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Message-ID: <1392042851.14618.YahooMailNeo@web181102.mail.ne1.yahoo.com>
Date: Mon, 10 Feb 2014 06:34:11 -0800 (PST)
From: John E Clifford <kali9putra@yahoo.com>
Reply-To: lojban@googlegroups.com
Subject: Re: [lojban] Individuals and xorlo
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This muddle has gotten out of hand. =A0At least the following words are bei=
ng used in at least two senses, often in the same sentence:"individual", "l=
ine (segment)", "among" ('me'), "plural". =A0Further, at least three langua=
ges are involved: ordinary English, mathematics and plural logic/mereology.=
 =A0I'm not sure that sorting all these out will help (there are deeply par=
adoxical notions here), but it might help get down to the real problems and=
 away from the superficial confusions.


________________________________
 From: guskant <gusni.kantu@gmail.com>
To: lojban@googlegroups.com=20
Sent: Monday, February 10, 2014 8:19 AM
Subject: Re: [lojban] Individuals and xorlo
=20


Le lundi 10 f=E9vrier 2014 21:38:06 UTC+9, selpa'i a =E9crit=A0:
la .guskant. cu cusku di'e=20
>> Le lundi 10 f=E9vrier 2014 00:55:01 UTC+9, selpa'i a =E9crit :=20
>> =A0 =A0 Let's say the original single line segment L looks like this:=20
>>=20
>> =A0 =A0 |----------------------------- ------------------| =A0 <- {lo li=
nji}=20
>> =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 L=20
>>=20
>> =A0 =A0 You seem to be saying that L is not an individual because we can=
=20
>> =A0 =A0 turn it=20
>> =A0 =A0 into multiple smaller line segments A, B, C, like this:=20
>>=20
>> =A0 =A0 |---------------| |---------------| |---------------|=20
>> =A0 =A0 =A0 =A0 =A0 =A0 =A0 A =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 B =A0 =A0 =
=A0 =A0 =A0 =A0 =A0 =A0 C=20
>>=20
>> =A0 =A0 Further, you seem to be saying that A, B, and C are all among L.=
 You=20
>> =A0 =A0 also seem to be saying that each of A, B, C are not individuals =
either,=20
>> =A0 =A0 because we can further split them, like this:=20
>>=20
>> =A0 =A0 |-------|-------| |-------|-------| |-------|-------|=20
>> =A0 =A0 =A0 =A0 =A0 M =A0 =A0 =A0 N =A0 =A0 =A0 =A0 O =A0 =A0 =A0 P =A0 =
=A0 =A0 =A0 Q =A0 =A0 =A0 R=20
>>=20
>> =A0 =A0 And that M and N are among A, and so on.=20
>>=20
>> =A0 =A0 Is this what you are saying?=20
>>=20
>>=20
>>=20
>> Yes.=20
>
>But how does that work? If the original {lo linji} (L) is an individual,=
=20
>then only itself can be among itself. On the other hand, if it is *not*=20
>an individual, then we cannot call it {lo linji} in the first place. You=
=20


The individuality is not an necessary condition for being {lo linji}. A spe=
cial {lo linji} such that {RO DA poi ke'a me lo linji zo'u lo linji cu me D=
A} is an individual.


=A0

>could say that {lo linji} is more than one individual, and then the same=
=20
>things that applied to the singular L would apply again for each of the=20
>referents of the "more than one individual" L. At some point through the=
=20
>taxonomy, you must arrive at an individual or individuals and then you=20
>can't go further and say that even smaller things are among that=20
>individual. Even the shortest line doesn't have {lo mokca} {me} it.=20
>
>


There is no shortest line. That is the point for proving that any {lo linji=
} in this universe of discourse cannot be an individual.


=A0
> For example, in the case of finite {lo ci prenu}, let us call the three=
=20
>> persons p1, p2, p3. In the universe of discourse. The following sumti=20
>> are all in the domain of plural variable that are prenu even if you=20
>> don't mention the sumti:=20
>> p1=20
>> p2=20
>> p3=20
>> p1 jo'u p2=20
>> p2 jo'u p3=20
>> p3 jo'u p1=20
>> p1 jo'u p2 jo'u p3=20
>
>Yes.=20
>
>But I don't quite see how this is the same case. If this is what you=20
>were going for with the {linji} example, then it doesn't show anything=20
>that qualifies as not being one or more individuals.=20
>
>The 7 possible plural values for {prenu} above are all one or more=20
>individuals. Listing infinitely many more would not change that.=20
>
>


Not an infinite number of {lo linji} itself but an infinite number of proce=
dures of affirming that {lo linji xi ny cu me lo linji xi my i ku'i naku lo=
 linji xi my cu me lo linji xi ny} do prove that every {lo linji} is not on=
e or more individuals.


