null quantification

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(originally from tu'o and relevant to discussions of tu'o and lo'ei and similar creatures.)

I don't understand how the meaning of the bridi can be determined without quantifying over the underlying set, unless the set is one-membered. Perhaps the idea is simply that the quantifier is left unspecified so that it is glorked from context? That seems reasonable, but it's not equivalent to lo'ei (e.g. mi nitcu tu'o tanxe is not equivalent to mi nitcu lo'ei tanxe). --And Rosta

  • If the set is one-membered, then you are still quantifying over that one member, though perhaps a bit trivially. I think that the idea (as xorxes has expounded) is that the quantifier is deleted, resulting in the intensional meaning of the selbri being added to the main bridi without extensionally quantifying over the underlying set. This is just what happens with lo'ei: mi nitcu lo'ei tanxe is defined as mi kairnitcu le ka ce'u tanxe. There is no quantification over lo'i tanxe there, only a quantification over lo'i ka ce'u tanxe, which, like every property, whether it obtains or not (or can possibly obtain), is inherently a singleton. -- Adam

If we think of 'sets' as groups instead (collectivities, = Lojban 'masses'), then we can just refer directly to the set/group without quantifiying over its membership. Regarding your analysis of tu'o and lo'ei, I don't get it. lo'ei always seems to reduce to lo with a narrow scope within that of some implicit predicate. In other words, I think I have a rough idea of how lo'ei works, but I can't make sense of your and xorxes's analysis of its working. Maybe this discussion should move to the lo'ei page, if you're arguing that tu'o is equivalent to lo'ei. --And Rosta

  • Mathematical sets cannot be used directly, and mathematical sets are what lo'i does. Also, in Lojban you cannot just use groups/collectivities/masses directly without quantification. For individual gadri (lo/le/la) you must pick out (quantify over) individuals from that group. For mass gadri (loi/lei/lai) you must pick out (quantify over) parts of that mass. xorxes's rewrite of broda lo'ei brode to kairbroda le ka ce'u du lo brode was an intermediate step, I think, in the ultimate goal of getting to kairbroda le ka ce'u brode. As xorxes says, if you don't understand that, take sisku, which is a primitive in standard Lojban: mi sisku le ka ce'u tanxe (=mi buska lo'ei/tu'o tanxe) doesn't involve any quantification over lo'i tanxe, it merely uses the meaning of tanxe as expressed in the property le ka ce'u tanxe, and adds it to the predicate sisku. --Adam

I don't mean that lo'i broda is a group rather than a mathematical set. I mean that if we conceive of categories as groups of individuals, then we can either quantify over the membership, or refer to the group directly. (This is how lei/loi ought to work.) Regarding sisku, as I've been saying in the discussions on Jboske, I don't understand sisku tu'o ka ce'u broda except as a way of expressing troci tu'o du'u co'e lo broda, so for me the analogy with sisku does not help at all in explicating the notion of null quantification. I understand that lo'ei is supposed to "use the meaning of tanxe as expressed in the property le ka ce'u tanxe, and adds it to the predicate sisku", but I can't make sense of this. We haven't found any examples from English that don't reduce to lo (or loi'e). --And Rosta