d from d.(Return to the Table of Contents)
Notes 262
In the previous chapter we talked about the ways in which a speaker could use the predicate apparatus of a language to make claims, to give information, to frame new insights, and so forth. But to use a predicate is also to indicate one's willingness to show one's listeners how to use or test the truth of the relationship or perception that it claims. If I tell you 'X is taller than Y' or 'Z is an intellectual dwarf', I must evidently be prepared to answer such questions as 'How do you know?' 'In what way?' 'How can I tell?' and so on. For if I am a knowing and responsible speaker, I must be able to follow up any such use of a predicate with such remarks as 'Well, if you talk to Z, you will find he is no intellectual giant', or 'If you put X and Y back to back and hold a carpenter's level over their heads, and then keep it level while you lower it, you will find that it touches X's head before it touches Y's.' In fact if I cannot follow up my predications with instructions of this--or some other--sort, people will begin to suspect that I don't know what I am talking about.
But you might also ask an entirely different kind of question about either of these same remarks. You might ask 'Who's X?' or 'Who's Z?' Obviously the most elaborate instructions for testing the claim that X is taller than Y, or the most illuminating comment on Z's dwarfed intellectuality, will not be of much use unless you know the identity of the individuals to whom these predicates are supposed to apply. And again, just by using such arguments as 'X', 'Y' and 'Z' in such remarks I am evidently indicating my willingness to help you locate the objects to which my predicates apply. For example, I might answer 'X is that red-haired fellow standing over there.' And again, if I am unwilling or unable to give you locating information of this--or some other--sort, people are likely to suspect that I don't know who I am talking about.
But the two kinds of information are very different. To tell you what I mean by a predication is to give you a recipe for testing it, on anything. But to tell you to whom or on what I intend that predication to apply, is to give you the address, so to speak, of just those objects. Predicates make claims. Arguments designate the individuals, or sets of individuals, those claims are about. By one linguistic convention or another, they help the listener to locate those things in space-time.
Suppose I say 'I am taller than you are.' You will not, if you understand English, have to inquire who or what I mean to designate by the arguments 'I' and 'you'. For you will know that anyone who uses 'I' in an English sentence means to designate himself, and here I am. Similarly, if I am gazing directly at you when you hear me say 'you', you will have no difficulty in locating the second object I have designated. For by a similar convention of spoken English you know that 'you' designates the person addressed, and here you are, too. In contrast, the references of 'X' and 'Y', like those of the pronouns 'he', 'she' and 'it', are not so easily located. Like the Loglan variables da, de and di, they require a context of previously-spoken sentences from which to infer what they mean. I can start out talking about you and me, for you know immediately who we are; but I cannot usually start talking to you in sentences in which the only arguments are 'he' and 'she' or da and de. For, as we shall see, the conventions of both Loglan and English require that I use these "third person" variables to refer to things which have already been referred to in some other way.
This, then, was the essential artificiality of the sentences we studied in the preceding chapter. None of their arguments designated anything; for no listener could have located the things to which those arguments apparently referred. We must now look more closely into these matters. We will find that very special conventions surround the machinery of designation in any language. When successfully used, these conventions lead to the possibility of the listener's locating the things to which the speaker has referred. Just how these locating conventions are arranged in Loglan is the subject of the present chapter.1
The simplest way a speaker can locate something for a listener is by pointing to it. Then if, in addition, he wishes to say something about the object at which he is pointing, most languages provide one or more convenient little words to serve as arguments of the predicate which says that thing. In Loglan the variables ti [tee] and ta [tah] serve this "demonstrative" function, as in the following sentences:
| (1) | Ti bukcu | This is a book. |
| (2) | Ta bakso | That's a box. |
Just as in English there are two of these words. The convention is that if two objects are to be demonstratively designated, ti will be used for the closer or the later of them, while ta will be used for the farther or the earlier. If only one object is to be referred to, either ti or ta may be used.
The relationship between both ti and ta and the thing it refers to is usually a transitory one. Thus in the same context of speech I may use the word ti many different times to refer to many different things. For example, I may walk down a row of objects on a shelf and refer to each of them in turn as ti, just as I may say 'This is a cat; this is a dog; this is a mouse' in English. In this respect, the demonstrative variables differ from the other variables we are about to study in that their references may vary within the same context of speech. They are in this sense the most variable of the Loglan argument forms.
Sometimes when we use 'this' and 'that' in English we aren't referring to objects in the world immediately around us but to something someone has said or alluded to. Thus when someone says something we agree with, we often say 'That's true.' In a logical language one must keep references of that kind distinct from references to the object world. This is the same difference--first pointed out by the positivist philosopher Rudolf Carnap--that philosophers now refer to as the difference between the "object language" and the "metalanguage". In its simplest terms the metalanguage is the language we use to talk about language. 'That's true' is an excellent example. We use the pair of demonstratives toi [toy] and toa [toh-ah] for this metalinguistic purpose in Loglan.
| (1) | Toi tradu | That's true (literally, this is true). |
| (2) | Toa falji [FAHL-zhee] | That's false (that earlier claim was false). |
On most occasions of their use, disyllabic operators like [toh-ah] will have "level stress"; that is, neither syllable will be stressed.
But there is still another kind of demonstrative pronoun. Suppose someone tells you 'John is sick today.' You say 'That's bad!' Is it da's sentence you are referring to? No; it is the situation described by that sentence that you are saying is bad. So neither Ta zavlo ('That object over there is bad!') nor Toa zavlo ('That sentence you uttered is bad, i.e., ill-formed') will do. In a logical language we need still a third pair of demonstratives to refer to the absent situations to which the sentences spoken in our immediate vicinity often refer. In Loglan we use tio [tyoh] and tao [tow] for this meta-metalinguistic purpose.
| (3) | Tio zavlo | This is bad (i.e., the situation just alluded to is bad). |
| (4) | Tao gudbi | That's good (the situation previously alluded to is good). |
In English we tend to use 'that' in both these situations. We say 'That's bad' and 'That's good' whether the allusion was made in the most recent sentence or not. Possibly this is because of the remoteness from the scene of speech of the meta-metalinguistical world.
So in Loglan we have three pairs of demonstratives: ti ta for immediately perceived things; toi toa for pieces of recent speech or writing; and tio tao for absent situations to which pieces of recent speech or writing allude.
As a speaker of a logical language you will find these distinctions very useful...even though the chances are very good that you have never made them before.2
These are the argument-forms that we used without comment throughout the previous chapter. You sensed in that context that they were very like the X Y Z's of the mathematician. This is correct; for unlike the English third person pronouns which they often translate, the Loglan free variables may stand for anything at all: single things or plural sets of things ('it' or 'they'), subjects or objects ('he' or 'him'), animate or inanimate things ('she' or 'it'), and males or females ('him' or 'her'). Moreover, each of the five free variables may be used in any of these ways.
Like English third person pronouns, Loglan free variables are usually introduced into speech as short replacements of other, longer designations that have already been made. For example, in the sequence of English sentences,
(1) Christopher Columbus visited the Queen of Spain.
(2) He persuaded her that the Earth was round.
the pronouns 'he' and 'her' in (2) replace the longer designations 'Christopher Columbus' and 'the Queen of Spain' that first occurred in (1). In Loglan we often make the same kind of replacement with free variables. As in English, they may replace (i) names, (ii) descriptions, and (iii) demonstratives. They may not replace each other or the Loglan equivalents of 'I' and 'you'. In a moment you will see why.
Now the reason that pronouns are often inflected for number and gender in the natural languages is primarily to allow the listener to make a fair guess at the identity of the name, description or demonstrative for which each pronoun is a substitute. For example, it is because we know the genders of Christophers and queens, that we can be fairly certain that 'he' replaces 'Christopher Columbus' and 'her' replaces 'the Queen of Spain' and not the other way round. But the Loglan variables are totally uninflected. Obviously, some other system of identifying the objects they replaced must be found.3
In Loglan the replacement system governing the references of free variables is based on the order in which they are used. It is as if, when speech commences, the five free variables were sitting on a shelf in alphabetical order in both the speaker's and the listener's mind. Then as speech progresses they are continually matched up with the arguments they might replace in the sentences that have already occurred. When a free variable is used to replace another argument, it is taken off the shelf, so to speak, and the others are shifted along it to form a new order. The matching with potential replacements then proceeds as before. Let us illustrate this process with an example.
Suppose someone commences a conversation by pointing to something and saying:
| (3) | La Djan, pa vedma ta le fumna | John sold that to the woman. |
In this sentence there is a name (La Djan), a demonstrative (ta) and a description (le fumna). All of them are replaceable by free variables. Let us see how.
Suppose the speaker now wants to add that the woman who bought the indicated object then gave it to a person named Pete. Well, the five free variables are all unused, and as he spoke sentence (3) the speaker unconsciously matched the first of them, da, with the last designation in the previous sentence, which is the one it may replace, namely le fumna. So da is now available to talk about the woman. But the speaker also unconsciously matched the second free variable, de, with the second-from-the-last argument used, namely ta. So de is available as a more permanent designation of that object than ta is. (Recall that the demonstratives are temporary designations and may not be used a second time to designate the same thing.) Finally, the third-from-the-last designation is La Djan; this has been matched by the speaker with the third variable di. And if he wanted to mention John again, the speaker could now do so by using the variable di.
But he doesn't. What he wants to say is that the woman--who is potentially da--gave the object--which is potentially de--to some new person named Pete. So he says:
| (4) | Da pa donsu la Pit, de | X gave Pete Y. |
Now because the listener--let us suppose, for our referential convenience, a woman--is playing by the same rules, she has also made this same unconscious matching; and she therefore knows that da refers to the same object as the last previous designation, namely le fumna, does, and that de replaces the second-to-the-last designation she has heard, namely ta. Moreover, had she heard the variable di she would have known that it referred to John. But she didn't.
Now as soon as these two variables, da and de, come off the shelves in the speaker's and listener's mind, then a new matching must be made. For if the speaker thinks back over what he has now said he will find that the last replaceable designation he has made is not La Djan in (3) but la Pit in (4). Consequently, after speaking sentence (4) a new matching set-up is formed in the speaker's and listener's mind in which di now matches la Pit and the fourth variable do now refers back to La Djan. Both of the other replaceable designations in these two remarks, namely le fumna and ta, have already been replaced by da and de and therefore stand outside the new matching scheme.
So the speaker may continue:
| (5) | Do pa mercea [mehr-SHEIGH-ah] da | W married (married-became to) X. |
And who is X? The woman once designated by le fumna. And who is W, the "designatum" of (that is, the thing or person designated by) the fourth free variable? Why John, of course. Had the speaker wished to say that it was Pete who married the woman X, he would have said:
| (6) | Di pa mercea da | Z married X. |
For at the time he spoke, di was matched with the name la Pit.
This seems tricky, but you will probably find it easy and natural to assign up to three free variables in this way. It will usually be clear to you when you are listening to or speaking Loglan just which among the five free variables have been used. The rest remain in alphabetical order on their shelf waiting for the speaker to use them. Thus after sentences (3), (4) and (5) the variables da, de and do have been used to replace le fumna, ta and la Djan, respectively. Throughout the rest of this conversation--or the current paragraph in text--these three variables will remain more or less permanently assigned to the objects and persons designated by the original expressions, i.e., to their designata. At the end of utterance (5) only di and du remain unused. These will be ready to be matched to whatever is the last and next-to-last replaceable designation, respectively, at any subsequent moment in the conversation. Experience has shown, however, that even a fourth free variable is rarely used in speech.
Writing is a different matter. With one's text in front of one, not only can all five replacing variables be rapidly assigned, but one can run out of variables fairly fast. When this happens, subscripted variables may be used. These are compounds like dacine [dah-shee-neh], dacito [dah-shee-toh], etc.--these compounds, too, normally get level stress--which are the Loglan equivalents of expressions like English 'X-sub-one', 'X-sub-two', and so on. There are in principle an infinite number of these, of course, so once the writer starts on them, da is not likely to run out of variables again. But the five unsubscripted variables da de di do du will suffice for organizing the references in most ordinary text.4
The personal variables of Loglan are much more numerous than the personal pronouns of English, but they are used in much the same way. The basic words are mi [mee] and tu [too] which, as you may easily guess, mean 'I' (or 'me') and 'you', respectively. Thus:
| (1) | Mi cluva [SHLOO-vah] tu | I love you. |
| (2) | Tu cluva mi | You love me. |
Note that neither of these words is inflected for its position in the sentence. It is as if we said 'Me love you' in English, as, in fact, some children and speakers of Pidgin English do.5
There is no distinction in Loglan between the formal and informal senses of 'you' as there is in French and German. In this respect Loglan is like modern English and unlike nearly all of the other European languages. For almost all these languages still carry this mark of the sharp class-distinctions amongst the people who spoke these languages in the past.6
A third personal variable is mu [moo], a phonemic mixture of mi and tu. Naturally it means 'we' or 'us'. In fact, mu is an abbreviation of the "mixed" argument form mi ze tu ('I and you jointly'), the exact meaning of which we will consider in Section 4.35. For the moment it is enough to know that this is the "proposing" or "planning" sense of English 'we' or 'us', as in the sequence 'Let's go. We'll visit Jack. Then we'll eat.'
There is another sense of the pronoun 'we' in English. For example, the sense of 'we' in the following sentences is not that of mi ze tu: 'John and I went to Spain. We stayed there for a while, and then we went on to Italy.' Obviously I do not mean to include you, my listener, in this "narrative" sense of 'we'. So for precision of reference we have another set of personal variables in Loglan which mean 'X and I', 'Y and I', and so on. These are mia mie mii mio miu [myah myeh myee myoh myoo]. As you may easily infer, these words are abbreviations of the mixed forms mi ze da ('I and X jointly'), mi ze de ('I and Y jointly'), and so on.
Like the free variables, replacement with these mixed variables is determined by order. Thus in translating the English narrative above, we would use mie for 'we' because the name 'John' in 'John and I went to Spain' is the second-to-the-last replaceable designation at the moment the replacement occurred ('Spain' was the last). Note that 'I', being a permanent designation of any speaker, is not replaceable and therefore is not counted in reckoning the replacement order of 'John'. Since all designations made with personal variables are permanent in the passages in which they occur, they are never replaced by free variables.
There is a third, less frequently occurring sense of 'we' in English for which Loglan also provides distinct words. This is the mu ze da sense of 'we': the mixed first, second and third person sense of the pronoun 'we' in 'We (you and I and the children) will visit the Louvre first, then we'll go to Notre Dame, then the Left Bank...' and so on. This is the "group planning" sense of 'we'. So this mixture of references is expressed in Loglan with the mua-series, mua mue mui muo muu [mwah mweh mwee mwoh mwoo]; and mua is, we see, a very compact abbreviation of mi ze tu ze da.
The final series of personal variables is one in which the members have the sense of English plural 'you' when it means a mixture of second and third person references: thus 'you (the listener) and X', 'you and Y', and so on. These abbreviations are of course generated from the mixed argument forms tu ze da, tu ze de, and so on, and are simply tua tue tui tuo tuu [twah tweh twee twoh twoo]. Again the rules of replacement for free variables apply.
The total number of Loglan personal variables is a formidable eighteen. But as fifteen of these come in five-member series, and as all but the primitive elements mi and tu are plain abbreviations of ze-linked phrases, they hardly have to be learned. Once the da-series and mi tu are in hand, then tui will be seen and heard as tu ze di. There is hardly any more to it than that.
With the personal variables we complete our account of the words which function as pronouns in Loglan. In summary, these are (i) the six demonstratives ti ta, toi toa and tio tao, (ii) the five free variables of the da-series da de di do du; and (iii) mi tu mu and their fifteen derivatives. There are many other variables, of course, since Loglan is a heavily mathematized language. The most numerous are the letter variables we will take up in the next section.
Loglan, which frequently uses those compact visual forms beloved by mathematicians, has an unusually large supply of letter variables: the 'a' 'b' 'c' 'd's of the mathematician and logician. Each letter variable is available in two forms, first as a word--in most cases three-letters long, e.g., bei--and second as a single-character written sign, in this case b. The Loglan letter words and letter signs are used exactly as the English number words ('one') and numerals ('1') are used, in that each numeral is a visually compact form of its corresponding word that is used optionally in print or writing. In fact, Loglan letter signs are called "letterals" on the model of the English word 'numeral'.
There are a hundred of these word/letteral pairs in Loglan. There are the 52 words for the 52 Latin letterals, the 26 lower plus the 26 upper case ones. (A and a are different letterals in Loglan, as indeed they are different graphs in English, and so deserve different words by which to speak them.) But there are only 24 three-letter words for the 48 Greek letterals, because the 24 capital letter words are made by prefixing gao- [gow] to the three-letter word for the corresponding lower-case letteral. This is because so few Greek capital letterals differ from the corresponding Latin capitals that there is little use for upper-case Greek letter-words.
The words loglanists use for reading letterals aloud--words like the seldom written but often spoken English 'tee', 'eks', 'eff' and 'cue', and the both written and spoken 'alpha', 'beta' and 'gamma' of Greek--are generated in Loglan by adding -ei [-ay] and -ai [-igh] to the lower and upper case Latin consonant letters, respectively. This generates the series bei cei dei... [bay shay day...] for the lower-case letterals and Bai Cai Dai... [bigh shigh digh...] for the capitals. The Latin vowel words are either the seven vowel letters pronounced according to their sounds, a e i o u w y as [ah eh ee oh oo eu uh], when it isn't important to distinguish them from the connectives a e i o u, and when case and language (Greek or Latin) doesn't matter, or by three-letter words formed by attaching -si and -ma to the vowel letterals when it is. Thus asi esi isi... [ah-see ess-ee ee-see...] are the three-letter words for the lower case Latin vowels, and Ama Ema Ima... [ahm-ah em-ah eem-ah...] represent the capitals. Again, the most typical pronunciation of these disyllables is with level stress.The Loglan words for the Greek letters--words which function like 'alpha', 'beta', 'gamma', and so on, in English--are formed in Loglan by adding the suffix -eo [-eigh-oh] to all the consonants except c because there is no sound in Greek that corresponds to Loglan [sh]. This generates beo deo feo... [beigh-oh deigh-oh feigh-oh...] for the lower-case Greek consonant letter-words. As mentioned above, gao- is added to these three-letter forms to make the occasional Greek capital. Thus gaoseo [gow-seigh-oh] is the word for capital sigma, whose letteral does in fact differ from Latin 'S'. Seo [seigh-oh] of course is lower case sigma. Greek lower-case vowel-words are made in forms parallel to the Latin ones by adding -fi to all the Loglan vowel-sounds except w--like c, Loglan w [eu] is not assigned to any letter in the Greek alphabet--whenever it is useful to distinguish between cases or languages: afi efi ifi... [ah-fee eff-ee ee-fee...]. The words for the Greek capital vowels--on the rare occasions when they are required--are gao,afi gao,efi gao,ifi... [gow-ah-fee gow-eh-fee gow-ee-fee...]. (Note the close-commas. This forces vowel-pairing from the left, and is one of the rare occasions when the "pair-from-the-right" rule mentioned in Section 2.15 is departed from in non-names. Because it is a departure from standard pronunciation, it is marked.)
