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xorxes: > Some considerations about LAhE and quantifiers. > > 1- lu'a an individual/member/component of > > CLL does not say anything (that I could find) about default > quantifiers for LAhEs. I won't assume any for now. > > I take lu'a to work thus: > > ro lu'a ko'a - each member of ko'a > ro lu'a ko'a e ko'e - each member of both ko'a and ko'e > ro lu'a ko'a a ko'e - each member of either ko'a or ko'e or both > > {ro lu'a ko'a e ko'e} is equivalent to {ro lu'a ko'a ku'a ko'e}, > each member of the intersection of ko'a and ko'e, and {ro lu'a > ko'a a ko'e} is equivalent to {ro lu'a ko'a jo'e ko'e}, each member > of the union of ko'a and ko'e. > > {ro lu'a ko'a enai ko'e} is each member of ko'a that is not a > member of ko'e, etc. > > Similarly {ro lu'a ro lo broda} is each member of every broda > (i.e. each member of the intersection of all broda) and > {ro lu'a su'o lo broda} is each member of at least one broda, > i.e. each member of the union of all broda. For these to make > sense, brodas have to be things with members. > > {su'o da zo'u ro lu'a da} is different from {ro lu'a su'o da}. > The first gives, for some X, each member of X. The second gives > each member of at least some X (i.e. everything). > > {ro da zo'u ro lu'a da} is different from {ro lu'a ro da}. > The first is for each X, each member of X. The second > one is each member of every X, (i.e. nothing). > > We can expand {PA1 lu'a PA2 da} as {PA1 de poi PA2 da zo'u de cmima da} All this has to be the default story, since it follows inevitably from the left-to-right scope rule & we would need a very very compelling reason to go against it. > 2- lu'i a set formed from > > Here I'm not so sure. Is {lu'i ko'a} some set that has ko'a > as one of its members, or is it the set that has ko'a as its only > member, or something else? The something else might be the membership qua Group. I think the *intent* of lu'i is clear -- it is somehow supposed to magic a distributive into a set. I.e. lu'i ko'a e ko'e is intended to be equivalent to ko'a ce ko'e. Getting that to work is quite a tall order, though. Here's how it might be done: (tu'o) lu'i ko'a e ko'e = the set that includes ko'a e ko'e and that excludes ro da poi ko'a e ko'e na du ke'a = the set {ko'a, ko'e} > If we take it to be the reverse of lu'a, we would expand > {PA1 lu'i PA2 da} as {PA1 de poi PA2 da zo'u de se cmima da}. > > So {ro lu'i ko'a} would be each set that has ko'a as a member, > not necessarily as its only member. I have no idea whether this > is a useful notion or not. {su'o lu'i ko'a} is some set that > has ko'a as one of its members. {ro lu'i ko'a enai ko'e} would > be each set that has ko'a as a member and does not have ko'e as > member, etc. {ro lu'i ro lo broda} is each set that contains all > broda, {ro lu'i su'o lo broda} is each set that contains at least > some broda. This is (a) correct & (b) pretty useless. However, redefining {lu'i} as "set that excludes everything except" gives more useful results. > If we take the complement to be the full list of the members, > we run into trouble with things like {lu'i ko'a enai ko'e}. > How is that different from {lu'i ko'a}? On my suggestion: {su'o lu'i ko'a enai ko'e} = a set that includes ko'a and excludes ko'e > And what is {lu'i ko'a a ko'e}? {su'o lu'i ko'a a ko'e} = a set that includes ko'a or ko'e and excludes everything thst is either not ko'a or not ko'e. IOW, something that is the set {ko'a} or the set {ko'e}. > A third possibility is that ko'a itself has members and then > that {lu'i ko'a} is the set whose members are the members of > ko'a. This view has been offered in the past, but I don't > think it is worth defending. Agreed. > 3- lu'o a mass formed from > > This one has possibilities analogous to those of lu'i. > > So, while {lu'a} seems to be fairly clear, the functioning of > {lu'i} and {lu'o} is not at all clear to me. I think my suggestion for lu'i, which would apply also to lu'o, is perhaps the best compromise between usefulness and consistency. However, whereas {lu'a} ought happily to take either a set or a mass as its argument, lu'i and lu'o would take only 'individuals' (i.e. members/constituents). So {lu'i lu'o} and {lu'o lu'i} would not convert a mass into a set and vice versa. --And.