XS gadri proposal

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XS gadri proposal: And's version is another exposition of the same proposal.

This version is by xorxes.

(Please keep comments and suggestions separate from the proposal itself, below the line. Thank you.)

lo = Kind

PA lo = avatar of Kind

le = Specific

PA le = members of Specific

Bare lo has no outer quantifier (or equivalently, an implicit tu'o). It refers to a single entity, the x1 of the description as a single individual encompassing all individuals. {lo broda} is "Mr. Broda". The inner quantifier is part of the veridical description. {lo re cutci} is "Mr. Pair of Shoes". examples of XS lo here are some examples.

PA lo quantifies over the avatars of the Kind, i.e. over all the instances of the single individual of bare lo. {PA broda} remains equivalent to {PA lo broda}. This is as in the traditional prescription, but now there is a difference in the interpretation of the inner quantifier: {ci lo re cutci} is "three avatars of Mr. Pair of Shoes", i.e. "three pairs of shoes".

Bare le has no outer quantifier (or equivalently, an implicit tu'o). It refers to a single entity, which can eventually be a group. The inner quantifier is part of the description, so for example {le re cutci} can be used to refer to a pair of shoes as a single entity, {le cino cipni} to a group of thirty birds as a single entity. {le cipni} could be one or more birds, as a single entity.

PA le quantifies over the members of a specific group. {ro le cino cipni} is "each of the thirty birds", {su'o le cino cipni} is "at least one of the thirty birds". {ro le cipni} is "each of the birds". This is just as in the traditional prescription.

Examples

lo jugypre cu te cmene lo ri panzi lo cmalu

The Chinese give their children short names.

which can also be said as:

lo cmalu cu cmene lo panzi be lo jugypre ri

Short names are given to the children of Chinese by their parents.

Doing this with quantification can be very messy, and almost impossible to

rearrange the terms unless the quantifiers are expressed in the prenex.

mi ta'e cpacu lo karni bu'u le zdani i ku'i ca le cabdei ky na tolcliva

isemu'ibo mi tcidu ky bu'u le briju

Usually I receive the newspaper at home, but today it didn't arrive,

so I read it at the office.

This is messy to do with quantification if we want to use anaphora. "It" refers to the newspaper that I usually receive, which is the one that didn't arrive today and that I read at the office. That's Mr Newspaper, with different avatars in each case.

(to be continued...)


Some part-whole type-of relationships

pagbu: x1 is a part/portion of x2

cmima: x1 is a member of x2

selsucta: x1 is an avatar/instance of kind x2 (by rules x3)

klesi: x1 is a subclass/subkind of x2 (with defining property x3)

For example {lo cixa cipni}, "Mr 36 Birds" has 36 "Mr Single Bird" as members, it has millions of groups of 36 birds as avatars, and it has innumerably many subkinds, such as "Mr 36 White Birds", "Mr 36 Pelicans", "Mr 36 Birds Flying North", etc. Portions might consist of some subgroup of members, like "Mr 12 Birds".

In this proposal, outer quantifiers on {lo} quantify over the avatars of the Kind. So {PA lo broda} can be analysed as {PA selsucta be lo broda}. Quantification over members can always be achieved with {lu'a}, so {PA lu'a lo broda} can be analysed as {PA cmima be lo broda}. There is no short form for quantification over subkinds, {PA klesi be lo broda}. A new LAhE could be introduced for this.

In the case of {le}, direct quantification is over members: {PA le broda} is equivalent to {PA lu'a le broda} and can be analysed as {PA cmima be le broda}. The new LAhE for subkinds could be used with specific references to Kinds as well, and perhaps another LAhE for avatars could be added for completness, so that we can quantify over avatars of a specific kind.

(If member, avatar and subkind each had its own LAhE, then eventually direct quantification could be made glorkable from context as to which of the three applies.)