=A0
> Similarly, the infinite number of {lo linji} were in the domain of=20
>> plural variable that are linji when the universe of discourse was given=
=20
>> first.=20
>
>Infinity does not preclude individualness. If you have an infinite=20
>number of "things", then you just have infinitely many individuals.=20
>


{lo linji} in that universe of discourse are not individuals but an infinit=
e number of=A0non-individuals, because every {lo linji xi my} has always an=
other {lo linji xi ny} such that
{lo linji xi ny cu me lo linji xi my i ku'i naku lo linji xi my cu me lo li=
nji xi ny}, and this proposition contradicts the condition for individual {=
RO DA poi ke'a me lo linji xi my zo'u lo linji xi my cu me DA}. Therefore, =
every {lo linji} is neither an individual=A0nor=A0individuals.
=A0
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<html><body><div style=3D"color:#000; background-color:#fff; font-family:ti=
mes new roman, new york, times, serif;font-size:12pt"><div><span>This muddl=
e has gotten out of hand. &nbsp;At least the following words are being used=
 in at least two senses, often in the same sentence:"individual", "line (se=
gment)", "among" ('me'), "plural". &nbsp;Further, at least three languages =
are involved: ordinary English, mathematics and plural logic/mereology. &nb=
sp;I'm not sure that sorting all these out will help (there are deeply para=
doxical notions here), but it might help get down to the real problems and =
away from the superficial confusions.</span></div><div><br></div>  <div sty=
le=3D"font-size: 12pt; font-family: 'times new roman', 'new york', times, s=
erif; "> <div style=3D"font-size: 12pt; font-family: 'times new roman', 'ne=
w york', times, serif; "> <div dir=3D"ltr"> <hr size=3D"1">  <font size=3D"=
2" face=3D"Arial"> <b><span style=3D"font-weight:bold;">From:</span></b> gu=
skant
 &lt;gusni.kantu@gmail.com&gt;<br> <b><span style=3D"font-weight: bold;">To=
:</span></b> lojban@googlegroups.com <br> <b><span style=3D"font-weight: bo=
ld;">Sent:</span></b> Monday, February 10, 2014 8:19 AM<br> <b><span style=
=3D"font-weight: bold;">Subject:</span></b> Re: [lojban] Individuals and xo=
rlo<br> </font> </div> <div class=3D"y_msg_container"><br>
<div id=3D"yiv575089944"><div dir=3D"ltr"><br><br>Le lundi 10 f=E9vrier 201=
4 21:38:06 UTC+9, selpa'i a =E9crit&nbsp;:<blockquote class=3D"yiv575089944=
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; Le lundi 10 f=E9vrier 2014 00:55:01 UTC+9, selpa'i a =E9crit :
<br>&gt; &nbsp; &nbsp; Let's say the original single line segment L looks l=
ike this:
<br>&gt;
<br>&gt; &nbsp; &nbsp; |----------------------------- ------------------| &=
nbsp; &lt;- {lo linji}
<br>&gt; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nb=
sp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; L
<br>&gt;
<br>&gt; &nbsp; &nbsp; You seem to be saying that L is not an individual be=
cause we can
<br>&gt; &nbsp; &nbsp; turn it
<br>&gt; &nbsp; &nbsp; into multiple smaller line segments A, B, C, like th=
is:
<br>&gt;
<br>&gt; &nbsp; &nbsp; |---------------| |---------------| |---------------=
|
<br>&gt; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; A &nbsp; &nbsp; &=
nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; B &nbsp; &nbsp; &nbsp; &nbsp; &nbs=
p; &nbsp; &nbsp; &nbsp; C
<br>&gt;
<br>&gt; &nbsp; &nbsp; Further, you seem to be saying that A, B, and C are =
all among L. You
<br>&gt; &nbsp; &nbsp; also seem to be saying that each of A, B, C are not =
individuals either,
<br>&gt; &nbsp; &nbsp; because we can further split them, like this:
<br>&gt;
<br>&gt; &nbsp; &nbsp; |-------|-------| |-------|-------| |-------|-------=
|
<br>&gt; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; M &nbsp; &nbsp; &nbsp; N &nbsp;=
 &nbsp; &nbsp; &nbsp; O &nbsp; &nbsp; &nbsp; P &nbsp; &nbsp; &nbsp; &nbsp; =
Q &nbsp; &nbsp; &nbsp; R
<br>&gt;
