(Originally appeared in Lognet 99/1)

The following paper continues the discussion of Sets, Multiples and Masses that appeared as “Sets and Multiples" (Lognet 95/2: 22ff), “Sets and Masses” (Lognet 96/1: 7ff), both by JCB, and “Sets, Masses and JCB’s Multiples” (Lognet 97/1: 23ff), by Randall Holmes, who was then our Cefli Lodtua (chief logician). Randall resigned this position in 1997 (see his letter, the first in this issue's Lo Lerci), and his place was taken by Emerson Mitchell.

A Brief History of the Word Set

By James Cooke Brown

For some time now there’s been discussion in and around the Keugru about what the English word set means and how we are entitled to use it in the E-speaking quarters of Loglandia. It may help to clarify this discussion—which has been at times fairly muddy—to make a brief historical survey of the senses the word set has been given in various Loglan documents.

1)  The uses of the word set in early Loglan documents—say in the earliest dictionary I can find in our archives, a 1963 one—make it clear that it was then being used as a genus term covering all collectivities of things or persons that are taken as either acting together, as in teams, groups, tribes, pairs, armies, nations, etc., or simply as thought about being together, as in species, classes, castes, etc. This usage appears in the 1963 dictionary, and it has been in my own idiolect with that meaning more or less forever.

2)  No logician—and several were consultants on the Loglan Project in those early years—ever objected to this usage of mine, either then or in the post-1975 years when John Parks-Clifford, a professor of logic, was the editor of The Loglanist, until Randall Holmes became our Cefli Lodtua (Chief Logic - worker) in the middle ’90s and famously delivered to us his dictum that “sets do not carry logs”. R’s allusion was to my favorite example of a set description: Leu to mrenu pa berti leva tristaga. The set of two men (I have in mind) carried that log. I meant this example to contrast with the parallel claim about multiples: Le to mrenu pa berti leva tristaga. (Each of) The two men (I have in mind) carried that log. Note that the L sentences made with Leu and Le sort out the two possible meanings of the ambiguous E sentence The two men carried that log.

3)  More particularly, two logicians—Parks-Clifford and a fellow named Richard Rosenberger—formed with me in the late ’70s what amounted to a committee of three to examine the exact nature of set designations in natural languages, and those discussions ultimately led to the 1980 forerunners of the 1989 pair of set-descriptors lea/leu that are given in Sec. 4.20 of Loglan 1, the 4th Edition, p 208 ff. Leu was to be the “intentional set descriptor”, to be used in ways parallel to le, while lea was to be the “exhaustive set descriptor” and parallel to ra. Le and ra are, of course—and always were—used for multiples. So the set of four operators therefore constitute a tetrad of logical possibilities: the two ways of describing multiples and the two ways of decribing sets.

4)  Interestingly, set description was a totally new addition to the post-1975 language, not having even been mooted in the 3rd, ’75 edition. It is also interesting that, when we did get around to discussing set designation, none of these earlier logicians found it necessary to make the “set1/set2” distinction between the ordinary and the logician’s senses of the word set that now seems to be so important. Sets, for logli workers in the ’70s, were always sets1. It was clearly set1 usages that we were providing for; that is, we were providing ways of designating collective entities that sometimes did in fact carry logs.

5)  In recent conversations with Randall Holmes and Emerson Mitchell, however, who are the two logicians now most active in Loglandia, it has become clear to everybody that the English word set is used in (at least) two distinct ways: one way, call it the set1-sense, is the way I’ve been using it in my documentations of Loglan for these many years; for it is the sense that accommodates the universal human habit of designating objects that have multiple elements or members that act together in some unitary way but are in principle separable from one another and so denumerable. Of such objects human speakers frequently wish to say that they are acting or being together, functioning as a unit, constituting a group, a class, or a team. Obviously in this set1 sense, some “sets” do carry logs. The second way set is used is in the set2 sense given it by logicians. Apparently a set2 is a mathematical object, a sort of ideal label or container that may be empty, and that exists outside of time and space (just as numbers are usually assumed by mathematicians to exist outside of time and space). Perhaps the most important way sets2 differ from sets1 is that the former may usefully and paradoxically be capable of having no members at all! Sets 1, in contrast, always have members, usually two or more. Sets2, having acquired this mysterious capacity to be empty, have apparently lost the capacity to carry logs.

6)  To accommodate Randall Holmes’ startling technical dictum in the middle ’90s (that sets do not carry logs) I suggested, as many readers of this journal will recall, the General Semantics solution to the problem of dealing with lexical ambiguities, namely, that we regularly subscript our English uses of the word set in our Loglandical counsels. Thus began the set1/set2 distinction in the dialect of English that is spoken in and around the Loglan Keugru.