  • This is a nice idea. PA LE is then always an abbreviation for PA LAhE (tu'o) LE. Very good: it removes the element of arbitrariness involved when choosing the interpretation of PA le and PA lo. --And.

le

  • And {le} now differs from old {le'i} how? It is useful to recognize that Lojban descriptions are typically of sets, but they are of sets taken distributively, so requiring -- except for singletons -- an implicit quantifer. Leaving that off makes the bare form of remarkably little use (very unZipfy).
    • The proposed {le} is indeed basically JCB's "eu". It differs from {le'i} in that it is not a Mathematician's/Logician's set, but simply a group which (unlike the abstract set) can carry logs or pianos for example. It is also equivalent to the collective Lojban {lei}. Under this proposal, quantifiers on {le} range over the members of the group, therefore as stated above the {PA le} forms have identical meaning to the old {PA le} forms.
      • ignotum per ignotius{leu} has meant more unclear things in rising 50 years than almost anything but {lo}: ther are no other sets than mathematician's sets, everything else is something else (as JCB was told fairly regularly from 1960 on). So, let it be a replacement for {lei} and leave "set" out of it. Now, however, you can't quantify over the members, because they are collective. So, {PAle} is an unanalyzable idiom whereas before it was just a naormal expression. And no new notions have been dealt with. Looks like a loss, except for freeing up another CVV.
        • The word 'set' is not used in the proposal, so we agree that the new {le} is clearly different from {le'i}. {PAle} is analyzable as {PA lu'a le} or as {PA cmima be le}. The gain is that {le broda} is now a constant instead of a quantified expression.
          • {le broda} always was a constant and was then and is now quantifiable (with fractionals), if I understand your proposal at all.
            • Maybe you're right, but my understanding was that {le broda} was {ro le broda}, i.e. always quantified. If this is not the case, then this proposal as far as {le} goes is nothing but the status quo as you understood it. But notice that a constant {le ci broda} means one object (for example a group of three broda), not a quantification over the members of that group. The constant itself, the group of three, is the argument, not each of the members.
  • (the insets were getting to me)The referent of {le broda} is the selected set. It is used to cover its members distributively and thus can be quantified to restrict the distribution (it actually expands it, but that is by the way). This is all standard stuff that never gets said very clearly (I see a long chat on the Medieval theory of supposition coming on). (The referents of {lei broda} and {le'i broda}are the same set, treated collectively and cumulatively. And all are just a convenient way of referrring to brodas.)
    • Ok. In the present proposal the referent of {le broda} without an explicit quantifier is not quantified and is treated collectively. (In the usual interpretation, the referent of {le broda} is always universally quantified, i.e. {le broda} is {ro le broda}.) In this proposal, quantification is only achieved explicitly, i.e. with {PA le}.
      • But then it is implicitly quantified with {piro}, as I suspected. Or else with {pisu'o} or with a fractional to be glorked. Only if the treatment is cumulative -- current {le'i} -- would an external quantifier be redundant (and one is possible even there). As long as the members are behaving separately to achieve what the set achieves, we can ask whether they are all involved or only a few or... and that is quantification. Or, of course, if the set is a singleton.
        • {le broda} is unquantified. I don't know what your understanding of {le'i} is. If {le'i nanmu} is something that can't carry logs and pianos, then no, {le nanmu} is not that. If it can, then maybe it is. (The usual understanding has been that {le'i nanmu}s don't carry pianos.) The important thing is that {le broda} is not quantified, it is a constant. So for example, {naku le broda} within a bridi is always equivalent to {le broda naku}, because constants can switch places with negation, but quantified expressions cannot.
          • I agree that le'i broda can't carry a piano -- that is, that its members' actions do not contribute to the actions of the le'i broda. For the rest, I don't see the point: if the members of your le broda (and how different from lei broda again?) do contribute to the actions of the whole, then it is quantifiable and so quantified (explicit, implicit or guessed). But that doesn't say anything about it being constant or not: one of the ways in which I think that {lo broda} differs from {da poi broda} and perhaps even {su'o lo broda} is that it is but they are not constant, i.e., unaffected by negation passage (though not by modal passages). It is still quantified (indeed is a particular quantifier on one view, but one with very very broad scope). And I can see the virtue of that with constitutive groups -- what I take your {le} to mark: if it is not the case that the trio moved the piano, then the trio failed to move the piano, not just some part of it failed (in spite of what the various accusations flying around may seem to say). However, the trio failing is compatible with two members of that trio forming a new constitutive group and moving the piano, since that is a new group. So, what you really want is not a new gadri but a new rule about quantifier scope, which has the virtue of not affecting the grammar, nor much usage (on a bet). Since I am more or less on that kick myself, I go along (that far at least -- but why not leave it {lei} rather than having to fididdle with {le} in several usages minutely distinguished?)
