An essay on gadri

On this page I have essayed an exposition of gadri to someone who is neither a novice nor completely sure of the differences among the gadri. Hopefully someone with superior pedagogical skills can retranslate this page for those who still find it indigestible.

As usual, please don't annotate the main text other than by the insertion of footnote references; add any comments at the end.

o-gadri and e-gadri. O-gadri (lo, loi, lo'e) and e-gadri (le, lei, le'e) can be defined in terms of lo'i and le'i respectively. lo'i broda refers to the set of all broda. le'i broda refers to a set that may be defined either extensionally, by its membership, or intensionally, by the entry criteria for membership. The truth of a statement that includes an e-gadri cannot be determined until the identity of the corresponding le'i has been established (either through context or through a sentence-internal identification). (Members of le'i broda needn't be broda: hence e-gadri are nonveridical. However, le'i du ku noi ke'a broda means the same as le'i broda except that this time the members are broda.) Similarly, 'a-gadri' (la, lai) can be defined in terms of la'i.

Definitions in terms of lV'i
|lo'e broda|= lo'e ro lu'a lo'i broda|_|le'e broda|= lo'e ro lu'a le'i broda|_|_|
|(su'o) lo broda|= su'o lu'a lo'i broda|_|su'o le broda|= su'o lu'a le'i broda|_|su'o la broda|= su'o lu'a la'i broda
|ro lo broda|= ro lu'a lo'i broda|_|(ro) le broda|= ro lu'a le'i broda|_|(ro) la broda|= ro lu'a la'i broda
|loi broda|= lu'o lo'i broda|_|lei broda|= lu'o le'i broda|_|lai broda|= lu'o la'i broda

Featural analysis
|_|-specific|+specific|cmene
|set|lo'i|le'i|la'i
|distributive|lo|le|la
|collective|loi|lei|lai
|generic (singularized)|lo'e|le'e|

The difference between -specific and +specific is the difference between o-gadri and e-gadri.
'Distributive': for lV broda cu brode, each member of lV'i broda is separately a brode.
'Collective': for lVi broda cu brode, the membership of lV'i broda is jointly/collectively a brode.
'Generic/Singularized': for lV'e broda cu brode, it is presupposed that lV'i broda has exactly one member, and that member is claimed to be a brode. In a version of the local world that is relevantly similar to the local world but contains exactly one lu'a lV'i broda (and may in fact be the local world), the one lu'a lV'i broda is a brode.

Redundancies and defaults
When lV'i has no members, only lV'e is sensical (or nonvacuous).
When lV'i has a single member, the distributivecollective distinction is redundant. Each gadri within the same o/e/a-series can be replaced other (non-set) gadri in the series, without affecting truth-conditions. However, the choice of gadri is not entirely arbitrary. lV'e avoids invoking the redundant distributivecollective distinction and thereby avoids implying that the distinction is relevant and that lV'i therefore has more than one member. And if the choice is between lV and lVi, lVi is preferable because, unlike lV, it does not involve quantification (and the complexities of scope that that can entail).
When lo'i has a single member, the distinction between o-gadri and e-gadri used veridically is redundant, since there is no possible contrast between lo'i and a subset of lo'i. Here, the o-gadri is preferable, both so as to avoid the potential nonveridicality of e-gadri and so as to avoid implying that the o-gadri/e-gadri distinction is relevant and that therefore lo'i has more than one member.

NB This discussion considers only semantic criteria in choosing default gadri. One may also consider phonological criteria (i.e. shortness). There are ideological differences concerning the desirability of considering phonological criteria.

