simple Gadri Solution

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Simple Gadri Solution

It seems that it has been decided that the CLL gadri system is totally broken and that a whole new one must be constructed, recycling old pieces any which way that seems convenient. Before working on a new system, it might be useful to review the old one and see what it does do and where it contains problems. What follows is my understanding of the CLL system. I think that it conforms to the main thrust of CLL and its usual interpretations historically, but admit that there are examples and occasionally comments that do not obviously fit it.

All of the description expressions refer to the member of some set, which is specified by the following phrase. The various types are identified by the nature of the phrase (the vowel in the lV[‘)i) and the way the members of the set are treated (which options is taken up).

Nature of the phrase

Called (a): things in the set involved are called the following phrase as a name. In the case of {la} the revocable assumption is that the set is a singleton.

Described as (e): things in the set have been selected beforehand and are described as satisfying the following phrase. The revocable assumption is that they do satisfy that phrase, if there are relevant items, or that the association with things that satisfy the phrase is obvious, if not.

Are (o): the things in the set do satisfy the phrase.

Treatment

Distributive attribution {lV}: what is attributed to the set as signified by the description is attributed to each member separately.

Collective attribution (lVi): what is attributed to the set need not be attributed to any member separately, but at least some members have attributes that materially contribute to the property attributed to the whole. In the case of {lei} the revocable assumption is that the selection was made of just those items that do contribute materially to the attribute of the whole.

Cumulative attribution (lV’I): what is attributed to the set is not attributed to the members but the members do contribute indirectly to the attributed property of the whole.

Quantifiers

internal (between gadri and phrase): indicate the cardinality of the set. Not permitted with Called cases. The default value is {su’o} for Described cases, {ro} for Are. Only cardinal quantifiers are allowed.

Problem: we often do not know the size of the set involved, even to whether it has any members

– even when we know what properties the members would have if there are any (e.g., neutrinos).

Possibilities of solutions: use {ni’u ro} as default with Are or assume that {ro} does not have

existential import or drop this specification altogether.

external (before gadri – or in place of {lo}):

  • cardinal – with {lV} gives the number of members of the basic set to which the given attribution is to be made. Default for Described is {ro}, for Are {su’o}.Undefined for the other gadri.

Problem: the default for Are is incompatible with the possibility that the set have no members.

Possible solutions: default to {ni’u su’o} or take {su’o} as non-importing

(pretty implausible without doing violence to the whole system) or treat unquantified {lo broda}

as different from {Q (lo) broda} – as a local constant (even if eventually quantified).

  • fractional: With {l(‘)i} the size of the set to which the attribution is made as a portion of the whole set. With lV, the fraction of each member of the original set that is a member of the set to which the attribution is made distributively.

Quantifiers inherently introduce inspecificity into a description: aside from {ro} and singleton sets, any quantification could be satisfied in several ways from any set. Specificity can be reintroduced by prefixing the e form to any quantified description.

Problem: The external quantifiers are not systematic: The {lV(‘)i} forms do not take cardinal quantifiers,

the {lV} forms treat fractional quantifiers differently from cardinals and from the way they work with

the other types. Consequently, the size subsets of {lV} can only be indicated cardinally,

not as a proportion of the whole, while the reverse holds for {lV(‘)i}.

Possible solutions: make all external quantifiers specify the size of the relevant subset,

whether absolutely or relatively. I suppose there are other possible solutions, but the only reason

I can think of for not using this one is that there is a better use for some of these locutions

(I can think of a few – see below – but fractions of members is not one of them).

Treatment hopping

Since the selection of subsets for each of the various treatments is independent of the selection for any other, even when the description is the same, we need a device for moving from one treatment to another while preserving the selection. This is done by some members of LAhE, which convert from one treatment to another, saving the selection involved and the nature of the description. Thus, {lu’a} moves to a distributive treatment of a set presented in another way, {lu’o}to a collective treatment, and {lu’i}to a cumulative one, retaining whatever selection has taken place through quantifiers or inherent in e.