7)  It was about this time, too, that we in the К asked our two logicians for, but sadly never got, a clear definition of set2, by which we meant a definition that could be put into LOD as the place-structure of lodsei (“logical set"), the L word I was proposing as the translation of E set2. To Randolph, a set was evidently a collection of none or more label-like entities—apparently akin to names on a written list of names, or some other indirect representation of the real objects that are assembled from members and then do carry logs—that do not themselves carry logs but are capable of being “manipulated” in the mathematical sense. (The distinction R makes between a set and its members is very reminiscent of the nota- tional distinction that logicians, following the early Quine, finally got around to drawing between names and the things they name. Are sets2 then just the names of sets1?) To Emerson, the word set is apparently an “undefined term”, one of the primitives of the deductive system with which E regularly works, and which E therefore chooses not to define. Neither of these observations leads to a usable dictionary definition, however. Still, clearer and clearer definitions of set1 have emerged from these strangely elusive remarks about sets2.

8)  It is clear now—thanks ironically to Randall— that setci (set1) may be defined in LOD as (4n) F is a denumerable collection of individuals of-type S, belonging-to-superset S, or having-property S, who number С and who are being or doing something V together. All four of these places—but no others, I submit—are sometimes necessary to demonstrate that F is indeed a set 1. E.g., Da setci lea darkra mur- ku lio ro gu lepo duvrai lo tcidi. = X is a set of / a subset of the set of all howler (far-crying) monkeys, that numbers many, and that is searching for food together. The 3rd and 4th places of this predicate seem often to be unnecessary; but sometimes they are necessary...simply to exhibit its denumerability or that its members are in fact “being or doing something together”, both essential features of sets1. Often the information in the 3rd and 4th places is incorporated in the 2nd: Da setci nenicu darkra murku ji titci. - X is a set of some ten howler monkeys that is eating.

9)  Going back to the history of these matters, a mistake was made by me—and, by guilt of association, soi crano, by all 11 of my critical readers—in revising the 3rd edition of Loglan 1 to make the 4th. For in the 4th Edition I failed to carry out, and they failed to see that I had failed to carry out, the implications of our having added two set descriptors leu/lea for the sections on lo and ze in the new book. This mistake is clearly lurking in Sec. 4.9 of the 4th Edition, which introduces lo, and it is in full bloom by the time we get to Sec. 4.35, where I equate La Djan, e la Pit with Le to mrenu (still ok), and La Djan, ze la Pit with lo to mrenu (now not ok). Of course I should have used the still-new-to-me operator leu instead of lo in this example; for what La Djan ze la Pit is really equivalent to is Leu to mrenu = The set of two men considered collectively. Thus the “mini-mass” of two men—quite sensible as a kind of kludge in the less well equipped 1975 language—no longer made sense (except in a nostalgic way) in the ’89 language, which was now equipped with a full complement of set1 descriptors.

10)  What does one do about late-discovered mistakes in one’s published work? One points them out to those who have been misled by them and corrects future editions of the work in question, and so, however belatedly, improves the effect of one’s work. For me, there never has been any real choice in such matter!.. Confession of error is a virtue in any intellectual worker but an obligation to a scientist. (I am told that one of my occasional graces as a college teacher was that, whenever someone discovered a mistake I had made—and in rapid blackboard work, while teaching, say, math, statistics, or logic, one frequently does make mistakes—I happily congratulated the discoverer and off we went again...for my part quite unabashedly. Evidently college students are happier with professors who know their feet are made of clay than with the other, “infallible” kind, who tend to be either mortified or catipulted into denial by any notice of their inevitable mistakes.) In fact, after a lifetime of discovering and correcting errors, discovering yet another now is a source of happiness to me. It’s the undiscovered errors I worry about! This policy has served me and Loglan well. It served me and my fellows when, as an Air Force navigator during World War II, the discovery of an arithmetic error was often a life-saving event for all of us; and later as a teacher, a scientist, and an inventor. Loglan, for example, is an organic invention of so many parts that I was bound to make mistakes in putting it together. Much of the history of the language, from my point of view, has been the gradual discovery and correction of its designer’s many errors.

11)  So, in my recent papers on sets, masses, and multiples I pointed out this unfortunate error in the 4th edition. Most logli I’ve heard from seem to view these papers as leading to a quantum leap in the clarity and transformational power of the language; and this has pleased me. But error discovery and correction is a process in which our logicians have also participated, and should be proud of the progress we’ve made as a consequence. For through our squabbles about the meaning of the word set, a good many muddy matters have been clarified, and so corrected.

