# mei

{PAmei} was originally introduced as simply a predicate to give the size of sets -- in the undifferentiated way that these were considered in Loglan, that is, any group, whether collective or cumulative. When the notion of a mathematical set got sorted out, mei continued to apply to the undifferentiated notion, set or mass, as we would say now. However, early in Lojban, it came to be specified for mass [although there is some evidence that that was still the undifferentiated notion under change of names). Further, details were added, giving the Wordlist definition "x1 is the mass formed from x2 whose n members are x3." This is several ways ambiguous and called for an interpretation. The one that was given was the less likely (an almost cetainly unintended) version: "x1 is the collective group whose members are exactly those of x2, whose (x2's, though also x1's) PA members are listed as x3" That is, the three arguments refer to the same objects in three different ways: mass, set and list. The more natural reading (and probably the originally intended one) would be "x2 is the mass of PA items drawn from set x2, specifically those in list x3." That is, all of the items in the mass are in x2, but not all x2 needs to be in x1. x3 is still the complete list of members, however. xorxes' discussions have suggested that it would also be sensible to allow x3 to be an incomplete list, giving only significant members, say. Other practical considerations suggest that x1 might better be either a set or a mass -- a group, in short, to allow for maximum usage (and to cover the difficulty in talking abut the cardinals of sets, which are, after all, cardinals home ground). So, ideally, {PA mei} should be "x1 is a PA membered group drawn from x2, having among its members x3"

- Is a "list" a third way of making reference to a group of objects, besides set and mass and different from quantification? I always took the x3 of PAmei to be a member, so {ta cimei fi ko'a e ko'e e ko'i}, which necessarily means that {ta cimei fi ko'a e ko'e} and also that {ta cimei fi ko'a}. If this is how it works, talking of a "complete list" makes no sense. Of course the property {le ka PAmei fi ce'u} will apply to the complete list of members, but only in the sense that it applies to each member individually, so x3 is a member not a list of members. If this is not how it works, then how do we express "complete lists" in Lojban? Is that perhaps what {jo'u} is for? And if that is the case, is there a corresponding gadri? This new gadri, say {le'o'u} would work like this: {le'o'u broda cu brode}: "each of the things that I describe as broda, and no other thing, is a brode." Something like that would be a gadri for "complete list". I don't think we have one in traditional Lojban. --xorxes
- I agree that there is a problem with this line however we work it out. We have no natural Lojban for a list per se, and such other forms don't work. Neither ko'a nor ko'e is PA members of the mass, each is one or some smaller number than PA (since the other is also needed). Nor do {ce} or {joi} work, since they give the mass again or the set again, but not the members. This seems to be yet another defect in the definition as given and I have seen too few (no?) instances of usage to know how it was resolved. So, another thing we need? (But surely we will find a gadri or a connective more related to {liste} if it comes to that.) Note that this is a problem regardless of whether we take "whose PA members are" as modifying x1 or x2. In this case, btw, a complete list will just be one with PA items on it.

- I don't think {mei} is all that helpful for talking about the cardinality of sets. If you really want to say something about the cardinality of some set ("The cardinality of set A is greater than the cardinality of set B" for instance) then {mei} is not of much help. We need a predicate "x1 is the cardinality of set x2". {terkancu} is not quite that, but we can say {lo terkancu be abu cu zmadu lo terkancu be by}. ({terkancu} really means "x1 is the cardinality of x2 as determined by x3 using units x4".) --xorxes
- As noted, it is sets that have cardinality in the first place, so saying what that is is important at that level (which is not much, given how little we really talk about sets). It is also nice to be able to talk about the cardinality of set as you do here -- if we are to talk about sets at all, but that is clearly not the point of {mei}, even when it is about sets. If we lack such expressions, that is a flaw in Lojban -- and not one that has an obvious easy solution. {terkancu} would work, if at all, only by zeroing out the third place (former first) and probably the fourth as well.

- Looking at the wordlist, I accidentally noticed the definition of {cimei} "x1 is a set whose three members are x2" The other defined {PAmei} are similar. That is, the enumerated is a
*set*and the second element is, somehow, the members and there is no mention of the set to which this is a subset. Even assuming that this is from so long ago that the official line was still that every plurality was a set (rather than the later that it was usually a mass), this suggests that the proposed definition is closer to what was intended originally. But it is still un realizable in current Lojban.

- Looking at the wordlist, I accidentally noticed the definition of {cimei} "x1 is a set whose three members are x2" The other defined {PAmei} are similar. That is, the enumerated is a