Generality

Among the gadri are a couple that describe their sets quasi-statistically. They appear to give a unique item but actually sum up the group. The system is rather limited in several ways. First it has one for Described sets ({le’e}) – but that is only the stereotype – and one for Are sets ({lo’e}) – but that is only typical . Clearly there “need” to be more of each type – at least typical Described and stereotypical Are. There might also usefully be averages of various sorts and probably others. The information can, of course, be conveyed without using these locutions, but the locutions are familiar and handy – so long as they do not lead to quantifying over the locutions or going looking for their supposed referents.

Generic

The search for these seems to be at the heart of the gadri resystematization. It is held that finding an expression for the generic broda will solve a variety of problems and that such an expression is not to be found among the already existing expressions in Lojban. It appears, however, that no one notion of generic broda will solve all the problems raised. I think also that at least some of the problems are already solved in CLL Lojban.

a broda – any one will do seems to occur only in intensional contexts (with “need”, “want,” “picture’” and the like or in imperative/precative uses or hypotheticals). It is just the quantified broda-phrase inside the context – rather than in this world – and is adequately dealt with by {tu’a}, however that is officially interpreted.

kind seems to cover a number of different desiderata, some of them still only nebulously formulated. But a few are clear:

  • Mr. Broda: does whatever any broda or group of brodas does, is spotted whenever one is and so on. It functions then like the collective of the whole set of actual brodas, {piro loi broda}. It might be nice to abbreviate this to a single gadri, but it is not needed and probably is not justified by usage. Note, it will not solve the “any broda will do” problem, since is restricted to actual brodas and the “any will do” may well involve sets with no actual members.
  • Stuff: this is present wherever any constitutive part of a broda is. It looks then like Mr. Constitutive-Part-of –any-broda. Again, a nice short expression would be nice, but usage is not yet sufficient to justify one. This seems to be the most likely thing for “Lo, Rabbithood” cases.

(I note a peculiarity that for some sets Mr. and Mr. Parts-of are the same, since the parts of the members are themselves members. I suspect these cases have led to several confusions when pressed to cases where this is not true.)

  • sub kinds: Describing sub kinds is a snap, they are just kinds on a subset, which subset is somehow set off -- typically by an additional predicate, or by shifting to an e form. The problem is rather to count them: “We drank two wines, a Chablis and a Beaujolais.” If we kept the present irregular external quantifier system, we could use the currently undefined cardinal quantifier on {loi} etc. But failing that – as we probably should – no convenient device is apparent within the CLL system.
  • ”I like chocolate”: This, almost the original problem (after “any will do”) still does not have a solution within the CLL system. It does not seem to be intensional (even though what I like is probably eating chocolate or some such) nor do kinds nor stuff seem to work – nor shifting to abstracts like chocolateness. The solution may lie in the logic of “like” (and some related words) and how they relate some of the critters laid out above – like the intensional cases – but no successful suggestion has turned up so far, even moving beyond the CLL system. Fortunately, these difficult cases seem rather limited.

I am sure that there are other cases that are not dealt with here, but this seems to me to be the main ones.


Nice description of the current prescription.

  • Thanks. If it is accurate, whence comes the need to completely redo it?
    • XS doesn't redo it. The only changes are:
    1. a new (more useful) reading for inner PA after lo
    1. the removal of the understanding that terms without an expressed quantifier are quantified
    1. a way to understand fractionators, which CLL doesn't quite provide

xorxes have a few questions:

pc:

internal (between gadri and phrase): indicate the cardinality of the set. Not permitted with Called cases. The default value is {su’o} for Described cases, {ro} for Are. Only cardinal quantifiers are allowed.

xorxes: Inner PA is permitted with {la}, as in {la ci cribe}, {lai ci cribe}, {la'i ci cribe}, and inner fractions are also permitted by the parser. By "not permitted" do you mean that they have no known meaning in that position?