12)  Sadly, Randall, at least, seems not to welcome our collective achievement. Randall wants us all to go back to the lo to mrenu usage for pairs of men, say log-carriers, who are involved as a single unit in a single act, and to use lo as the companion of ze in making what we would henceforth be obliged to call “(partitioned) masses” and not “sets” at all. In short, following R, we would all call what natural languages call “sets, groups, pairs, troops, armies, and nations” by its new name, “partitioned masses”, and leave the word set entirely in the hands of logicians.

13)  This sounds draconian, like a move in a turf war. Besides, this move—reinterpreting lo as the set1 descriptor—would leave the classic Trobriand use of lo without direct expression. Yet it was reading Quine’s Word and Object, a book in which Q’s analysis of Trobriand-like usage of the mass term— that is, the Trobriander’s apparent use of mass description as a universal designator—that led to my invention of lo in the first place; and, by all accounts that have been published by its users, lo is one of the adornments of the language. Randall realizes all this, and has proposed, in private correspondence with me, the use of the indirect address operator lue—I think this is what R proposed; but I’ve just looked for this memo of R’s but can’t find it, uu, so I’m obliged to reconstruct R’s proposed “Trobriand operator” from memory—in something like the following way;

Let lue lo preda be interpreted as The “address of” (which generalizes to “signs of”) the mass of (all? or just those I have in mind among?) the predas.

Thus, if R’s Trobriand operator were adopted by the K, instead of saying Lo simba! when you heard the grunt of a lion, you’d be obliged to say Lue lo simba! = Signs of the partitioned-mass of all lions!, Lo simba! now meaning that you had observed, or were perhaps only thinking about, the entire scattered mass of all lions...clearly quite useless as a real-world observative.

14)  My reconstruction of this recommendation of Randall’s is probably accurate enough to be commented on; (a) It’s un-Zipfean, for it replaces a currently short (one-syllable) expression with one that is substantially longer (two syllables longer) for a usage that is exceedingly common, namely our use of the “Trobriand” sense of lo (in Lo fagro!, Mi pazda lo taksi., Ea mu godzi lo sinma., etc.). (b) It reveals a fundamental flaw in the logic of R’s proposal as well. For in collapsing the distinction between all the members of some property-defined set (the “exhaustive” sense of description now conveyed by lea) and just those members of it that the speaker has in mind (the “intentional” sense now conveyed by leu), R’s would introduce a transformational opacity into the language that was not there before. Thus, the lea/leu distinction is evidently now to be abandoned; for if R’s proposal were adopted, we would have to express both these senses of set1 description by lo. But this is the same distinction as the one we have had “forever” between the two multiple designators ra/le. To destroy that distinction just to get lo safely reinstalled in its R-approved role—the mistaken (and I will now star it) *lo to mrenu role—is, I suggest, draconian in the extreme. Worse than that, it is to take a step backwards in our program of facilitating accurate transformations in our logical language.

15)  Even so, there is one valid reason for continuing to use lo to mrenu as one’s own preferred way of translating the first argument in the sentence Together the two men carried that log., though it is essentially a sentimental one. Those who learned their L from the 3rd Edition of LI have every sentimental reason to continue to use the mass descriptor—not in its Trobriand sense, now, but in its equally legitimate local minimass sense—in this remarkably vivid and poetic way: Lo to mrenu pa berti leva muegro tristaga. The local mass of exactly two men carried that enormous log. I can buy this. I can feel this. I can understand the desire to continue this poetic usage, and, frankly, I expect it never to die. Languages grow like Topsy...even logical ones. And historical accidents leave marks upon their corpora just as surely as planned changes do.

16)  At the same time, ever since 1989—ever since the publication of TL 4/3 with its “Supplement to Loglan 1 ” in November 1980, in fact—the exact way, the logical way, the poetically dull way of saying in Loglan that two men carried that log is Leu to mrenu pa berti leva tristaga. The set of exactly the two men I have in mind carried that log. And what I taught 1975 students of L on pp 260-261 of the 4th Edition of Loglan 1 in 1989 is simply wrong.

17)  In the meantime, while we are getting used to the fact that this error occurred, and trying to extirpate its effects, I hope it will be clear to everyone that whenever I—or anyone else, for that matter, who is speaking for the Keugru—use(s) the word set without qualification, it is the set1 sense of that slippery little word that I, he, or she probably has in mind.

—Hue Braon Djim

Copyright © 1999 by The Loglan Institute. All rights reserved.