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Posted by pycyn on Tue 27 of Sep., 2005 20:53 GMT posts: 2388

A primary occurrence of a sumti is one not in the scope of a negation, abstraction, modal or non-assertive speech act. In general, primary occurrence sumti can serve as the premise of a particular generalization: from {sumti broda} to {da broda}. The usual upshot of this is that sumti refer to things that exist in the world for which the sentence is being evaluated.

In xorlo, some primary occurrences of sumti which do not refer to things existing in the evaluation world are nonetheless true: certainly {lo pavyseljirna cu pavyseljirna}, probably {lo pavyseljirna cu simsa lo xirma}, maybe even {lo pavyseljirna cu blanu}. These are all strictly false in prelo, the previous interpretation of {lo}. However, there are a variety of workarounds. For xorlo we could change the domain of descriptions to, say, one in which every well-formed sumti had a referent and – insofar as possible given existence constraints – where that sumti indicated what sort of thing the referent should be, it was that sort of thing ({lo pavyseljirna co se darxi be mi} would be a unicorn but not – in this world — one hit by me, since what is hit has to exist in the world of the hitting). The quantified variables would then range over this domain. Thus, the first inference would go through, but the second (from “there is a” to “there exists a”) would not, in any case. There are some inconveniences with having things this way, but some with not having it as well. And the inconveniences with having it are practically less than theory suggests, since so many interesting predicates require that significant places be filled by reference to existents, not just to beings.

For prelo, the standard workaround has always been that if we are talking about unicorns then we are in a world where unicorns exist. But that only works sometimes; clearly if someone rushes in saying “I just saw a unicorn” and we reply “Not likely, since they don’t exist” we have not made the shift. More satisfying for the certain cases is the notion that tautologies, like “unicorns are unicorns” are true even with vacuous terms: even “brumpfs are brumpfs” is true whether or not we have any idea what brumpfs are. Strictly speaking this takes advantage of the fact that anything can be omitted in Lojban (if “it is clear from the context”) and modals and the like are particularly apt to fall under this, so here we have omitted an “obvious” {ca’e} (assuming that is the right thing for definitional claims and closely related items like tautologies). The second claim above, that unicorns are like horses, can similarly be justified as a hidden {ka’u}. The third, that unicorns are blue, is harder, since this goes against cultural norms (unicorns are typically white and, at worst, run through horse colors in the cultural understanding). But the claim is also, for those very reasons probably false, even though it is logically possible that there be blue unicorns (and on the broad domain view there certainly are since {lo blanu pavyseljirna} is a well-formed sumti and nothing prevents its referent from being blue any more than from being a unicorn). That is, the practical difference between xorlo and prelo in this area is vanishingly small and comes down eventually to slightly different interpretations, differences that will appear within each of the positions standing alone (i.e., the difference between the two systems is no greater than between different instances within a given system).

Such easy relief does not appear for the other case of difference. To say that I want a unicorn in prelo requires {tu’a}: {mi djica tu’a lo pavyseljirna}, while xorlo can say just {mi djica lo pavyseljirna}, what used to be a malglico solecism. In this case, the fact that there are no unicorns in the evaluation world is not crucial; the same problem arises with {mi djica lo mikce}. Nor does expanding domains help any here: even in the widest domain, the move from {mi djica lo broda} to {da (poi broda) zo’u mi djica da} does not work in general, for it can be shown for every broda, fub, even in the extended domain that {la fub zo’u mi djica fy} is false even when the original is true — because I would have been as satisfied, my desire met, by any other broda every bit as well as this one.

The problem is, of course, that of intensions. For expressing them there are generally two solutions: intensional places or intensional expressions. English does a mix; Lojban aims at doing the second, though even in unchallenged areas there are exceptions. For a logical language to use places would seem to require that those places be overtly marked to prevent by formal interdiction the objectionable inferences (and to allow unmarking where appropriate). Merely learning a list (even if guaranteed exhaustive) does not seem sufficient. So, for Lojban, the suggestion that {djica2} is intensional is at variance with the program, to be taken up only as a last resort (it also does not allow marking cases where the inference goes through).

But there is the other choice, namely to take expressions in {djica2} as referring to intensional objects. One doesn’t want to do this across the board, since that would again preclude a marking for the generalizable cases and, more to the point, some expression pretty much have to refer to particular, identifiable things (even though occasionally nonexistent ones) where the inference usually goes through with only the existence problem (for which solutions are available). That is, most kinds of sumti refer unambiguously to extensional objects (or abstracta considered extensionally). In fact, the severe problems arise only with {lo}, which, because of its generality, is particularly liable to the sort of fallacy sketched above. Thus, much of the problem presented is solved if {lo broda} is taken to refer to an intensional entity, say the broda species or brodahood or brodaness (what happens in these case differs somewhat but the overall pattern is pretty much the same; in what follows we will stick to brodaness, the property of being a broda). That is, {mi djica lo broda} describes a relation between me and brodaness, a relation involving a tension that would be resolved just in case I come into some (unspecified, but covered by having) relation with something that has brodahood, su’o broda.