  • pc: Glad to hear it. I couldn't find an example in sections on LA or internal quantifiers, so went with the general perception that what comes after LA is name all the way to the pause.
    • x: {la ci cribe} does not require any pause. Names with cmevla can't have an inner PA, I suppose that's what you meant, but names with regular selbri can.
      • Is {la ci cribe} one guy name Three Bears or three guys named Bear? Intuition and analogy pull both ways and the parse is, as all too often, of no help.
        • In CLL, it would seem to be "each of the three guys named Bear". I suppose that the XSive reading would be "the entity named Three Bears".

pc:

external (before gadri – or in place of {lo}):

  • cardinal – with {lV} gives the number of members of the basic set to which the given attribution is to be made. Default for Described is {ro}, for Are {su’o}.Undefined for the other gadri.

xorxes

"The attribution" is what follows the quantified term, right? For example, in {re broda cu brode ci brodi vo brodo}, we have:

there are exactly 2 broda x with the following attribution:

there are exactly 3 brodi y with the following attribution:

there are exactly 4 brodo z with the following attribution:

brode(x,y,z)

So there might be up to 24 brodo involved in the brodeing, right? And in fact the statement does not contradict that maybe seven other broda are brode to exactly 2 brodi and 6 brodo, for example. In other words, the kind of precision achieved in {re broda cu brode ci brodi vo brodo} is highly unnatural, and we would not expect it to be used much, if at all.

  • pc: There might be as many as 24 or as few as 4. I agree that it is going to be rare, but we need it for that occasion. It could be longer though without doing much damage. But cases with just one numerical quantifer or several traditional ones are not rare.

pc:

  • fractional: With {lV(‘)i} the size of the set to which the attribution is made as a portion of the whole set. With lV, the fraction of each member of the original set that is a member of the set to which the attribution is made distributively.

xorxes: Given {lo'i broda}, there are in general many different subsets of that set that have half the size of that set. Is {pimu lo'i broda} "at least one half-subset of all brodas", "every half-subset of all brodas", or something else?

  • I tend to take it as an unspecified subset half the size of the whole, but it should in fact be at least one. Doing one of anything is so damned hard in Lojban without using {pa} all over the place -- and I am not sure how I would use {pa} in this case anyhow.
    • On third thought, I go back to the original, it is some one such subset -- this indefiniteness only goes so far
    • {pa lo pimu lo'i broda}?
      • That would do it, but I take it that the {lo} reintroduces the plurality that I claim was lost in the simpler form.

Is {pimu lo plise} "at least one apple-half", "every apple-half", or something else? Can we quantify over apple-halves?

  • We can certainly quantify over apple halves, though the principle of individuation is a bit obscure -- unless we means the halves of apples that have been physically split in half. Score another point against that particular reading, in addition to being unsystematic. My guess is that it means all or some of the halves of the members of whatever set (some subset of the set of all apples) {lo plise} refers to. Since I want to get rid of this reading, I am not about to spend a lot of time figuring out which it is, especially since I am pulled both ways by equally impressive (or unimpresive)considerations.
    • I'm sure not defending that reading either. :)

pc:Treatment hopping

Since the selection of subsets for each of the various treatments is independent of the selection for any other, even when the description is the same, we need a device for moving from one treatment to another while preserving the selection. This is done by some members of LAhE, which convert from one treatment to another, saving the selection involved and the nature of the description. Thus, {lu’a} moves to a distributive treatment of a set presented in another way, {lu’o}to a collective treatment, and {lu’i}to a cumulative one, retaining whatever selection has taken place through quantifiers or inherent in e.

xorxes: If {lu'a re lo broda} is just {re lo broda}, what is {re lu'a re lo broda}?

Do outer PA of LAhE make any sense at all? Is {lu'a lo girzu} the same as {lo girzu}?

  • pc: I suppose that {lu'a re lo broda} is incongruous, since the descriptor is already distributive. But it ought to factor out as you suggest. Then {re lu'a re lo broda} ought to mean the same as {ro lu'a re lo broda}. And that, in turn, looks to be just {re lo broda} again -- though, if {lu'a re lo broda} were specific it might be a bit more. But surely, {pa lu'a re lo broda} does make some sense, though it would differ very little from just {pa lo broda}, if at all. {pa lu'a le re lo broda} would be more interesting, though not different from {pa le re lo broda}. In short, I think that {lu'a} in front of an already distributive descriptor reduces to that descriptor.

