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Date: Sat, 8 Feb 2014 13:47:58 -0800 (PST)
From: John E Clifford <kali9putra@yahoo.com>
Reply-To: lojban@googlegroups.com
Subject: Re: [lojban] Individuals and xorlo
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There several logical systems which are formally indistinguishable but whic=
h differ in metalanguage and informal chat. =A0They also extend in differen=
t ways when they are built into something like Lojban, =A0Mixing the differ=
ent metalanguages or the different chat or the different extentions makes f=
or results that are even more paradoxical than already happens in any one o=
f the systems. For present purposes, lets just consider two relatively typi=
cal systems, plural quantification ala McKay and mereology ala Lesniewski (=
there are other plural quantifications and other part-whole theories). Plur=
al quantification (and plural reference, which goes with it in McKay, thoug=
h need not) starts with a domain of =A0individuals but then specifies refer=
ence and evaluation not as functions but as relations, =A0Thus, "term A ref=
ers to" is a predicate which may be true of several thing simultaneously an=
d similarly "variable X evaluates as". =A0Mereology begins with wholes
 and introduces individuals, if at all, only as wholes which are their only=
 parts. =A0The mereological metalanguage is normal, using functions rather =
than relations. =A0Talking about sets in either system is a bit misleading.=
 In plural reference, there is no entity (in terms of the system) between =
=A0individuals and the role they play, so no sets. =A0In mereology, there i=
s no separate type between individuals and what plays the role, so no (spec=
ial class of ) individuals. =A0In fairness to terminology, the wholes of me=
reology are sometimes called sets or some such thing, but are definitely no=
t the same as the usual, Cantorian, sets. =A0Similarly, in nontechnical dis=
cussions in English, it is almost impossible to talk about several things s=
imultaneously with out introducing some collective expression: "plurality" =
or "bunch" (my favorite) or ... .=A0The fundamental internal relation in th=
e two systems are "among" for plural reference (a relation between some
 individuals simultaneously and some individuals simultaneously) and "is pa=
rt of" in mereology (between two wholes). =A0A moment's thought will show t=
hese are going to behave exactly the same, if you understand the system (if=
 you don't see they behave the same, then we need to go back to the two sys=
tems in more detail). =A0All this being the case, it turns out that, for =
=A0informal discussions, at least, it is most efficient to use one of those=
 handy English expressions to talk about the system without specifying whic=
h version you are using. =A0But, since there is a temptation to take these =
terms literally, it is probably best to avoid freighted expressions like "s=
et" or "group" or "mass" (this is why I like the unfreighted "bunch"). =A0B=
ut the problems with literality are obviously different in the two cases: i=
n one you call into existence some intermediate type, in the other you call=
 into existence some fundamental individuals. =A0Lojban seems to split the
 difference, talking as though there were things of the intermediate type (=
you can't actually says some plural reference sorts of things in grammatica=
l Lojban "A, B among A,B, C," for example) but sometimes talking as though =
there were ultimate individuals (counting what is in lo broda, for example)=
. =A0But at other times (or, perhaps, with some predicate but not others) i=
t goes with indefinitely extensible partness (as when 'lo gerku' can refer =
to dabs of stuff on my bumper from running into a pack of dogs). =A0I think=
 any effort to resolve this kind of tension in general, rather than on each=
 particular occasion, is going to fail, since we clearly want and need both=
 approaches. =A0So the quest for THE meaning of a Lojban expression -- othe=
r than its formal role -- seems a not very promising task. =A0One of the ni=
ce things about that pedantic definition of 'lo broda', "the salient node o=
f the upward semi-lattice ..." is that covers just about every kind of
 case.=A0


________________________________
 From: guskant <gusni.kantu@gmail.com>
To: lojban@googlegroups.com=20
Sent: Saturday, February 8, 2014 9:34 AM
Subject: Re: [lojban] Individuals and xorlo
=20