            • The idea is to have a simple rule: normal scope quantification always corresponds to explicit outer PA. The absence of explicit outer PA corresponds to a constant (or very very broad scope quantification, if you prefer, but always of a single entity, be it a kind, a group or an individual, a group of one.)
    • (the insets got out of hand again) A single thing composed of one or more individuals is simply the set (lV'i), or, if the actions of the members constitute the action of the thing, the constitutive group (lVi). Both of these are fractionally quantified, though what happens with negation passage on fractional quantifiers is markedly unclear. Obviously, from what I have said in various places around here, I like the idea of unquantified items taking on a certain fixed status and quantified ones behaving "normally." But,as noted, that is a change in conventions about quantifiers, not in grammar nor -- significantly -- in interpretation of forms.
      • Yes, the changes involved are minor: Eliminate default quantifiers, and re-interpret inner PA after lo.
        • Well, what I had in mind was more along the line of making unexpressed quantifiers (they are going to be there whether we like them or not)have widest scope and eliminating unexpressed inner quantifiers (but that is a separate point).
          • As long as the unexpressed widest scope quantifiers are always "the one and only", I don't see a problem. If the unexpressed widest scope quantifiers can be something else, I see all sorts of problems arising from the order that these unexpressed quantifiers may have among themselves. I want {le mi gerku cu terpa lo cipni} and {lo cipni cu se terpa le mi gerku} to have the same meaning, namely "my dogs are afraid of birds"/"birds scare my dogs", i.e. "my dogs are afraid of Mr Bird"/"Mr Bird scares my dogs". I want no complications with any ordering of quantifiers.
    • Well, does every bird -- even every bird that has been relevantly in your dogs' environment -- frighten your dogs or only some? Is it all your dogs or only some? Do some birds frighten one dog and others another?
      • I'm not saying. Is it today, yesterday or usually? I'm not saying either. Lojban allows me to not specify what needs not be specified. If "my dogs are afraid of birds" is not informative enough in a given context, you can ask for more precision.
    • Or is there a monstrous entity such that any?, every?, some? part of it frightens the dog entity (all or some part of it).
      • No, just normal birds and dogs.
        • Then what is Mr. Bird?
          • Whatever "birds" is in "my dog is scared of birds". We've been caling it Kind. Other names are "Unique" and "generic".
            • "Unique" and "Generic" can hardly meaningfully be applied to the same thing. But then that "birds" is a hard one in English -- part of the reason to be very careful about what we do in Lojban. Creating new hypostates without indication how they are based on reality does not seem a good idea.
    • Remember, however we word this we have eventually to get back to individual objects: your various dogs and individual birds -- at least in theory.
      • I think you don't always have to get to avatars, but I agree that often you can be more specific if you want or need to.
        • Oh, we often don't need or want to get back to objects. The point is that it has always to be possible to do so in theory. And the clearer the path is the better.
          • That remains unchanged: explicit quantifiers.
            • But explicit quantifiers don't explain how to get back to objects from Kind, even though there must be a route if Kind is a legitmate expression.
              • This seems to have become clear in the parallel discussion on And's page. It's quantification over what really are avatars of the Kind.
    • Quantifier problems are going to arise as long as we have groups, giving the group the status of an individual only means that the quantifiers are fractional rather than cardinal.
      • Fractional quantifiers don't help here. The idea is to use constants. When I talk about John I may be saying something that applies to a fraction or an instance of John, but I'm not really quantifying over fractions or instances, I simply talk about the individual. The same thing can be applied to Mr Broda.
        • The problem is that Mr. Broda is not an individual, any more than the average man is; "Mr Broda" is a way of talking about brodas and we will get into trouble taking the language too literally (notice, even {la djan} is directly about a set, with the usual convention that it is a singleton).
