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Date: Fri, 12 Sep 2014 13:39:34 -0700
From: "'John E Clifford' via lojban" <lojban@googlegroups.com>
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Subject: [lojban] C-sets
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I was reading up on xorlo today, trying
to figure out what it says as opposed to what  various people seem to
think it says  =E2=80=93 and possibly what later changed actually make it
say, when I was reminded that Lojban still has C-sets in its
repertoire.  The not said that these are little used.  What a pity!=20
C-sets have some advantages over L-sets (mereological hola,
pluralities, etc.) which could be exploited in some situations rather
handily.  The problem is that we tend to take sentences involving
them in a fairly literal way, following (Cantorian) set theory rather
than Lojban.  In set theory of the usual sort, the only properties
that sets can have are size and taking things as members or other
sets as subsets (and various things derivative from these).  But
there is no reason, other than habit, why a set can't be said to
carry a piano or surround a building.  Allowing this, that letting a
C-set to have properties that grow out of the properties of its
members, has certain advantages in some cases.  The simplest is that
C-sets have two =E2=80=9Camong=E2=80=9D relations, one exclusively for
individuals and another not.  This removes =E2=80=93 or at least alleviates
=E2=80=93 a lot of complexity with L-sets, which has to keep shifting back
and forth on the issue (quantifiers on L-set expressions =E2=80=93 some of
them anyhow =E2=80=93 are restricted to individuals, even when subsets
might be more handy, for example.).  Another useful feature of C-sets
is that they can be empty, so that, unlike 'lo no broda', 'lo'e no
broda' is a meaningful, referential, expression.  Exactly what all
sets might be used for and just how to exploit them is not clear,
though I think all the needed pieces already exist and are
grammatical.  For now, I just want to place the possibilities into
the mix of expanding consciousness for usage.

--=20
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<html><body><div style=3D"color:#000; background-color:#fff; font-family:He=
lveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;fo=
nt-size:12pt"><div style=3D"margin-bottom: 0in" class=3D"">I was reading up=
 on xorlo today, trying
to figure out what it says as opposed to what  various people seem to
think it says  =E2=80=93 and possibly what later changed actually make it
say, when I was reminded that Lojban still has C-sets in its
repertoire.  The not said that these are little used.  What a pity!=20
C-sets have some advantages over L-sets (mereological hola,
pluralities, etc.) which could be exploited in some situations rather
handily.  The problem is that we tend to take sentences involving
them in a fairly literal way, following (Cantorian) set theory rather
than Lojban.  In set theory of the usual sort, the only properties
that sets can have are size and taking things as members or other
sets as subsets (and various things derivative from these).  But
there is no reason, other than habit, why a set can't be said to
carry a piano or surround a building.  Allowing this, that letting a
C-set to have properties that grow out of the properties of its
members, has certain advantages in some cases.  The simplest is that
C-sets have two =E2=80=9Camong=E2=80=9D relations, one exclusively for
individuals and another not.  This removes =E2=80=93 or at least alleviates
=E2=80=93 a lot of complexity with L-sets, which has to keep shifting back
and forth on the issue (quantifiers on L-set expressions =E2=80=93 some of
them anyhow =E2=80=93 are restricted to individuals, even when subsets
might be more handy, for example.).  Another useful feature of C-sets
is that they can be empty, so that, unlike 'lo no broda', 'lo'e no
broda' is a meaningful, referential, expression.  Exactly what all
sets might be used for and just how to exploit them is not clear,
though I think all the needed pieces already exist and are
grammatical.  For now, I just want to place the possibilities into
the mix of expanding consciousness for usage.</div><div class=3D"" style=3D=
""><br class=3D"" style=3D""></div></div></body></html>

<p></p>

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