Remember that each of the 100 three- and six-letter words so generated may be represented in text in two ways: first, as a phonemically spelled word--Tai, for example, which translates the phrase 'capital tee' in English--and second, by its single-letter abbreviation, in this case the letteral T. Both representations are pronounced as the word itself is spelled, in the case of T and Tai as [tigh]. Thus the two differently written sentences:
| (1) | Tai ditca [DEET-shah] | Tee is a teacher (unusual in English text, but understandable). |
| (2) | T ditca | T is a teacher. |
are read aloud as the same utterance. This is exactly what we do when reading numerals aloud in English, of course. Thus 'He ate 3 doughnuts' and 'He ate three doughnuts' evoke exactly the same sounds.
A common use of letter variables in Loglan is to shorten longer designations, often as an alternative to using the replacing variables described in Section 4.4.7 Thus T in (2) might well have been an abbreviation of the longer designation la Tam in
| (3) | La Tam, merji le kicmu [KEESH-moo] | Tom is married to the doctor. |
(La is the Loglan name operator, and le is a "descriptor" like English 'the'. These are operations which we will consider more carefully in the next two sections.) Thus we could rewrite (3) as
| (4) | Tai merji le kicmu | Tee is married to the doctor. |
Conventionally, upper case letter variables are used to abbreviate names, while lower case ones are used to abbreviate predicates used as designations, as kicmu is used in le kicmu. Thus (4) could be further shortened by using a second letter word--this time a lower case one--to abbreviate le kicmu:
| (5) | Tai merji kei | Tee is married to kay. |
or even to
| (6) | T merji k | T is married to k. |
in text.
The text is now in the maximally condensed visual form we see in mathematics books. But the sentences of (6) are pronounced exactly like those of (5)...in both languages. Note that the case information in the Loglan letter words is not conveyed in the spoken English ones. That is to say, we do not say 'Capital tee is married to lower-case kay' in English. In effect, we do in Loglan...thus doubling our kit of speakable letter variables.
The mathematized style of Loglan is still being explored. At the moment, using letter variables is neither more nor less admired than using the replacing variables of Section 4.4, which, although more difficult to keep track of, seem somehow to be more natural. Which system of third person pronouns will be preferred in what contexts remains to be seen. Perhaps both systems will have permanent roles.
In replacing a longer designation with a letter word, the Latin letter is used first. The Greek one is used only after the corresponding Latin letter has been assigned. For example, to abbreviate the designations in,
| (7) | Le kicmu pa furvea [foor-VEIGH-ah] le ketpi le ditca | The doctor bought (2nd converse of sold) the ticket from the teacher. |
we use kei for the first k-initial predicate, keo for the second, and dei for the d-initial one. Rewriting (7) with those letter words we get:
| (8) | Kei pa furvea keo dei | Kay bought kappa from dee. |
If text is to be printed, and if the fonts available to the printer include Greek letterals as well as Latin ones, then the following even more abbreviated textual form is possible:
| (9) | k pa furvea d | k bought from d. |
Greek letterals have, of course, been routinely used in science and mathematics for several centuries. As the century of the computer unfolds, the use of such fonts in ordinary home-generated text may well spread to non-mathematical domains.
We must now make explicit a convention that we have used informally for some time. That convention is that when names are used as designations in Loglan, they are preceded by the little word la [lah]. For example, the presence and absence of la is the only difference between the following two sentences:
| (1) | La Djan, godzi | John goes. |
| (2) | Djan, godzi | John, go! |
In sentence (1), the name operator la has made a designation out of the name-word Djan which follows it. That is, La Djan refers to something, namely to a person named John. Since it refers to something, it is an argument, namely the first argument of the predicate godzi. Therefore the sentence as a whole is a statement; it claims something to be true of John, namely that he goes.
In sentence (2), however, the name-word Djan is used vocatively, that is, used to call the attention of someone named John. This leaves the predicate godzi without a first argument; and, as we will see in detail later, a sentence whose predicate does not have a first argument is not a statement but an imperative. It forms the injunction 'Go!'. Evidently the presence or absence of the little word la makes some difference in Loglan.
The distinction between the designative and the vocative use of names is not regularly drawn in the natural languages. And yet there is a very important difference in meaning. People designate someone by using da's name in much the same spirit that they describe someone by using some predicate that fits da. Thus we may designate someone by saying 'He's the fat one over there' or by saying 'He's the one named John over there.' Thus having a name is a kind of property, namely the property shared by all who have that name. We use this property in using names to make designations. We say, in effect, 'the one named John'.
This is exactly what the name-operator la does in Loglan. In sentence (1) La Djan means literally 'The one person I mean whose name is John'. This is a mouthful, and no one would ever translate Loglan into English in this way. But English is not explicit about these matters. Loglan is. It perhaps expresses the sense of the Loglan best to write sentences like (1) as 'The John goes' whenever a literal translation is desired. Again, this is not a routine one would care to impose on unwarned ears. But it does suggest, as 'John goes' does not, the sense in which the Loglan sentence, but not the English, explicitly recognizes that there are many Johns.
Just as names may be used to form designations, so may predicates. Thus the little word le [leh] operates on predicate expressions to make designations out of them in a way that is similar to the way la operates on name-words. We will call the designations made with le descriptions, and le itself, the descriptive operator. For in this context we are using predicates, not to say things about the world, but to locate those things in the world about which we have something to say. Thus with la we locate things by naming them; with le we locate things by imputing other properties to them. For example, in
| (1) | Le fumna pa cluva le mrenu | The woman loved the man. |
the predicate words fumna and mrenu are not predications, for they claim nothing. Instead, they function in this sentence to help the listener locate the two objects in the world about which the speaker does have something to say, namely that one of them loved the other. Thus, descriptions are not true or false of the things they describe, but merely helpful or not helpful. This can best be seen by considering a fanciful example.
Suppose someone who looks like a woman is arrested by two detectives on suspicion of some crime. Later the suspect is more thoroughly examined and found to be a man. Suppose the first detective reports this fact to the second by saying 'That woman was a man.' Is this a contradiction? Certainly not. For by describing the suspect as 'that woman' the first detective has not said that the suspect is in fact a woman. It is not the linguistic business of designation to assert facts, but to use facts, or apparent facts, to help listeners locate individuals. The fact is that the suspect looked like a woman. And that fact is useful in locating him.
For we can now ask a very different kind of question. Was it useful to the listener to have the suspect described to de as 'that woman'? Certainly. For this is exactly what de needed to know in order to locate the person who was in fact a man. Suppose the second detective had been told 'That man was a man.' Would this have been useful to de? We suppose not. We suppose, in fact, that nothing would have been more misleading to that as yet uninformed listener. For it is worse than useless to be told to locate an object by means of a property you think that object does not have!
Notice that the sentences 'That woman was a man' and 'That man was a man' are both true under the circumstances we have assumed. But only one of them has any chance of communicating that truth to the listener; and that is the one that uses a "false" but useful description as the designation of the individual the sentence is about.
But, however these matters may be interpreted in English, the sentence
| (2) | Le fumna pa mrenu | The woman was a man. |
is not a contradiction in Loglan. The reason is that the descriptive operator le does not simply mean 'the', or 'the one that is', but more exactly 'the one thing, or set of things, which I intend to designate with this phrase and which is apparently a...'. Thus there are many women, and many things which look like women, but the speaker of sentence (2) intends to designate just one of them, and a certain one of them, when da says that it was a man. That one intended thing is the reference of the descriptive phrase. And the sentence containing that phrase is true or false depending only on whether its predicate, not its description, is true of that intended thing.8
Now any untensed and unspecified predicate expression of the language can become the basis of a description with le. Thus the predicate expression bilti cmalo ge nirli ckela provides the description
| (3) | Le bilti cmalo ge nirli ckela | The (thing that is) beautifully small for a girl's school. |
and nirli ckela go bilti ce cmalo provides the basis for another slightly different description:
| (4) | Le nirli ckela go bilti ce cmalo | The girls' school that is beautiful and small. |
Similarly, the verbal notion of the predicate kukra sucmi [SOOSH-mee] ('quickly swims') becomes a noun-like notion in the description:
| (5) | Le kukra sucmi | The fast swimmer. |
And the adjectival notion of the predicate mutce [MOOT-sheh] blanu ('is very blue') becomes a noun-like one in the description:
| (6) | Le mutce blanu | The very blue thing. |
In short, one must occasionally make rather radical adjustments to the English in transporting a predicate notion into or out of a Loglan description. But so long as the Loglan predicate expression is (i) untensed and (ii) unspecified, no grammatical adjustment whatever is needed to make a Loglan description out of a Loglan predicate, or vice versa. In later sections we will take up the adjustments that are necessary just in case the descriptive predicate is specified or tensed.
In Chapter 3 we observed that predicate strings with "kekked head predas" were not allowed in predicate expressions but were permitted in descriptions. It is easy to see why. A predicate expression with a kekked head preda is impossible to say because the listener will always take it for a kekked predicate expression. Thus, the speaker of
(7) Da ke gudbi ki sadji mrenu
may intend it to be understood as
(7') *Da [(ke gudbi ki sadji) mrenu]9
but nobody will parse it that way (and so I have starred it). Instead everyone will hear it as
(7") Da [ka gudbi ki (sadji mrenu)]
But no problem arises with kekked head predas in descriptions:
| (8) | Le ke gudbi ki sadji mrenu pa hijri | The both good and wise man was here. |
The reason this sense is unequivocal in descriptions and not in predications is that kekked whole predicate expressions may not be made the basis of descriptions. Thus there is no rule in the machine's grammar that allows kekked predicates to be operands of descriptors. In descriptions, therefore, the scope of a kek is always the next pair of individual words, or the next pair of expressions that may replace individual words. Thus, in the case in hand, the parser will hear (8) unequivocally as
(8') (le [[ke gudbi ki sadji> mrenu]) (pa hijri)
and now
(8") *(le [ke gudbi ki [sadji mrenu>]) (pa hijri)
will be impossible for it to hear.10
Suppose we say in English 'Butter is soft' 'Water is wet' and 'Man is in trouble.' Are the words 'Butter', 'Water' and 'Man' descriptions? In a sense they are, for they use predicates (in the Loglan sense) to help us locate--or think about, for such objects are mighty hard to locate--the peculiar objects they do designate. And what are these objects? Well, if you think about it, anyone who talks like this in English is talking about all the butter there is, all the water there is, and all the human beings there are, for this is the sense of the English noun when it is used without an article. (Contrast 'The man is in trouble.') But is this a legitimate way of talking? Perhaps; but it is certainly a different way than talking about pieces of butter, glasses of water, or individual human beings.
In Loglan we recognize this important difference explicitly by providing a different operator lo [loh] to form these mass descriptions, as we will now call them. (To English-listening ears [loh] has a very abrupt, even truncated sound. It is not, for example, the sound of English 'low' [loh-oo].) Let us consider some examples.
The Loglan predicate batra means 'is a piece, portion or lump of butter'. The predicate cutri means 'is a drop, portion, body or expanse of water'. The predicate humni means 'is a human being'. Thus le batra, le cutri and le humni designate the particular lump of butter, the particular drop (let us say) of water, and the particular particle of humanity which the speaker has in mind. But lo batra, lo cutri and lo humni designate just what the English words 'butter', 'water' and 'man' designate when used without articles, namely those three massive, widely distributed but discontinuous individuals composed respectively of all the butter, all the water, and all the human beings there are. Looking back, we will now call descriptions made with le particular descriptions, to contrast them with the mass descriptions with which we are now concerned.
English permits us to talk of these massive individuals in a wide variety of ways. In the case of what some grammarians call the "uncountable" nouns--substance words like 'butter', 'sand', 'wood', 'meat', 'iron', etc.--the procedure is very simple. One simply uses the unadorned noun, as in 'Iron is hard.' What is awkward in the case of these nouns is talking about individual pieces. For one must say in English 'The piece (lump, fragment, chunk) of iron', not simply le fernu ('the iron-thing') as one can in Loglan. For other nouns--the "countable" English nouns like 'book', 'chair', 'spoon', etc.--we sometimes use the plural to express this massively constructed individual ('Books are important to man'), and sometimes the singular with the definite article ('The lion is found all over Africa'). It is usually obvious from the context that the speaker does not mean to talk about all or any books or lions as individual particles. Thus it is not the case that every book is important to humankind, and it is certainly not true that any particular lion is found all over Africa. It is the mass individual Felis leo who has spread his tawny presence over Africa. But the trouble with these English designations is that they are not very distinctive. Thus with the same grammatical constructions one can also designate quite particular things or sets of things ('The lion roared', 'Books were on the table'). The English listener must, as usual, guess from context what kind of creature the speaker has in mind...although we are so used to doing this in English that it does not seem to us to be a very difficult thing to do.
In Loglan a distinct grammatical form exists for each of these distinct mechanisms of designation. There can be no doubt that the Loglan speaker who says lo simba is designating lion-kind, and that lo bukcu means that massive individual composed of all the books there are or have been or ever will be. For there is no restriction in Loglan on the kind of predicate to which the lo operator may be applied. Even the most countable things can be massified, and the most uncountable things particularized; for Loglan does not divide the world up in this way.
Before we leave mass descriptions it is worth pointing out that the languages of some preliterate peoples apparently employ the idea of mass description as the elementary meaning of their basic predicate words. Thus the Trobriand Islanders are reported to place this interpretation on all their nouns; whence the curious world-view arises that what we Indo-Europeans would call a single instance of a thing is, to them, nothing but a part, or reappearance, or manifestation of the same, massive individual thing. Thus every rabbit is just another appearance of Mr. Rabbit; every yam just another manifestation of Mr. Yam; every baby just a part of Mr. Baby all over again. I don't know if many Trobrianders will learn Loglan, but if they do they will find an apparatus readily available in it with which to describe the world exactly as they see it. And the lo-operator will be as common in their speech as le will be in yours and mine.11
In the last three sections we have discussed three very similar ways of forming designations in Loglan: (i) naming with la, (ii) describing particular things with le, and (iii) describing masses of things with lo. There is a fourth kind of designation, namely description by quotation; and for this we will need the marks li...lu [lee...loo], liu [lee-oo] and lie [lee-EH], the second syllable in the last word being nearly always stressed.
Not only are all punctuation marks spoken words in Loglan, as we have observed before, but the affinities of quotation marks with the other descriptive operators of Loglan is phonemically clear. Thus the very sound of the word li suggests that it is related to the descriptors la, le and lo, all in some sense meaning 'the'. And so it is. For just as le means 'the one I mean that is...', and la means 'the one I mean named...', so li means 'the thing I mean that looks or sounds like...'. Thus quotation is really description by imitation.
| (1) | Li, Kristobal Kolo'n, lu logla namci la Kristobal Kolo'n | 'Kristobal Kolo'n' is the Loglan name of Christopher Columbus. |
In (1) the speaker has imitated a portion of Loglan speech or writing--perhaps copied it from a book--and put the imitation between the marks li, and , lu in order to quote it. Note that pauses--represented as usual by commas in text--are also required around the quoted string. This style of quotation is called weak quotation. With it any string of well-formed Loglan may be unambiguously quoted.
But sometimes we wish to quote ill-formed strings...including some that might have an extra lu in it, which would baffle the machine. Even foreign utterances, in which there's no predicting how many stray lu's there might be, also need to be quoted. For these two occasions Loglan has a more robust style of quotation called strong quotation. This is done with lie X, ..., X, in which the repeated boundary marker X is any arbitrary Loglan word, usually a letter word, that does not occur within the quoted string. For example,
| (2) | Lie gei, Christopher Columbus, gei gleca namci la Kristobal Kolo'n | 'Christopher Columbus' is the English name of Christopher Columbus. |
Here gei (g) has been chosen as the repeated letter-word because the quoted string is an expression of English (gleca [GLEH-shah]) and because the sounds [gay] of gei do not occur in it. If we had quoted the Spanish (spana) name of Christopher Columbus, or the German (dotca) one, we could have used sei or dei because neither [say] nor [day] occur in it as well. For example,
| (3) | Lie sei, Cristobal Colo'n, sei spana namci la Kristobal Kolo'n | 'Cristobal Colon' is the Spanish name of Christopher Columbus. |
The second and fourth pauses are optional; the ones before and after sei are required to make strong quotation work.12
Note that the argument la Kristobal Kolo'n designates a once-living person, while the arguments Li, Kristobal Kolo'n, lu; Lie gei, Christopher Columbus, gei; and Lie sei, Cristobal Colo'n, sei all designate portions of human speech, namely a Loglan, an English, and a Spanish name. Kristobal Kolo'n, 'Cristobal Colo'n' and 'Christopher Columbus' are different names; but they name the same person, namely Cristobal Colo'n.
Weak quotation with li and lu is used much as ordinary quotation marks are used in written English. The chief difference is that in Loglan they are spoken words. In fact li and lu are used exactly as the words 'quote' and 'end quote' are used in certain styles of spoken English, especially the style that is invoked when the speaker wishes to be very certain that someone else's words are not mistaken for his own.13 In Loglan the motivation of the speaker's use of li and lu is logical, and hence less circumstantial. For there is a difference between the name of a thing and that thing. This difference is fundamental in a logical language. So quotation marks are never omitted in Loglan even when their presence might be thought to be assumed. Thus, of the two sentences,
| (4) | Liu Djan, corta purda | 'John' is a short word. |
| (5) | La Djan, corta purda | John is a short word. |
only one is true if, as we assume, John is not a word of any length but a man. Here liu (a blend of li and lu) is the single word quotation operator and may always be translated 'The word '...''. Liu may only be used with confidence on Loglan words.14
In spoken English all these clarifying marks are commonly left out. The usual form of the sentence which means (4) is spoken exactly as it would be spoken if the speaker had meant (5). We rely on the "good sense" of the listener not to infer that the speaker actually meant (5). Again, the interpretation of English depends on context. Loglan does not. In Loglan we wish to be able to speak nonsense when we want to.15 Thus (4) and (5) in Loglan are invariably distinct forms.
In some forms of written Loglan the words li and lu may be replaced by their signs '«' and '»'.16 So written, (1) becomes:
(6) «Kristobal Kolon» logla namci la Kristobal Kolon
But, as always, such signs are pronounced as words in speech.
Summarizing, there are three kinds of quotation words in Loglan: (i) ordinary or weak quotation with li...lu; (ii) single word quotation with liu; and (iii) strong quotation with lie X...X. In the latter X is any exactly repeated boundary marker that does not occur in the quoted string. When convenient X may be the letter word for the initial letter of the Loglan predicate for the language of the quoted string. Strong quotation can handle any kind of quoted string including nonsense and non-Loglan.