Paradigm gaps and experimental gadri
pa'ei. When lV'i has a single member, but we don't know whether lo'i has a single member, which gadri is it best to use? We don't want to use lo'e, because that would mean that lo'i has a single member. We could choose le'e, but le'e could be seen as implying that the o-gadri--e-gadri distinction is relevant and that therefore lo'i has more than one member or the description is nonveridical. As an option for this circumstance, pa'ei is proposed: it is veridical, refers to a single individual, but does not say that this individual is the only member of lo'i.
la'ei. There is a gap in the gadri paradigm for a lV'e-series a-gadri — a generic/singularized cmene. la'ei fills this gap.
lau'i-series. If le'i broda is seen as a +specific subset of lo'i broda, then there is a gap in the paradigm for gadri based on a nonspecific subset of lo'i broda (i.e. da poi ke'a klesi lo'i broda). To fill this gap, lau'i and a series of gadri based on it are proposed.
|lau'e broda|= lo'e ro lu'a lau'i broda
|su'o lau'a broda|= su'o lu'a lau'i broda
|(ro) lau'a broda|= ro lu'a lau'i broda
|lau'o broda|= lu'o lau'i broda
If lau'i were extensionally defined and had only a single member then it would simpler to use lo rather than an au-gadri. Therefore the use of an au-gadri implies that lau'i either is intensionally defined or has more than one member.

Full gadri paradigm
|set|lo'i|lau'i|le'i|la'i|
|distributive|lo|lau'a|le|la|
|collective|loi|lau'o|lei|lai|
|generic (singularized)|lo'e|lau'e|le'e|la'ei|pa'ei

Stats
For a message to Jboske from a while back, I compiled some statistics of my gadri usage in a text that uses only the official gadri but uses them according to the principles and preferences described above.
|total lo'e|208|
| lo'e before du'u/ka|_|102
| lo'e elsewhere|_|106
|lo|48|
|loi|6|
|le'e|61|
|le|2 (both {su'o le}|
|lei|9|
|lo'i|3|
|le'i|0|
I seem not to have collected stats on la/lai/la'i, but there are lots of lai and no la or la'i.

--And.

I (nitcion) like the start and not the end. In particular

• lo'e to me is still marked, and moreover is marked for squinting: extrapolating properties from a population that do not necessarily apply to each given individual, and conversely, missing out on properties that may apply to every individual. In that sense, it looks highly misleading to me as the preferred article applied to a singular population, as you propose it; and the misleadingness is more salient than what you claim for lo and loi.
  • I think your view is reasonable, but I would hope that we come to think of lo'e as primarily generic, and squinting as the mechanism you need in order to get from a nonsingleton to a singleton.
  • But generic still implies to me something to generalise amongst, which is highly marked when the population is already a singleton. That's why I said lo'e for singular populations is odd to me.
• pa'ei, I take it, is reasonably close to the. But I'll need more information before I am anywhere near liking it.
  • Yes, I think it is pretty close to singular the.
  • If were going to have an exp.cmavo for 'the' (and we may or may not need it - most ppl, I suspect, are still treating le as definite), I'd much rather it be the iota quantifier, which is much more useful. (To anyone listening: this is how Bertrand Russell resolved "how do you say 'the' in logic" - by making up a quantifier, alongside "for all" and "exists", picking out the one entity you want to talk about.
• I don't think people have been clamoring for la'ei, and I suspect naming already involves a notion akin to singularisation --- singling out; so I don't think names even want a singulative.
  • The la:lai distinction implies that names aren't inherently singular. I would be happy to dispense with la and la'i and just have lai, deriving the others by means of LAhE. People have absolutely been clamouring for la'ei. As things stand, this is because only a small handful of Lojbanists appear to have much understanding of gadri and to have applied that understanding to their usage. But even if that changed, the demand for la'ei would be minimla. But popular demand is only one rationale for experimental cmavo; gap-filling is another.
• lau'i is what, a certain kind of X and I don't know which? You'll have to demonstrate why we need to be able to say such a thing; you haven't yet.
  • lau'i is either some nonspecific kind of X, or else some nonspecific set of X. In English, they correspond to nonspecific indefinite plurals.
  • *shrug* as do Lojban masses already (loi), without positing phantom classes. You'll need to explain more.
• And, the older I get, the more I luuurve structuralism; but not every gap in a system cries out to be filled. The rest goes into the latest local rant against exp cmavo; I will add to it here, though, that exp cmavo does occur in a social context, and thereby are an easy currency to debase.