          • But {la djan} can be used to talk about "ten-year-old-John" as much as about "today-John", and those two can be taken as avatars of la djan.
            • I think they are just constitutive parts of John; John actually is an object after all, so we don't need to work with avatars and the like, even though those are analogically based on the part relationship.
              • We don't need to, but we can. It is simply a useful comparison.
                • Actually, I don't think we can; real individuals don't have avatars -- Lord Krishna notwithstanding.
    • Now, we might reformulate Lojban ontology so that everything was stuff or kind, but my limited experience with that sort of language suggests that hacking out the right pieces for individuals is harder than mushing them together.
      • Nobody is proposing to do away with the explicitly quantified forms, so that would not be a problem.
        • But quantifiers don't get to individuals until individuals have been recreated out of stuff or kind and that is the problem.
    • And, of course, we would have rewrite the whole dictionary and large chunks of CLL (and all the text to date).
      • I would have to rewrite my {lo'e}s as {lo}, but other than that I don't see much that would need re-writing. Could you cite some concrete examples?
        • My menory is that your {lo'e} are not Lojban, so that is not an interesting case. But notice that the rewrite is hypothetical, based on changing ontologies, and then virtually every description has to be rewritten to get the right carving up of the stuff.
          • A hypothetical rewrite does not seem to be very problematic. Are there examples of things that would require concrete rewriting?
            • Well, supposing that the basic notion, {le/lo} is about kinds, then all of the original writings where that is about objects has to be revised, and similarly (but even more difficultly) if the basic is about Stuff.
              • {lo} for Kind, {le} for Specific. I can't imagine what sort of problems you envision without a concrete example to examine.
                • If what is basic is kinds, the quantifiers are going to be over kinds. How then do I say what I now say with {lemi gurku}?
                  • XS's {ro le mi gerku} corresponds to CLL's {(ro) le mi gerku}. Quantification in {PA lo} is by definition over avatars, not over subkinds. Quantification in {PA le} is over members of a specific in-mind group.
                  • But remember, we have changed what quantifiers quantify: it is Kinds now, not objects. So how do we get down to object, now that Kinds are not composed of objects. Once the ontology changes, the whole langauge changes and, as I said, saying what we normally want to say is very difficult.
  • The members of the set lo'i broda are the real avatars of the Kind lo broda, so I'm afraid I don't see the problem. We are quantifying over the same things as far as I can see.
    • I stuck the external quantifier bit in by the way just because I am trying not to tick the {lo broda} = {su'o broda} folk off completely. I really think these guys get simply assigned at the beginning of the context and are fixed throughout -- though locally modifiable (we can talk about three of the twenty things we started with, for example). I think we pretty much agree on what we want to say and differ on how to say it, but I am not at all sure. But thanks for an example to see what this is all about now.
      • There are more examples with the proposal.
        • Yes, but they were only fragments or else -- in the newspaper case -- very heavily wrapped up in another whole range of problems (type-token -- though this may be the same one). In any case, what you want to convey is that any bird then comes within the ken of any of your dogs frightens it (maybe with different quantifiers: "most birds," "a certain one of your dogs," etc.) We can drop the "that comes within the ken" bit from either conversational conventions or the logic of "frighten" or perhaps implicit subjunctiveness. Now the question is how to say that in some other words -- or perhaps how to say something that ranges over a wide variety of quantifiers in the text without specifying which one is meant -- but without using quantified expressions. At first glance,{loi cipni cu se tirpa leimi gurku} seems to work, though second thoughts immediately say that this would be true if there was only one bird that once frightened one of my dogs -- but that is true of Birdkind or Mr. Bird as well. I look forward to hearing what I have overlooked.
          • Indeed the proposed {lo} is one of the readings of {loi}, the ancestral one, the one that corresponds to JCB's {lo}. But almost anything has been Lojban {loi} at some point or another: at least Substance (Stuff), Collective (the piano carriers), and Kind (Mr).
            • Well, almost everything was JCB's {lo}. As for the rest, I think we have been substantially correct about {loi} but rather careless: all of these things are {loi}-- with "collective" being the central notion -- but {loi} is not exclusively any one of them.