We are now ready to deal with the abstract entities we left hanging in Chapter 3. You may recall that the abstract operators po, pu and zo which we discussed in that chapter permitted us to form predicate expressions like pu gudbi which meant '...is a property of being good', but that "goodness-in-general", or what we there called "virtue", was still beyond us at that time. But we are now ready for 'virtue'. Surprisingly, it is a mass term. For it is used exactly like the word 'butter' is used in English and evidently designates the mass individual manifested in all the particular instances of virtue that there are. Consequently, the Loglan designation that translates this word is made with the compound operator lopu, which is lo + pu and usually pronounced [loh-poo]; and 'virtue' in Loglan is lopu gudbi /lopuGUDbi/, or the mass composed of all the properties of anyone's or anything's being good that there are. Similarly, we would expect lopo gudbi to be used when the mass individual was to be composed of all the acts, states or events of goodness that there are, and to be best translated into English by 'goodness'. Finally, we would expect lozo gudbi to be used when the mass individual was to be composed of all the measurable quantities of goodness that there are, the latter being translatable by no English word or simple phrase because no such concept is readily available to speakers of English. To translate lozo preda we have to use a circumlocution...as I just have.
Note that some of the constructions we are now encountering are more complex in Loglan than they are in English. And rightly so. For the ideas that underlie them are in fact complex. Because they seem very simple in English, words like 'virtue', 'courage', 'weight', and 'length' are logically very troublesome to our English-thinking minds. Where are these individuals? What does it mean to "love" virtue, or to "have" weight? In Loglan it is plain that these individuals are complex creations of the human mind.17 To love lopu gudbi is to love a massive, discontinuous, widely distributed individual composed of all the instances of just that property by which all the phenomena that ever exhibit it may be said to be good. That is possible...in Loglan as well as in English. But in Loglan it is obvious that it is a very different enterprise than loving John.
On the other hand, some uses of abstract words in English obscure some very simple ideas. For example, to "have weight" is simply to weigh something, and no abstract entity is involved in doing that. Thus the abstract creature we call 'weight' is lopu tidjo in Loglan; for in more explicit English, weight is all the heaviness there is. But to say that X "has weight" is simply to say
| (1) | Da tidjo | X is heavier than (something). |
which doesn't involve abstraction at all. Thus the Loglan speaker is usually not inclined to speak in this unnecessarily abstract English way. Even so, da could translate such English expressions literally if da wished to. Here is one way to do it:
| (2) | Da katli lopu tidjo | X has (is characterized by) Mr. Heaviness. |
Talking abstractly about things that can be talked about concretely is not a very satisfactory procedure in any language. On the other hand people do have genuine attitudes toward abstract things, if only because the structure of their language tempts them to see the world in an abstract way. Thus to say
| (3) | La Djan, cluva lopo sucmi | John loves swimming. |
is a perfectly sensible thing to do in English, though a curious one in Loglan. But presumably in both languages what John loves is just this abstract, massively distributed thing composed of all the events of swimming that there are. (Notice that we are now using the event-operator po.) But if what John really loves is his swimming, then in Loglan we would say so:
| (4) | Da cluva lopo da sucmi | He loves the mass of all events composed of his swimming. |
In pidgin-style English, 'X love mass-event X swim.' Similarly, to love the color blue, as in
| (5) | Da cluva lopu blanu | X loves blue. |
is easier to do in English than in Loglan. For the word 'blue' functions in such English sentences as if it were a proper name (e.g., 'X loves Mary'). But it is possible to love blue even in Loglan. It may be a little more troublesome to do so, for it is necessary to perform two distinct grammatical operations on the naked predicate blanu with which the Loglan mind begins. Even so, such designations can be formed.
We may expect, therefore, that our customary European attitudes toward abstract entities will survive in Loglan, but with a finer set of discriminations than we are used to in English. For if you're going to love virtue in Loglan you must first decide whether it is the mass of all goodnesses that you love, or all states of being good, or all quantities of goodness, or, a little more concretely, the mass of all good things. Thus
| (6) | Mi cluva lopu gudbi | I love the property that good things have. |
| (7) | Mi cluva lopo gudbi | I love good states-of-affairs. |
| (8) | Mi cluva lozo gudbi | I love all the quantities of goodness in good things. |
| (9) | Mi cluva lo gudbi | I love good things. |
are your choices. For each might be said to be a legitimate translation of 'I love virtue' into Loglan. Again we see that Loglan embraces English but exceeds it, and in ways that will probably lead to greater awareness of the nature of abstraction than is usual among speakers of English. For if a thing is an abstract entity and not a concrete one, it will be obvious in Loglan that it is, and in just what ways. We suppose there will be some advantage in this arrangement for the thinker.18
We can now go back to deal with a matter that we left unsettled at the end of Section 4.8. In that section we dealt with particular descriptions formed with le, and we concluded by saying that any untensed and unspecified predicate expression of the language could be made the basis of a description with le without adjusting it in any way. Mass descriptions with lo, we later implied, could be constructed from predicates selected from the same broad domain. But now suppose we do want to form a description with a specified predicate, that is, with a predicate that has one or more of its arguments shown. Suppose, for example, we want to use the specified predicate farfu la Rabrt, as it might occur in the sentence Da farfu la Rabrt ('X is the father of Robert') as the basis of a description. That is, we wish to designate someone who is--or is locatable as--the father of Robert. What adjustment must we make, and why?
First let us see what happens if we try to describe the father of Robert in the usual way. Suppose we simply precede the predicate expression farfu la Rabrt with le as follows:
| (1) | Le farfu la Rabrt | ??? |
But what have we designated? Not one thing, but two. For if we now try to use the string we formed in (1) as an argument of some multi-place predicate, for example with the predicate godzi ('...goes to...from...') as below,
(2) Da pa godzi le farfu la Rabrt
we then see that the single designation we thought we had formed breaks up immediately into two: le farfu and la Rabrt. In (2) we hoped to say the X went to the father of Robert; instead what we actually said was that X went to the father from Robert. For Robert has changed allegiance. No longer is he the father's son; he is now the point of departure from which X went.
To avoid this kind of confusion, Loglan uses two little linking words to attach the arguments of specified descriptions to the main descriptive term. Je [zheh] is the first of these and links second arguments to descriptions. Thus what we failed to say in (2) we may now say by using je:
| (3) | Da pa godzi le farfu je la Rabrt | X went to the-father-of-Robert. |
It is as if we had hyphenated the whole phrase. For le farfu je la Rabrt now functions everywhere as a single term. To attach two specifying arguments to a description, we use je and the second linking operator jue [zhweh] as follows:
| (4) | Da pa godzi le farfu je la Rabrt, jue la Meris | X went to the-father-of-Robert-by-Mary. |
and je and jue now hold the entire description le farfu je la Rabrt jue la Meris together. And to attach three or more arguments to a description, we use je first, and then as many instances of jue as we require:
| (5) | Da pa godzi le vedma je le horma jue la Djan, jue lo nema dalri | X went to the-seller-of-the-horse-to-John- for-the-hundred-dollars. |
I have hyphenated the whole English phrase starting with 'the-seller-' and ending with '-dollars' to show that the Loglan construction is similarly linked by its je's and jue's into a single term. Jue is the general link for all arguments in third or higher places of a descriptive predicate. (The word nema, by the way, is a number word meaning 'one hundred'.)
Now a world of English ambiguities is avoided by this device. For though the number of English prepositions is very large, they do not work as effectively in keeping descriptive meanings straight as the pair of Loglan linking words je and jue.
For example, suppose I say in English 'I talked to the teacher of many things.' What do I mean? That we talked about many things? Or that the teacher taught many subjects? In English, one cannot be sure. In Loglan, one cannot be in doubt. The little word ro means 'many'; and the predicate bekti is the general word for 'thing'. The predicate takna means '...talks to...about...'. Therefore, the two possible interpretations of the English sentence can be said unequivocally in Loglan in these two ways:
| (6) | Mi pa takna le ditca ro bekti | I talked to the teacher about many things. |
| (7) | Mi pa takna le ditca je ro bekti | I talked to the teacher-of-many-things. |
(Both pauses are phrasing pauses.) The difference, of course, is the presence in (7), and the absence in (6), of the linking operator je. Accordingly, the phrase le ditca ro bekti in (6) represents two arguments, the second and third arguments respectively of the predicate takna ('...talks to...about...'). While in (7) the linked phrase le ditca je ro bekti ('the teacher of many things') functions as a single argument, namely as the second argument of that same predicate. What could be clearer? A little experimentation with the linking operators will show that they settle nearly all prepositional ambiguities of this kind. For example:
| (8) | Le furvea je le kamla je la Romas | The buyer of the thing that comes from Rome. |
| (9) | Le furvea je le kamla jue la Romas | The buyer of the thing that comes...from Rome (as the seller). |
Here English 'from' does not succeed in distinguishing the two ways in which Rome is linked in these descriptions, despite the pause that we hopefully introduce in (9). In Loglan, however, the difference between je and jue clearly shows that la Romas is the second argument of kamla in (8), that is, a place of origin, and the third argument of furvea in (9), that is, the seller of whatever came. This is tricky...but in English, not in Loglan.
Incidentally, mass descriptions may also be specified. But to do so may severely limit the extent of their "massiveness". Thus, when unspecified, the description lo farfu designates a massive object with many parts (as in 'Fathers of the world unite'). But should we now specify the predicate farfu, as in lo farfu je la Rabrt, we would find that the corporate entity we have now designated (as in 'Fathers of Robert unite') is exactly the same entity as the single person we might have designated with le farfu je la Rabrt. But again it is a matter of biology, not grammar, that people have only one father. So the distinction between le farfu je la Rabrt and lo farfu je la Rabrt exists to tease the fancy, if not the factual mind.
There is one variety of specified description that deserves and gets special treatment in Loglan. This is the specified abstract description formed with a compound operator made by joining any descriptive operator to po, pu or zo. The most widely used form of this construction is called event description and is made with the compound operator lepo (typically pronounced [leh-poh] with level stress), a word that may always be translated 'the event, state or condition of...'. Thus the unspecified description lepo sucmi means 'the particular event of swimming which I have in mind', or simply 'the swim'. Similarly, lepo prano means 'the run', and lepo mrenu means 'the manhood (of some particular person)'. Obviously we shall sometimes want to specify such predicates as richly as we can. For we shall often want to anticipate such questions as: Whose manhood? Who ran? And where did he run?
Now the special treatment consists in this. Where the specification of concrete descriptions is limited to the second and higher order arguments of a predicate (le farfu je la Djan), the specification of abstract predicates may include the mention of first arguments as well. Thus we say
| (1) | Lepo da sucmi | The event of X's swimming, that is, X's swim. |
| (2) | Lepo da mrenu | The state of X's being a man, that is, X's manhood. |
as well as the more abundantly specified forms
| (3) | Lepo da prano de di | The event of X's running to Y from Z. |
| (4) | Lepo la Djan, pa traci la Espanias, la Frans | John's trip (i.e., the event of his travelling) to Spain from France. |
We now observe that the constructions which form the basis of these descriptions are not simply predicate expressions, but whole sentences: Da sucmi; Da mrenu; Da prano de di; and La Djan, pa traci la Espanias, la Frans. Obviously this is a very flexible form. Notice something else. The specified arguments in (3) and (4) evidently do not require the linking operators je and jue which we learned to use in specifying descriptions in the previous section. Why is this?
The reason is that event descriptions are formed, not with predicate expressions, but with what we may usefully think of as whole sentences. The sentence may be incomplete, even totally without arguments, as in lepo sucmi, or it may be complete with all possible arguments mentioned, as in lepo da sucmi de di do ('the event of X's swimming to Y from Z by route W'); but any sentence whatever may be used to form an event description with the phrase lepo. Special punctuation rules we will study later guard this construction against ambiguity.19
We sense immediately how convenient this new form is. For we now have a form in which any conceivable event, state or condition, whether actual or imaginary, may be easily designated simply by preceding any sentence which asserts it with the phrase lepo. One consequence of this way of designating events is that imaginary states of affairs may be designated without asserting their existence. Thus with event descriptions we can talk about the events which people fear, hope or expect, or the states of affairs in which they believe, whether these events or states are ever realized or not. As usual we can do so in a more straightforward way than is possible in English.
In English we say 'John believes that it will rain.' But what is it in which John believes? English grammarians call this kind of thing "indirect discourse", suggesting that there is a sentence somewhere which the speaker does not bother to quote directly but in the truth of which da is saying John believes. But this is not a very satisfactory account of the meaning of this clause. Suppose there is no sentence. Suppose John goes to the window, looks at the sky, gets his raincoat, and goes out. Observing this, we may say with some confidence 'John believes that it will rain.' But the object we are designating with the phrase 'that it will rain' is certainly not discourse of any kind.
In Loglan, we say
| (5) | La Djan, krido lepo fa crina [SHREE-nah] | John believes that the event of raining will happen. |
For we suppose that what is related to believers by predicates of this kind are events or states-of-affairs, and not sentences at all. Thus we may also say:
| (6) | Da pa spopa lepo de fa kamla | X hoped that Y would come (that is, that the event of Y's coming will happen). |
| (7) | Mi djano lepo la Ter, bamfoa [bahm-FOH-ah] | I know that the Earth is round (ball-form), that is, that the state of the Earth's being round obtains. |
All Loglan predicates which express the ideas of English 'know', 'believe', 'hope', 'fear', 'expect', 'want', 'wish', and the like, may take event-descriptions as arguments in Loglan.20
But suppose we want to say that someone believes in the truth of an actual sentence. Can we do so? Of course; but by the same kind of precise construction that is required to make this unusual claim in English:
| (8) | Mi djano lepo li, La Ter, bamfoa, lu tradu | I know that 'The Earth is round' is true. |
In Chapter 5, on utterance forms, we will see how event-descriptions figure importantly in the construction of subordinate clauses. But for the moment we will deal with them as if they were simply another kind of Loglan argument form.
We now consider what happens to a description when it occupies the first place of an unadorned predicate. For example, suppose we wish to say that some particular wise person is a man in the same time-free sense that we already know how to say that X is a man, namely
| (1) | Da mrenu | X is a man. |
If now we wish to substitute the description Le sadji ('the wise one') for Da in (1), we get:
| (2) | Le sadji mrenu | ??? |
Does this mean what we intend? Or does it mean 'the wise man', which is not a sentence at all (it claims nothing) but a more elaborate description? Obviously the expression Le sadji mrenu will be interpreted as a description no matter what we intend. It is clear that we have uncovered a major source of ambiguity were no special provision made to prevent such--evidently futile--intentions from arising. That special rule is that whenever a predicate word is the last word to appear before an unadorned predicate expression, then we use the marker word ga in the position of the tense operator to mark the point at which the description ends and the predicate expression begins:
| (3) | Le sadji ga mrenu | The wise one is a man. |
This is an awkward rule;21 but it preserves the economy of such expressions as Da mrenu and La Djan mrenu which require no marker word. It is the price we willingly pay for the logical advantage that all predicate words in Loglan belong to a single part of speech.22
We can now consider several other varieties of description. In Section 4.8, where we first talked about description, we said that only untensed predicate expressions could become the basis of descriptions. This seems arbitrary. Suppose we do want to add a time particular to some description, as in 'the present king of England'. Can we do this in Loglan? Of course; but it turns out to be more parsimonious, grammatically, to generate a set of tensed descriptors--such as lena [leh-nah] ('the present'), lepa [leh-pah] ('the-former') and lefa [leh-fah] ('the-future')--to do this work, rather than permitting tense operators to occur within descriptively used predicates. But with these modified descriptors one may make tensed descriptions in Loglan after all:
| (1) | Lena bragai [BRAH-gigh] je la Inglynd [EENG-gluhnd] | The present king (born-ruler) of England. |
| (2) | Lepa ditca | The former teacher. |
| (3) | Lefa matma | The future mother. |
and even tensed mass descriptions as in
| (4) | Lofa humni | Future humanity. |
| (5) | Lona simba | Present lionkind. |
Notice that when a stressed syllable precedes a predicate word it must be separated from the predicate by a pause. As noted in Chapter 2, this is a general rule. No stressed syllable may pauselessly precede a predicate.
Perhaps more important for translating English than the tensed descriptors, however, are the spatially particularized descriptors formed with vi and va. As we saw in the chapter on predicates, these two little words mean 'here' and 'there', and are used in many ways as tense operators are used in Loglan. Like tense operators, they may be combined with either le or lo to form just those demonstrative descriptions which we would translate into English with 'this' and 'that', as in the sentences below:
| (6) | Levi bukcu ga redro | This book (i.e., the-here book) is red. |
| (7) | Leva fumna ga mrenu | The-there woman is a man. (That woman is a man.) |
and even:
| (8) | Lovi cutri ga kofhatro [kohf-HAHT-roh] | The (mass of) here water is warm (comfortably-hot). (The water here is warm.) |
The distinction between lovi cutri and levi cutri ('the mass of all the water here' and 'this particular puddle of water here') will not seem immediately useful to the English mind. For the noun 'water' seems incorrigibly masslike in English and the adjective 'this' in the phrase 'this water' does little to particularize it. But the Loglan mind starts with integral bits and pieces of water and will therefore be tempted to use lo cutri and lovi cutri only when some synthesis of these elementary bits and pieces is intended. In short, to use this apparatus intelligently we shall have to think about the distinction between le and lo in a Loglan way.23 The distinction between these operators arises, of course, from the fact that every Loglan predicate is a general term. Thus while the Loglan mind starts with pieces of water and bits of better-than, it can be carried by abstraction and mass description to whatever lofty abstractions of "waterness" and virtue we Indo-European thinkers might require. And by the operations of specifying predicates, or tensing them or locating them, we can stop anywhere we like along the way. Thus with lovi cutri we pause to glance at the local mass of water on our way.
The mechanism of "possession" in language ('my hat', 'your mother', 'John's book', etc.) is a widely misunderstood phenomenon. It is unfortunate that the grammarians who first studied it called it "possession", for usually the relationship it specifies has nothing to do with possessing things at all. Thus, in English I can talk of my son's clothes (which he doesn't really own any more than I own him), of your mother (whom you certainly don't own), of my skin (which is simply attached to me) or even of his corner of the room (which is where he is). Thus a huge variety of predicate relations is evidently hidden in these slippery little "possessive" words.
Even so, if we are to translate from the natural languages, we need the "possessive" descriptors, for they provide a useful kind of brevity. But let us be clear about what they are abbreviations of. If you think about it, you will see that when you say 'my hat' you are designating it; and you are doing so by implying that it is a hat that is related in some way to you. You may have several, but this is the one you mean. Moreover, your designation is a description. It utilizes the predicate 'is a hat' in a perfectly regular way. It also uses another fact about that hat in a second but implicit description, namely that it is related somehow to you. Probably the essence of your relation to your hat is that you are the only one who uses it. But whatever that relation is, it is not explicitly predicated in your designation 'my hat'. Thus you have used two properties of your hat to describe it: one explicitly (that it's a hat), the other implicitly (that it is related somehow--you haven't said how--to you).
