# discussion of the Conservative Extension

• la xorxes:
• The correspondences (I don't dare say equivalences) now seem to be:
XS CE
lo loi (=? lu'o loi)
lo PA PA loi (=? lu'o PA loi)
lo pa lo (=? pa loi, =? lu'o pa loi)
PA (lo pa) PA (lo) (=? PA lu'o pa loi)
PA lo PA lu'o loi
PA1 lo PA2 PA1 lu'o PA2 loi
• la xorxes:
• XS uses outer PA always as a normal quantifier, while Conservative Extension sometimes uses it for other purposes (as in PA loi, PA lei).
• pc:
• True, though the anomolous uses are tentative, trying to deal with some issues you've raised. The sense of the difference is that for universal groups, the subgroups defined by adding predicates are more interesting than those defined by size, so ought to have easiest expression. For distributive groups, the opposite seems to be the case - indeed, the subgroups defined by predicates turn out to be simply different selections, not subgroups at all.
• As for the correspondences, The first is what I understand to be going on (and, yes, I think the collpase goes through, though similar thoughts elsewhere have proven wrong). For the second, third, and fourth I cannot speak, since I don't know yet what they mean - and wonder why pa is separated from the rest of PA. Is it an anomolous case? If I understand what you are up to, then the fifth is right, but your use of external PA is now different from what it is elsewhere (assuming I have figured out what that is, which I doubt - a subgroup of size PA, I would have guessed.
• The pa case is not anomalous within the XS scheme. It is separated simply because there is a special expression in CE that corresponds to it. pa broda lo pa broda in XS is the Kind "Mr One Broda". lo pa broda PA lo pa broda is quantification over real avatars of that Kind. lo pa broda ro lo pa broda is "every single broda".
• So, there is no Mr. Two-Broda? But you are going to say there is in the next step. Presumably an avatar of Mr. One-Broda is a singleton, a set containing exactly one broda. lo pa broda ro lo pa broda then is "every broda singleton" not every single broda in either sense of that expression (absolutely all of them or each one taken singly). Assuming that what you say here is a correct reporting of what you mean. Nothing in CE corresponds to pa broda lo pa broda in this sense, certainly not broda lo broda, which is some group of brodas fixed for the context though not by the speaker. Its referents are the brodas themselves, not their singletons.
• I notice that I have now changed the meaning of lu'o and so probably of lu'i from "the mass with the same members as ..." to "a mass with only members from ...". And the last one is obscured again. One of the reasons for setting out that strange ontology was to have a single reference point to which we could trace back all these complicated expressions, but you won't use it and I can't figure out what your system amounts to in its terms.
• I tried to use the ontology, but you stumped me by saying that you don't allow things like ka ce'u remei le ka ce'u remei as columns, and therefore you don't have single rows that correspond to groups or to Kinds. If you allow me to extend the ontology so that truly any property is allowed as a column, then I can use it to explain XS: each of le and lo always point to a single row of this extended ontology. lo PA lo quantifies over the set of rows that correspond (via the property "is an avatar of lo broda") to the row selected by lo broda. le PA le quantifies over the set of rows that correspond (via the property "is a member of le broda") to the row selected by le broda.
• Well, since there are only first order things, it must be the case that, if ka ce'u remei le ka ce'u remei means something at all, it means something about such things, in this case something about considering things two at a time (cumulatively or collectively). Exactly what will depend upon what else you say in the sentences that include this phrase. I don't have lines corresponding to groups or to Kinds, because they are just ways of considering things and i want to figure what ways they are. But now that you propose an extended ontology - but still want the same things to happen, so the internal structure is now monstrously more complex - lets see what I can make of it. We have a column for "is a doubleton" and so there are rows (and thus things) that have this property. And what others? Presumably things like "have things marked for broda as members" - and, if there is more than one of these, than there must be something else that distinguishes one from the other.
