(From Lognet 96/1. Used with the permission of The Loglan Institute, Inc.)

Sets and Masses

By James Cooke Brown

This is the second of two essays on the several ways of handling plurals in Loglan. The first, which appeared in Lognet 95/2, examined the difference between sets and multiples. In this second article the author examines the difference between sets and masses.

The title of last issue's essay was "Sets & Multiples". But there is a third kind of collective entity created by language, namely the so-called "mass individual". These objects, too, are apparently composed of many elements, and so are easily confused with sets if not with multiples. It is time we talked about masses.

Like sets and multiples, masses have no independent existence in nature. They, too, are created by language. They are the things we designate with the "mass designators" of human languages; and they are very easy to confuse with sets. I know; I've done it, soi crano. At least one source of the current confusion is to be found in my own writing. Even as short a time ago as 1989, I occasionally confused these two sorts of designata. For example, in Sec. 4.35 on Mixed Arguments with ze in the 4th Edition of Loglan 1 (pp.260-62), I talked about the designatum of la Djan, ze la Pit, who, having jointly painted a house together, could be treated as a team. That was okay, because these "ze-creatures" are teams; and all teams are sets. But then, in specimen (4) on page 261, I used Lo to mrenu as a designation of that same team. That was a mistake. As I argued in last issue's article on "Sets and Multiples", all these ze-creatures--and that is exactly what they are: things created by ze--are best treated as sets. But back in 1989 I was apparently suggesting that the best description of such a team of house-painters was Lo to mrenu. As I say, this extraordinarily bad example of how to speak Loglan is probably the source of at least some of the present indistinctness in Loglandia between sets and masses.

What was wanted then, of course, was Leu to mrenu. The uses of leu had already been described in Sec. 4.20 on Set Description with loe leu lea of the 4th Edition (pp. 208-9 ); but I was not familiar with this new operator yet; so in Sec. 4.35 I failed to heed L1's earlier lesson! Thus specimen (4) on page 261 was bad Loglan even then. Leu should have replaced Lo in that example. The leu/lea pair had been in principle available since 1978, when these two additions to the descriptor set (but written with other phonemes) had been proposed by two logicians, John Parks-Clifford and Richard Rosenberger; and they were adopted by John and me in The Loglanist of that year. By1989 the descriptor set had settled down, and the definitions of nearly all our present kit were to be found in the 4th Edition. According to Sec. 4.20 of that edition what Leu to mrenu means is The set composed of the two apparent men I have in mind. Leu is therefore an "intentional designator" just as le is. So Leu to mrenu is what should have replaced La Djan, ze la Pit in specimen (4) of Sec. 4.35. In replacing it with Lo to mrenu, I lapsed into an older habit...creating an ontological error that now, some six years later, I find myself obliged to confess. I herewith do.

Unlike more ordinary mistakes, this one is not obvious. (It was apparently not obvious to anyone, soi crano, for no one pointed it out to me in the intervening years!) Perhaps the "invisibility" of this error is due to the inherent difficulty of the set/mass distinction for E-shaped minds. In any case, this little slip has had some amazing fallout! I now hear logli arguing that everything we have been designating as sets should now be considered as "partitioned masses" and designated with lo. This essay is partly an effort to correct this novel misconception.

That Leu to mrenu is a correct "co-designation" of La Djan, ze la Pit--i.e., an expression that can legitimately be used to designate the same designatum--is now plain. But why Lo to mrenu is a not a similarly good co-designation of this same designatum--this same two-man team--may not be so plain. To see why it isn't, let's briefly review how Loglan generates the fiction of the "mass individual" in the first place, how it got its lo-operator, what the original purpose of this kind of designation was, and how the general availability of mass-designating machinery in Loglan allows logli to say many useful things clearly that are difficult to say at all in natural language. Only then will we be able to see how the current confusion between sets and masses probably arose. Having glimpsed its origins we may then try to dispell it.