lo

  • More useful than the corresponding thing with {le}, but now almost to {loi}: the only difference is using quantifiers in the predicate rather than cardinal predicates. we still need a distributive notion, since that is the most useful -- but can hardly be called a kind (as the collective can).
    • The distributive notion is obtained by quantifying over the avatars.
      • See above. By the way, {lo re cutci} like {lo cutci remei} is not the pairs, only the dyads -- pairs and couples are special sets that need a raft of other conditions met -- even for the bad jokes.
      • I take avatars to be merely members of the underlying set, treated distributively. So, maybe what we need is a rule that allows us to refer directly to members of a constitutive group without the intermediate {lu'a}. But I wonder if the frequency of use justifies the change.

part-whole relations

All of the examples given are of relations analogical to part-whole but not part whole. {pagbu} is the part-whole relationship -- or as near as Lojban comes, since this talks about masses as well as individuals, and we haven't more than a vague clue what "mass" meant when this definition was written. Whether "avatar" and "subset" are even analogs depends upon what gets built into them, and that is still unspecified. The apparent rules -- once the strange use of internal quantifiers is passed -- do not look promising: I don't see how a Mr.One-Bird is a member or part or whatever of Mr.36-Bird, but the avatars looks OK. The complications to get back to objects seem excessive, but we seem to need it for lVi and lV'i so I can't complain, exccept to wonder why we can't just use the simple forms more often.

  • Another "member of Kind" example:

mi cpacu lo re karni i go'i pa lu'a ky ca le cerni i go'i le drata ca le vanci

I receive two newspapers, one in the morning and the other in the evening.

    • How does this compare with "I receive two New York Times, ..."? That is, how are two types of newspaper differentiated from two tokens of the same type and that from another step down that trail: "I receifved two New York Times this week, one on Tuesday and one on Saturday."?
      • Using {braplisykarni} for "x1 is a New York times (with date x2...)"

mi cpacu lo re braplisykarni ca lo pa djedi

I receive two New York Times a day.

mi cpacu re braplisykarni ca le ca jeftu

I received two (avatars of the) New York Times this week.

As noted elsewhere, subkinds are just kinds with additional predicates, so they present no separate problems.

  • Example of quantification over subkinds:

mi'a pu pinxe re klesi be lo vanju

We drank two wines. (Not two quantities/glasses/bottles, two kinds.)

    • Ahah! This clarifies that point and my comment does not help here.

I can't think why a portion of Mr, 36-Bird would be body parts of 36 birds. While I don't believe it, it would be more reasonable to think that that was Mr. OneBird (among others)rather those being members. But I may be foolishly confusing Mr 36-Bird with loi cipni cixamei.

  • I agree. Fixed it.