• Yes, plenty of things. "Carried the piano yesterday", for example. None of the objects in the original table will have a positive in that column, but there will be one of the new rows that has a positive in "cimei" and in "carried the piano yesterday". Lots of other rows with positive for "cimei" won't have a positive for "carried the piano yesterday", of course.
• There is, of course, a predicate "carried the piano yesterday" and so some things that have it, though probably nothing real. There are also a number of predicates about what the various members of the cimei actually did that resulted in/amounted to carrying the piano when their activities are considered together collectivly. What they actually did get lost in the focus on the result of those activities (which might not have been their intentions at all, for example)but they are what really happens - the rest is gravy. (see below for some attempt to make some sense of your desired ontology)
• Are any of the basic rows marked positive for "carried the piano yesterday" in any way interesting? Are any of those rows in any way helpful to relate this property to the various members of the cimei that did what resulted in the piano being carried? How do we connect, in the basic ontology, the rows that are members of the cimei with the property "carried the piano yesterday", which none of those rows has?
• I find Samson types interesting, though, I admit, this one is probably not real. But, oh how interesting he (and in some cases, she) would be. In various worlds in which these things coexist, their doing their various things results in the piano going from here to there in their various hands.
• If the Samson type is a thing (a row, but not an object) that carries the piano, how are the Samson types connected to the actual members of the cimei (which itself is not even a thing) that carries the piano?
• I didn't say he wasn't an object just that he is not real, i.e. doses not exist in this world. He has no connection with in cimei except that a group that included him could surely carry a piano.
• xorxes: So in the basic ontology, where groups are not things, there is no way to connect the column corresponding to the property "carries the piano" with the rows corresponding to the three men that carried the piano.
• Right, because none of them does. they do other things which, in some worlds at least, amount to carrying the piano as a group.
• An intersting current case. It now appears that six switches blacked out the eastern US (and part of Canada). They each did what they normally do: cut out power surges, but whne these happened more or less simultaneously we got the blackout. In countless other worlds inn which they do their thing there is no blackout and their synergies go unremarked until forced on our notice. Then we "take them together" and, lo, a collective!
• For sets that can be only members, so we now have to say as a property in this array that something has as members things that are defined by the array itself. This is the favorite home of paradoxes - defining members of incompleted sets in terms of the completed set they will be members of, impredicative definitions. That is why I don't want second order vocabulary as primitive. Having as properties "is a property" is even worse, if possible. But back to seeing what could be done but for these problems: "le and lo each point to a single line, each names a thing - with what properties?
• In the case of le, no properties are given, it is just something that the speaker has in mind. The description is provided just as an aid for the listener. In most cases the description will correspond to a true property of the row in question. In the case of lo, the row is one that has the property "is a Kind corresponding to the property given by the description".
• (see below) what le refers to will be a number of objects, even if there is not common property involved.
• The idea proposed in XS is that le points to a single row (in the extended matrix). If that row has a number of objects (other rows) associated to it as members, then you can go on and quantify over them. If not, not.
• Le'ssee: le refers to a second order row marked for distributive and a number (perhaps 0?) first order objects (columns now). OK - but you get the same result if you just say it refers to the first order objects distributively and you save a whole level of unreality.
• You do get the same result when quantifying, that's what I said from the start. You don't get the same result when you just use broda le broda unquantified.
• Why not? Did I allow le to go into the universal domain rather than just the existents? That was an accomodation to one of your problems. Since I now think that your problems are self-inflicted, I am happy to withdraw that if it gets a satisfactory result.