Le samedi 8 f=E9vrier 2014 19:57:39 UTC+9, lojbab a =E9crit=A0:
On 2/6/2014 8:58 PM, guskant wrote:=20
>>=20
>>=20
>> Le vendredi 7 f=E9vrier 2014 06:22:09 UTC+9, xorxes a =E9crit :=20
>>=20
>>=20
>> =A0 =A0 On Thu, Feb 6, 2014 at 1:34 AM, guskant <gusni...@gmail.com> wro=
te:=20
>>=20
>>=20
>> =A0 =A0 =A0 =A0 Although it will become out of topic, I have another sug=
gestion=20
>> =A0 =A0 =A0 =A0 related to the BPFK page of gadri.=20
>>=20
>> =A0 =A0 =A0 =A0 "Any term without an explicit outer quantifier is a cons=
tant"=20
>> =A0 =A0 =A0 =A0 should be changed to=20
>> =A0 =A0 =A0 =A0 "Any term without an explicit outer quantifier can be a =
constant",=20
>> =A0 =A0 =A0 =A0 because an usual predicate logic has an axiom on a const=
ant c=20
>> =A0 =A0 =A0 =A0 that "F(c) {inaja} there is at least one (individual) x =
such=20
>> =A0 =A0 =A0 =A0 that F(x)";=20
>>=20
>>=20
>> =A0 =A0 That applies to singular constants, whereas unquantified terms n=
eed=20
>> =A0 =A0 not be singular, but the version with plural quantifiers will st=
ill=20
>> =A0 =A0 be valid.=20
>>=20
>>=20
>>=20
>> Actually, there is no explicit plural qiantifier in Lojban, though=20
>> implicitly there are.=20
>
>su'ore is the plural quantifier=20
>


