Lojban
The Logical Language
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Y’know, Lojban is a funny language. To take one point, it was designed to test the Sapir-Whorf Hypothesis, yet it is more an SAE language than any actual SAE language. I has only objects and there properties and connections. It has only count nouns, no mass nouns. Even abstracts are just things on a par with the most concrete. Yet, for all of this, the language does not have an obligatory singular-plural distinction. These can pose problems for someone used to the more generous ontology of even English, not to mention Chinese or Hopi or Menominee. The first line of response to this problem seems to have been the system of articles, which provides means of introducing reference to at least some entities other than simple objects (the second line is the abstractions, but that is a later issue). And so there have come to be a number of suggestions about how to change that system to allow other kinds of talk than are presenty possible (or at least easy enough that we know how to do them). The suggestions are so numerous that it may be worthwhile to go back to the original system to see what it lacked and what it had that seemed misguided aand then trace the various moves from there to the proposals now around. The basic system is about the formula (PA1) L (PA2) PRED, with PA1 pred as a degenerate case. The basic plan with this formula (this is a reconstruction, since the official statements are at least occasionally confusing or contradictory) is that L PRED refers to a group of things that somehow fall under PRED. PA2 refers to the number of things that thus fall under pred, the cardinality of the group. PA1 enumerates some members of that group in some way for further use. In the original system, both PA slots were always filled, even if not overtly. That is, there was a default value to be understood when no number was explicitly given. There are nine versions of L (for the moment) and each of these has some variations on these general rules, specifying what is left vague here and, occasionally, even denying the rule. The nine Ls fall into three groups of three. Where V is any of “a,e,o,†there are {lV}, {lVi}, and {lV’I}. The V= “o†cases are those where the group involved is of things that actually have the property referred to by PRED. The V = “e†cases are those where the user of the term has selected certain objects which s/he chooses to refer to as PRED (with a range of pragmatic restrictions on what circumstances allow using PRED for things which are not actually PRED). The V = “a†cases are those in which the objects in the group are called “PRED†(PRED in this caase being enlarged to include NAME). These last cases do not allow PA2 in the usual sense; a number in the PA2 slot is taken as part of what the objects are called. Where there is a PA2, they function slightly differently between o and e versions, corresponding to the difference between “is†and “is said to be.†That is, for the o version, PA2 is the actual cardinality of the group involved. When not stated, it is assumed to be just all of the things that fall under PRED, so the default is {ro}. For e, PA2 is as much under the non-veridicality as PRED is, so it gives merely the size the speaker is claiming for the group. In default, the speaker is at least claiming that the group has some members, so the default is {su’o}. Conversely, for the e version (and the a), we usually want to talk about all the members of the group (why select these critters if we have nothing to say about some of them?) and so PA1 should implicitly be {ro}. On the other hand, we rarely (it was said) want to talk about all the things that have a certain property, so the implicit quantifier on o cases should be {su’o}. Finally, the simple lV cases are about the members of the group taken separately; {lV broda cu brode) is true just in case each member of the group referred to by {lV broda} brodes. PA1 enumerates the members of a subgroup who individually meet the outer predicate. (Fractional PA1 tell the size of the predicate-satisfying part of a single member of the group.) The lVi cases treat the members of the group collectively, that {lVi broda cu brode} is true if the collective (think “teamâ€) has the property, even though no member does – but also if even one member does. Finally, {lV’i broda cu brode} is true just in case the set whose members are the so-called broda brodes. Usually, the properties of lV’l broda are not – even cannot be – properties of brodas (which usually are not sets), though ultimately they do depend is some way on the brodas (cardinality, intersection and the like). The same is usually true of lVi, though less indirectly. PA1 for lV(‘)i is fractional -- implicitly {pisu’o} for lVi and {piro} for lV’i – marking the size of the subcollective or subset referred to relative to the size of the whole. Integral PA1 are undefined here. That is the system (with a few minor further features that do not yet play a role). What, then is wrong with it for what it sets out to do? That is, quite aside from what it does not (obviously) do, what does it do poorly? Here are a few that have led to suggested