In English none of this is clear. It can be found out by analysis, of course, for we have found it out in English. But the semantic structure of the English possessive pronouns cannot be seen either in their word forms or in their grammatical inflections in that language. Here is a sentence with a Loglan possessive form:
| (1) | Lemi bukcu ga blanu | My book is blue. |
The first thing we make clear is that the expression lemi bukcu is a description ('the-me book'). For it involves the descriptive operator le in a most obvious way. Secondly, by using bukcu in lemi bukcu just as we use it in le bukcu, we also make clear that the predicate bukcu is the basis of this description, too. Whatever additional properties it may have, the thing we intend you to look for is at least a book. Thirdly, the auxiliary role of the word mi in the descriptive operator lemi suggests to the listener--on the model of levi and lena--that an abbreviation of something else is afoot. It is. That something else is that I am related somehow to the designated thing. Thus, look for it in my hand, on my desk, or where I left it. And that is all. You must not expect me to furnish the deed.24
With lemi as a model, we can now interpret some of the other possessive constructions of the language:
| (2) | Donsu mi lotu bukcu | Give me your books (all of them). |
| (3) | Da pa donsu de leda mroza | X gave Y his hammer (X gave Y the-X hammer). |
| (4) | Le la Djan, horma ga kukra lemu horma | John's horse is faster than our horse. (The-John horse is faster than the-we horse.) |
| (5) | Lemi da gudbi letu de | Mine (the-me X) is better than yours (the-you Y). |
In sentence (5) a curious thing happens. A possessive description has been formed, not with a predicate, but with a variable in the usual place of the predicate (da in lemi da). What this means is that the explicit portion of the possessive description has been omitted, and we are left with its implicit portion only: namely that I am referring to some X that is related in some way to me. This is, of course, exactly what we mean by 'mine'.
Now you have probably sensed that the utility of the possessive form lies not only in its economy but in its vagueness. For it is not only simpler to say 'my hat' than 'the hat which I regularly use' in both English and Loglan (lemi kapma as opposed to le kapma ce nu plizo je mi = 'the thing which is a hat and used by me'), but just as in English, the very vagueness of the unspecified relation is sometimes useful. Suppose I don't know how Johnny is related to the car I see him driving (it is probably owned by his father). When I call it le la Djanis, tcaro ('the-Johnny car') I avoid committing myself on this delicate matter. But suppose there is no doubt about the relationship which I want to impute. Suppose I am talking about his mother. Do I say le la Djanis, matma in Loglan?
I may do so if I wish; but it is an unnecessary circumlocution for what can easily be said directly, in Loglan. For le matma je la Djanis ('the mother of Johnny') provides what will almost always be a better designation in Loglan of Johnny's mother, that is, a more useful one, than le la Djanis, matma is. For le matma je la Djanis is a specified description which relates Johnny as an offspring to his mother: a much more exact relation than "possession". Similarly, the predicates for body-parts are all two-place predicates in Loglan. It is therefore unnecessarily vague to say lemi barma ('the-me arm') when you can say le barma je mi much more explicitly. One is not related to one's arm vaguely, at least not in Loglan.
Mass descriptions may also be possessive in Loglan. Thus lo resfu means 'clothing in general' (resfu = 'is a garment, an article of clothing'), whereas lomi resfu means 'my clothing'. This is another momentary specialization of a mass term--or partial massification of a general term, as we might now prefer to say--which is similar in mood and structure to the located mass term lovi cutri. Thus semantic parallels often exist between one grammatical construction and another in Loglan, and these are usually reflected in their having similar structures in a Loglan-viewed reality.
The possessive form le la Kristobal Kolo'n, botsu ('Christopher Columbus's boat') is as clumsy an expression in Loglan as it is in English. A simple operation exists to reverse these terms...in both languages:
| (1) | Le botsu pe la Kristobal Kolo'n | The boat of Christopher Columbus. |
Notice the structural parallel between this designation and the following one:
| (2) | Le matma je la Kristobal Kolo'n | The mother of Christopher Columbus. |
Now je warns us that Christopher is related in a very definite way to his mother; that is, she bore him. But pe [peh] is a kind of vague, all-purpose linking marker saying only that he's related in some way to his boat: that he owns it, sails around on it, goes to sea in it, is its captain or its cabin-boy.
But now suppose that we wish to talk of that man's boat. 'That man' is easy enough; it is leva mrenu. But if we put leva mrenu in the position of la Djan in le la Djan botsu, we encounter a difficulty. For *le leva mrenu botsu seems to say 'the that man type of boat', which says nothing at all in Loglan. Obviously we need to terminate the internal description leva mrenu with some kind of marker. We may do so with the comma-word gu [goo], and gu may or may not be accompanied by a pause.
| (3) | Le leva mrenu gu, botsu | That man's boat (the that-man boat). |
But we may feel that this, too, is clumsy, especially if we want to say more about the man. So we might prefer the inverse possessive forms with pe:
| (4) | Le botsu pe leva mrenu | The boat of that man. |
| (5) | Le botsu, pe le bilti ce cmalo ge nirli ckela | The boat of the pretty little girls' school. |
Thus pe is used most effectively when the speaker wishes to designate the "possessor" with a longer and more elaborate construction than da plans for the "possessed."
A maneuver that looks like description but is not is to use the name operator la to turn a predicate or predicate expression into a name. The predicates used for this purpose are always predicates that may be used as calls, that is, to call the attention of someone, just as we may use the predicate 'father' to call 'Father!' in English. We will learn how to make attention-calling expressions of this kind (vocatives) in the next chapter. But in this one we are concerned with how predicate names may be used to talk about the people whose attention may be called with them.
In English we express our intention to make a name out of a predicate by dropping the article and capitalizing its initial letter when we use it in writing. 'Father', we say or write, 'got back last night.' In Loglan we accomplish this same purpose by using the name operator la in both speech and text and capitalizing the predicate word or words in text:
| (1) | La Farfu, pa favgoi [FAHV-goy] na lepazi natli | Father returned (reverse-went) last night. |
(Pazi means 'just preceding', so lepazi natli means 'the-just-past night'. There will be more on this kind of maneuver in Chapter 5.) How different this is from the same sentence with the ordinary descriptor le:
| (2) | Le farfu pa favgoi na lepazi natli | The father returned last night. |
Sentence (1) suggests that the speaker is one of the father's offspring, or at least a member of his household...one of the few people, at any rate, who are entitled to call him by that name. Sentence (2), in contrast, suggests that the speaker is a detached observer, perhaps a detective staked-out in front of the Jones house, say, who is reporting that the father of the family has returned.
In general, to use a predicate as a name rather than as a description connotes familiarity, even intimacy: the intimacy reserved for those who have the right to use such words as names. 'Father', 'Mother', 'Man', 'Woman', 'Husband', 'Darling', 'Sister', 'Brother', 'Son', 'Fatty', 'Boy', 'Big Guy', and so on, are among the numerous English predicates that turn up as names in that language.
The intimacy effect of using predicate names is often exploited by tellers of children's stories.
(3) Rat told Dog he was going fishing with Cat.
'(To) tell' is to '(to) knowledge-give' in Loglan; so this word is djadou [jah-DOH-oo] from djano donsu. '(To) go fishing with' is '(to) fish-hunt-accompany'; so this one is ficyjankii [feesh-uh-zhan-KEE-ee] from ficli janto kinci. The predicates for 'rat', 'dog' and 'cat' are ratcu, kangu and katma, respectively. So this line could go into a Loglan children's story as:
(3') La Ratcu, pa djadou la Kangu lepo de fa ficyjankii la Katma
With these examples I have let us get slightly ahead of our grammar. We do not really know how to make three-term complexes like ficyjankii ('fish-hunt-with') or modifying phrases like na lepazi natli ('in the-just-past night'), or how and when to use them. These topics will be treated in the next chapter, which is on the structure of utterances. But in the next section we will consider how we can make shorter names for use in such stories once we do know how to write them.
We are still concerned, in short, with the ingredients of utterances rather than their structure.
A name in Loglan is any consonant-final word. Therefore a very natural way of making names is to drop the final vowel or vowels from a predicate word, getting Mren from mrenu, for example, or to add a final consonant to a little word, getting Tun from tu. We may call the names made in these ways internal names because they come from inside the language. Most Loglan names, of course, are borrowed.
For example, The Institute has a dog named Cimr [SHEE-mrr] and it once had a cat named Gro'katm [GROH-kah-tmm]. The name Cimr was made from the predicate cimra [SHEEM-rah], which means 'summer' and fits the sunny temperament of its referent. The predicate grokatma [groh-KAHT-mah], which means 'big-cat', was the source of Gro'katm...with its abnormal and therefore marked stress, notice. Grokatma, from groda katma, was a complex derived on the spot for that monstrous cat.
Tun itself is an excellent example of an internal name made from a little word. It is the name of You, or of whatever person the speaker can get the attention of by shouting it. Spoken like 'You, there!' into a crowd of inert bystanders, Tun is the temporary name of whoever will respond. We'll see in Section 4.27 how numerical names, like Ten and Fon ('Three' and 'Four') may also be made by the consonant-adding route. Conventionally, the consonant that is always added to make little word names is n.
All the predicate names in the last section could have been made as calls first by the vowel-dropping route. Thus, la Farfu could have been la Farf or la Far, 'Mom' could be Mat or Matm ([MAH-tmm] to rhyme with Gro'katm), and the name of the personage called Rat in the children's story could have been rendered with either Loglan Rat [raht] or Ratc [rahtch] as the writer preferred. Similarly, the character of Dog could have been Loglan Kan or Kang [kahngg], with the hard [g] after [ng] definitely pronounced, and Cat could have been Loglan Kat [kaht] or Katm, again as the writer preferred.
Indeed, using a predicate as a name is a rather formal thing to do, just as 'Father' is formal in English. But dropping a vowel, or a vowel and a consonant, from the same predicates is an informal, even familiar move. It yields Mat and Far, which, like 'Mom' and 'Dad', amount to nicknames. So with Loglan words like Rat, Kan, Kat, Fum, Mat and Far we enter the affectionate world of nicknames.There are three other little words that have grammatical distributions which are identical to that of le and lo, and these are the set descriptors loe leu lea [loh-eh, leigh-oo, leigh-ah]. Each has a special variety of 'the' to convey that lends precision to description in Loglan. Each involves sets in some way. In the following discussion we will use the Loglan word preda to stand for any Loglan predicate expression and the English nonce word 'preda' for its translation into English as a common noun.
Loe preda designates the characteristic or typical individual preda which best exemplifies the set of predas in the given context. At bottom this is a statistical construct. For instance,
| (1) | Loe femdi cimpanizi [sheem-pah-NEE-zee] ga forli loe mendi ce humni atlete | The (typical) female chimpanzee is stronger than the typical) male human athlete. |
would require the mounting of a fairly extensive experimental enterprise in order to confirm or refute it. Indeed, (1) might be the conclusion of such an investigation, or a result remembered from reading about one.
In English we would usually say 'The chimpanzee female is stronger than the human male athlete' and leave the listener to figure out what sensible thing we might have meant. In Loglan we must do better than that. We make such statements more precise by using loe, a special kind of 'the' in which the notion of typicality is built in.
Leu preda designates the set of predas--not the individual predas, note, but the particular set--which the speaker has in mind. It means 'the set of some (predas)'.
| (2) | Leu monca gorla ga cmalo [SHMAH-loh] | The (set of) mountain gorillas (I have in mind) are few (literally, is small). |
Like le-designations, leu-designations are intentional. That is, they designate whatever set the speaker intends to designate with da's description. But unlike le-designata--the things that le-phrases designate--leu-designata are sets, not individuals. Thus, we may compare their properties with those of other sets, for example, in size, diversity, longevity, and so on. Certainly the speaker of (2) does not mean that any particular mountain gorilla is small, much less that all of them are, as Ra monca gorla ga cmalo ('All mountain gorillas are small') would claim. The universal quantifier ra will be taken up in Sections 4.23 and 4.24.
Lea preda designates, for any preda, the non-empty set of all the predas. It is universal, not intentional. Like leu, its designatum is always a set, not the members of some set. Unlike leu, it means 'the set of all (predas)'.
| (3) | Lea ficli ga laldo lea mamla | Fishes are older than mammals. |
Certainly we would not mean to claim by this English sentence that every fish is older than every mammal, or even that any individual fish is. We could only sensibly mean that the non-empty set of fishes has endured longer, i.e., has had members in it longer (on this planet, anyway), than the non-empty set of mammals.
In Loglan we wish to make these ideas clear.25
One of the cleverer things we do with language is to apply numbers to arguments. Thus when I say in English 'Those ten men are teachers' I have said something that is strictly equivalent to looking at each of them in turn and saying 'That man is a teacher' ten times. But this is not the only way in which numbers may be used. Numerical concepts may also occur as predicates (for example 'We are three', 'It was a football eleven', 'He was first in line'), as proper nouns ('The number three', 'The year 1937'), and also as indefinite descriptors ('I saw three men', 'One of the teachers smoked'). We will provide for all these uses in due course. But we must first supply the basic number words themselves. Here are the digits from zero to nine:
|
|
There are some obvious regularities. First, note that the digits are divided into five pairs and that each pair has a characteristic consonant: n t f s v. Second, note that the odd-numbered member of each pair (ne, te, fe, se and ve) ends with e. Third, note that all the even-numbered digits except ni, that is, to, fo, so and vo, end with o. The word ni (zero) is evidently the one irregular word in the system. But this makes sense. Zero is the sign of the re-cycling of the system with every tenth member and so ought to be different. Thus 'ten' is neni (10), 'twenty' is toni (20), 'thirty' is teni (30) and so on; but 'twelve' is simply neto (12) and 'one-hundred-and-twenty-three' is simply netote (123).26
For larger numbers there are two extra "zeros", as we might call them: ma (
) which represents multiplication by a hundred, or the double zero ('00') in English; and mo (
) which represents multiplication by a thousand, or the English triple zero ('000'). Thus 'one-hundred' is nema (1) in Loglan, 'a thousand' is nemo (1), 'two-thousand' is tomo (2), 'twenty-thousand' is tonimo (20), 'two-hundred-thousand' is tomamo (2), 'two million' is tomomo (2), and so on. Normally, compound number words, like compound little words generally, receive level stress. Thus [toh-mah-mah-HOOM-nee] and [veh-moh-moh-HOOM-nee] are the usual pronunciations of the Loglan phrases corresponding to 'two-hundred-thousand humans' (tomama humni) and 'nine-million humans' (vemomo humni), respectively, in which there are no pauses and in which only the penultimate syllable of the predicate word is stressed. On the other hand, any syllable in a number word may be emphasized to mark contrast: [TEH-veh-moh-moh-KAHT-mah] 'thirty-nine-million cats'. Such emphasis is often shown by underlining the emphasized syllable in text: tevemomo katma.
To round out the number system, the little word pi represents the decimal point, so that 'point-five' is pife (.5) and 'twelve and thirty-four hundredths' is simply the compound word netopitefo [neh-toh-pee-teh-foh] (12.34). Similarly, there is a set of arithmetic operators of which kua [kwah] ('divided by'), tia [tyah] ('multiplied by'), piu [pyoo] ('plus'), niu [nyoo] ('less'), pea [peigh-ah] ('positive') and nea [neigh-ah] ('negative') are the most useful. (The complete set of mathematical operators will be found in Loglan 6.) So nekuato [neh-kwah- toh] (1/2) is 'one-half'. What could be simpler? Let us now consider the uses of these number-words as argument quantifiers.
Quantification is the art of applying numbers to arguments. Sentences with quantified arguments, or, as we shall sometimes call them, plural sentences, are equivalent in meaning to those same sentences without quantified arguments (singular sentences) repeated n times; and the number of repetitions n is always equal to the product of the numbers used as quantifiers in the original sentence. Thus if I say:
| (1) | Levi to fumna ga corta leva ne mrenu | These two women are both shorter than that one man. |
what I have said is equivalent in meaning to the singular sentence,
| (2) | Levi fumna ga corta leva mrenu | This woman is shorter than that man. |
spoken twice. But if I say
| (3) | Levi to fumna ga corta leva te mrenu | These two women are (all) shorter than (each of) these three men. |
then what I have said is equivalent to speaking sentence (2) six times.
There are several things to notice about this. First, there is evidently no plural form of the Loglan descriptors levi and leva, and no plural inflection of the Loglan predicate. For with levi to fumna we are evidently not literally saying 'these two women', but 'this two woman'. Again, Loglan sounds like pidgin. There is a logical advantage as well as an obvious simplicity in this grammatical plan. For it reveals more clearly than English does what the claim of such plural sentences is about. For note that the equivalently repeated sentence--sentence (2) above--is identical to both (1) and (3) except for the presence in the latter two of the number words. Second, the meaning of the Loglan quantifier evidently includes the meaning of such occasional clarifying phrases in English as 'each of', 'all', 'both', and so on. We will see why this is so in a moment. Finally, note that the two things designated by the quantifying phrase levi to in (1) and (3) are definitely designated. For suppose I had said:
| (4) | To levi fumna ga corta ne leva mrenu | Two of these women are shorter than one of those men. |
| (5) | To levi fumna ga corta te leva mrenu | Two of these women are shorter than (some) three of those men. |
Notice that if any two of the women designated in (4) are each shorter than some one of those men, then (4) is true. And if there exists a pair of women and a trio of men belonging to the two sets designated in (5), such that each woman of the pair is shorter than each man of the trio, then that sentence is true. We will have a look at the mechanism of indefinite quantification more closely in Section 4.24 on indefinite description.
Just as in English, the indefinite quantification of an argument may be freely alternated with its definite quantification. Thus, the following forms are all possible.
| (6) | Le te fumna | (Each of) The (set of) three women (I have in mind). |
| (7) | Te le fumna | (Some) Three of the (set of) women (I have in mind). |
| (8) | To le te fumna | (Some) Two of the (set of) three women. |
| (9) | Le to le fumna | (Each of) The (subset of) two of the (set of) women. |
| (10) | Le to le te fumna | (Each of) The (subset of) two of the (set of) three women. |
And so on. Note that in these sentences le has the sense of the English phrase 'the set of', whether we are then told how many members the set has (as in Le te fumna), or not (as in To le fumna). Thus when we say To le fumna it is assumed that there are enough women in the set to yield at least two. Again we need no plural inflection of the predicate word to make this idea clear.
So far we have been concerned with quantifications of descriptions made with the particular descriptive operators le, levi and leva. But now let us consider the effects of quantifying descriptions made with the mass operator lo. As usual, we will approach our problem obliquely by first considering an English ambiguity. Suppose I tell you:
(11) The two men carried that log.
