD2, not UD1.


=20

> >     And maybe this helps: Do you see a difference between "referent" an=
d=20
> >     "individual"? What do you consider the difference to be?=20
> >=20
> >=20
> >=20
> > Yes. The identity of referent is defined as follows:=20
> > "X are the same thing as Y" =3Dca'e {X me Y ije Y me X}=20
> >=20
> > On the other hand, "an individual" is defined as follows:=20
> > "X is an individual" =3Dca'e {RO DA poi ke'a me X zo'u X me DA}=20
>
> Each s_x satisfies the definition of "individual". Any pair of {s_x,=20
> s_y} fails the "sameness" condition. The two definitions don't exclude=20
> each other.=20
>
>

The universe of discourse in which each s_x satisfies the definition of=20
"individual" is UD2, not UD1.


=20

> Every sumti has certain referents, and it might have the same referents=
=20
> as another sumti, in which case the two sumti are "the same", or they=20
> might have different referents, in which case the two sumti are not the=
=20
> same. In either case, the referents themselves are individuals.=20
>
>

In UD2, yes. In UD1, no. It depends on our choice of universe of discourse,=
=20
on the context, not on the language.


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<div dir=3D"ltr"><br><br>Le vendredi 14 f=C3=A9vrier 2014 20:59:56 UTC+9, s=
elpa'i a =C3=A9crit&nbsp;:<blockquote class=3D"gmail_quote" style=3D"margin=
: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;">la .=
guskant. cu cusku di'e
<br>&gt; {lo sidbo} does not refer to one or more individuals, because, for=
 every
<br>&gt; {lo sidbo xi my}, there is another {lo sidbo xi ny} such that {lo =
sidbo
<br>&gt; xi ny cu me lo sidbo xi my i naku lo sidbo xi my cu me lo sidbo xi=
 ny},
<br>&gt; &nbsp; therefore {lo sidbo xi my} does not satisfy the condition f=
or being an
<br>&gt; individual {RO DA poi ke'a me lo sidbo xi my zo'u lo sidbo xi my c=
u me
<br>&gt; DA}. It means that there is no individual {lo sidbo} in this unive=
rse of
<br>&gt; discourse. Therefore {lo sidbo} is neither an individual nor indiv=
iduals.
<br>
<br>To me it looks more like this entire process of sub-grouping is a=20
<br>strawman. I don't see why I should be forced to sub-divide {lo sidbo}=
=20
<br>into infinitely large {lo sidbo be ny} when I could just as well just=
=20
<br>look at each individual {sidbo} in isolation.
<br>
<br></blockquote><div><br></div><div><br></div><div>It is because the follo=
wing proposition is given as an axiom in the universe of discourse (UD1) on=
 the current topic.</div><div>P1:&nbsp;</div><div>ro'oi da poi ke'a me lo s=
idbo ku'o su'oi de zo'u de me da ijenai da me de</div><div><br></div><div>I=
n this universe of discourse, the following proposition is a theorem.</div>=
<div>P2:</div><div>naku ro'oi da poi ke'a me lo sidbo zo'u lo sidbo cu me d=
a</div><div><br></div><div>As long as talking about UD1, we are forced to t=
hink that P2, that is, there is no individual {lo sidbo}, because it is a p=
roved theorem.</div><div><br></div><div>On the other hand, it is also possi=
ble that we talk about such a universe of discourse (UD2) that the followin=
g proposition is an axiom or a theorem.</div><div>P3:</div><div>ro'oi da po=
i ke'a me lo sidbo zo'u lo sidbo cu me da</div><div><br></div><div>In UD2, =
{lo sidbo} is an individual, and a negation of P1 is proved.</div><div><br>=
</div><div>Because neither P1 nor P3 is tautology, we are not forced to thi=
nk that one of them is always true for all the universes of discourse. We h=
ave freedom to choose non-logical axioms and a universe of discourse accord=
ing to context.</div><div><br></div><div><br></div><div>&nbsp;</div><blockq=
uote class=3D"gmail_quote" style=3D"margin: 0;margin-left: 0.8ex;border-lef=
t: 1px #ccc solid;padding-left: 1ex;">[ s1 , s2 , s3 , ... ]
<br>
<br>Why can't I just look at s1 by itself, and s2 by itself and so on? For=
=20
<br>each s_x, it holds that:
<br>
<br>&nbsp; &nbsp;ro'oi da poi ke'a me s_x zo'u: s_x me da
<br>
<br>So each s_x is an individual.
<br>
<br></blockquote><div><br></div><div><br></div><div>That is UD2, not UD1.</=
div><div><br></div><div><br></div><div>&nbsp;</div><blockquote class=3D"gma=
il_quote" style=3D"margin: 0;margin-left: 0.8ex;border-left: 1px #ccc solid=
;padding-left: 1ex;">&gt; &nbsp; &nbsp; And maybe this helps: Do you see a =
difference between "referent" and
<br>&gt; &nbsp; &nbsp; "individual"? What do you consider the difference to=
 be?
<br>&gt;
<br>&gt;
<br>&gt;
<br>&gt; Yes. The identity of referent is defined as follows:
<br>&gt; "X are the same thing as Y" =3Dca'e {X me Y ije Y me X}
<br>&gt;
<br>&gt; On the other hand, "an individual" is defined as follows:
<br>&gt; "X is an individual" =3Dca'e {RO DA poi ke'a me X zo'u X me DA}
<br>
<br>Each s_x satisfies the definition of "individual". Any pair of {s_x,=20
<br>s_y} fails the "sameness" condition. The two definitions don't exclude=
=20
<br>each other.
<br>
<br></blockquote><div><br></div><div><br></div><div>The universe of discour=
se in which each s_x satisfies the definition of "individual" is UD2, not U=
D1.</div><div><br></div><div><br></div><div>&nbsp;</div><blockquote class=
=3D"gmail_quote" style=3D"margin: 0;margin-left: 0.8ex;border-left: 1px #cc=
c solid;padding-left: 1ex;">Every sumti has certain referents, and it might=
 have the same referents=20
<br>as another sumti, in which case the two sumti are "the same", or they=
=20
<br>might have different referents, in which case the two sumti are not the=
=20
<br>same. In either case, the referents themselves are individuals.
<br>
<br></blockquote><div><br></div><div><br></div><div>In UD2, yes. In UD1, no=
. It depends on our choice of universe of discourse, on the context, not on=
 the language.<br></div><div><br></div><div><br></div></div>

<p></p>

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