changes, in no particular order. Default PA1 quantifiers. Since they are invisible, they are easily forgotten about, with the result that we find ourselves saying things we did not intend. Thus, negation boundaries and word order often lead from what we meant to something very else. Thus, {le nanmu cu prami lo ninmu} is not the same as {lo ninmu se prami le nanmu} for the same reason that {ro da broda de} is not the same as {de se broda ro da} and even though {ko’a broda ko’e} is the same as {ko’e se broda ko’a}. Similarly {lo broda na brode} is not the same as {lo broda naku brode}, just as {su’o da na brode} is not {su’o da naku brode}. Suggested solution: do away with PA1 quantifiers, requiring all quantifiers to be overt. But that leaves bare {lV((‘)i)} uninterpreted, so needing some explanation – and presumably one that is not equivalent to some quantifier. Leave that in abeyance for the moment to see whether other problems and their solution may fill this need in. PA2 quantifiers. At least in the o and oi cases, where the group is all the things satisfying the sumti predicate, they are pretty useless. We rarely know how many of them there are in fact and rarely even care. So these could be dropped without much loss. We do often want to know about the size of selected groups (the e cases), so those might well stay in place (although, if there were another way to show this that did not involve a quantifier between gadri and predicate, it would be useful as being applicable to the a series as well). Solutions to the PA2 problem don’t seem to say much to this one. But in any case, PA2 need not be obligatory, in the sense that we have to read some default value when there is no overt one. This may in practice amount to saying that the default value is always {su’o}, but PA2 is unaffected by order or negations, so no practical problems arise. The e - o distinction. E cases differ from o cases in two ways: the objects in the e group are identified and selected beforehand as individuals, those in the o group are recognized only insofar as they satisfy the sumti predicate. As a consequence, the predicate used to talk about the e group does not have to be one all in that group satisfy, so long as it enables the hearers to pick out the right objects, while that in the o cases is, by definition, one that the objects in the group actually do satisfy. This leads to a double problem (in theory at least, and perhaps occasionally in practice): a reasonable predicate for indicating a selected group is taken veridically and the hearer goes to a different group or claims that there is nothing to meet the need or, conversely, a veridical use of a predicate is taken as merely indicative and so a different group is heard of than that spoken of. The specific – inspecific distinction is the important one here and is often needed; why complicate matters? Solution: require e cases to be veridical as well. Since this would result in immediate duplication, we would also require that {le} is used only for actually distinguished or guaranteed unique groups, not for just any group of broda that we might think to pick. Even so {lo’i broda} duplicates {le’i broda} apparently. But we can patch athat up. More problematic is that we lose the ability to say certain often very useful things: {lo melbi ninmu cu nanmu} as Mike Hammeer discovers at the end of some early Mickey Spillane. We could put in a warning that we are using the words here not merely specifically but also loosely. But that telegraphs the punch line – and means that all the earlier references to Juno, which were made when we thought she was a woman, are strictly incorrect. We could presumably spell out some pragmatic conditions here: speaker believes the predicate applies or at least believes the hearer believes so or believes that the hearer believes the speaker believes or… Again, let’s see what other solutions turn up that may be useful here. Unreal things. {le} was devised originally to deal with the problem of useful “the so-and-so†expressions when there is no so-and-sos. In real-life cases, we say {le broda} in the belief that there are brodas and, in particular, that the things we have in mind are some of them. That we may be wrong on the latter point is discussed above, but what about the cases where there are no brodas at all and yet we say {lo broda} ? These seem to be immediately false or else meaningless, whatever the rest of the sentence says. And yet there are cases where we want to say meaningful and even true things in this way: {lo pavyseljirna cu blabi} (meaningful, maybe even true), {lo pavyseljirna cu xanri danlu} (meaningful and clearly true) {mi kalte lo pavyseljirna} (meaningful and possibly true). The standard solution was to say that talking about things that do not exist means shifting to talking about a possible world in which they do. But that is clearly wrong for many cases: it works for the white case, but would make the imaginary animal case false (in a world where unicorns are real) and would not allow me to go unicorn hunting in this world (even though I am guaranteed not to succeed). There are piecemeal solutions to particular problems (shifting to another world