The question immediately arises: Together? Or separately? It makes a difference. For if I mean that a team of two men has carried that log, I have asserted only one thing, namely that a single individual thing--albeit two-headed--carried that log. But if there had been a log-carrying contest, say, and each of two men succeeded in carrying that particular log, then I am, in effect, asserting two things when I say "they" carried it. Namely, that one of them did, and that the other of them did, too, presumably on different occasions.
Now the second of these interpretations is, as we have seen, exactly the meaning of the Loglan quantification with le. Thus,
| (12) | Le to mrenu pa berti da | Each of the two men carried it. |
expresses the notion of two successful occasions exactly. For this is indeed the sentence form that is equivalent to itself without to spoken two times. And now, just as you might expect, the sense of the two-headed individual having carried the log is neatly accomplished with lo:
| (13) | Lo to mrenu pa berti da | The mass individual composed of two men carried it. |
This parallel use of le and lo with quantifiers completely avoids the major source of ambiguity in the use of numbers in English. Suppose we say 'The two men went to London.' Did they go as a group, or separately? The English sentence doesn't say. 'The four women played bridge.' Are you saying four things? Or only one? The English sentence doesn't say, though in this case, we would usually guess from context that the best Loglan translation was to be made with lo.
Thus whenever a number of individuals are involved in such a way that they function together as a group, then the Loglan translation will usually be made with lo. But wherever sets of individuals are involved in such a way that we have something to say about each individual member of the set, then the Loglan designation will usually be made with le. The ambiguity of the English quantified form 'The two men carried it' can of course be resolved in English by the use of such qualifying phrases as 'each of', 'separately', 'together', 'as a group', and so on. But such maneuvers are not necessary in order to speak clearly in Loglan. Thus le to mrenu means 'each of the two men' without further qualification, and lo to mrenu means 'the two-man group' and not really 'the two men' at all. Again we find that Loglan makes a logical distinction clearly and explicitly that is implicit in English, but obscurely and irregularly handled in that language.
The Loglan words meaning 'all', 'some', 'many', and the like are used grammatically in exactly the same ways that the Loglan numerical quantifiers are used. Eight of these non-numerical quantifiers are presently defined:
| ra | all, every, each of |
| ro | much, many of |
| re | most, more than half of |
| ri | little, several, a few of |
| ru | enough, a sufficient number of |
| sa | about, around, almost all of |
| su | some, at least, at least one of |
| si | at most, up to, at most one of |
The five r-words may be used in place of numbers, but they may not be used next to a number word. Thus one does not say 'All three of the men' in Loglan (*Ra te le mrenu), simply because Te le mrenu already means all of some three of the men. Similarly Ra le te mrenu ('All of the three men') is acceptable but redundant because Le te mrenu already means 'Each of the three men'. So the quantifier ra does not often accompany Loglan descriptions, being implicitly present in nearly all of them. But Ri le se mrenu ('Several of the seven men'), Lo ro mrenu ('The mass individual composed of many men'), and Re le ro mrenu ('Most of the many men'), are all useful forms. On the other hand, each of the three s-words sa, su and si may be usefully prefixed to numbers. When they are, they become part of a compound number word, as in the following sentences:
| (1) | Sanema le mrenu pa kamla | About a hundred of the men came. |
| (2) | Suto le fumna pa ditca | At least two of the women were teachers. |
| (3) | Sive le botci pa kamla le sitci | At most nine of the boys came from the city. |
But sa, su and si may also be used like r-words in place of numbers. When they are used alone in this way, they are always abbreviations of longer expressions. Thus sa alone means sara ('almost all'), su alone means sune ('at least one' or 'some'), while si alone means sine ('at most one' or 'one or none'). For example:
| (4) | Su le mrenu pa turka | Some of the men were workers (that is, at least one of the men was a worker). |
| (5) | Sa le nirli pa godzi lo ckela | Almost all of the girls went to school. |
| (6) | Si le fumna pa merji | At most one of the women was married. |
When ro and ri are used with particular descriptions, they mean 'many' and 'a few' or 'several'. Thus:
| (7) | Ro le mrenu pa no turka | Many of the men were non-workers. |
| (8) | Ri le mrenu pa kamla la Italias | Several of the men came from Italy. |
But when these same words are used with mass descriptions, they must be prefixed by pi- to turn them into fractional quantifiers. In this form they mean 'much' and 'a little':
| (9) | Piro lovi batra ga no nu titci | Much of the butter here is not edible. |
| (10) | Piri lo kolme ga nu titci | A little (of the mass of all) coal is edible. |
Similarly, pira lo humni means (redundantly) 'all of mankind', pire lo humni means 'the major portion of mankind', and of course, piru lo humni means 'enough of mankind'.27
You will encounter no particular difficulty in understanding constructions made with the non-numerical quantifiers. And constructing them is scarcely more difficult.
Indefinite descriptions are made in Loglan by putting either a numerical or a non-numerical quantifier in front of a predicate expression. No other descriptive operator is involved. For example, Ne mrenu = 'One man', as in
| (1) | Ne mrenu pa kamla | (Exactly) One man came. |
is such an indefinite description. What descriptions of this sort usually do, in both languages, is tell the listener that the described individuals are hard to find. This is a useful move for the speaker to make when information about how to locate them would be difficult or impossible to provide. In languages like English which have "indefinite articles" ('a' and 'an')--not all do; for example Russian doesn't--those articles are always among the words used to form its indefinite descriptions; but these always include the number words and certain other quantifiers like English 'all' and 'some' as well. To the best of my knowledge, all languages have indefinite descriptions of some kind.
A typical English use of indefinite description is in the sentence 'I just now saw one man in the street' as this might be spoken by someone looking out a window. The observer is apparently quite definite about da's seeing what da takes to be a man. Da is also definite about the number of men da sees: exactly one. But we may infer from da's choice of the indefinite form 'one man' over the definite form 'the man' that da is quite unable to identify the man da has just seen. Da could not, we feel confident, give us the address of that man, or his name, or indeed any other locating details. So by the usual rules of the designating game, no designation is really going on here. There is quantification (the number 'one') and there is description (the predicate 'man'). But there is no designation. The speaker is evidently quite unable (or unwilling...it amounts to the same thing) to help the listener locate the individual this sentence is about. It is for this reason that we call such structures indefinite descriptions. They describe but do not designate.
In Loglan we form indefinite descriptions in exactly the same way as English does:
| (2) | Mi pazi vizka ne mrenu le trida | I just saw exactly one man in (i.e., against the background of) the street. |
The reader may perhaps remember from Chapter 3 that to see something in Loglan is to relate the seer, the seen thing, and the background against which it is seen.
Any quantifier may be used as an indefinite descriptor:
| (3) | Su sagro smabru pa hijri | A(t least one) cigar smoker (smoke-breather) was here. |
Cigar smoke in the room, perhaps? Another way of translating su in (3) would be to say 'Some cigar smokers were here.' In Loglan we might even prefer to use a mass-term and say Lo sagro smabru pa hijri ('Cigar-smokers were here'). The next sentence is more specific:
| (4) | Sunema sagro smabru pa hijri | (At least) a hundred cigar smokers were here. |
Lots of cigar smoke, obviously...or a speaker given to exaggeration.
Finally, we come to that most mysterious of all indefinite descriptions, the one that is so vast that it becomes nearly definite, namely the one made with 'all' in English and ra in Loglan:
| (5) | Ra humni ga razdou [rahz-DOH-oo] | All humans reason (i.e., give reasons). |
We will see in Section 4.28 on the non-designating variables how there are other, logically more manipulable ways of saying (5). But for the moment let us simply note that the grammatical structure of (5) reflects by far the most common way of expressing universal claims in natural language. Indeed, what (5) claims is clear enough but rather reckless, namely that there isn't a human being anywhere who doesn't, in appropriate circumstances, give reasons.
More realistically we might claim
| (6) | Sa humni ga razdou | Almost all humans reason. |
always a safer claim; or even
| (7) | Ro humni ga razdou | Many humans reason. |
And we would be doing so with an indefinite description in each case.28
The three final uses of numbers in language are as predicates ('We were three'), as numerical descriptions ('She loved the number three'), and as names ('He came at three'.). We will deal with numerical predicates in this section, with numerical descriptions in the next, and with numerical names in the one after that. This will conclude our discussion of numbers...which cut a fairly wide swath through the language.
If we say 'It was a football eleven', 'We made a foursome at golf', or 'Those are five-gallon cans', it is clear that we are using numbers, not to quantify arguments, but to predicate numerical properties of things. In English we use the same words to quantify arguments ('The five men came') as we use within descriptions ('Those are five-gallon cans') and this leads to a widespread class of ambiguities, e.g., 'Bring me those five gallon cans.' We must obviously design such ambiguities out of Loglan. Moreover, since numbers used as predicates are predicates, and therefore participate in the whole grammar of predicates, it is clear that we would introduce an unfortunate inconsistency into the morphology of the language if we decided to use the two-letter number words, which are among the shortest of the operators, as predicate words. For both these reasons, then, numerical predicates are formed in Loglan by adding suffixes to number words.
The first series of numerical predicates are the cardinal predicates. These are formed by adding the suffix -ra to any number word. Thus 'onesome', 'twosome', 'threesome', and so on--or, alternatively, 'monad', 'dyad', 'triad', etc.--are simply nera, tora, tera, and so on, in Loglan.29 The Loglan words are used exactly like any other predicate words:
| (1) | Mu tera | We are three (that is, a threesome). |
| (2) | Ta fera galno30 veslo | That's a five-gallon can (i.e., a fivesome gallon container). |
| (3) | Da pa futbo nenera | X was a football eleven. |
Thus the cardinal predicates may be used alone, as in (1); they may modify other predicates, as in (2); and they may be modified by other predicates, as in (3). No particular difficulty attends the use of these words. They are obviously one-place predicates; they may be used in particular descriptions (le fora = 'the foursome'), or in mass descriptions (lo tora = 'pairs', that is, 'all the twosomes there are'); and they may even figure in abstract descriptions. For example, lopu tera means 'threeness', or the property that all threesomes share. Obviously, there is an infinite number of such abstract individuals. They may, in fact, be nothing more than the abstract creatures called numbers themselves.
Like all predicates, the numerical predicates are stressed penultimately. This means that their front-ends must be protected from accidentally absorbing whatever number words may precede them. How do we say 'Bring me those five five-gallon cans' in Loglan? And do so in such a way that our listeners will know that we don't want the fifty-five-gallon cans? The answer is simple. We pause in the first case, and scrupulously fail to pause in the second. (After all, fefera = 'fifty-five-some' is a single word; and we know that pausing inside a word can sometimes be misinforming.) These are the two utterances we seek:
| (4) | Kambei mi leva fe, fera galno veslo | Bring me those five five-gallon cans. |
| (5) | Kambei mi leva fefera galno veslo | Bring me those fifty-five-gallon cans. |
Note that it is clarifying to stress the last syllable before the crucial pause in (4). The stress needn't be emphatic; but there should be at least a slight rise in the stress contour immediately before the pause. Whether one uses a comma (,) or not to mark these obligatory pause in text is optional.
The second class of numerical predicates are the ordinal predicates like 'first', 'second', 'third', and so on, in English. These are the predicates which describe the positions of things in ordered series. In Loglan they are formed with the suffix -ri: neri, tori and teri, and so on.31 Like the cardinals, the ordinal predicates are handled grammatically like all other predicates; and like them, too, they have initial stress. Unlike the cardinals, the ordinals are two-place forms:
| (6) | La Djan, pa neri | John was first. |
| (7) | Da pa neri lepo prano | He was first in the race (that is, in the running). |
| (8) | Mi pa neniri le clina | I was tenth in the line. |
For obviously, if one is to be tenth in something, there must be something to be tenth in. Perhaps not quite so obviously, that something must be a series long enough to have ten members. This consideration, incidentally, shows that there are not only an infinite number of ordinal predicates, but also an infinite number of converse ordinal predicates of the following form:
| (9) | Da nu neniri | X is a series with ten or more members. |
| (10) | Da nu teri la Djan | X is a series in which John is third. |
Now there is no reason why we cannot also apply the suffixes -ra and -ri to the non-numerical quantifiers of the preceding section and produce even more of these predicates. Thus Da rara means that X is literally everything (that is, an "allsome"); Da rora, that it has many members (a "manysome"); Da sura, that it has at least one member (a "somesome"); and so on. The non-numerical ordinals are even more interesting. For example, Da rari must mean that X is the last member in some series, for literally it is the "allth" member. We can also talk in Loglan of the "manyth" member (Da rori), and even of the "fewth" member (Da riri); for nothing prevents our extending the ordinal ideas of Loglan in this curious direction, too. Again, in the effort to accommodate the natural languages, we have overshot them. And if someone asks you (in Loglan) if your position in the movie queue is close enough to the box office to make success probable, you have the splendid opportunity to reply laconically:
| (11) | Mi ruri | I am "enoughth". |
Apart from these curiosities, there are a great many quite ordinary English expressions that can be translated into numerical predicates with great directness. A 'big group', for example, is simply a set with many members, that is, a 'manysome' or rora. A 'little group' is clearly one with few members, that is, a 'fewsome' or rira.
Note that ordinals, too, are penultimately stressed.
Sometimes one wishes to separate a number from the designation that it might be used to quantify and talk about it separately. For example, instead of talking about sixteen apples (neso pligo) one might wish to say that "the number of apples" in some set is sixteen. In such styles of speech the number sixteen itself requires to be designated. In Loglan we do this with the numerical descriptor lio ([lee-oh] or [lee-OH]). It means 'the number...'. The predicate konte means 'is the count of...'. So we may say
| (1) | Le pligo ga nu konte lio neso | The apples have a count of sixteen. |
Or more directly,
| (2) | Lio neso konte le pligo | Sixteen is the count of the apples. |
Lio may operate on any quantifier, indeed on any mathematical expression. Thus Lio to and Lio sokuate ('The number two' and 'The number six divided by three') designate the same individual. We know this because we know that a true identity sentence can be set up between them:
| (3) | Lio to bi lio sokuate | The number two is identical to the number six-divided-by-three. |
(There is more on identity sentences in Chapter 5.) Notice that the whole numerical description made with lio is penultimately stressed. Thus the phrase lio to is stressed as [lee-OH-toh] or, phonemically, /liOto/, while the longer phrase lio sokuate is stressed as /liosoKUAte/ with level stress on lio. It is as if the descriptor lio were a prefix that attached itself to the number word and the compound word so formed were then required to be penultimately stressed. This makes sense. Numerical descriptions may be indefinitely long. But they must not be allowed to absorb the quantifers that happen to follow them. Penultimate stress reckoned over the whole of such expressions allows their endings to be uniquely determined; and of course the lio-segment itself marks their beginnings.
The two descriptions equated in (3) designate the same individual, namely the number two. Which designation we choose to use in any given case will be governed by the same kinds of considerations--about what the listener may be expected to know, what will be useful to da, and so on--as governs our choice between La Djan and La Djek, or between Leva mrenu and Leva fumna in the sentence Leva fumna pa mrenu. In short, that there are many names for the same number should give us no pause.
In English translation, the word lio has roughly the sense of the phrase 'the number' in such sentences as 'The number one trillion is hard to think about.' But notice that the phrase 'The number...' is not obligatory in such sentences in English. One may also say 'One trillion is hard to think about' with approximately the same effect...although perhaps in the latter case one is tempted to ask 'One trillion what?'. It is not at all clear that it is the number one trillion that is designated in the second sentence.
In any case, lio is obligatory in similar sentences in Loglan. Saying Fo kurnuu /fokurNUu/ without it--kurnuu means 'is a square number'--will not convey what you intended if what you intended to say is that the number four is a square. What you have actually said is a designation, an argument without a predicate such as might be the answer to a question. Fo kurnuu could be translated correctly, if laboriously, into 'some four instances of the set of square numbers', or more neatly 'four squares'. So it is important to say lio in Loglan when you mean it.
Another kind of ambiguity that is resolved by lio is illustrated by the following pair of sentences:
| (4) | Da cmalo | X is small. |
| (5) | Lio da cmalo | The number X is small. |
In (5) the variable da is used mathematically; that is, Lio da is the designation of a number whose identity is (usually) unknown. Perhaps all we know about it is that it is small. But in (4) the argument da may designate anything the speaker wishes to designate...including a number. One may also use letter variables as the operands of lio-descriptions. For example, lio b-- pronounced [lee-OH-bay]--means 'the number b'.
Another important use of lio is in connection with the scalar predicates. These are the words in every modern language that name the units of our numerous measurement scales. Some examples are dalra ('is a dollar/be worth...dollar(s)'), metro ('is a meter/be... meter(s) long'), gramo ('is a gram/weigh...gram(s)'), and we have already encountered galno ('is a gallon/be...gallon(s) in volume'). The "default" value of the argument in the second place of all scalar predicates is lio ne /liOne/, that is, 'the number one'. Thus Ti dalra is short for Ti dalra lio ne /tiDALraliOne/ and means 'That's a dollar' or 'That's worth a dollar', or in literal translation--which is always worth trying to figure out for each new usage you encounter--Ti dalra means 'This is worth in dollars exactly one'...a dollar-bill, perhaps. Similarly, Ta gramo means 'That's a gram' or, literally, 'This weighs in grams exactly one'...a one-gram weight, almost certainly. (Hardly anything else comes out that neatly!!)
But if, now, we wish to say that something that we have weighed with some care weighs 33.1 milligrams, say, description with lio is available to help us do it: Ti milgramo lio tetepine /timilGRAmo.liotetePINe/, or, in the abbreviated textual style we prefer for numerical expressions in both English and Loglan, Ti milgramo lio 33.1. The second expression is, of course, read aloud in exactly the same way as the first. And remember that stress remains determinedly penultimate in lio-descriptions whether it falls on a decimal point or not.
The affix mil- in the scalar predicate milgramo comes from milti 'is a thousandth part of...'. Milti is one of a series of multiplier predicates, which includes pikti, nanti, mikti centi, and decti on the small side, and dekto, hekto, kilto, mirdo, megdo and gigdo on the large side. These provide Loglan renderings of the familiar scientific measurement affixes: pik- ('pico-'), nan- ('nano-'), mik- ('micro-'), mil- ('milli-'), cen- [shen-] ('centi-'), dec- [desh-] ('deci-') as well as the ascending series dek- ('deka-' or 'deca'), hek- ('hekt(o)-'or 'hect(o)-'), kil- ('kilo-'), mir- ('myri(a)-'), meg- ('mega-') and gig- ('giga-'). So Loglandia, too, can eventually learn to spend its gigdalra. The multiplier predicates themselves predicate metrical properties of individuals or sets. Thus, if I say Da gigdo de di, I am saying that X is a billion times bigger than, or more than, Y on dimension Z. If Z is not mentioned, it is usually assumed that the dimension is numerical; that is, that set X has a billion times more members than set Y. Similarly, Da nanti de di says that X is a billionth part of Y on dimension Z...whence De gigdo da di. In short, nanti = nu gigdo; decti = nu dekto; and so on.