• But then we have "lo PA lo quantifies over the sets of rows that corresond to lo" But lo points to a single row. OK, so among the properties of a given line are a bunch of the form "has A as an avatar" for some other line a (which presumably includes the property "is an avatar of ..."). lo PA lo then quantifies over set of rows like A. That is, lo PA lo quantifies over the things that are referred to in the avatar way by lo. So the only question left is what is "referred to in an avatar way." But if you can answer that question, we didn't need all the rest of this stuff. And if you can't, then your system is still impenetrable.
• I'm not sure I understand the question. How do you manage, in the original table, to identify those rows? You can use the same method now, because they will be the same old rows. lo pa PA lo pa gets you to exactly the same rows as lo PA lo did in the original table. (At least for those broda that existed in the original table. In the original table lo remei ci lo remei was meaningless because there was no column for remeis.)
• Which rows? the ones that correspond to your lo aren't there, I think. The ones for CE broda lo broda will be some selection from the rows with a plus (only}} in the broda column, lo broda PA lo broda will be some such selection of PA such rows. If you really mean what you really say, then there will be nothing corresponding to XS lo pa broda PA lo pa broda because there will be no rows that are for singletons - or any other sets - of objects, as pa broda lo pa broda seems to require. They certainly won't be the same rows as picked out by CE lo broda PA lo broda since these are all brodas themselves.
• And the problems come at just the places where I don't understand what you are aiming at. So, what is the practical upshot, in terms of objects of Mr. One Broda as opposed to Mr. Two Broda or even just Mr. Broda (I note in passing, as part of my problem, that you have already denied that Mr One Broda was anything like Mr. Broda Pamei or Mr Pamei be le'i broda, which, while weird, are accessible.)
• If I denied that Mr One Broda is Mr Broda Pamei, I retract my denial. They are the same thing as far as I can see. (Mr Pamei be le'i broda is a different matter because it is based on a specific set.)
• Sorry, broda lo'i broda.
• As I said somewhere else, broda lo'i broda will not work either, with the current place structure of mei. be lo'i broda pamei be lo'i broda makes sense only if broda lo'i broda is a singleton set, which for most broda it is not. The x2 of PAmei is not simply some set from which the members of x1 are extracted. It is the one set that has all the members of x1 and no other member. A fairly useless definition, but that's what it is.
• If what you say about mei is true - and it doesn't reflect usage but the word;lsit and CLL are, as usual, not as clear as might be - then the definition of mei has to be revises to "drawn from x2."
• You are most welcome to try to convince Lojbab and John Cowan of that.
• Well, I can just put it in LoCCan. But even they can see (well, maybe not, given history) that the definition -if it goes as you say - is useless. My list says of x2 "the mass formed from x2 whose n members are x3." I read - and have always read - that as saying it is the set with members exactly x3, all of which are members of x2. I can, with some effort, read it the other way - taking "whose n members are x3" as modifying "x2", rather than "the mass," but I have to put in a comma to manage it.
• I wouldn't know what the original intention was. I can only tell you that lojbab and John say that The PA in PAmei gives the cardinality of set x2.
• (repeated ad lib) Surely they mean x3 - even more surely x1.
• Both x1 and x2. The relationship would be: re nanmu cu remei le'i re nanmu ro le re nanmu lei re nanmu cu remei le'i re nanmu ro le re nanmu. The mass of two men is a two-some from the set of two men with each of the two men as members. But x3 is of course about each member separately: re nanmu cu remei le'i re nanmu la djan e la bil lei re nanmu cu remei le'i re nanmu la djan e la bil = re nanmu cu remei le'i re nanmu la djan ije lei re nanmu cu remei le'i re nanmu la bil lei re nanmu cu remei le'i re nanmu la djan ije lei re nanmu cu remei le'i re nanmu la bil. So djan te remei la djan te remei says that djan is a member of a two-some. x1 (la djan) is not a set and so does not have cardinality.
• I assume that if the PA is of any interesting size, x3 will be given as a named group, not individually, so what goes in will be brode (PA)le/lo brode - a subset of the brodas, of course.