<br>&gt; &nbsp; &nbsp; And that M and N are among A, and so on.
<br>&gt;
<br>&gt; &nbsp; &nbsp; Is this what you are saying?
<br>&gt;
<br>&gt;
<br>&gt;
<br>&gt; Yes.
<br>
<br>But how does that work? If the original {lo linji} (L) is an individual=
,=20
<br>then only itself can be among itself. On the other hand, if it is *not*=
=20
<br>an individual, then we cannot call it {lo linji} in the first place. Yo=
u </blockquote><div><br></div><div><br></div><div>The individuality is not =
an necessary condition for being {lo linji}. A special {lo linji} such that=
 {RO DA poi ke'a me lo linji zo'u lo linji cu me DA} is an individual.</div=
><div><br></div><div><br></div><div>&nbsp;</div><blockquote class=3D"yiv575=
089944gmail_quote" style=3D"margin:0;margin-left:0.8ex;border-left:1px #ccc=
 solid;padding-left:1ex;">
<br>could say that {lo linji} is more than one individual, and then the sam=
e=20
<br>things that applied to the singular L would apply again for each of the=
=20
<br>referents of the "more than one individual" L. At some point through th=
e=20
<br>taxonomy, you must arrive at an individual or individuals and then you=
=20
<br>can't go further and say that even smaller things are among that=20
<br>individual. Even the shortest line doesn't have {lo mokca} {me} it.
<br>
<br></blockquote><div><br></div><div><br></div><div>There is no shortest li=
ne. That is the point for proving that any {lo linji} in this universe of d=
iscourse cannot be an individual.</div><div><br></div><div><br></div><div>&=
nbsp;</div><blockquote class=3D"yiv575089944gmail_quote" style=3D"margin:0;=
margin-left:0.8ex;border-left:1px #ccc solid;padding-left:1ex;">&gt; For ex=
ample, in the case of finite {lo ci prenu}, let us call the three
<br>&gt; persons p1, p2, p3. In the universe of discourse. The following su=
mti
<br>&gt; are all in the domain of plural variable that are prenu even if yo=
u
<br>&gt; don't mention the sumti:
<br>&gt; p1
<br>&gt; p2
<br>&gt; p3
<br>&gt; p1 jo'u p2
<br>&gt; p2 jo'u p3
<br>&gt; p3 jo'u p1
<br>&gt; p1 jo'u p2 jo'u p3
<br>
<br>Yes.
<br>
<br>But I don't quite see how this is the same case. If this is what you=20
<br>were going for with the {linji} example, then it doesn't show anything=
=20
<br>that qualifies as not being one or more individuals.
<br>
<br>The 7 possible plural values for {prenu} above are all one or more=20
<br>individuals. Listing infinitely many more would not change that.
<br>
<br></blockquote><div><br></div><div><br></div><div>Not an infinite number =
of {lo linji} itself but an infinite number of procedures of affirming that=
 {lo linji xi ny cu me lo linji xi my i ku'i naku lo linji xi my cu me lo l=
inji xi ny} do prove that every {lo linji} is not one or more individuals.<=
/div><div><br></div><div><br></div><div>&nbsp;</div><blockquote class=3D"yi=
v575089944gmail_quote" style=3D"margin:0;margin-left:0.8ex;border-left:1px =
#ccc solid;padding-left:1ex;">&gt; Similarly, the infinite number of {lo li=
nji} were in the domain of
<br>&gt; plural variable that are linji when the universe of discourse was =
given
<br>&gt; first.
<br>
<br>Infinity does not preclude individualness. If you have an infinite=20
<br>number of "things", then you just have infinitely many individuals.
<br>
</blockquote><div><br></div><div><br></div><div>{lo linji} in that universe=
 of discourse are not individuals but an infinite number of&nbsp;non-indivi=
duals, because every {lo linji xi my} has always another {lo linji xi ny} s=
uch that</div><div>{lo linji xi ny cu me lo linji xi my i ku'i naku lo linj=
i xi my cu me lo linji xi ny}, and this proposition contradicts the conditi=
on for individual {RO DA poi ke'a me lo linji xi my zo'u lo linji xi my cu =
me DA}. Therefore, every {lo linji} is neither an individual&nbsp;nor&nbsp;=
individuals.</div><div>&nbsp;</div></div>


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