secretly, as noted, or insisting that certain contexts ({xanri1, say, or {kalte2}) are opaque even in the absence of the usual sorts of indicators, or insisting that certain expressions are merely mistakes for others ({kalte lo pavyseljirna} for {pavyseljirna kalte}, for example). But what of a uniform solution? One suggestion, in the context of the original system, is to say that, while we are dropping PA2, we drop the assumption built into it that the default is always at least {su’o}. Leave it so open as to allow even {no} as the cardinal of the group talked about. This does not make {lo [no] broda} automatically false or meaningless, but it does make sentences involving such ecxpressions hard to evaluate: since no unicorns are blue, is {lo [no] pavyseljirna cu blanu} true or false? There are a variety of solutions to these issues, some of which might impinge on solutions to other problems, so this is a factor to keep in mind. Opaque contexts. One of the places where unreal things turn up is in opaque contexts, places where it is invalid to 1) perform the usual quantifier operations on terms in that context (generalize over them at the beginning of the sentence in which the context lies, instantiate external universal to them – nor internal universal to terms outside them, move quantifiers in them to the front of the whole sentence – even if no other quantifiers or negations intervene) or 2) interchange things that are in fact identical. Many of these contexts arise from “mental†predicates – about thinking or dreaming or imagining – or creative ones, like talking about or describing or picturing or… -- or intentional ones – goal directed activities where one intends something – or the opposite – those defined in terms of something missing. And the list can go on. For the first of these at least – and for some of the others – the context is a place of a predicate that takes an abstraction as sumti. An object mentioned in that place is then understood to be buried in that abstraction – a fact signalled by {tu’a}, which stands for the rest of the abstraction. For many of the other cases, however, this move is not at all plausible, at least in the crude form that works with mental predicates. And even for some of them it is a bit far-fetched. The original gadri system clearly does not do this well, although the terms involved seem to be exactly like terms in other contexts. So perhaps this is not something the original system was meant to deal with – appearances to the contrary notwithstanding – and a solution to this may be added as a desideratum. (It is not perfectly clear what a solution would be. Minimally it would be that we can always recognize an occurrence in an opaque contexts as such, perhaps with a special gadri or a generalization of the {tu’a} approach but with a different, more general, underlying rationale. The ideal seems to be to produce sentences that did not look different ordinary sentences and contained terms that did not behave differently from ordinary terms, but which were still true just in the cases wanted. This may, of course, be impossible, since opaque contexts do occur (indeed, are fairly important) and do have a different logic from transparent ones, but the present patchwork des not seem to be an adequate effort.) The meaning of {lo broda}. Or perhaps better, the right use of {lo broda}. {lo broda} is about as inspecific as one can get, even with the assumed PA1 of {su’o}. In the texts that have accumulated over the years, however, two patterns – both legitimate precidings of that vagueness -- have emerged as standard (counting, for the moment, only the unquestionably non-erroneous uses). These uses correspond remarkably well with the English “a(n)†for inspecific concrete singular cases (“A moose and a lobster walked into a bar…,†“I caught a fly ball.†And so on) and indeterminate generalizations (“A climber who has not taken a fall hasn’t learned much,†“A child should respect his eldersâ€) and not a few cases (like the climber case, to be sure) which might be either, but are probably one or the other. Which of these is correct? In fact, with {su’o} as implied limit on the the range of possibilities, both are legitimate. They are, however, so different in their pragmatics, at least, that they should be distinguished clearly. In English, the first line of distinction is often in the verb (timeless presents vs progressives or past tense, for example) and, of course, considerable reliance on context. So, one suggestion is to add a “tense†for “in general†to the general cases (or “in particular†for the others, or use both to be nondiscriminatory). But this would virtually make these tenses obligatory, a very unlojbanic change. Another suggestion is a new gadri for one or the other or a better use of what we have: mainly to use {loi} or {lo’e} for the general case. As they stand, using {loi} includes the general at the cost of also including the particular (it holds if any member holds) and so is no improvement, while {lo’e} is about the typical, which need not be anything like the same notion as the general (the typical cat is female, for example, but cats are not generally female). A third suggestion would be to introduce the distinction into what is – in the original system – a virtual redundancy: {lo broda} and {su’o broda} seem to be at least materially equivalent, true or false in exactly the same cases. But introducing any devise to distinguish the two cases would discard some sizable portion of existing usage. Still something needs to be done. (This is also arguably a desideratum – the original language may not have intended the gadri system to make this distinction; if we use it to do so, this would be an added feature.) Typical. Beyond the basic system as above, the original system had two more gadri (well, several more, but two to look at): {lo’e}, “the typical†and {le’e}, “the stereotypical.