There is another, sometimes more convenient, way of talking about numerical facts than using either scalar or multiplier predicates; and this requires another kind of predicate, the dimension predicate. Fewer than the scalar predicates but more commonly used, they are the words for the various dimensions humans have so far succeeded in measuring. Examples are langa [LANG-gah] ('is longer than...by amount...'), laldo [LAHL-doh] ('is older than...by amount...'), tidjo ('is heavier than...by amount...'), nerji [NEHR-zhee] ('has more energy than...by amount...'), and so on. Notice that, when specified, the third arguments of all these dimension predicates will be designations of amounts. To be meaningful, these amounts must, of course, be expressed in units appropriate to that particular dimension, that is, they must be dimensioned numbers. For example, 'three inches' is a dimensioned number in English, which, when properly expressed in Loglan, might be used with the predicate langa. In another example, '33.0 cg', which we would read aloud in English as 'thirty-three-point-zero centigrams', might be suitable for use with tidjo; and '700 MYA' which, if we know what the English letters stand for, we would read aloud as 'seven-hundred-million years ago', might be appropriate to one of the many scales on which lopu laldo is measured. Loglan, too, has a full array of dimensioned numbers. The ingredients from which they are made will be found in Appendices A, B and D.
With both dimension predicates and dimensioned numbers we can now make quantitative comparisons. Suppose that brass object over there is a standard 5-kilogram weight. Suppose this sack of flour weighs 8.1kg. Then we can say
| (6) | Ti tidjo ta lio 3.1kg | This is heavier than that by 3.1 kg. |
Lio 3.1kg is, of course, the Loglan designation of the international dimensioned number 3.1 kg, a designation which could be translated literally as 'the number 3.1 kg'. We might think that the numerical part of the Loglan expression was just another instance of the familiar Loglan quantifier, but in fact the expressions 3.1kg and 3 have exactly the same grammatical privileges in Loglan. Both may be preceded by lio. Both may function as quantifiers. Thus we may speak of 3.1kg sulfo ('3.1 kg of sulfur') as readily as we may speak of 3 sulfo ('3 sulfurs', three lumps of sulfur, perhaps?), and of course a good deal more precisely. For example, we may now say
| (7) | Nensea [nen-SEIGH-ah] 3.1kg sulfo | Put in (in-set) 3.1 kg of sulfur (any 3.1 kilograms). |
just as we may still say
| (8) | Nensea 3 sulfo | Put in three sulfurs (any three lumps, handfuls, etc.). |
more roughly and with the same construction we may use to say
| (9) | Ridle te bukcu | Read 3 books (any 3 books). |
With the dimensioned numbers we reach the level of precision required by science. Yet no grammatical novelties are afoot here. Sentences (6) through (9) have exactly the same grammatical structure. Evidently a Loglan quantifier may be any mathematical expression whatsoever.
Let's now look at the dimension part of dimensioned numbers. The kg part of the expression 3.1kg stands for the pair of letter-words keigei [kay-gay]. These are the words for the lower-case Latin letterals that constitute the Loglan, as well as the international, symbol for this unit of measurement, the kilogram. The Loglan scalar predicate for this unit is kilgramo as it might be used in Ti kilgramo, 'This weighs a kilogram.' The word is derived from kilto gramo = 'thousandfold-gram', with obvious affinities with English and French 'kilogram(me)', Spanish 'kilogramo', Italian 'chilogramma', and so on. But when loglanists read the written expression 3.1kg aloud, they will read it, not as tepine kilgramo on a misleading analogy with the English 'three-point-one kilograms', but as the compound little word tepinekeigei /tepineKEIgei/; and this spoken word may always be generated simply by reading the individual numerals and letterals in the textual expression aloud. It is just as if we read '3.1kg' aloud as 'three-point-one-kay-gee' in English. We don't but could, and in Loglan we do.
Tepine kilgramo does mean something, of course, but not 'three-point-one kilograms'. It means '(any) three-point-one things that weigh one kilogram each'. There are contexts in which this curious designation might be useful. In any European supermarket, for example, there are many things that weigh (approximately) 1 kilogram. Any 3.1 of them would satisfy this designation.
The utility of comparative measurements like (6) is fairly limited, however. More frequently we wish to say that this single object in our hand, for example, weighs 30 grams, or is 5 inches long, or is probably 37,000 +/- 500 years old, without comparing it to anything else. In short, we wish to report our measurement of it directly. There is a third group of predicates that enable us to do that, namely the measurement predicates. These are all complex predicates made by attaching mel- or mely-, a prefix derived from merli = '(to) measure...to be...on scale...', to some dimension predicate like tidjo, langa or laldo. For example, melylanga [mel-uh-LAHNG-gah] means '...is measured-in-length to be...'.
| (10) | Ta melylanga lio 5i [lee-oh-feh . EE-see] | That is 5 in (5 inches) long. |
The letter word isi, being the pronunciation of the letteral i and vowel-initial, requires the briefest of pauses--usually a glottal stop--between it and the preceding number word. The letteral i is the symbol assigned to the scalar predicate inca [EEN-shah], an obvious borrowing. We might translate (10) more exactly as 'That measures-in-length the-number five-inches.' Here's another measurement statement:
| (11) | Ti meltidjo lio 30g | This weighs 30 g (30 grams). |
Phrase for word, such a sentence might be translated 'This measures-in-weight the-number thirty-grams.' It is good to "loglanize" one's English in this way from time to time.
| (12) | Ta melylaldo lio 37 ± 5n | That measures-in-age 37,000 ± 500y (years). |
The expression piuceniu [pyoo-sheh-nyooo] means 'plus-and-minus' and translates English 'plus-or-minus'; the Loglan connective is the correct one because it defines a range.
The Loglan scalar predicate for 'year', or rather for 'lasted... years', is nirne. So the international unit for years is represented in Loglan by the symbol n (read [nay]). Note from the pronunciation of (12) that pauses may be optionally introduced into a numerical description. They may occur at any point between its head-mark /lio/ and its stressed penult, in this case /MA/. This is because the appearance of the head-mark ultimately followed by a stressed vowel is sufficient to resolve such strings uniquely no matter how many pauses occur between them.
But even forms like (10)-(12) are of limited utility. In fact, they are chiefly useful for translation from the natural languages. This is because the equivalent forms made with the simple scalar predicates
| (13) | Ti inca lio 5 | This is in inches 5. |
| (14) | Ti gramo lio 30 | This is in grams 30. |
| (15) | Ti nirne lio 37 ± 5 | This is in years 37,000 ± 500. |
are much more economical in Loglan, and in both writing and speech. They are apparently the most natural way of reporting measurements in Loglan. Indeed, they have a uniquely Loglandical air, since the order of the semantic elements--designation, scale, number ('This inch five')--is quite unlike that of any other language.32
Expressions like (13)-(15) lead readily to further descriptions:
| (16) | Le nirne je lio neni | The years of the number ten (the ten-year interval). |
And this same idea may be entirely differently expressed as
| (17) | Le nirne nenira | The year-tensome (the ten-some made of years). |
Again Loglan gives options to its speakers and scope to their inventions.33
The last class of number words need not detain us long. These are the names of the objects we sometimes wish to hail by their numerical properties. Years are such objects; times of day; musical compositions ('The Beethoven Quartet') and groups ('The Dreadful Dozen'); and last but certainly not least, those abstract creatures called numbers themselves.
All such objects are very simply named in Loglan. As suggested in Section 4.19, we may always make a name from a little word or little-word compound by adding the suffix -n. Thus Nen, Ton, Fon, etc., form an infinite class of names which may then be used exactly as the name-words Djan, Pit, Bab and Kat, Kan, Rat and Far are used. If you want to talk to something with a numerical name, you may address it by using that name vocatively ('Oh 1988, how cruel you have been!'). But more frequently, you will want to talk about these things, and this requires the use of the name operator la. Thus la Ten may be used to designate the number three, the local musical trio, three in the afternoon, or anything else that has three parts or members. For it may serve, of course--just as 'John' does--as the name of many things. Thus la Ten is often used in Loglan as the translation of 'three o'clock', and la Nevevoven /laneveVOven/ is one of the expressions you may use if you wanted to talk about, and not to, the year 1989. Normally, of course, polysyllabic names are penultimately stressed.
The loglanist should remember, however, that anything that may be given a numerical name (la Nevevoven) may also be given a predicate name of roughly the same import by using one of the numerical predicates. Thus la Nevevoveri /laNEvevoVERi/ would mean '(the) Nineteen-Eighty-Ninth (Year)', and the Dreadful Dozen might be more mellifluously named la Nu Firpa Netora /lanuFIRpaneTORa/, using the techniques of Section 4.18, than la Nufirp Neton /laNUfirp.NEton/, using those of 4.19 and this section. Mellifluousness may not be what is wanted here, however.
But whatever is wanted, the Loglan name-coiner has many colors on da's pallette.
Occasionally we designate something by pointing to a sign or address of that thing. We say 'Bring me 129' when what we really want is something with that number pasted on it or written next to its name on a list. This is indirect designation. We first designate something that can serve as a sign of something else--a label or a title or an address, or a bit of smoke in the room--and then indicate that it is the thing behind that label or title or bit of smoke that we really want to talk about. In English we can do this quite openly by saying 'Bring me the car with the number 129 pasted on the windshield'; but we seldom bother. We content ourselves--as we often do in natural language--with saying something that we don't really mean, confident that the listener will understand that we mean something else.
In Loglan we would like to do better than that...especially as we will sometimes be talking to computers. So we have an indirect designator lae [lah-eh], and we use the argument-form lae X to designate anything of which X may be taken as a sign. X might be a designation of a street address, for example. In that case, lae X could be used as a designation of the "occupants". X may be of any grammatical type whatever: a description, a quotation, a name, number, or even a variable. But whatever X points to directly must be something that can then be taken as a sign of what the speaker really means to designate.
Here are some examples:
| (1) | Kambei mi laeliegei, War and Peace, gei | Bring me 'War and Peace'. |
The English speaker isn't really saying what da means, of course, and would be disconcerted--perhaps even vastly annoyed--if handed a slip of paper on which the words 'war and peace' had been quickly scribbled. The Loglan speaker is saying what de means, however, for de has, in effect, asked de's listener to look for something to which, or on which, the words 'War and Peace' will serve as some kind of sign--they will be printed in gold letters on its cover, perhaps--and to bring de that thing, please.
In the next few sentences we're going to need the predicate for 'tell' or 'inform', which is "knowledge-give" in Loglan, or djadou [jah-DOH-oo] from djano donsu.
| (2) | Djadou mi laelepo tu crano | Tell me about (whatever is behind) your smile. |
What the English speaker has said outside the parentheses is 'Tell me about your smile.'...which is pretty vague. In Loglan this vague enquiry would be conveyed by speaking (2) without lae, or Djadou mi lepo tu crano = 'Inform me (give me knowledge) about your smile.' What the English parenthetic clause and the Loglan lae operator both convey, however, is that the speaker wants to know what the listener's smile is a sign of. In short, what invisible thing is going on inside the listener of which di's smile is possibly the only outward sign.
| (3) | Mi danza lepo helba laelevi racbao [RAHSH-bough] | I wish to help whoever this suitcase (travel-box) is a sign of. |
The English translation of (3) is really quite odd. An English speaker would more often say 'I wish to help whoever owns this suitcase.' But the Loglan speaker has evidently seen the suitcase as a sign of someone da is looking for. This someone is evidently someone whom da believes will need da's help...perhaps someone da has been sent to meet and transport somewhere else. So da speaks to that unknown someone de by broadcasting a message in which da designates de indirectly through de's suitcase...now sitting at da's feet. 'I wish to help whoever's "address" is this suitcase.'
A final example of a lae-designation.
| (4) | Djadou mi lae tu | Tell me about whatever you are a sign of. |
This very Loglandical remark might be used by a speaker who saw something about the listener--da's costume or uniform, perhaps--that served as a pointer to something else...something of which the listener might be a part: a military unit, for example, or a sports team. More explicitly we might say to such a person 'What does your presence mean?'. We don't know how to ask questions yet in Loglan. (Questions and similar matters will be dealt with in Chapter 5.) But we do know how to say with djadou and lae 'Tell me of what you are a sign.'
The operator sae works in the opposite direction from lae. It produces a designation of a sign of a thing from a designation of that thing. Thus if some Loglan expression X is a designation of something X, then sae X is a designation of some sign of X...X's name, for example, or a label, or the smoke trailing behind X as X passes. Thus
| (5) | Mi sutsae [soot-SAH-eh] sae da | I smell (odor-sense) a sign or signs of X. |
differs subtly from Mi sutsae da ('I smell X') in that the second version claims that X, not just some of X's signs, has been perceived by me through smelling (odor-sensing). The claim of (5) is weaker; it says I smell things that could be signs of X.
Perhaps the most common current use of sae is as an alternative means of designating human discourse. Language, after all, is made up of signs. Thus, one may say
| (6) | Da pa cutse sae lepo de pa hijri | X said, in effect, that Y was present. |
instead of the more usual
| (7) | Da pa djacue [JAH-shweh] lepo de pa hijri | X claimed (know-said) that Y was present. |
Sentence (6) is more specific than (7). It says that X spoke "signs", i.e., words, to this effect. Sentence (7) uses the complex predicate djacue (from djano cutse = 'know-say') to report that da claimed to know that someone else was present, that is, that that state-of-affairs obtained.34
Just as le and la turn predicates into arguments, so the little word me [meh] turns arguments into predicates. It "predifies" them. Like lae and sae, me accepts any sort of argument as its operand. This includes names, descriptions, quotations, numbers...even variables. Usually, me- is prefixed to the arguments it predifies. Thus the cryptic 'That's me' as said by a speaker trying on a costume--in the sense of suiting da or expressing da--has an almost literal translation into Loglan:
| (1) | Ta memi | That's me. |
Similarly,
| (2) | Ta metu | That's you. |
in the sense of being like you or characteristic of you, could be said by a knowing friend of a particular mannerism that you have. Take a third example. Suppose we want to use a proper name as a predicate, as in 'Einsteinian Relativity':
| (3) | Ta mela Ainctain | That's Einsteinian. |
or even
| (4) | Ta mela Kraislr | That's a Chrysler. |
Such predicates are vague...often intentionally. For me-predicates are often meant to be used until a literal predicate is built to do the same job. Probably (4) is short (in both languages) for the slightly more literal
| (5) | Ta mela Kraislr, tcaro | That's a Chrysler car. |
Letter variables also work as operands of me:
| (6) | Ta meSai | That's S-shaped. |
| (7) | Ti meJai korva | This is a J-curve. |
Sometimes me-predicates are used to express such fleeting notions that there would be no point in ever building literal predicates for them. Predified quotations are often instances of such ephemeral predications:
| (8) | La Kan, pa meli, Mi danza lepo hasfa godzi, lu bleka mi | Dog "I want to go home" looked at me (i.e., gave me that "I want to go home" look). |
In this last sentence, the whole phrase meli, Mi danza lepo hasfa godzi, lu has been predified by its leading me, and the predicate it precedes and therefore modifies is the main predicate of the sentence bleka = 'looks at'.
In English, we don't quite know what to make of such constructions...especially when we try to use them in text. Sometimes we hyphenate them ('He gave me that I-want-to-leave look'); sometimes we put them in a different style of quotation marks from the ones we use for ordinary speech ('She shot back a "Don't be silly!" frown'); and sometimes (in despair) we capitalize the initial letters of the principal words in the predified phrase to indicate that something special is afoot here but we don't quite know what: 'It was God Save the King week when we arrived in London.'
In Loglan, the predifier me always makes it clear what we are doing. We are turning these bits of copied or invented speech into predicates, and we are then free to use them in any way that other predicates might be used to get the job done. Often the semantic effect is pleasantly vague. But as mentioned above, we often make do with predified arguments because we don't know of any proper predicates with which to say what needs to be said.
In sentence (8) a speaker might feel that the long predified term might be more conveniently spoken last. To put it last, da may invert the predicate string with go just as if the me-ed expression were a single predicate word:
| (9) | La Kan, pa bleka je mi go meli, Mi danza lepo hasfa godzi, lu | Dog looked at me I-want-to-go-home-ishly (i.e., in an "I want to go home" sort of way.) |
But to do this, notice that we must first link mi to bleka with je. This is because when a deferred modifier is to be linked to its modificand with go, the modificand must first be linked to all its (soon to become internal) arguments with je...jue...(See Section 4.12). Notice how linking with je advises the ear that an adverbial go-phrase is probably coming up. There is no other reason to link arguments to the main predicate of a sentence than that they are about to become internal.
Finally, here's a me-expression that is applied to me itself:
| (10) | Ba pa meliu me forma holdu le lengu | There was (i.e., something was) a "me"-shaped hole in the language. |
After me was invented in 1978 many loglanists felt that way. How had we ever gotten along without it?35 In fact, how does English get along without it now? Obviously these are historically new constructions, in the natural languages, whose grammar has not yet jelled.
When a speaker of English wants to talk about something or someone da cannot properly designate, da frequently uses the words 'something' or 'someone'. In Loglan the four variables ba be bo bu are used for this same purpose. (Note that bi is missing from this series; bi is the identity operator and will be discussed in the next chapter.)
| (1) | Ba pa ditka mi | Something bit me. |
| (2) | Ba na kokfa be | Someone's cooking something. |
| (3) | Ba pa crina | Something rained. (Usually 'It rained'). |
All these sentences express in both languages the speaker's inability to locate the thing or things the sentence is about. Or, as we might say from sentence (1), da doesn't know what bit him. All da knows is that da was bitten. And da infers from this that there exists something x that did the biting.36 Similarly, who is prepared to designate the cloud from which rain falls? We will use the lower-case letters x, y and z in English text to represent these non-designating variables.
Logicians call sentences which make claims of this kind existential propositions. Their claims are minimal. For all that is necessary to establish the truth of (1), for example, is to find that there exists something somewhere that bit the speaker.37 How different this is from the same sentence with a definite designation:
| (4) | Da pa ditka mi | X bit me. |
For sentence (4) accuses a definite culprit, X, where (1) only vaguely proposes that the crime occurred. As a consequence, (4) is easy to refute, for the accused--whom we can presumably locate--is either guilty or da is not. In contrast, (1) is almost impossible to refute. For how many "somethings" do we have to examine before our failure to find one that satisfies some given predicate may be taken as conclusive? The answer is, all of them. And that is everything there is. It is in this sense that existential propositions make minimal claims about the world.
Logically, the non-designating variables are very important. For example, they permit the clear expression of just these minimal claims that are often disguised with the indefinite article in the Indo-European languages. Thus the mystery of English 'a' and 'an' is resolved at once with this device. For consider what it means to say:
(5) A man came.
Is it not equivalent to saying?
(6) Something was a man and came.