• But now the question is, what is the use of Mr. One-Broda? I just rarely see or deal with singletons as opposed to individuals.
• It is useful in that now you have a whole series: Mr One-Broda, Mr Two-Broda, Mr Three-Broda, Mr Many-Broda, ... as well as Mr Half-Broda, Mr Fraction-of-Broda, ... All for the same price. I can't tell what difference there might be in seeing broda pa broda or seeing pamei be fi pa broda paboi pamei be fi pa broda. Is there one?
• Neat, I have this series. But what will I do with any of them? I could have had them with (revised) PAmei. Why are they valuable enough to get this compact expression. Indeed, what value have they at all? In whose language are we to compare meanings? I can't speak for yours, but for me broda pa broda refers to a broda and broda pamei pa broda pamei refers to as et whose only memvber is a broda. I can (depending on what broda means}} probably see the former; in no case can I see the latter.
• But pamei lo pamei are not sets but "masses". Tell me how you make a difference in treating the members of a singleton collectively or distributively. I don't see how you could. A singleton set is a different matter, and I agree that you can't see it, but how is le pa broda viska le pa broda different from lei pa broda viska lei pa broda?
• Touche! Usage has been so bad at making that distinction and the set reading has always been so much the most common that I forgot the actual words. If, at the time this was written down, the mass-set distinction was clearly in mind (which I doubt, since it often is not even now), then you are quite right. I do wish you had mentioned this at some earlier time when I called it a set and saved some todo.
• I didn't notice. For me it has always been obviously a collective, given that it is much more useful. And since x2 is supposed to be the set with exactly those same members, it would make no sense that x1 was the same set.
• I wonder how one says that a set is PA-membered? PAmei se PAmei if your reading is correct?
• Yes, that's one way. That is often inconvenient though, sometimes we want to say something about the number of members, which that form of expression won't allow. When I've needed the relationship "x1 is the number of members of x2" I've used kancu te kancu, or kancu be fi zi'o te kancu be fi zi'o, "x1 is the count of x2".
• But does this help beyond the case of Mr. One-Broda? If these are all collective, then that you get Mr. Two-Paper everyday will be true even if you always get only one paper on any given day, since the collective group has the properties attributed to each of its members as well as the ones that require collaboration.
• That's not how I understand collectives. I get a collective group of two papers only if I get the collective group of two papers, not if I get one member.
• But now you are changing the meaning of the collective relation - not a bad idea perhaps, but one that takes a warning note beforehand. This also means that there are non-object avatars and that is going to require some working over - how to reduce that back to talk just about objects. In this case, it is pretty easy - the avatar is not the collective group as you say, but the ditributive one: something is true of an avatar of Mr.Two-Papers (and so of Mr. Two-Papers itself?) just in case it is true of each of two papers. Others will be harder, I suspect.
• No, I take an avatar of Mr Two-Papers to be a collective group of two papers. A collective groups does not automatically inherit all the properties of its members. If you don't accept collective groups as objects, then I'm afraid there are non-object avatars. In other words, I take da remei su'o da remei as true: at least one "thing" is a two-some, there are twosomes. Do you hold that da remei no da remei?
• (etc)I have no problem with talking about collective groups as things, even quantifying over them, I just want to know what such talk means in each case. I take da remei su'o da remei to mean that things are sometimes taken together as couples and da remei no da remei to mean that they never are - the first blatantly true, the other equally obviously false. As noted before, the particular case involves changing the usual meaning of "collective", but that is problably desirable. It also reduces to the simple "Each day there are two papers that i get" without the metaphysics.
• But da remei su'o da remei says that at least one thing is a couple, not that things are sometimes taken as couples.
• I know what it says; my concern is with what it means.