†These seem to be in the gadri section because they are in English (etc.?). They are about groups of individuals but taken statistically (as it were) rather than individually or collectively or even as a set. Even CLL falls back on adverbial phrases to explain these: {lo’e broda cu brode} as “Broda typically brode.†In any case, the {lo’e} (and even less the {le’e}) claim does not purport to be about any individual, but rather sums up information – accurate (o) or merely taken to be accurate (e) about a group. Exactly how this is done – in the {lo’e} case --has never been spelled out completely successfully, though it seems to be something more complex than counting cases (the genuinely statistical method) in that some cses appear to weigh more heavily in the upshot than others. And also in the fact that the counts are not ever actually made (it is a desideratum to have marks for genuinely statistical summaries – at least the mean of “the average man†sort). For the subjective case, {le’e}, there is the question whether this “said to be accurate†is an individual or a grpoup matter. The official line seems to favor the group; the look favors the individual. So that needs to be nailed down. In any case, neither will do for generality, since clearly they do not apply to at least the deontological cases like “A child should obey his elders.†What the original system is said to be missing, over and above solutions to the problems given, are ways of dealing with at least species and substances -- both of which seem to impinge on the issue of generality (another issue to be dealt with) – and a crisp way to deal with several groups of objects more or less at once (“divide the class into three groups of five eachâ€). The first and last of these have solutions already in the original system, but those solutions are inelegant at least. And the need for something for substances (even though this too has a partial solution in the original system) seems to open the possibility of dealing with the others. The partial solution for substances takes care of many of the cases that correespond to English mass nouns. These are defined typically as “x1 is piecee broda,†in the pidgen form: “a bit of , a volume of , a quantity of,†and the like, chopping up what we think of in English as a basically continuous mass. So, what we can do is put the pieces back together acting as a unit: {loi broda}, in short. And this gives pretty much the right result, whether or not {loi} picks up the properties of indivduals, since almost any “individual†of this sort can viewed as already being a couple close together and actin in concert. But it does not obviously work as well for typees of things we take as having natural individuations, that come in stable discrete chunks. So, while loi prenu may move a piano, it does not – we feel – fill the interstices between the relics of floor and run down the side of the wreck (and get inhaled by rescue workers, to continue the story). And stories like that one exactly show the sorts of cases where this would be useful to have. These cases are perhaps rare enough that a brivla solution would be appropriate: {se spisa} looks like the best candidate, but clearly is not quite there (and how can we fill {spisa2} if we have no substance words anyhow?) The solution for groups of groups is simply to explicitly talk about groups, using the {-mei} suffix usually. So, the above problem is met by {ci lo mumei be lo se ctuca} with the possibility of moving the subordinate sumti into the predicate: {ci lo se ctuca mumei}. However, the basic form is rather longer than the usefulness of the notion would suggest and the short form is ambiguous – maybe even in context. Further, it is unclear what kind of group {-mei} alludes to: oner word list calls it a mass formed from a set (so {lo’I se ctuca}) and “mass†seems to usually mean a collective group ({loi}), while the group given here is not obviously of that sort (and we are unsure what vbeing of that sort entails anyhow). It may also be possible to deal with these cases by double gadri: {ci lo mu lo se ctuca}, or some such construction. Even so, a new notation would be clearer. Species is more complex, as its nature suggests. We want to say that a species is represented (or even present) wherever a specimen occurs and, in some sense, does whatever a specimen does. On the other hand, a species is an abstraction and, as such, interacts with other abstractions in peculiarly abstract ways. The first factor could