Is {lu'a ko'a e ko'e} the same as {lu'a ko'a lu'u e lu'a ko'e}? What about {lu'a ko'a ce ko'e}?

  • pc: I can't work the grammar well enough to tell how it will parse this, i.e., whether {lu'a} goes with {ko'a} only or with both KOhA
    • It goes with both: {lu'a ko'a e ko'e lu'u}.
  • -- and, however it parses, I am not sure what the expansion should be.
    • My reading has always been {lu'a <sumti>} = {lo cmima be <sumti>}, so in this case simply {lo cmima be ko'a e ko'e} = {da poi ge da cmima ko'a gi da cmima ko'e}. But this is in conflict with your reading.
  • My inclination, barring some good clear reason not to do it this way, is to say "Yes" to your question and reserve {lu'a ko'a lu'u e ko'e} for the other reading.
    • My question was not meant as to the scope of {lu'a} but as to its distributiveness. You take it as distributive, I see. I don't.
  • I would also expect the {lu'a} in {lu'a ko'a ce ko'e} to cover the whole set created by {ce} and (possibly with some conditions on the nature of ko'a and ko'e) to collapse to {ko'a e ko'e}.
    • I would take {ro lu'a ko'a ce ko'e} as {ko'a e ko'e}, and {su'o lu'a ko'a ce ko'e} as {ko'a a ko'e}. In fact, there is a quantifier for every symmetric connective:

ko'a .e ko'e = ro lu'a ko'a ce ko'e

ko'a .a ko'e = su'o lu'a ko'a ce ko'e

ko'a na.enai ko'e = no lu'a ko'a ce ko'e

ko'a na.anai ko'e = me'i lu'a ko'a ce ko'e

ko'a .onai ko'e = pa lu'a ko'a ce ko'e

ko'a .o ko'e = rojano lu'a ko'a ce ko'e

But that won't work with your reading of {lu'a}.

    • Very pretty. As you say somewhere, LAhE needs some more work or at least discussion. I took {lu'a} as distributive because I took it to make a {lo}, on the analogy with the other relevant LAhE, which clearly make a {loi} and a {lo'i}.
      • But which lo'i? If ko'a is a set, is {lu'i ko'a} the same set, or the set that has ko'a as its only member? If I say {le'i broda cu selcmi}, can I then use {le selcmi} to refer to the set le'i broda? Is lu'i le selcmi the set le selcmi or the set le'i selcmi? Also, we pretty much don't want {tu'a ko'a e ko'e} to split as {tu'a ko'a lu'u e tu'a ko'e}, so we would end up having special rules for each LAhE, which for me is a bad thing. Plus a lot of other questions when <sumti> (in LAhE <sumti>) is quantified or has connectives in it. I'll try to summarize it in a new page.

Comments from And:

pc:

a broda – any one will do seems to occur only in intensional contexts (with “need”, “want,” “picture’” and the like or in imperative/precative uses or hypotheticals). It is just the quantified broda-phrase inside the context – rather than in this world – and is adequately dealt with by {tu’a}, however that is officially interpreted.

  • The problem with this is that the referent of tu'a is a bridi, yet x2 of nitcu and pixra is an object, not a bridi.
    • Well, the wordlist is inspecific at this point, so either is possible -- but the reading I give forces a bridi. Its virtue is offering a general solution for a range of problems; its vice is that it is counterintuitive at first glance. However, trying to solve the problems raised by the intuitions seems enough to throw us back to this solution -- failing a better, which we still seem to be.
      • I fully agree that the most accurate paraphrase of 'Any' is tu'asu'o (or full bridi) in a sumti place that requires a bridi. But what do we do with predicates like nitcu, pixra, etc. when the relevant sumti place doesn't take a bridi? Either revise the place structure, or be unable to express intensional readings, or use Kind, or find some other as yet unfound solution.
        • Well, {nitcu} and {pixra} permit a bridi and {nitcu can always (I think)have a plausible brid reading, but {pixra} cannot: a mass of blobs of paint may be a picture of a horse somehow, but not of any particular event involving a horse (I think again). Maybe horseity. I'm not sure that Kind works better, since there is probably not horse in there -- even a possible one -- that this is a picture of.