Loglan's lo-operator is a very early feature of the language. In fact, its arrival in Loglan was a few years earlier than ze's, so the two ontological operations were not historically--and probably not even conceptually--related. Lo was present in the first Loglan dictionary (1963); ze was not. But lo was not present--at least not with that meaning--in the 1956 specification of the language, which was the version that resulted from my efforts to rewrite Otto Jesperson's catalog of "grammatical curiosities" (in his 1937 Analytic Syntax) in the predicate calculus. These dates suggest to me that lo came into the language shortly after, and probably as a consequence of, my reading of W.V.O. Quine's Word and Object, which took place shortly after its publication in 1960. I remember with telling vividness Quine's elegant demonstration that there is no (quick) way (though ultimately there is a way) of distinguishing behaviorally--that is, by a stimulus-response experiment--between the world-views of the users of two languages, L1 and L2, one of which, say L1, defines each of its predicates as claiming the presence of some (specified) mass individual, and so enables claims that are said to be true when and only when some "manifestation" of that mass individual is present, e.g., when some manifestation of Mr. Rabbit, say a vanishing hindfoot of a particular rabbit, is present. The other language, L2, uses our more familiar Indo-European predicate apparatus and treats all its predicates as "general terms", and so enables claims only about "instances" of such terms. Thus in L2 it takes a whole rabbit to satisfy a claim made with the predicate is a rabbit. Despite this substantial difference in their "ontologies" (theories of existence), the external performances of L1 and L2 are virtually the same. But--and this is the Whorfian metaphysical point--the internal worlds of L1-speakers and L2-speakers are vastly different! Quine probably had in mind the Trobriand Islanders as the prototypical L1-speakers. I, too, had encountered the Trobrianders in my anthropological reading, and had been impressed by this amazing linguistic phenomenon, one which apparently populates the worlds of those who speak L1-type languages with "mass individuals". I had found the Trobrianders in the works of Branislaw Malinowski and Dorothy Lee, two anthroplogical linguists who had described their language. One of them, Lee, was so struck by the remarkable "metaphysics" of these Melanesian people, and the way it affected the whole of their cultural and personal lives, as to formulate something very like the Sapir-Whorf hypothesis long before Sapir and Whorf did. Such is the riveting effect of the existence of this particular linguistic system on the mind. If languages can do that, Lee must have told herself, then languages must be very powerful mental tools indeed!

Well, I, too, had been enthralled by Lee's account of the Trobriand world-view, and I resolved--quite idly, I think, but very early on--to enable it as a "metaphysical option" in L. (In Whorf's terms, of course, that's an oxymoron; metaphysics are obligatory; that's what makes them so.) Lo is that universal enabler. It makes it possible for any speaker to turn any predicate expression into a mass individual any time it pleases him or her to do so. At the time, I had no notion of how powerful this device would turn out to be...how it would translate nearly impeccably, for example, the surprisingly numerous Trobriand-like expressions of other languages. All the substance words of E, for example--indeed all the words for abstract individuals like Wit and Virtue that populate the minds of E-speakers--turned out to be mass terms in Loglan.

But by 1975 it had still not become clear to me where the sensible limits of lo-usage lay. It wasn't until a few years after the publication of the first Loglan paperbacks in 1975--not until 1978, in fact, when John Parks-Clifford and I were discussing the merits of Scott Layson's proposal that we add a formal "observative" to the language (Scott's proposal had been that we enable our observative with a regular inflection of the predicate)--that both of us discovered, more or less simultaneously, that we already had an observative! We had lo. It was then that Lo fagro! and Lo simba! entered the language. To mean what? Well, of course to mean the purest of Trobriandic ideas, namely that some manifestation of Mr. Fire or Mr. Lion is prowling in the neighborhood. Not much of these gigantic individuals need ever be observed to precipitate observations of them. We shout Fire! or Lions! in English--Lo fagro! or Lo simba! in Loglan--at the merest whiff or cough. A big toe--or a little toe, for that matter--is enough to precipitate the observation that the "giant" to whom it "belongs" is in the neighborhood. This discovery--for the L observative was in truth discovered, not invented (we already had it, remember; it was Scott's invention that we didn't adopt)--made it very clear to me that the limits of lo-usage in L ought to be as similar to those of the Trobriand Islanders as we could make it. Accordingly I personally began to use lo, and to urge others to use it, in observative-like ways: that is, to celebrate any manifestation of these giants--as in Mi pazda lo taksi and Ea mu godzi lo sinma--by using the lo-forms...not as species-words, not as words with which to discuss the distribution of the "parts" of these massive individuals; for that, in fact, is what the lo mechanism cannot do well and what the language of sets is perfectly-suited to do. Thus, when it really doesn't matter which manifestation of some mass individual gets involved--as it doesn't in waiting for a taxi or in going to the movies--lo is the word to use. But when it does matter, when the actual distribution of some such "composite individual" is involved, then the vocabulary of sets--usually the word lea--is the one to use. Thus the designatum of lo simba is what snoops around your campfire; but it is the designatum of lea simba that is to be found all over Africa. Remember, sets are teams of individuals who are to be considered as acting or being together, and when we speak of those teams--as we do with leu mrenu ji va (that set of men over there)--it is because we wish to speak of whatever it is they are collectively doing or being. Together, they may be building a house; or together, they may be found all over Africa. Happily there are still a sufficient number of these tawny beasts left in the designatum of lea simba so that they still can be found "all over Africa." Notice that no single lion can, just as no single housebuilder--or very few housebuilders, anyway--can build a house alone. Ne simba being found all over Africa is a little like one hand clapping.