be dealt with by taking the species as the set of its specimens and discussing the activities of one, some, many or all its specimens in terms of intersection and (probably non-null) inclusion. That the some broda brodes would then be just that Species Broda ({lo’i ro broda}, say) intersects the Species Brode (similarly identified). And, indeed, we might require that the intersection be of some (probably unspecified) extent before we would take note of it (the law is not concerned with the odd case or some such reading of “de minimis non curat lexâ€). For the second part, we have to turn to properties and the notions of pervasion and overlap (and several other such notions but with varying terminologies). If Broda intersects Brode, it must be the case brodaness overlaps brodeness. But the reverse does not follow, for brodaness may lie conceptually on the line between brodeness and non-brodeness (brodeness is relevant to, but does not pervade, brodaness). Indeed, then brodaness may overlap both brodaness and its (relevant -- we don’t, for example, talk about the color of non-physical objects, though we might say they are all pervaded by non-coloredness and similarly for all the particular colors) complement. In short, the set part is about what is true of brodas, the property part about what is possible for them. Lojban has good vocabulary (well, a little edgy, but adequate) for the set portion and nothing that is obviously of use for the property part. A species combines both aspects, that is, one notion that fits with both vocabularies. Had we a decent property vocabulary, we might propose to use it for the property portion and reflect the set side in the ordinary vocabulary, using some tell-tale gadri. Thus we might say {X brod cu brode} for the intersection, rather than {X broda cu kruca X brode} and then {X broda cu [overlaps] X brode} for the purely conceptual part. Some of the problem cases for the old system could thus be absorbed thus more or less, especially those that are at the intersection of the two sides of species. For example, Xanri by its meaning, defines the empty set, but conceptually takes in any number of species that overlap it and whose intersection with Zasti is null. And so, though it looks like a factual statement and, as such would presumably be indeterminate in truth value, it can be seen as a complex conceptual claim, without raising at least one kind of problem (though it will raise others). Even though we have a good set vocabulary, taking it as the overt use and the conceptual end as covert behind ordinary talk {X broda cu brode} for {X broda [overlaps] X brode}, is less successful, since the oridianry talk is normally about what is rather than what is possible and the longer set talk would be far more commonly needed. But a little vocabuary adjustment would allow all of this to be put into play. Now, what can be done to correct these missteps and omissions? Some moves clearly make no significant changes either in usage or concepts. Others make some, but manageable. Some require a lot of reworking of either usage or concepts or both. Of the nonproblematic changes, the clearest is the elimination of obligatory PA2 in {lo} sumti. Sure, every group is some size or other, but we usually don’t know or care what it is. When we do we can put it in. This step changes nothing at all, all the sumti without out this PA can continue to be read as they were. Since this PA is not affected by moving the sumti around, no claims are altered. This change extends to {loi} and {lo’i} without added complications. The next move does ,make a change, however slight. That is to take the PA2 not as the size of the whole set of predicate-satisfying things, but of some (highly unspecified) subset of that set. Thus, {lo PA broda} would no longer claim that there are PA broda but only that the group referred to has PA members (like {le} but veridical); the whole set comes with {ro} as PA2. No previous correct usage is affected by this, except some may now contain superfluous PA2. On the other hand, spome usage that was previously incorrect because the PA2 was for a subset , not the whole, now become correct. Only this good affect on usage seems to follow. The conceptual change is insignificant. The same cannot be said for two extensions of this step. One such further move is to take {lo PA2 broda} to refer not to some members of a distributive group of PA brodas but to the group itself. Thus, the PA1 would not be partitive: PA1 members out of a group of predicate-satisfying with PA2 members, but rather multiplicative: PA1 groups of PA2 predicate-satisfying things. This change would, of course, go against any correct past usage of {PA1 lo PA2 broda}. Such cases would probably be rare because PA2 is so rarely mentioned. It would also replaces the occasional use of {PA1 (lo) broda PA2mei} and longer versions. But these will continue to be correct, so no harm is done there. Even the cases here PA2 is omitted will not be seriously problematic; the assumption is that (pragmatically at least) {PA1 lo broda} is {PA1 lo pa broda}. Now, a group with one member – whether distributive or collective – behaves just like its member (except perhaps