From cowan Sat Mar 6 22:46:09 2010 Subject: Re: TECH: lambda and "ka" revisited To: lojban@cuvmb.cc.columbia.edu (Lojban List) From: cowan Date: Tue, 12 Dec 1995 11:08:36 -0500 (EST) In-Reply-To: <199512101602.LAA09173@locke.ccil.org> from "ucleaar" at Dec 10, 95 03:47:24 pm X-Mailer: ELM [version 2.4 PL24] Content-Type: text Content-Length: 2729 Status: OR X-From-Space-Date: Tue Dec 12 11:08:36 1995 X-From-Space-Address: cowan Message-ID: 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.