Of course, {lo broda} does not refer to brodahood only in {djica2}(and other intensional places, as it were), for that would recreate the problem of unmarked opaque places, which we are trying to avoid. Thus, {lo broda} refers to brodahood in all places where there is no mark that it does not (assuming we want to have some such places). In particular, since it is brodahood in {djica2} it must be brodahood in all places of all predicates (else we would have unmarked places). On the other hand, for example, {lo broda} as part of a more complex description: {Q lo broda} can be given an extensional reading, if that is desired (in any case the whole expression is extensional).

Now ordinarily, we say that {sumti brode} is true just in case the referent(s) (in the evaluating world) of sumti is/are in the set of things assigned the predicate {brode}, that is, have the property brodeness in the evaluating world. This will not work for the intended purpose of {lo broda cu brode} – to say that brodas have the property — however, since generally brodaness – the referent of {lo broda} -- will not have the property brodeness, even if all the brodas do (or may have it even when all the brodas lack it). So, for xorlo to work, we need a different rule the truth of {lo broda cu brode}. Since we want this to sometimes be true even when there are no brodas, this new rule cannot appeal directly to “things which have brodaness” or the like. It must rather be written in terms of the relation between brodaness and brodeness directly, that there is a semantic or conceptual overlap. Now this overlap, to be effective in the way intended can come about in either of two ways: by conceptual inclusion (as in {lo pavyseljirna cu pavyseljirna} and perhaps {lo pavyseljirna cu blabi}) or by factual overlap (as in effect happens in the usual way of doing way of evaluating truth things that fall under one property fall also under the other).

Having introduced this intensional definition of truth for {lo} expressions, we need either to find a way to apply it to all other sumti expressions or to recognize that there are two radically different definitions of truth involved here, where there was only one with old {lo}. It seems clear that we cannot make the intensional definition work with many sumti expressions – or can do so only with the introduction of considerable ad hoc complexity. Variable by their nature do not fall under some concept to be used. Neither do names (unless you have “named so-and-so” as a concept, which seems to be straining the notion of “concept” a bit). And {le} expressions are specified exactly by their referents, not by any concept (unless again “is called such-and-such” is a concept and even that has content only by pointing to the intended individuals). So, it seems we must recognize that we have a more complicated and doubled conceptual apparatus with xorlo. Of course, this makes no practical difference in using the language, only in theory; so, if it brings about some simplification in use, it is probably acceptable.

As noted earlier, one change that is achieved is only a theoretical advance: the various things that can be said about nonexistents work as well in prelo as in xorlo and, at least in some cases, the same hidden devices are needed: elided modals or the like. As for the intensional cases, we still need {tu’a} for those desires that are referred to by other expressions than {lo}s: {mi djica le mikce} or {mi djica la djinis} or even {mi djica da} all immediately have – as they do in prelo – the reading equivalent to the fronted form: {le mikce zo’u mi djica my}, {la djinis zo’u mi djica dy}, {da zo’u mi djica da}, even when this is not meant (Jeanie may be only in my dreams as may be the doctor that I want and I can obviously want something without there being something I want). And, lacking {tu’a} with {lo} we are deprived of the possibility of quantifying out that is available for other sumti: I cannot say directly that the thing I want is something recognizable even separate from my wants. {mi djica lo broda} = {lo broda zo’u mi djica by} in prelo but not in xorlo, since the special reading of application in terms of property overlap applies only to {lo} expressions and {by} is not one, but rather is merely coreferential with one and so has me wanting a property. Since, this problem will arise with every anaphora of a {lo} expression} we can expand our rule of interpretation to cover such anaphora as well, although this requires that we always know what sort of an expression is being anaphorized (perhaps, to keep this all formally correct, we should require different anaphora for {lo} expressions so we can always tell). In a similar way, we need special variables for generalization of {lo} expressions. Otherwise the generalization from {lo pavyseljirna cu pavyseljirna} would be {da pavyseljirna} which says there are unicorns as things, not just about the overlap of properties. This is all to complicate the language and either put strain on the cmavo space or complicate the structure of pronouns and variables. Or, of course, we could ignore these problems and regularly use expressions that are ambiguous at a fundamental logical (and ontological) level.

So far, I have seen no concrete suggestions about how either to deal with these problems or to circumvent them. On the whole then, I think it would make sense to do away with xorlo and return to prelo. The one change that this makes at a practical level (aside from not needing the duplication of pronouns and variables) is the use of {tu’a} in all cases except those where the existence of a particular object is stressed and this was already a part of Lojban. And the theory is greatly simplified, with all sumti functioning in the same way – the way we naturally think they function anyhow.