Message-Id: <199512121602.SAA21629@xiron.pc.helsinki.fi>
Date:         Tue, 12 Dec 1995 11:08:36 -0500
Reply-To: John Cowan <cowan@LOCKE.CCIL.ORG>
Sender: Lojban list <LOJBAN@CUVMB.BITNET>
From: John Cowan <cowan@LOCKE.CCIL.ORG>
Subject:      Re: TECH: lambda and "ka" revisited
To: Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
In-Reply-To:  <199512101602.LAA09173@locke.ccil.org> from "ucleaar" at Dec 10,
              95 03:47:24 pm
Content-Length: 2773
Lines: 55

la .and. cusku di'e

> > Whereas sets must be abstract, because they have no empirical
> > correlates, events and forks are concrete (in the sense of being
> > observable).
> > Forks are concrete: I can point at them, pick them up, etc.  Event
> > abstract objects are not.
>
> Events can be pointed to, albeit not picked up. Event abstract objects
> and fork abstract objects can be pointed to if they're real; the fork
> abstract object, if real, can also be picked up.

I think it is only the concrete fork, not the "fork-type abstract object", which
can be picked up.  To tell the truth, I have no idea what a "fork-type
abstract object" might be; I only say that Lojban has a way of referring
to such objects if anyone finds it useful to postulate them.

I do not think event abstract objects can be pointed to, or only by a kind
of metonymy of pointing, whereby you point at some concrete object involved
in the event.  You can point at me, and you can point at me-who-is-breathing,
but I don't see how you can point at my breathing.

> > > Events and forks can be either real or imaginable, whereas for sets
> > > reality and imaginability amount to the same thing.
> > I again disagree, but from the other side now.  I can imagine the set
> > of all sets ("lo'i girzu"), but Cantor's paradox guarantees its
> > nonexistence.
>
> Should that be {lohi se girzu}? I had an idea that x1 of girzu is the
> group and x2 is the set of its members. But my gismu list has "x1 is
> group/set defined by property (ka)/membership (set) x3", which is
> stange both in the absence of x2 and in the "group/set" gloss.

The current definition makes both of us wrong: "x1 is a group/cluster/team
showing common property (ka) x2 due to set x3 linked by relations x4."
I had thought that "selcmima" was a set defined extensionally (relationship
between set x1 and each member x2) and "girzu" was a set defined
intensionally, but apparently a "girzu" is some kind of projection of a set.
I'll have to ask lojbab what he had in mind.

> As for Cantor's paradox, it is metaphysically curious. lohi girzu
> exists in the world of the imaginable, and no sets (or all sets)
> exist in the world of the real. I'll go off and revise my metaphysics.
> Maybe you can't imagine the set of all sets - rather, you can imagine
> a method of generating it (which wouldn't work).

Maybe so.  But your "no sets/all sets" dichotomy is just what I reject.
Depending on your set theory, you can accept the existence of some sets
but deny others, or more precisely, you accept that some membership
conditions (e.g. "x | x is on my desk") determine sets, and some
(e.g. "x | x is a set") do not.

--
John Cowan                                      cowan@ccil.org
                e'osai ko sarji la lojban.