for being a pamei), so {PA1 lo broda} amounts eventually to {PA1 broda}, as earlier usage would have it. Older correct usage would thus be preserved. The only major problem would be with cases of bare {lo PA2 broda}, which, as noted, some groups with PA2 members, not some members of a group with PA2 members. But again, such usage was probably rare since we so rarely mention group size with {lo}. The problem is rather how to recapture the old sense, the members of the group distributively. We have {lu’a} to be sure, even though it has been so little used that I don’t know how to use it; is {(PA1) lu’a lo PA2 broda} – or does it need another gadri? In any case, the phrase is unzipfily long for a usage which is surely at least as common as the reference to a number of groups of a size. And it breaks the parallelism of {lo} with {le} (which already would go with the different functions of PA2). The other move related to deobligating PA2 is deobligating PA1, doing away with the default quantifiers to be read when nothing is in the slot explicitly. This would leave bare {lo (PA2) broda} unspecified as to whether it referred to each or some or some particular number or maybe even none of the broda (or, perhaps – se above – PA@ broda). The same hold for {le} and the other gadri. This move is said to 1) simplify quantifier problems, since only the visible one are affected by movements and 2) provide a natural resource (in the {lo} case) for generalities. The first idea is that, since there is no quantifier there even implicitly, we do not have to worry about passing through negations or passing by other quantifiers; {lo broda} would behave like a logical proper name (not an ordinary proper name, which does not quite live up to this billing). But does it – can it – really work that way in practice. Is, for example, {lo broda na brode} the same as {lo broda naku brode} (that is, to show the move more clearly, this latter and {naku lo broda cu brode}). Well, consider what happens is we are looking to express generality with {lo broda cu brode}: {lo broda na brode} claims that that earlier claim is false, that brodas are not generally brodes. But that hardly means (as we understand {lo broda naku brode) to mean) that brodas are generally non-brode. Humans are not generally female, but that does not mean they are generally non-female (= male, but the point is the same even if there are other alternatives). Similar problems arise for other possible reading of the bare {lo broda} either the same pattern or the reverse implication, or composition or distribution ({lo broda cu brode ije lo broda cu brodi} and {lo broda cu brode gi’e brodi}). And the genuinely unspecified version leaves us without any guidelines for determining whether a claim involving the sumti is true or not – no number of instances (except all and none, perhaps) can decide the issue either way, nor, in the case of generality, can a weighting a la “typical†help (we can easily reproduce the {na}-{naku} case with plausible weightings as well). To be sure, someone might object to the above argument that I have misplaced the “generally,†that the generality of a {lo}-containing sentence is at a top-level, not a level subordinate to sentence negation. That is, {lo broda cu brode} is not “It is not the case that broda are generally brode†but rather “Generally it is not the case that broda are brode.†But this only makes matters worse. It might lead to “Generally broda are non-brodeâ€. Both of these might well turn out to be nearly vacuously true, for generally brodas are not in a position to brode or not; it is not very intersting to know that generally bears eat fish (or not), if this is based on the fact that generally bears are not eating. The connection between generality and bears has been lost. To solve this problem is to take generally (and related notions) into counterfactuals: “if a bear were eating (and in the wild and near a stream and…) then it would be eating fish.†This is very likely the correct tale about “generally†but, since we don’t know what to do with it, we can not call upon it to guide in this. Rather we have to work out what to do in this case to guide our thought about (some) counterfactuals. In short, dropping quantifiers does not eliminate the need to deal with logical operations for sumti and does not open a way to generality (which also does not eliminate logical operations). In short, eliminating the default PA1 solves no problems and creates new ones and does not work as advertised. So, for the nonce at least, we leave {lo (PA2) broda} as short for {su’o lo (PA2) broda}, without commenting on whether this some brodas out of a group or some groups of a certain size. We can dispose of a couple of other suggestions fairly easily. The {le}-{lo} distinction, perhaps because it is slightly odd, is something that most users of the language have gotten right early on and generally used correctly, so there ia considerable usage tht would have to be scrapped for any change (though certainly not all correct usage, for most are probably cases where {le broda} refers to selected actual broda). And the literary value of the potential to shock is probably enough to keep it, even if no one translates “I, the Jury†or “The Crying Game.