And this in turn finds its very clear expression in Loglan:
| (7) | Ba mrenu, e pa kamla | Some x is a man and came.38 |
As we saw in Section 4.24 on the art of indefinite description, we may also translate (5) into Loglan with what amounts to Loglan's indefinite article, the quantifier su ('at least one'):
| (8) | Su mrenu pa kamla | At least one man came. |
Logically (7) and (8) make identical claims, and the Loglan speaker is free to use whichever form da pleases. (8) is a little more economical than (7) in that the implied connective e and its associated pause do not have to be spoken in the Su preda-form. On the other hand, the Ba preda e-form is logically more explicit, and loglanists will often prefer to use it for that reason.
In choosing between forms like (7) and (8), one must also be wary of the temptation to follow one's English habits, some of which, I am sorry to say, are almost certain to be bad. For example, the English translation I have given for (8) ('At least one man came') is often an incorrectly abbreviated form of quite a different English claim:
| (9) | At least one of the men (I have in mind) came. | Su le mrenu pa kamla |
Many English speakers regularly use the English of (8) when they mean the English--and therefore the Loglan--of (9). If you have such speech-habits in English, it would be wise to use the more explicit existential form of (7) when making claims of this kind in Loglan.
The difference between the claims of (8) and (9) is not trivial. Its importance may be sensed if we remember that (8) is actually an abbreviation of
| (10) | Su le ra mrenu pa kamla | At least one of the set of all men came. |
And when we also consider that the sets involved in sentences like (9) hardly ever have more than ten or a hundred members, the large logical difference between the two kinds of claim becomes apparent. Sentences like (10) claim the existence of an unknown and unlocatable man that came, hardly more. Sentences like (9) identify the man that came as a member of a locatable set. That is a long way toward having his address.
In short, it is alright to use Su preda when one really does mean to make the minimal existential claim of (7) and (10), but at no other times. The logically safest bet--in any language--is to speak existentially (i.e., with 'something's and 'someone's or ba's and be's) when one's claim is existential. So in a logical language, the Ba preda e-form of (7) may come to be preferred over the simpler indefinite description of (8).
There is another reason why the longer Ba preda e-form may be favored by loglanists who are attracted by the idea of "talking symbolic logic". The original English sentence (5) seems to involve only one predicate idea, namely that something came. But as (6) and (7) suggest, two claims are actually afoot here, namely that something came and was a man. How obscure the English form with the indefinite descriptor 'a' really is! For on the misleading parallel with a very similar sentence containing the definite article,
(11) The man came.
we are tempted to think in English that sentence (5) uses the predicate word 'man' in a designation, and hence that it is not part of the speaker's claim at all.39 This is the first error. The second is that we are tempted to think that the phrases 'a man' and su mrenu are designations, but "indefinite" ones, as an English-speaking grammarian might call them. They are indefinite quantifications, as we have already seen. But the set over which the quantifiers su and 'at least one' operate is the set of all men; and so to qualify as some man, one must be something x which really is a man; and this is not designation but predication.40 We are claiming that this indefinite something x, whoever and wherever it may be, actually is a man.
This is an important and subtle difference. The thing I mean when I say 'The man came' needn't be a man for my sentence to be true. That man may be a woman. But the thing I mean--but do not know the location or identity of, and therefore cannot designate--when I say 'A man came' must be a man for my sentence to be true. Thus two predications are afoot in the sentences with indefinite descriptions as we originally surmised. And unlike all other variables, the non-designating variables ba be bo, with which we make such claims, do not designate anything at all. Hence their name. Their use reveals, in fact, the speaker's intention not to designate--not to give the perpetrator's location away ('Someone broke it')--even when da can.41
Another use of the non-designating variables is in "universals." These are the general claims about the world that people make when they are feeling incautious ('All crows are black') or didactic ('All whales are mammals'). Here is an instance of the incautious variety, first in rather literary English:
(12) All who love the Sun, love Spain.
Then in a style of English that is logically more sophisticated:
(13) If anyone loves the Sun, then he loves Spain.
Then in Loglan:
| (14) | Raba cluva la Sol, noa la Espanias | Each something x loves the Sun only if (it loves) Spain. |
(The pause before /esPANias/ is the one required everywhere in Loglan before vowel-initial words, and is usually very short: a glottal stop.)
Now we may observe two things about this Loglan sentence. First, by quantifying the non-designating variable ba with the "all"-operator ra, we are suddenly talking about everything there is. For every something x is indeed everything, for each something x can be anything at all. This apparently reckless move is called "universal quantification",42 and we will deal with it more fully in Chapter 5 (specifically, Section 5.17). But for the moment we need only remark that it allows us to convert the weak existential claim of
| (15) | Ba cluva la Sol, noa la Espanias | Something x loves the Sun only if (it loves) Spain. |
into a conjunction of an infinite number of such claims about all the somethings that there are. It is in this sense that Ra ba means that for every something x, some specified thing about each x is true.
Second, note that each time we apply (14) to a new something it says only that if that particular something is a lover of the Sun, then it is (also) a lover of Spain. But this implication will almost always be trivially true. For the vast majority of somethings--including your pencil, the Moon, and the electron hovering at the tip of your nose--do not love the Sun; and this makes it true of them that if they love the Sun (as they don't) they also love Spain (but don't have to). It is the genius of modern logic to have discovered that an infinite number of trivialities, plus a few non-trivialities--and these concern in this case those relatively few somethings that love the Sun--adds up to something that is not trivial, namely a generalization. In this case, what is non-trivial is the generalization we can now make about Sun-lovers without designating them--or even pretending that we can--namely, that whoever and wherever they are, they all love Spain.
Logicians call such sentences universal propositions; and though they are built, as you see, on the same non-designating variables as the existential sentences are, they claim much more.
Here are some further examples of universals built with Raba and noa:43
| (16) | Raba mrenu, noa razdou [rahz-DOH-oo] | Each something x is a man only if (it) reasons (gives reasons). ('All men are rational.') |
| (17) | Raba mrenu, noa nu matma be | Each something x is a man only if (it) is mothered by something y. ('Every man has a mother.') |
| (18) | Raba simba, noa miotci [MYOH-chee] | Each something x is a lion only if (it) meat-eats. ('Lions eat meat.') |
The grammar of these Loglan remarks is plain. Each involves a connected predicate formed with the implicative connective noa; and each involves a non-designating variable of the ba-series which is quantified with the universal quantifier ra. Other argument terms may be involved, and these may either be designations, like la Sol in (14), or other non-designating variables, like be in (17). But the essential requirements of a universal claim in Loglan are that it contain, first, at least one universally-quantified non-designating variable, and second, a connection made with noa. As we have already suggested with sentence (14), and as we will see in detail in the next section, this essential connection may involve one of the arguments instead of the predicate of the sentence.
But how elegant the natural languages are! 'Lions eat meat' is surely a most satisfying abbreviation of the complex notion shown explicitly in Raba simba noa mitro titci. But also how obscure! For 'Lions live in Kenya' (some lions do, but some do not) and 'Lions are found all over Africa' (lionkind is so distributed, but no individual lion or set of lions is) are English sentences which use the same grammatical form to make entirely different claims. In Loglan we have sacrificed this elegance to penetrate this obscurity; and the result is sometimes clumsier but always clear. Besides, we can imitate the Indo-European languages fairly closely when we want to, and we will often want to when translating from these natural tongues. Thus
| (19) | Ra simba ga miotci | All lions meat-eat. |
| (20) | Le ra simba ga miotci | Each of the set of all lions meat-eats. |
(which make the same claim) are available for these natural-language-imitating purposes. Thus we do not insist that the good loglanist "talk symbolic logic" every time da open's da's mouth. Logicality is a style of Loglan speech that is available to any loglanist should de wish to use it.44
But Loglan has an even more telling advantage over English in the matter of universals. For observe that nearly every grammatical form of the English noun can be used to make a universal claim. Thus, not only the plural noun without an article, as in 'Lions eat meat', but also the plural noun with an article can be used to make the same claim:
(21) The lions eat meat (as opposed to the zebras, say).
But we also say,
(22) The lion eats meat.
and mean exactly the same thing, though grammatically this is now the singular noun with the definite article. And even the singular noun without an article is occasionally used to make a universal claim:
(23) Man eats meat.
This last sentence definitely suggests the sense of the mass description in Loglan. Even so, it may be argued that in some contexts sentence (23) might be used to make a universal claim about individual men. But curiously enough even the singular noun with an indefinite article sometimes expresses a universal claim. For
(24) A man eats meat.
in the same sense that 'A man fights back' ('if he is a man', we are tempted to add) also makes this universal claim. In fact there is only one form of the English noun construction that, so far as I know, is never used to make a universal claim; and that is what is called the "indefinite plural" form in 'Some men eat meat.' Thus five out of the six ways in which nouns are used in English are occasionally employed to make universal claims.
But the riotous way in which the speaker of English uses noun constructions to make universal statements suggests that something has gone wrong. It suggests that the frequency of use of universals has increased markedly since the grammatical bones of the language were laid down, and that the grammar of the language has not kept up with these new needs. At least something in the English mind seems to resist the explicitly provided universal form 'All men eat meat' in favor of the wildly-varied but abbreviated noun forms we have just surveyed. Perhaps the transformational clumsiness of the "all"-form compared to the elegant transformability of the more precise conditional, as in 'If something is a man then it eats meat', has already been felt by users of English. The suggestion of a suppressed conditional in the form 'A man eats meat (if he is a man)' seems to forecast even further development along this line.
However this may be in English, or may become in the English usage of the future, the preferred form of the universal claim in Loglan compositions--as distinct from translations into Loglan from the natural languages where more imitative styles may be preferred--is the conditionally expressed claim with the universal quantifier:
| (25) | Raba mrenu, noa miotci | Each something x is a man only if (it is) a meat-eater. |
For this is the form that is most readily transformed into other forms. Many variations on this theme are possible as we shall see. But all of them involve the non-designating variables and a connection made with noa, or some other connection equally capable of expressing the conditional idea.45
The prepositions that sometimes precede the arguments of Loglan predicates are called case tags. They "tag" selected arguments for their role in the sentence, especially when those arguments are out of their standard order. The standard order of the arguments of a Loglan predicate is, of course, the order in which they are spoken when that predicate is unconverted and its arguments are untagged. This is the "dictionary order" in which you have been shown the places of at least some of the predicates we have used. It is also the order in which you will find the places of predicates shown in Appendices B-F.
Here is a sentence in which a tagged argument is not in standard order:
| (1) | Da pa donsu, beu [beigh-oo] de di | X gave object Y (to) Z. |
The standard order of the arguments of donsu is donor-recipient-gift. This is the same as the unmarked order in English: 'X gives Z Y.'46 But by tagging de with the case tag beu, which we have translated 'object', we make it clear that Y is the gift. So we are free to put the new designation of the recipient, which is beu de, in an unusual position, namely in second position instead of third, which is the usual order of the designation of a gift in both Loglan and English.
Once the gift is tagged, we may also tag the recipient:
| (2) | Da pa donsu, beu de, dio [dyoh] di | X gave object Y to recipient Z. |
This move would seem unnecessary to a loglanist unless da suspected da's listener de might profit from this "extra" information...as de would do if de were a learner, say. For the benefit of that learner, da might even tag the giver place and speak all the arguments in their standard order:
| (3) | Kao [kough] da pa donsu, beu de, dio di | Actor X gave object Y to recipient Z. |
Although rare in English, this move gives the learner a maximum amount of information about the place-structure of the predicate de is learning. A similar move might be made by an instructor attempting to teach the idioms of English to foreigners.
Let's look at a more usual English sentence involving the same predicate notion:
(4) John gave his sister the puppy.
All the arguments in (4) are untagged. While the character of their designata allows us to guess who is giver, what is gift, and who is recipient, in the end it is the order of the unmarked arguments that determines their role in the sentence. To see this, let us exchange the second and third arguments of sentence (4) while leaving them unmarked:
(5) John gave the puppy his sister.
The claim is still clear enough. It's an absurd one now, or at best a sentimental one expressed metaphorically. But clearly with (5) the speaker is making a sharply different claim from that of (4). What emerges from exercises of this kind is that it is the position of an unmarked English argument that determines its role in the sentence.
Now let us see the effect of tagging. If we tag 'his sister' in (4) with the preposition 'to', we may successfully speak its claim in two quite different orders:
(6) John gave the puppy to his sister.
(7) To his sister, John gave the puppy.
We might even try the unusual move of putting the tagged argument before the verb:
(8) John to his sister gave the puppy.
That would also be understood in English. Tagged arguments are evidently quite mobile...in both languages.
We might try to explain the mobility produced by tagging in the following way. English prepositions like 'to' are evidently signs of particular English "cases", where by case we mean a category of sentential roles: for example, the roles played by subjects, objects, indirect objects, and so on, in sentences. 'To' is often a sign of the "dative" case in English; and that is the case to which all sorts of indirect objects--which include designations of destinations, beneficiaries and other recipients--are always assigned. English has several such cases, but only its pronouns are ever inflected for them. For example, 'he/him/his' and 'I/me/my' are the "nominative", "accusative" and "genitive" cases, respectively, of two English pronouns. But unlike the nouns of Latin and Greek, English nouns are never inflected for case. So if we want to mark English nouns and noun phrases for case--that is, for their role in the sentence--we must tag them with prepositions. (Notice that these are called "prepositions" because in English they are positioned before the objects they tag.) Once tagged, English nouns and noun phrases may be moved around at will without losing their case-identities.
This is just what we do in Loglan. Loglan, of course, is a completely uninflected language. Moreover, it has no nouns, just predicates which may be used as arguments. But, like English, Loglan does have a set of optional prepositions with which speakers may tag the cases of their arguments when they want to move them around.
Unlike the English tagging system, the Loglan case tag system is formally complete. That is to say, it will assign a case, and hence a tag, to any place of any predicate. This is more than can be said for English, for example, some of whose noun cases, e.g., those of the subjects and direct objects we have already mentioned, are almost always unmarked. Loglan has eleven cases, and each is uniquely represented by a preposition that is used for nothing else; see the list at the end of this section. Among them, all the roles ever played by arguments in Loglan sentences are exhaustively provided for.
On the other hand, case-marking is never required in Loglan as it often is in English. Indeed, there are some English cases that are never untagged. In contrast, the Loglan case system is optional in the strong sense that the entire system may be dispensed with if a speaker or writer wishes to. A milder way of saying this is that the arguments of every Loglan predicate have an unmarked form. Indeed, the order of arguments in that unmarked form is their dictionary order, the order in which you will find them whenever that predicate is being defined. In contrast, relatively few complete English predicates even have an unmarked form. The verb '(to) give' happens to be one that has; but most do not. Try saying that Jack is the father of Sally through mother Jane without using prepositions. There is no unmarked English sentence that conveys this meaning. But in Loglan, as we know, this and every other multi-place claim may be made without using a single preposition: La Djek, farfu la Selis, la Djein
But let us return to giving. Here is the Loglan version of sentence (4):
| (9) | La Djan, pa donsu leda sorme le cinkau [sheen-KAH-oo]. | John gave his sister the puppy (infant-dog). |
Like (4), (9) is entirely untagged. But now let's tag the three arguments of this sentence and then permute them as we did in the English sentences (5)-(8). The tags we will use were introduced in sentence (3), where we used them without comment. Let's examine the origins of these three particular tags now.
The tag used to mark the Recipient Case in Loglan is dio. Dio is derived from dirco ('direction') which suggests a pointing to something or someone and so serves as an easily remembered cue to the notion of a receiver. The Recipient Case includes, of course, not only receivers but destinations...anything at all toward which things move. The Actor Case is marked by kao, which is similarly derived from kakto ('act'). It includes all sorts of agents, doers and perceivers. The first place of many Loglan predicates--but certainly not of all--are in the Actor Case. The Patient Case, which is used for all parts, passives and properties--of which gifts, because of their passivity, are instances--is marked by beu. Beu is derived from bekti = 'thing', which suggests passivity. Thus the completely tagged form of (9) is
| (10) | Kao la Djan, pa donsu dio leda sorme beu le cinkau | An Actor, John, gave to a Recipient, his sister, a Patient, the puppy. |
This is of course much more information than anyone but a learner of the language will ever require...especially as the arguments are still in their standard order. But notice that, once the three arguments have been tagged in this way, we may now speak the four elements of the new sentence (the predicate and its three tagged arguments) in any order we like:
| (11) | Beu le cinkau kao la Djan, pa donsu dio leda sorme | A Patient, the puppy, an Actor, John, gave to a Recipient, his sister. |
| (12) | Dio leda sorme beu le cinkau kao la Djan, pa donsu | To a Recipient, his sister, a Patient, the puppy, an Actor, John, gave. |
| (13) | Kao la Djan, beu le cinkau dio leda sorme pa donsu | An Actor, John, a Patient, the puppy, to a Recipient, his sister, gave. |
| (14) | Dio leda sorme pa donsu beu le cinkau kao la Djan | To a Recipient, his sister, gave a Patient, the puppy, an Actor, John. |
| (15) | Pa donsu kao la Djan, dio leda sorme beu le cinkau | Gave an Actor, John, to a Beneficiary, his sister, a Patient, the puppy. |
These are only six of the 24 ways in which four distinct elements may be arranged. But the other 18 orders are equally understandable.
Now the thing to notice from this exercise is that our understanding of these sentences is not dependent on their being presented to us in any particular order. Despite our minds having been trained in the ways of an order-dependent language like English, we are apparently able to understand the giving relationship between John, his sister, and the puppy he is giving her when its participants are mentioned to us in any order...provided only that the role of each in that relationship be known. It is this remarkable fact about our "sentence understander"--remarkable, that is, to those of us who speak order-dominated languages like English (it would not surprise an ancient Roman...Latin poetry, for example, apparently exploits the freedom to be disorderly in a most exuberant way)--that makes the optional case system of Loglan workable. In short, order is dispensable. And that is a surprise.47
Table 4.1 gives the eleven Loglan cases. Each is represented by its letter symbol, its tag, the Loglan source of the tag--a predicate which is also the name of that case in Loglan--an English keyword which gives a clue to the meaning of the case name, some English prepositions commonly associated with that case (if any are), and examples of typical roles played in sentences by arguments assigned to that case. Notice that the case letteral is always the initial letter of the Loglan tag but not always of the case name. We will often use these letterals to tell the reader what case assignments have been given the places of some predicate in which we are interested. For example, case letterals are often used as dummy variables in Loglan dictionary entries.
| B | beu | Bekti | (object) | '-/in' | Patients, Parts, Properties |
| C | cau | Canli | (quantity) | 'by/for' | Quantities, Amounts, Values |
| D | dio | Dirco | (direction) | 'to/for' | Recipients, Beneficiaries, Destinations |
| F | foa | Folma | (full) | 'in/of' | Wholes, Sets, Collectivities |
| J | jui | Junti | (young) | 'than' | Lessers in greater/lesser than relations |
| K | kao | Kakto | (act) | '-/by' | Actors, Agents, Doers |
| N | neu | Nerbi | (necessary) | 'under' | Conditions, Fields, Circumstances |
| P | pou | Proju | (produce) | '-' | Products, Outputs, Purposes |
| G | goa | Groda | (big) | 'than' | Greaters in greater/lesser than relations |
| S | sau | Satci | (start) | 'from' | Sources, Origins, Reasons, Causes |
| V | veu | Vetci | (event) | 'by/via' | Events, States, Deeds, Means, Routes, Effects |
We may expect loglanists to use their optional case system under at least three circumstances: (1) When the argument so-tagged is to be used out of its standard order, as may be desired to preserve the natural word-order in a translation, for example, or for writing poetry, when the freedom of maximum disorder may be desired. (2) When the tagged argument is a fourth or higher-order argument of its predicate. Experience has shown that the meanings of the first three places of even long predicates are easily remembered, but that later arguments--sufori ones, as we might say in Loglan--are easily confounded. The habit of routinely tagging the sufori arguments of sufora predicates prevents this. (3) When the listener is suspected of not knowing the place-structure of some predicate, as is often the case, for example, when the speaker is a teacher and the predicate is still new. In most other circumstances we expect that many loglanists will be charmed, as logicians and mathematicians often are, by the transformational elegance of Loglan's preposition-free forms.