Pc: From other papers around here, I wonder why ko'a e ko'e lu'i ko'a e ko'e should be a single set with these two members rather than a couple of sets, of one of which ko'a is the only member and the other ko'e (following the usual expansion of embedded connectives).

pc: But I think the main question here is whether ko'a lu'i ko'a is, if ko'a refers to an object, the singleton or just a set of which ko'a is a member, or even some group of sets of each of which ko'a is a member. I take it that if ko'a is a set or mass then lu'i ko'a is the set with the same members as the named set or mass, and if ko'a refers to a distributive group (lo/le) then lu'i ko'a is the set with exactly those members. So, in general, lu'i ko'a seems to be a unique set, hard as that may be to say in Lojban.

• You don't say what happens when ko'a is both a set and a distributive group, as in the case of te cuxna le te cuxna.
• In the case we have been considering, te cuxna le te cuxna is a distributive group of a single set, so the whole behaves like the set (a distributive group has the properties every one of its members has, and here there is only one member, so it behaves like that). Something can't be a set (a cumulative group) and a distributive group, but a distributive group can behave like a set if that set is its only member (or, indeed, if all its members are sets).
• So I still don't know what you want to do with le te cuxna lu'i le te cuxna. Is it choice-1 ce choice-2 ce choice-3 ..., or is it set-of-choices-1 ce set-of-choices-2 ce set-of-choices-3 ...?
• I am drawn both ways and have not worked out what will happen in each case. I should add that the example above also opens the possibility that it is intersection of the sets as well as the possibilities already discussed (which includes the union, I see). Maybe, if we get some basics taken care of, this will become clearer. And maybe, going back to e ko'a ko'e e ko'a we will discover - as we have often done in logic - that the surface English "and" is something quite else ("or" or a set operations, say) logically.

If these Mr. things are collectives, why 1) take one of the gadri that we actually understood pretty well away from that use and put it in for something we don't underatand at all and 2)pass up a gadri that has had this meaning forever (mixed with others to be sure, but this one has always been separated out as one possibility)? Starting afresh would have made sense, but this shuffling things around just seem perverse.

• Mr things are not collectives. Collectives and Mr, together with Stuff, have been traditionally conflated in Lojban loi, but this conflation is precisely what we want to sort out.
• Right, that is why I ask. Now, what exactly are the characteristics of the Mr.-avatar relation that distinguish it from collective, etc? (The point about using lo remains, even if that about loi does not.)
• I invite you to read the archives of the jboske list to answer that.
• Why do you think I am asking? I have slogged through reams of crap - yours and others' - without any concrete explanations and with constantly shifting requirements and examples. It may be that there is a coherent reading to all of that or to all of someone's reading in that, but it has never been pulled out or laid out precisely. I am trying either to do that or to get someone who believes this junk to do it. In short, you are not inviting me to a solution, only to a thorough muddling of the problem.

pc expands on the ontology.

There is a way of getting sets and the like into the ontology set up before (there is nothing sacred about that ontology, by the way. It was just a way to generate all the things that were likely to be needed in any conversation). To avoid impredicate definitions, we use recursion: creating each new whole and then defining the next level only in terms of what is on lower (completed) levels. In this case, we take the objects generated at the first stage - the one actually given before - and make them the column heads, along with a number of properties that say how new objects are to relate to old ones: distributively, collectively, cumulatively, as Mr. to avatar, as Kind to instance, as Stuff to hunk and so on, for as many of these as we need. Now the new rows will be things that have one of the kinds of relations to the items marked on that row. So, there will be, for every predicate, broda, a row that takes all of the things which have broda in each of the several ways possible. And also a row for each group of brodas, down to the rows which have only one broda marked but take it cumulatively, the singleton of each broda.

Now we take the objects (rows) so generated and add them as column headings to the objects already there. And we create all the rows across these columns, so we will have all kinds of groups of groups and groups of objectds, and mixed groups. Among all these will be, for each broda a set which deals as Mr. to avatar with its checked items and its checked items will be all those lines from the previous round that take exactly one broda cumulatively. That is, Mr. One-Broda will turn up in the third pass. But the procedure for getting the third pass from the second can be repeated to make a fourth pass and so on as long as needed to explain whatever needs explaining. This ought to include enough things to take care of any problem. To be sure, "is a threesome" is not a property on any column, but it is a property that rows after the first array have and all that can be done with it can be accounted for in some array.