See Simple Gadri Solution

Here is a table of correspondences between determiners from the Simple Gadri Solution and the XS gadri proposal: (where PA stands for a quantifier, and piPA or PA1 fi'u PA2 for a fractional)

SGS XS

??? lo

(su'o) lo su'o (lo pa)

PA (lo) PA (lo)

??? lo PA

lo...PA mei / PA loi? su'o lo PA

PA1 (lo)...PA2 mei PA1 lo PA2

(pisu'o) loi su'o lo

ro lu'a piPA loi / piPA (lo)? piPA (lo)

??? lo piPA

(su'o) lo...piPA si'e su'o lo piPA

PA (lo)...piPA si'e PA lo piPA

lo piPA (undefined)

??? lo piPA lo

piPA loi su'o lo piPA lo

PA lo piPA loi? PA lo piPA lo

PA1 lo PA2 PA1 fi'u roPA2

(su'o) lo PA su'o fi'u roPA

(pisu'o) loi PA su'o lo su'o fi'u roPA

lei le

lei PA le PA

PA lei? le PA le

PA le PA le

PA1 le PA2 PA1 le PA2

le ro le

le PA ro le PA

ro lu'a piPA lei? piPA le

??? lo pipa le

piPA lei su'o lo piPA le

It would seem that everything sayable in SGS with lo/le/loi/lei is sayable in XS with lo/le, some things sayable in XS are not (AFAICT) sayable in SGS. Some basic forms in SGS are as yet undefined.

  • Thank you for this chart. It nicely points out where I do not understand what you mean and, perhaps, where you do not understand what I mean.
  • I worked out how to fill in most of the question marks but the wiki ate the page rather than saving it and it is too late in the day to do all that again.

The remaining question marks are all of those expressions that in XS begin with {lo}, because there is no discernible way in CLL to refer to Kinds.