†The difference in meaning between (though not exactly the meanings of) {lo’e} and {le’e} has been clarified, one about the things themselves, the other about societies beliefs about those things (as understood by the speaker, to be sure). So, {lo’e} probably entails (but certainly is not entailed by} {su’o}. {le’e} is connected to real cases neither way (the earlier psychological histories of opinion-makers is too vague to count). Dealing with substance hardly seems useful enough to make any major change for and adding a new gadri seems major in this context. For your favorite mass nouns, {loi}, indicating an unspecfiedly large collective of unspecified (and perhaps changing) bits, serves well. For the rest, a predicate giving the desired sumti ought to be enough. The suggestion that {lo tu’o broda} with the undigit to indicate that number was not relevant at all (as might be the case for substances is clever, but we do want to talk about the flesh of six victims and the like, so further complications need to be added to make the whole case. And by that time, I think the result will be more complex that the new predicate. This leaves unreal things, opaque contexts, species, generality and the meaning of bare {lo broda} (if not to be left as it traditionally was). Of course, it would be nice to have one solution that covered all of these and there have been proposals along that line, species and Mr. Broda being the developed ones. As noted, what we want to say directly about the species Broda can be said using {lo’i ro broda} and {lo [or {le} – this is one problem not resolved above] ka ce’u broda} ({…du’u …} a problem from another corned of the map). Insofar as what a species does is dependent upon what specimens do, insofar as what is said avbout a species is about what actually happens involving specimens, a species can be viewed as entering into the same sorts of relations with other species as set does with set: intersection and inclusion being the central notions. Insofar as what a species does is dependent upon the properties that delimit the species – its superior genera (this is not a tree where there will be only one such immediately above) and differentia (which turn out to be other genera in may cases) – are like the relations between properties, pervasion and overlap (in varying vocabularies). These sum up what is possible and necessary and natural and so on for a species. In their pure form, there is no conflict between these two facets; they use (would if it were available in Lojban) separate vocabularies. But, to solve the other problems listed, we need to project some of this talk about species onto talk that looks like that about specimens. The species Rabbit is not really white, but the set of rabbits (and so also the species) intersects the set of red things (the genus Red) and this corresponds to some rabbits being white and might, in controlled circumstances, be expressed in almost the same way: {lo ractu cu blabi} say, rather than {su’o ractu cu blabi} (moving immediately to using bare {lo} for species). More complexly, although the species Unicorn intersects with no set (the corresponding set is empty), it is pervaded by at least the genus Animal. As a result, the species could be said to be an imaginary animal (in this world, though in another, where the species intersected differently, it might be a real animal – but always an animal; the property part does not change): {lo pavyseljirna cu xanri danlu}. Note that his is a special case, since the ordinary rule is only for inclusion-intersection. The exceptions are unmarked here; they depend entirely on the meanings of the words involved and so have to be learned individually. For example, that unicorns do not exist looks like the same sort of case but is in fact only about intersection, {lo pavyseljirna cu kruca no da} (or just {na kruca lo zasti}, which, by a semantic rule amounts to the same thing). [I am, by the way, not a bit happy with {kruca} for this kind of intersection but have not come across a better, and {kruca} was used as base for {ku’a}, the set term.] A similar trick works for opaque contexts, which generally have to be expanded (as {xanri} was above) to make the relation clear: I need a doctor when I have an experienced void which would be filled by any object which was a locus of lo mikcu (in the property sense, as “locus†– another missing word – shows). Note the subjunctives here to, which need not be explained for this to work. Finally, the move from species talk to apparent thing talk ({lo} with ordinary predicates), need not happen – indeed be allowed – when only minimal conditions apply. That is, one white rabbit need not make lo ractu white (though if all rabbits were white it would be, and, if it is, then at least one rabbit is to), nor does lo ractu being white mean that all rabbits are. In short, quantifiers do not apply directly to {lo ractu}. But, alas, for getting rid of opaque contexts, they do apply in just the way that those contexts don’t allow (the property moves prevent Leibniz’s laws from working, though).
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