• In this expanded ontology, XS le is used to point to a single row from any of the levels, whichever row the speaker has in mind. (If the speaker is going to use a quantifier with it, then they better pick a row that has members.)
• Well, presumably the one at the appropriate level - the one next higher than the highest member. CE le just picks the members directly.
• In the expanded ontology, broda lo broda picks the row that corresponds to Broda Mr Broda.
• The row next higher than brodas (note that there is no Mr. Mr., or, rather, one at each level after the second but no comprehensive one) which is marked for Mr.-avatar relation and marked for all and only broda columns. Is the Mr.-avatar column just the collective column? That would make subkinds pretty easy but wouldn't give Mr. Two-Paper.
• Mr avatar is not the collective. Mr Newspaper is usually light enough to carry. The collective of newspapers weighs millions of tons.
• Well, each avatar of Mr. Newspaper is light enough to carry, so, by the usual rules, Mr. Newspaper is too, even though it also weighs many millions of tons. I suspect that what you are getting at is that Mr-avatar only carriees upward the properties of avatars, while collectives carry upward both those and various intermediate collectives. But, on the other hand, you do seem to want to carry up some intermediate collectives as well: avatars of Mr. Two-Newspapers, whatever that is, are also avatars of Mr. Newspaper, are they not? Certainly Mr. New-York-Times works as an inclusive sub-Mr. Or is it that Mr. carries only the properties of ALL its avatars, and sub-Mr.s just over subsets, so with fewer avatars and ths more properties. If something like that, then this will not do as a replacement for CLL lo (the putative reason for reusing that word) since it will rarely make for true sentences.

But in fact the use of lo seems to be the correct thing and the metaphysical argle-bargle about Mr. Broda to be just that. what seems best to satisfy the conditions you are laying down is just old broda lo broda: a bunch of brodas (a distributive group of them, if you like), new for each occasion. Maybe we want the long scope on that, so that for a given context the reference remains the same. But otherwise, what (that does not involve the dubious metaphysics essentially) is said using Mr. Broda that this does not cover without paradox? (Hey, it even makes loPA come out right.)

• So how would that fit with: "I usually receive Mr Newspaper at home but today He didn't arrive, so I read Him at the office." If long scope can deal with that, then maybe it's equivalent. I just don't understand how you can do that with long scope quantifiers rather than with a constant.
• Hey, I said that did not involve the metaphysical presuppositions in the formulation. I assume you mean "I usually receive a copy of the newspaper, but none arrived to day so I read a copy at the office." "Usually there is a copy of the newspaper that I receive at home, but today there is no such copy so at the office there is a copy that I read ." Just sheets of paper, no Mr. Newspaper, no "he" or "it" as though there were a back reference to something that went before. And yet it says the same thing - absent a fondness for metaphysical eyewash, or a strictly translated idiom.
• It's just avoiding the making of distinctions when no distinction is necessary.
• What is? My formulation get rid of a whole bunch of stuff that isn't real, so that is getting rid of distinctions that aren't necessary. Your sentence - even if I figure what the reference of "it" is - is ambiguous and I doubt tha this is the one you intend, but my thesis is the only thing around that meets the condition.
• Constants are long-scope quantifiers, but in this case they are inappropriate, since the references to newspapers arre in three different situations at least, if not worlds. One is inherently in the scope of "usually," a temporal quantifier, another is in the scope of "today," another temporal, and the third in "at the office," a spatial that contrasts with "at home" in the previous two sections. In short, there is no one thing, here at all, but a large number of different things.
• And yet conveniently seen as one thing because there is no distinction worth making among the avatars. Similar to "John usually comes to visit me in the morning, but he didn't come today, so I talked to him on the phone." Obviously it is not the same stage of John that I see each morning, no stage came today, and there was one stage (not one that ever came to visit me) with whom I talked on the phone. But when speaking of people we find it convenient not to consider them as a number of stages but just as single individuals, we refer to them with constants. The idea is to do the same with Kinds. It simplifies the logic when the details of the avatar distribution is obvious or irrelevant.
• John is an object from the git-go. He is not a collection of stages although he can be thought of that way for some purposes. Your case is not one. Mr. Newspaper is not an object and making him one serves no vidible purpose so far as you have shown. There may be a purpose for which using Mr. Newspaper would achieve real a real efficiency. Your case is not one.
• To take it as one thing misses the whole point of the sentence. Now, if you want to talk that fanciful way, be my guest, but don't use up all the stuff needed for talking plainly for the artsy-fartsy stuff and leave plain talking to periphrasis and prolixity. Put Mr. Broda in CVV'V somewhere where he is available but doesn't do any harm. And be explicit about what you mean by it all, so us logic types don't have to go through all this again. (The change in the meaning of "collective" does seem a good idea, though - an unreal thing that has some clear uses.)
• In short, Mr. Broda - in this example at least (but it seems typical)- is just broda su'o broda with shortest possible scope, so that two occurrences of broda su'o broda or any anaphoric back references to one are independent of one another.