  • So far as anything you have said goes, I do not see why your {lo} is not my {loi}-- possibly with the wide scope quantifier reading that I would prefer (since the wide scope quantifiers in fact get fixed content, the possibilities of scope overlaps does not arise). Similar comments apply to {lo PAmei} and so on.
    • I'm not sure what happens when you have two wide scope quantified terms in the same expression. Does the order of the terms change anything? If it does, then it's a different thing. The other difference is that the Kind includes all avatars, real or not.
      • In my view (very wide scope) the order of the occurrent expressions would not affect their referents. Having unreal avatars of Kind leads to problems, for example, that either everyone or no one who is not eating chocolate like chocolate.
        • So everyone that likes babies likes John?
          • I don't quite see how you get to this, but, if it holds in your system then there is something seriously wrong -- worse than what I saw earlier. I assume it doesn't so hold; did you get to it by reading the fact that someone likes the kind to that they like each avatar? I never accused anyone of that, I hope. But it sometimes appears that anyone who like John, a baby, likes babies.
            • I'm simply reasoning about Mr Chocolate as I would about John. The different avatars of Mr Chocolate are like the different stages of John. Disliking Mr Chocolate does not preclude there being some irrelevant avatar of chocoate that one likes, just as disliking John does not preclude there being some irrelevant stage of John that one likes. So I may not like John, who is not now a baby, even though I would have liked or did like him as a baby. In {mi na'e nelci la djan} I don't specify times, similarly in {mi na'e nelci lo cakla} I don't specify avatars. In both cases context is needed to get exactly at what I mean. What does liking or disliking John involve? A lot of complex things about hypothetical situations probably. Similarly for Mr Chocolate.
            • But Mr. Chocolate is not an object and John, presumably, is. So the same rules don't apply, though many analogical ones do. What you say about Mr. Chocolate and John is, in this case, a good parallel up to a point. Some cases -- real and hypothetical -- don't decide the issue of liking. Nor are all needed (some cases don't decode the issue of not liking either). It just is not clear to me that liking chocolate is any closer to being solved by reference to Mr. Chocolate than it was by reference to the typical chocolate, as indeed, the case of John might well be more nearly solved by the typical John, John as he usually is or the like. Of course, that implies that liking John has something to do with what John is like, which may simply not be the case. I think that liking has to complex a logic to be worked out here and the best we can do is find a neutral idiom for saying it -- one that does not lead to generalization nor even identification, so an intensional context. I am not sure if Kind does that, though if it includes everything it is.
  • I do not understand what {za'u} does in {su'o lo za'u; guarantee that {lo} is not empty?
    • To guarantee plurality, {za'u} is "more than one". But if collectives of one are acceptable, it is not needed, so I have now removed it.
  • I am not sure what {lo piPA} means, but it looks like I ought to match it with {loi piPAmei}which out to be a collective of fractions of something. (This may push {mei} but is legal apparently.) Or maybe it should be {si'e}as you use later and attribute to me.
    • {lo pimu plise} is Mr Apple-Half, the kind corresponding to half an apple. I assumed that its avatars would correspond to {lo plise pimusi'e} in SGS. I'm not sure how else to talk about apple fractions. The problem with {pimumei} is the place structure of {mei}, which is terrible.
  • {piPA (lo)} is defined in CLL as {lo piPAmei/si'e}, which sucks. A conservative correction would be to take it as a subset piPA the size of the original set, treated distributively -- just like the corresponding {lV(')i}.
    • That's exactly what piPA (lo) does in XS.
  • {lo piPA} and {le piPA} are undefined and should just be eliminated, I think. Along with {lV PA}.
    • If inner PA should be eliminated, why not put it to use as a convenient mei/si'e?
      • They only go away as obligatory categories, they are still optional, though the fractional ones don't make much sense.
  • {PA lV(')i} is undefined in CLL. I take it to be a PA sized subset of the original set, treated as the gadri given prescribes, just like the corresponding {lV}
    • So {mu loi plise} would be some five apples treated collectively. That's {su'o lo mu plise} in XS.
      • Yes.
  • For {lo pipa le}, as near as I can shift back and forth among the various meanings of the same apparent words, comes out {lu'o pipa le}, but I wouldn't want to swear to it -- nor to the accuracy of many of your translations. I do not, for ecxample, know what has happend to the relevant LAhE in these contexts.
    • LAhEs need another page. There are lots of issues to deal with about them.
      • One thing at a time, unless it throws some light on this problem.

I like the new version of the basics better. The use of {tu'a} is strictly superfluous and even misleading, since these are always in an alternate world but not always in a recognizable situation, which is what {tu'a} is about. pc

  • I think you may be confusing {tu'o} with {tu'a}. I use {tu'o} simply as an explicit indication of no quantification. It is not needed if the bare gadri are not assumed to have default quantifiers.
    • Right you are. I am all for doing away with default quantifiers but I am not sure we can: {le} will have {ro} and {lo} {su'o}. What is required of the bare gadri is that they do never have explicit quantifiers and that is nicely covered here.
      • I'm happy with the interpretation of le broda and lo broda as constants, you are happy with the interpretation of special-scope quantifiers. As long as we end up using the same forms for the same situations I don't see a problem.
      • Both quantifiers and constants are functions from incomplete propositions to less incomplete propositions; that is, a constant can be seen as binding a variable just as a quantifier does. So I have no problem with seeing constants and quantifiers as two varieties of the same sort of logical element. --And.

The "different avatars in each case" just is the different short-scope quantifiers at each occurrence.

  • Indeed. But just as I don't focus on short-scope quantification over stages when referring to la djan (though I could), I prefer not to focus on the avatars when referring to lo broda (though I could). BTW, I didn't make any changes to the original version of the basics, all I did was add a link to some examples, so your liking it better is not so much of a new version as of your new approach to the same old version.
    • Probably true. Though I am willing to stop if you keep pressing that silly analogy between Mr. Whatsis and real objects. I think that the best plan is to stop the metaphysical chit-chat altogether, since then there is some concord about the language.