sumti Places Requiring Sets

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[20:31] <rlpowell> Now, get rid of gismu places that require sets: *fuck* yes. But only the requirement, not the places. 

[20:33] <Melvar> Do the places make sense without sets? 

[20:33] <rlpowell> vensa: Also, I *do* try to listen, and respect people's objections and stuff. :) Just be nice, and I'll be nice back. 

[20:34] <rlpowell> Melvar: They make sense with any distributive group. 

[20:34] <Melvar> Exactly. 

[20:34] <rlpowell> Which isn't just sets. 

[20:34] <Melvar> What then? 

[20:35] <rlpowell> In fact, most of them make *way* more sense with loi than lo'i 

[20:35] <Melvar> Huh? Masses, distributive? 

[20:35] <rlpowell> Example: kampu: x1 (property - ka) is common/general/universal among members of set x2 (complete set) 

[20:36] <rlpowell> Erm, yes? That's their entire purpose? 

[20:36] <rlpowell> Masses are for "the students surrounded the building". Use that example as your analogical case and you can't really go wrong. :) 

[20:36] <rlpowell> No one student is doing the surrounding. The *set* of students certainly doesn't surround anything, because sets only have membership and cardinality. 

[20:37] <rlpowell> Lojban calls the non-distributive plural "masses". 

[20:38] <rlpowell> vensa: ^^ and that's why sets are kind of pointless. 

[20:38] <Melvar> Have you contradicted yourself or am I not understanding something important? 

[20:39] <rlpowell> The *only* attributes sets have are membership and cardinality. This makes them almost useless to say anything with outside of math. 

[20:39] <rlpowell> Melvar: As far as I know everything I said makes sense; what doesn't make sense to you? 

[20:40] <Melvar> It seems to me that once you called masses distributive, and another time nondistributive, or else I misassigned a response … 

[20:41] <rlpowell> You're absolutely right. 

[20:41] <rlpowell> < rlpowell> Melvar: They make sense with any distributive group. -- I meant non-distributive. 

[20:45] <paldanyli> Why does kampu make more sense with masses than sets? 

[20:46] <rlpowell> paldanyli: Because sets only have cardinality and membership. 

[20:46] <rlpowell> They have no other properties. 

[20:47] <rlpowell> The only thing that's "common" to a set is, I dunno, the most frequent member or something? It doesn't even really make sense. 

[20:48] <Melvar> The way I thought of it is that the concept of membership makes a set act as a distributive. 

[20:49] <paldanyli> It makes sense to me. We're talking about the members, no? 

[20:49] <rlpowell> Distributiveness is exactly not-helpful here; that's why you can't do "kampu mi .e do", because that distributes to "kampu mi" and "kampu do" 

[20:49] <rlpowell> Yeah, the idea is it's supposed to be "common among the members of the set", but "among the members of the mass" works just fine too. 

[20:49] <rlpowell> And "common to the mass" also. 

[20:50] <paldanyli> That doesn't make much sense to me. How could something be common in a mass? Perhaps I think of masses differently than everyone else. 

[20:51] <Melvar> Masses don’t have members, do they? 

[20:51] <rlpowell> How could they not? 

[20:51] <Melvar> ∈ is not defined on them. 

[20:51] <rlpowell> I mean, if sets have members, I don't see how a mass could possibly not; they're both plural abstractions. 

[20:51] <rlpowell> Umm. Nothing mathematical is defined on masses; we made them up. 

[20:52] <paldanyli> Wouldn't be much use if masses didn't have members. But if the purpose is to aggregate their properties, using them to get at their members properties seems strange. 

[20:53] <rlpowell> That's true for sets, too. :) 

[20:53] <paldanyli> Not to aggregate their properties. Just to indicate the membership. 

[20:54] <rlpowell> To me, a mass of something has all of the properties of its members, in proportion to their frequency. So the mass of rats is mostly X inches long, but somewhat Y inches long. 

[20:54] <rlpowell> That view is probably idiosyncratic, though. 

[20:54] == mode/#lojban +o kpreid by ChanServ 

[20:54] <paldanyli> That was my view as well. Which is why kampu on masses confuses me. 

[20:55] <rlpowell> Well, something that is common to all of them is clearly a major part of the mass, yeah? 

[20:55] <Melvar> kampu: p ↦ A ↦ ∀a∈A:p(a) 

[20:55] <rlpowell> I can't see most of that, sorry. 

[20:56] <Melvar> Wait a sec. 

[20:56] <paldanyli> I don't think there's any reason that masses couldn't serve as sets, but it's not what I think of their purpose as being. It's confusing to me to make a set then "break it apart". 

[20:56] <paldanyli> Make a mass, rather. 

[20:56] <rlpowell> Right, but whether you use a set or a mass there, you're asking about the members, not the set or the mass. 

[20:56] <rlpowell> So I don't see that it matters much. 

[20:57] <paldanyli> Probably not. I can't think of a property of sets that wouldn't apply to masses. 

[20:58] <rlpowell> And this all is why I wouldn't suggest getting rid of sets; if it's this easy to argue about, it's not clear cut. :D 

[20:58] <Melvar> $kampu: p \mapsto { A \mapsto \forall a \in A : p(a) }$ approximately. 

[21:01] <paldanyli> I suppose the cardinality of a mass of masses would be in question. 

[21:02] <paldanyli> Likewise its membership? 

[21:03] <rlpowell> Hadn't thought about it. 

[21:05] == tom has changed nick to _wtw_ 

[21:08] <Melvar> You could say I see sets as enumerable, but not masses. 

[21:10] <rlpowell> Which I think is a valid POV. 

[21:10] <rlpowell> I just don't know if that's how the language works. :) 

[21:11] <rlpowell> I'd love it if you could summarize all this to the appropriate BPFK page, btw. Perhaps the gadri one.