## Attempted summary

#### le

1. We agree about le PA2 broda PA1 le PA2 broda: normal quantification over members of a specific group of PA2 broda.
• Check!
2. XS PA broda le PA broda is equivalent to CE PA broda lei PA broda: the PA members of a specific group treated collectively.
• OK, but why use le for this rather than lei? le has never had this meaning, lei always had, though mixed with other things, for which we now need new treatments
• The XS scheme uses lo and le only.
3. CE PA broda le PA broda: the PA members of a specific group treated distributively with very long scope quantification (presumably with long scope ro?).
• Yes.

#### lo

1. We seem to agree in how it should be used, i.e. we have not been able to find any examples where XS broda lo broda would be used and CE broda lo broda would not, or viceversa.
• Actually, I'm not sure we do. I now see it as being used in at least two different ways and thus to be ambiguous, whereas I think you see it as being used in one uniform - though very odd - way.
• How do you propose to disambiguate? What would be an example where you would use broda lo broda and I wouldn't, or viceversa?
2. You don't understand the explanation of lo as a constant. (Basically, that Mr Broda is treated as an individual.)
• I understand it just fine; I just deny that it ever actually occurs in Lojban any more than in English in the corresponding places. Well, all right, I never did understand the relation betweeen Mr Broda and individual brodas. I now think that was because there is no one such relation but rather a confuison of several others dealing with other things. (I have to admit I am having my doubts about Trobriand Islanders: Malinowski was no linguist and even linguists are not logicians, so he might have gotten misled by superficial features of the language. A careless reading of English could lead to the same metaphysics, which is unsupported elsewhere in English culture - or by native speaker analysis. I wonder if there is anything else in Trobriand culture to support the notion of Mr. Rabbit.)
3. I don't understand your explanation of lo as short-scope quantified with literal replication by anaphora. Or rather, I can't see a difference between that and a constant.
• A constant refers to the same thing every time, a short-scope quantified expression refers to a different thing every time. Since, in the cases you have cited, there is no one thing referred to on all occasions and there clearly is a different thing each time, I take it that that is what is going on in, for example, the newspaper case - and the Chinese naming one, too, as well as several others in the literature.
• Of course. I meant that I don't see a difference between using short-quantification over avatars with literal replication and using a constant kind. We could similarly use short-quantification over stages plus literal replication when referring to people and obtain the same result as using constants. A name refers each time to a different stage too.
• Ahah! You've caught on, too.

pc's summary on lo (with the note that he objects to using a perfectly good CLL word in this non-CLL usage, while forcing that usage onto a more complex expression - even though it seems to be the more common.)

broda lo broda means either

1. Mr. Broda, a thing which has all the properties of any broda in any accessible world. broda lo broda is a constant, unaffected by negation passage, etc. But, since it extends into other worlds, it cannot be bound by quantifiers in this world (absolute intial ones) nor does the fact that in this world every broda is also a brode and conversely mean that broda lo broda can be replaced by brode lo brode(It is an intensional thing). All anaphoric pronouns tied to broda lo broda mean this same thing.
2. Extreme short-scope particular quantified broda, quantified into an explicit or implicit accessible world. Each occurrence of broda lo broda or its anaphora is a new quantifier in a new world (except accidentally), consequently these terms cannot be moved to absolute initial position - or even joined together - nor can equivalents be interchanged.

It turns out which of these reading you choose makes no difference to the information you convey; they differ only in how you talk about the language, not in the language. Logicians prefer the second version as being simpler in terms of what the logic already has available and so as falling in with Ockham's Razor. The Mr. Broda version requires more things and leaves some as yet unexplained items: the Mr.-avatar relation, for example (unless it is just as noted above), but can presumably be completed to work just as well as the other.