Mr. Broda: does whatever any broda or group of brodas does, is spotted whenever one is and so on. It functions then like the collective of the whole set of actual brodas, {piro loi broda}. It might be nice to abbreviate this to a single gadri, but it is not needed and probably is not justified by usage. Note, it will not solve the “any broda will do” problem, since is restricted to actual brodas and the “any will do” may well involve sets with no actual members.

  • Jboske has come to use 'Mr Broda' as a label for Kind, and it is agreed that a Kind need not have any avatars in this world. So while it is true that 'Mr Broda' by your definition does not cover 'Any', on the jboske definition it does serve as a nonpropositionalist way of rendering 'Any'.
    • Interesting and useful, though hard to cope with directly, since it involves intensions again. I suppose that will work provided that 1) there is a way to separate out Mr. Real Broda from Mr. Any Broda, so that the temptation to generalize for Mr. Broda to some broda or even something can be blocked or permitted as need be.

”I like chocolate”: This, almost the original problem (after “any will do”) still does not have a solution within the CLL system. It does not seem to be intensional (even though what I like is probably eating chocolate or some such) nor do kinds nor stuff seem to work – nor shifting to abstracts like chocolateness. The solution may lie in the logic of “like” (and some related words) and how they relate some of the critters laid out above – like the intensional cases – but no successful suggestion has turned up so far, even moving beyond the CLL system. Fortunately, these difficult cases seem rather limited.

  • Jboske consensus was that Kind was the best thing for the job. In this instance what makes it do the job is the way it turns the membership of a category into a single individual, so that "I like chocolate" is as straightforward as "I like Bill".
    • OK, but only if we allow that we cannot generalize on either of these absolutely. There is also the problem that it does seem to compel that a person who once liked one bit of chocolate and never before nor since liked any is going to end up liking chocolate, which is surely not allowed by what was intended: one avatar does for all. (I dislike "avatar" by the way, though I can't find a cogent reason for the dislike.)
      • The model for the logic of Kinds is (IMO) the logic of individuals. Does a person who once liked Arnold Schwarzenegger during one particular encounter. but never before or since, like Arnold? I'd say no, unless context restricts focus to the occasion of that one particular encounter when the person did like Arnold. I don't want to insist on the rightness of this last sentence, but I do want to insist on the rightness of the first (even if it holds good only by virtue of Kinds being defined as individuals).
        • Well, there are similarities -- even analogies -- between membership or inclusion (I'm not sure which applies to Kinds) and part-whole, but they are not the same. As I understand it (when I don't get it confused with {loi}) the components of a kind are also kinds for example, but the components of an individual are not necessarily individuals. The Schwarzenegger case cuts both ways: if the person does no longer like Schwarzenegger, then no one not now enjoying chocolate like chocolate. On the other hand, if he does still like Schwarzenegger, then our hypothetical one bit liker does like chocolate. Worse, if Kind includes all possible avatars, then it included the chocolate that everyone likes, and so everyone likes chocolate. Though I don't believe it myself, "the typical bit of chocolate" seems a better shot at the moment.
          • As long as your reasoning about liking Arnold and liking chocolate is parallel, I am content. It is an essential property of Kinds (at least as defined by their proponents on jboske) that they are individuals. Beyond that, we are not pushing any particular logic of individuals.
            • I think (hope) that what you mean by "is an individual" is what xorxes means by "is expressed by a constant." Otherwise I have trouble imagining what kind of idndividual a Kind might be. If all you want is freedom quantifier problems, that is easy to do (and I want to do it for all {lV[')i)} anyhow) but what you have are still sets with members to reference to which all claims about Kind must eventually be reduced.

Historical notes on mei, lo, loi