Denumerability, as Randall Holmes is fond of saying, is an essential feature of the members of any set, whether they be the designatum of a leu-description--like two hands clapping or that team of house-builders--or of a lea-description, like all the free-living lions to be found in Africa (lea rezlii simba ji vi la A'frikas). In either case, we must in principle be able to count the members of any set before we can speak of them collectively...which is the only reason we ever talk about sets. Not so with the lo-giants who populate the Trobriand world. The parts and appearances of Mr. Yam are not countable--not even in principle--and those of Mssrs. Wind and Fire? Well, it is hard to know how one might even begin to count their parts! In fact, in the-world-according-to-Trobriand very little is denumerable. Manifestations of Mr. Fire, Mr. Lion, Mr. Taxi, and Mr. Cinema simply do not come in countable forms. Any old whiff, sniff, or glimpse will do. It's nice, of course, if the taxi that arrives is a whole taxi with four wheels and an intact back seat. It's also nice if the celluloid substrate of the film we have just sat down to watch does not burst into flames. But even if it does, we have still "gone to the movies". Even if the arriving taxi doesn't have a back seat, we have still been waiting for "it". Questions of wholeness, like those of denumerability, are simply not among the truth-conditions of reports about lo-giants...any more than the wholeness of one or more of the potatoes we eat is one of the truth-conditions of our claim that mu titci lo palto (we eat potatoes).

It is from such Trobriandic considerations as these that I have come to believe that we logli should confine our uses of the lo-operator to nondenumerable manifestations of these glimpsable giants, no matter how slight those glimpses might sometimes be. It simply doesn't take much in the way of smoke or smell to precipitate the Lo fagro! alarm in any of us. We are all Trobrianders when it comes to fires! Those huge, discontinous, usually widely distributed individuals that lo creates for us do not have to show very much of themselves in order to get talked about. But, at the same time, we shouldn't use lo for those assemblages of countable objects about which we do have something collective to say. In other words, we shouldn't use lo for those equally imaginary objects we call sets whose members own houses together, who play tennis or bridge together, and are found all over Africa. For these, we have ze, leu, and lea. And we should learn to use these designators just as readily as we now use lo, e, le, and ra.

That is why it was wrong in 1989 to transform La Djan, ze la Pit, pa pinduo le hasfa into Lo to mrenu pa pinduo le hasfa. They don't say the same thing at all! Given what I will now call "the Trobriandic interpretation of lo", for the second specimen to be true, a glimpse of any skulking two-man pair or a smelly old tennis shoe belonging to any one of such a pair would count as "a manifestation of the mass composed of any two men"; and such things simply don't paint houses. So only Leu to mrenu pa pinduo le hasfa = The set/team/dyad composed of the two apparent men I have in mind painted the house makes a useful claim about this pair of named men. Leu to makes a testable claim out of this remark as Lo to does not.

I'd like to end this paper with a brief demonstration that all members of the class of cardinal numbers are also "mass individuals", and in precisely the Trobriandic sense I have just developed. That it is to say, cardinal numbers can be accurately designated with a lo-form, in particular, with the mass-property descriptor lopu. To show that such designations "make sense"--that is, that they work to locate their designata in the minds of our auditors--is in fact very easy to do. We start with the cardinal predicates: nera, tora, tera, fora, ... . We now observe that a thing is a fora, say, if it can be perceived--by us, or by some other animal observer--as a set with exactly 4 denumerable members. These may be four eggs in a nest, four puppies in a litter, or a key, a button, a paper clip, and a coin on a dresser top...or any other assemblage that has, as we say, a "numerosity of four". (It is a surprising and important fact about numerosities that those up to five can be immediately perceived, i.e., without counting, not only by humans but by the members of surprisingly many other taxa of animals, including birds and elephants. Numerosities of six or more must be counted; but these, alas, can only be counted by humans and--so far at least--by specially trained chimpanzees.) Now if we ask what sort of thing "a numerosity of 4" is, we can answer immediately, if our minds are loglaform--perhaps with a little hesitation if they are not--that a numerosity of 4 is a manifestation of an "abstract property", one exhibited by some "concrete" thing, no doubt, by virtue of which we know that it is a fora...or in more usual E, a tetrad. Perhaps the concrete thing is a nest with 4 eggs in it. Call it X. Then the property Y by which we know X to "have tetradicity" is predicable in L by pu da tora, and the claim that Y is such a property may be expressed in L by De pu da tora. So far so good. But now we wish to designate an imaginary mass individual whose presence is manifested by any of these specific tetradicities. It is the mass of properties by which all tetrads are known to be so. Isn't each of these separate tetradicities, no matter how different it may be from some other tetradicity (just as a lion's cough is different from a flash of tawny pelt), a manifestation of this same mass individual? And can we not designate it in L with Lopu tora? Doesn't each of these concrete tetrads give us one more glimpse of this mysterious giant looming in the shadows? And isn't that looming giant exactly what we mean to designate when we say the number four?

What I am proposing here is that just as every cough, odor, roar, and flash of tawniness emitted by a lion is a manifestation of that also unseen giant, lo simba, so every fora is a manifestation of the unseen giant we call "the number four". If so, we can designate it precisely in L with the expression Lopu ba fora. We know where to look for it; we know where it hides. We can then claim the following identity:

Lio fo bi lopu ba fora.

which may be translated as:

"The number four" co-designates (has the same designatum as) "the mass individual formed of all the properties by which 4-membered sets x may be known to be so".

If a set1 is that kind of "abstract object", we are in clover! But see this space next time for the rebuttals I expect this argument to elicit from our friendly neighborhood platonists! --JCB

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