That is a singular quantifier. I did not mean it by "plural quantifier". I =
meant that of plural logic.
=A0
--=20
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--=20
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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>There seve=
ral logical systems which are formally indistinguishable but which differ i=
n metalanguage and informal chat. &nbsp;They also extend in different ways =
when they are built into something like Lojban, &nbsp;Mixing the different =
metalanguages or the different chat or the different extentions makes for r=
esults that are even more paradoxical than already happens in any one of th=
e systems. For present purposes, lets just consider two relatively typical =
systems, plural quantification ala McKay and mereology ala Lesniewski (ther=
e are other plural quantifications and other part-whole theories). Plural q=
uantification (and plural reference, which goes with it in McKay, though ne=
ed not) starts with a domain of &nbsp;individuals but then specifies refere=
nce and evaluation not as functions but as relations, &nbsp;Thus,
 "term A refers to" is a predicate which may be true of several thing simul=
taneously and similarly "variable X evaluates as". &nbsp;Mereology begins w=
ith wholes and introduces individuals, if at all, only as wholes which are =
their only parts. &nbsp;The mereological metalanguage is normal, using func=
tions rather than relations. &nbsp;Talking about sets in either system is a=
 bit misleading. In plural reference, there is no entity (in terms of the s=
ystem) between &nbsp;individuals and the role they play, so no sets. &nbsp;=
In mereology, there is no separate type between individuals and what plays =
the role, so no (special class of ) individuals. &nbsp;In fairness to termi=
nology, the wholes of mereology are sometimes called sets or some such thin=
g, but are definitely not the same as the usual, Cantorian, sets. &nbsp;Sim=
ilarly, in nontechnical discussions in English, it is almost impossible to =
talk about several things simultaneously with out introducing some
 collective expression: "plurality" or "bunch" (my favorite) or ... .</span=
><span>&nbsp;The fundamental internal relation in the two systems are "amon=
g" for plural r</span>eference (a relation between some individuals simulta=
neously and some individuals simultaneously) and "is part of" in mereology =
(between two wholes). &nbsp;A moment's thought will show these are going to=
 behave exactly the same, if you understand the system (if you don't see th=
ey behave the same, then we need to go back to the two systems in more deta=
il). &nbsp;All this being the case, it turns out that, for &nbsp;informal d=
iscussions, at least, it is most efficient to use one of those handy Englis=
h expressions to talk about the system without specifying which version you=
 are using. &nbsp;But, since there is a temptation to take these terms lite=
rally, it is probably best to avoid freighted expressions like "set" or "gr=
oup" or "mass" (this is why I like the unfreighted "bunch").
 &nbsp;But the problems with literality are obviously different in the two =
cases: in one you call into existence some intermediate type, in the other =
you call into existence some fundamental individuals. &nbsp;Lojban seems to=
 split the difference, talking as though there were things of the intermedi=
ate type (you can't actually says some plural reference sorts of things in =
grammatical Lojban "A, B among A,B, C," for example) but sometimes talking =
as though there were ultimate individuals (counting what is in lo broda, fo=
r example). &nbsp;But at other times (or, perhaps, with some predicate but =
not others) it goes with indefinitely extensible partness (as when 'lo gerk=
u' can refer to dabs of stuff on my bumper from running into a pack of dogs=
). &nbsp;I think any effort to resolve this kind of tension in general, rat=
her than on each particular occasion, is going to fail, since we clearly wa=
nt and need both approaches. &nbsp;So the quest for THE meaning of a
 Lojban expression -- other than its formal role -- seems a not very promis=
ing task. &nbsp;One of the nice things about that pedantic definition of 'l=
o broda', "the salient node of the upward semi-lattice ..." is that covers =
just about every kind of case.&nbsp;</div><div style=3D"color: rgb(0, 0, 0)=
; font-size: 16px; font-family: 'times new roman', 'new york', times, serif=
; background-color: transparent; font-style: normal; "><span><br></span></d=
iv><div><br></div>  <div style=3D"font-size: 12pt; font-family: 'times new =
roman', 'new york', times, serif; "> <div style=3D"font-size: 12pt; font-fa=
mily: 'times new roman', 'new york', times, serif; "> <div dir=3D"ltr"> <hr=
 size=3D"1">  <font size=3D"2" face=3D"Arial"> <b><span style=3D"font-weigh=
t:bold;">From:</span></b> guskant &lt;gusni.kantu@gmail.com&gt;<br> <b><spa=
n style=3D"font-weight: bold;">To:</span></b> lojban@googlegroups.com <br> =
<b><span style=3D"font-weight: bold;">Sent:</span></b> Saturday, February 8=
, 2014 9:34
 AM<br> <b><span style=3D"font-weight: bold;">Subject:</span></b> Re: [lojb=
an] Individuals and xorlo<br> </font> </div> <div class=3D"y_msg_container"=
><br>
<div id=3D"yiv577315774"><div dir=3D"ltr"><br><br>Le samedi 8 f=E9vrier 201=
4 19:57:39 UTC+9, lojbab a =E9crit&nbsp;:<blockquote class=3D"yiv577315774g=
mail_quote" style=3D"margin:0;margin-left:0.8ex;border-left:1px #ccc solid;=
padding-left:1ex;">On 2/6/2014 8:58 PM, guskant wrote:
<br>&gt;
<br>&gt;
<br>&gt; Le vendredi 7 f=E9vrier 2014 06:22:09 UTC+9, xorxes a =E9crit :
<br>&gt;
<br>&gt;
<br>&gt; &nbsp; &nbsp; On Thu, Feb 6, 2014 at 1:34 AM, guskant &lt;<a rel=
=3D"nofollow" href=3D"">gusni...@gmail.com</a>&gt; wrote:
<br>&gt;
<br>&gt;
<br>&gt; &nbsp; &nbsp; &nbsp; &nbsp; Although it will become out of topic, =
I have another suggestion
<br>&gt; &nbsp; &nbsp; &nbsp; &nbsp; related to the BPFK page of gadri.
<br>&gt;
<br>&gt; &nbsp; &nbsp; &nbsp; &nbsp; "Any term without an explicit outer qu=
antifier is a constant"
<br>&gt; &nbsp; &nbsp; &nbsp; &nbsp; should be changed to
<br>&gt; &nbsp; &nbsp; &nbsp; &nbsp; "Any term without an explicit outer qu=
antifier can be a constant",
<br>&gt; &nbsp; &nbsp; &nbsp; &nbsp; because an usual predicate logic has a=
n axiom on a constant c
<br>&gt; &nbsp; &nbsp; &nbsp; &nbsp; that "F(c) {inaja} there is at least o=
ne (individual) x such
<br>&gt; &nbsp; &nbsp; &nbsp; &nbsp; that F(x)";
<br>&gt;
<br>&gt;
<br>&gt; &nbsp; &nbsp; That applies to singular constants, whereas unquanti=
fied terms need
<br>&gt; &nbsp; &nbsp; not be singular, but the version with plural quantif=
iers will still
<br>&gt; &nbsp; &nbsp; be valid.
<br>&gt;
<br>&gt;
<br>&gt;
<br>&gt; Actually, there is no explicit plural qiantifier in Lojban, though
<br>&gt; implicitly there are.
<br>
<br>su'ore is the plural quantifier
<br>
</blockquote><div><br></div><div><br></div><div>That is a singular quantifi=
er. I did not mean it by "plural quantifier". I meant that of plural logic.=
</div><div>&nbsp;</div></div>


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ut</a>.<br>
</div><br><br></div> </div> </div>  </div></body></html>

<p></p>

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