But again we must be prepared to be surprised. The interesting scientific question is, How will the Loglan case tags actually be used? What kinds of users will use them and in what contexts? Again, we have the outcome of an interesting natural experiment to observe.48
In Chapter 3 we saw how predicate expressions could be connected in an afterthought way with the connectives e, a, o, u, and noa. This same apparatus is available for connecting arguments as well. For just as we can say Da mrenu, e farfu, and mean that Da mrenu and Da farfu are both true, so we can say:
| (1) | Da, e de mrenu | X and Y are men. |
and mean that Da mrenu and De mrenu are both true. Recall that connections made with e are called conjunctions. We may also form alternations with a, equivalences with o, independencies with u, and implications with noa between argument pairs:
| (2) | Tu, a mi fa ditca | You or I--and possibly both--will be teachers. |
| (3) | La Djan, o la Meris, fa godzi | John--if and only if Mary does--will go. |
| (4) | La Djan, u la Meris, fa godzi | John--whether Mary does or not--will go. |
| (5) | Raba cluva la Sol, noa la Espanias | Each x loves the Sun only if (it loves) Spain. |
This is the list of connectives we had available at the end of Chapter 3. We can now make several additions, all of which will apply retroactively, as it were, to predicates.
As the expression 'only if' in the English of sentence (5) suggests, we find it awkward to form afterthought implications between arguments in English. It is in any case not nearly so easy to assert this important connection as an afterthought in English as it is in Loglan. But there is another form of implication that is readily asserted between English arguments. Consider the following sentence:
| (6) | Raba cluva la Espanias, anoi la Sol | Each x loves Spain if the Sun. |
Thus with 'if' and anoi we make exactly the same claim in (6) as we make in (5) with 'only if' and noa; but in (6) the arguments la Espanias and la Sol ('Spain' and 'the Sun') are put in an order that somehow seems more understandable, or at least more convenient, in English.49 Now the connection that is made so neatly with English 'if' is called converse implication, for it is the same as implication (A implies B) with its terms reversed (B is implied by A). Similarly, the Loglan compound connective anoi is nothing but the converse of the connection made with noa. For if the defining form of noa is no A a B, as we learned in Chapter 3, then all we need to do is switch the terms around to get B a no A. This then provides the defining form of the word for 'if' or anoi. The final vowel -i is necessary in this compound word to keep it from breaking up, so to speak, into the two words a and no. Thus,
| (7) | Godzi la Romas, anoi la Paris | Go to Rome if to Paris. |
differs from
| (8) | Godzi la Romas, a no la Paris | Go to Rome and/or not to Paris. |
only by that single letter. And note that (7) and (8) are grammatically distinct forms, even though they make exactly the same claim. Notice, too, that in Loglan it is obvious that they do. That their translations are also equivalent is not at all obvious in English.
Now just as we can construct the connectives noa and anoi from the negative affixes no- and -noi, so we can construct other compound connectives from these same affixes by attaching them to other bases. Here are some of those other compounds:
| (9) | Godzi la Romas, onoi la Paris | Go to Rome or Paris, but not to both. |
The word onoi expresses the "exclusive" sense of English 'or'. This is the sense of 'or' we use when we tell our children that we can go to the mountains or the seaside, but not to both. Since the word onoi is formed on the base o, you may assume that the connection of exclusive 'or' is based on the notion of equivalence even in English...that it is, in short, negative equivalence. We can see this best by breaking the word onoi in Sentence (9) into its parts:
| (10) | Godzi la Romas, o no la Paris | Going to Rome is equivalent to not going to Paris. |
And in English we would like to add 'and vice versa'. In short, a negative idea (not going to Paris) is said to be equivalent to the positive expression of another idea (going to Rome). Since what equivalence requires is that both its terms be true (not going to Paris and going to Rome) or both false (not not going to Paris and not going to Rome, or going to Paris but not to Rome), we see that this is exactly what we mean by the exclusive sense of 'or' in English. We shall call this connection disjunction, to distinguish it from the inclusive sense of 'or', or alternation.
We may now observe that onoi and anoi are parallel forms. We might think of them as negative equivalence and negative alternation, respectively. This is true logically in English, but not lexically. For it is impossible to tell from their verbal forms alone that both '...or...but not both' and '...if...' involve an implicit negation of their second terms. You will have to take it on faith that they do, or take a moment to study the generating formulas of the Loglan forms.
Let us now consider some more transparently negative forms. There are several senses of negative conjunction in Loglan. One of them is '...and not...' or enoi [en-noy]; the other is 'not...and...' or noe [no-eh]:
| (11) | Godzi la Romas, enoi la Paris. | Go to Rome but not to Paris. |
| (12) | Godzi la Romas, noe la Paris | Go not to Rome but to Paris. |
The claims of these Loglan compounds are both obvious in English. As usual, they are equivalent respectively to the expanded forms:
| (13) | Godzi la Romas, e no la Paris. | Go to Rome and not to Paris. |
| (14) | Godzi no la Romas, e la Paris. | Go not to Rome and to Paris. |
But what does doubly negated conjunction with noenoi [noh-en-noy] ('not...and not...') actually mean? Does it have a useful meaning? It turns out that it does. This double negation is just what we mean in English by 'neither...nor...':
| (15) | Godzi la Romas, noenoi la Paris | Go neither to Rome nor to Paris. |
And if a doubly negated conjunction is meaningful, what about doubly negated alternation with noanoi [noh-ahn-noy] ('either not...or not...and possibly both are false')? This is a rare connection, but we do assert it now and then in English with the expression 'not both...and...are true', or some equivalent phrase:
| (16) | Godzi la Romas noanoi la Paris | Don't go to both Rome and Paris. |
There are other compound forms, principally the varieties of independence formed on the base u. But these are less interesting and need not detain us here. The reader is again reminded that the complete connective system may be examined in Appendix B.
We have now defined eleven of the fourteen Loglan connectives in afterthought form: e, noe, enoi and noenoi; a, noa, anoi and noanoi; o and onoi; and finally u. These eleven words form most of the logical connections in Loglan, both between arguments and between predicates. Their c-marked forms (sheks) may even be used to connect predicate words within predicate strings. So, retrospectively, the forms noce cenoi nocenoi [noh-sheh shen-noy noh-shen-noy], canoi nocanoi [shahn-noy noh-shahn-noy], and conoi [shohn-noy] may now be added to the kit of internal connectives ca ce co cu and noca that was introduced in Section 3.16. But all these infixed connective forms have limitations. They cannot be used to express certain complex sequences of connected ideas unambiguously. For example, what does it mean to say 'Bob or John and Pete if Joe were students' in English? We will see in the next section how such riddles are solved in Loglan.
The reader will recall that certain k-marked connections (which we there called keks) were used in the previous chapter to make forethought connections between predicates, i.e., to "kek" them. These were ka ke ko ku and kanoi as derived from the basic set of five afterthought connectives a e o u and noa (often called eks). All the keks were to be positioned before the pair of elements to be connected and the infix ki was to be placed between them. Thus, ka...ki... meant 'either...or...', ke...ki... meant 'both...and...', and kanoi...ki... meant 'if...then...'. (Please note in passing that the phonemically similar ...anoi... is also translated with English 'if'.) Let us now extend this set of five keks by deriving an additional six k-connectives from the six compound eks, namely anoi enoi onoi noe noenoi and noanoi, that were derived in the previous section.
Take anoi = '...if...'. To get the kek that corresponds to anoi, we prefix /k/ to its significant vowel a, getting ka, and then add -noi to the infix ki, getting a new infix kinoi. Thus the whole kek that corresponds to anoi is ka...kinoi.... This makes sense if we remember that the defining form of anoi is ...a no.... Thus ka...kinoi... expresses the same connection as ...a no... does but with the forethought version of the connective. Similarly, the keks for enoi and onoi are ke...kinoi... and ko...kinoi..., both of which also use the new infix kinoi.
But now let us derive the kek for noe = 'not...but...'. Here the defining form is no...e.... Just as we derived kanoi...ki... ('if... then...') from noa and no...a..., so we will now get kenoi...ki... from no...e.... Similarly, the kek for noenoi will be kenoi...kinoi..., and noanoi gives us the kek kanoi...kinoi.... All these new keks apply retroactively to Section 3.18 on kekking predicates, of course, and all these same keks, new and old, may now also be used to kek arguments. For example,
| (1) | Ke la Djan, ki la Pit, stude | Both John and Pete are students. |
| (2) | Ke la Djan, ki ka la Pit, ki la Meris, ditca | Both John and either Pete or Mary are teachers. |
Sentence (1) is of course equivalent to
| (3) | La Djan, e la Pit, stude | John and Pete are students. |
But (2) is not equivalent to
| (4) | La Djan, e la Pit, a la Meris, ditca | John and Pete, or Mary are teachers. |
but to
| (5) | La Djan, e ka la Pit, ki la Meris, ditca | John and either Pete or Mary are teachers. |
For, since all unmarked connections are to be interpreted as afterthoughts in Loglan, the listener will group the elements of (4) in the following way:
(4') [(la Djan e la Pit) a la Meris] ditca
This rule is quite general. Any string of unmarked connections in Loglan will group naturally to the left...; or, as we will sometimes say, such strings are left-associative. Thus in A e B a C the association must be as (i) [(A e B) a C] and not as (ii) [A e (B a C)]. The reason is that in afterthought mode each new connected element must be connected to a construction that is in some sense already complete. So to get the right-associativity of (ii), one must use a marked connective to embrace the final pair of elements in a group (ka B ki C), and this expression may then be connected as an afterthought to the initial element A. This produces (iii) [A e (ka B ki C)] which has the same right-grouping as (ii); and this is the interpretation of (2) and (5) already given. Indeed, (5) will parse as:
(5') [la Djan e (ka la Pit ki la Meris)] ditca
If now we go back and look at the twice k-connected (2), we see that it, too, will evidently parse as:
(2') [ke la Djan ki (ka la Pit ki la Meris)] ditca
Thus both (2) and (5) are right-associated groupings of the same elements and so make the same claim. Evidently kekking the conjunction in (2) was unnecessary. Of the two equivalent forms, the minimally kekked form used in (5) tends to be preferred by loglanists over the one with the unnecessary kek in (2). In general, it is considered good style in Loglan to use unmarked connections when the normal left-associativity of the language accomplishes what is meant, and to kek connections only when the abnormal condition of right-associativity is required.
Let us consider a somewhat longer example of a sentence with unmarked, and therefore left-grouped, connections.
(6) La Bab, a la Djan, e la Pit, anoi la Djos, stude
This can only mean '([[Bob or John> and Peter] if Joe) were students' whatever may be the case with similar unmarked strings in English.50 If, therefore, we want to express a different grouping pattern than the simple left-associative one which the listener will assume on hearing (6), we must use one or more marked connections. (In the next few examples we will translate ka...kinoi..., which is the marked form of ...anoi... = 'if', with the curiously backward expression 'then...if...'. This is by analogy with 'if...then...' which translates kanoi...ki..., the converse of ka...kinoi.... There is no marked form of '...if...' in English. So we have to invent one to translate the Loglan.) Thus both of the following sentences
| (7) | La Bab, a la Djan, e ka la Pit, kinoi la Djos, stud | [(Bob or John) and (then Pete if Joe)] are students. |
| (8) | La Bab, a ke la Djan, ki ka la Pit, kinoi la Djos, stude | (Bob or [John and [then Pete if Joe>]) are students. |
are minimally marked. By this I mean that the groupings intended--here shown by parenthesizing the English--cannot be expressed with fewer keks...given this order of elements, anyway. As you may now guess, the most difficult connections to understand are precisely those in which the stylistic sin of unnecessary kekking has been most exuberantly indulged, namely the completely kekked left-associated pattern. For in these, of course, no kekking at all is really necessary. Here is an extreme example of such "bad form":
| (9) | Ka ke ka la Bab, ki la Djan, ki la Pit, kinoi la Djos, stude | (Then [both [either Bob or John> and Pete] if Joe) are students. |
Both the English and the Loglan specimens are very nearly incomprehensible (although the parenthesizing does help us glimpse the meaning of the English). But since (9) is equivalent to (6), which is readily comprehensible in both languages, (9) is hardly likely to occur.
In general, then, one uses marked forms for right-associative structures in Loglan, letting the left-associated ones take care of themselves. This avoidance of redundantly marked connections is a little like our reluctance to use the predicate grouping operator ge unnecessarily even though doing so is perfectly grammatical; see Section 3.12.
Here is an example of a sentence which is sparingly kekked in both languages:
| (10) | La Bab, ditca, e stude, e kanoi gudbi stude ki gudbi ditca | Bob is a teacher and a student, and if a good student, then a good teacher. |
Note that the claim, though complicated, is quite comprehensible. The single kek is necessary, by the way; for the wholly unmarked version
(11) La Bab, ditca, e stude, e gudbi stude, noa gudbi ditca
does not make the same claim as (10). The reader may enjoy figuring out what claim (11) does make and deciding whether it is likely to be a true one. Again, the reader is reminded that the full connective system may be examined in Appendix B.51
In the two previous sections we used negative arguments without comment in such sentences as:
| (1) | Mi pa godzi la Romas, e no la Paris | I went to Rome and not to Paris. |
The advantage of using no in such positions is that it allows us to express two related claims economically in the same sentence. But how are we to interpret no before arguments in sentences which have no connectives? Consider the following sentence:
| (2) | Mi pa godzi no la Paris | I went not to Paris. |
Clearly this is one of the two sentences (the other being Mi pa godzi la Romas) which have been implicitly connected to form the compound claim of sentence (1), the legitimacy of which we have already accepted. We are plainly obliged to accept its constituent (2) as a grammatical form as well. Yet the English version of sentence (2) has a curiously archaic ring. When we revive this archaism in Loglan we do so to obtain certain transformational advantages, not the least of which is the disentangling of just such negative connections as occur in (1). There are other advantages, but before considering them let us first be clear what no means before argument terms. Consider the next three sentences:
| (3) | No la Paris, pa nu godzi mi | Not Paris was gone to by me. |
| (4) | No, la Paris, pa nu godzi mi | It is not the case that Paris was gone to by me. |
| (5) | No, mi pa godzi la Paris | It is not the case that I went to Paris. |
Sentence (3) is obviously the converse of sentence (2), the one in which we first found the argument la Paris negated. In (3) we brought the negative argument to the head of the sentence. Sentence (4) is evidently a permissible transform of (3) in which the scope of the negation has been extended to the whole sentence. Evidently this can be done simply by pausing after the now-initial No. Sentence (5) is apparently a reconversion of (4) back into the original order of arguments as they appeared in sentence (2) but with the negative no left at the head of the sentence. Are we justified in doing this?
By the rule of conversion given in Section 3.l8 it is clear that (3) makes the same claim as (2),52 although with the different emphasis expressed by the new order in which the arguments la Paris and mi now appear. But the interesting thing is that no, which has accompanied la Paris in its migration to the position of first argument in sentence (3), has now turned up at the head of the sentence. In this new position we may recognize No as a potential modifier of the entire sentence, and turn it into one simply by pausing after it and generating sentence (4), which is evidently what No was implicitly before. In (4), No with its following pause now has the sense of contradicting the whole sentence. So we may translate the No-comma sequence in sentence (4) by that curious phrase 'It is not the case that' which occurs so frequently in the argot of logicians. Such phrases occur only rarely in everyday speech and then mainly in argument ('That's not so!') and often very awkwardly ('What you said when you said that John came to dinner just isn't true!'). The truth is that the Indo-European languages have no simple operator by which unequivocal contradictories of given sentences may be formed.
But in Loglan we need one. Sentence (5), which is the reconversion of (4), shows that no before at least some kinds of arguments has this sense of the sentential contradictor ('It is not the case that'); and the transformation rule by which we can always get from sentences of type (2) to sentences of type (5)--without bothering to go through such intermediate forms as (3) and (4)--is called the "rule of exportation." We may now state this rule explicitly: No before designative arguments may always be exported to the head of the sentence.53
But negatives before non-designative arguments may not be so easily exported. Suppose we wish to claim that some people are not fathers using the non-designating variables of Section 4.21:
| (6) | Ba farfu no be | Something x is the father of no something y. |
If, now, we export this no to the head of the sentence we get:
| (7) | No, ba farfu be | It is not the case that something x is the father of something y. |
which means no one is a father. This is not what we intend. Evidently the easy transformation leading by double conversion from sentence (2) to sentence (5) is not applicable to sentences with non-designating variables. Let us see why.
Suppose we try to convert the predicate of sentence (6) as follows:
| (8) | No be nu farfu ba | No something y is fathered by something x. |
But this means that no one has a father! Evidently we are not allowed to convert predicates with non-designative arguments. To do so would clearly be to change their meanings.54
The reason is that every non-designating variable is an implicit sentence quantifier--which is a matter we will take up in Chapter 5 when we consider quantified sentences--and the order of these quantifiers is often very important in logic. Conversion changes their order, sometimes illegitimately. Suppose, for example, we rewrite the English portions of sentences (6) and (8) in the style of English speech that is favored by logicians. Sentence (6) then becomes
(9) There is an x such that there is no y such that x is the father of y.
or, less tediously, at least one x is not a father. Sentence (8) becomes
(10) There is no y such that there is an x such that x is the father of y.
Or no one has a father. But the only difference between (9) and (10) is the order of the quantifying expressions 'there is an x such that' and 'there is no y such that'. Evidently the order in which such quantifications are applied to the same basic sentence makes some difference to those operations of the human mind that collectively we call logic.
If, now, we examine the Loglan sentences of (6) and (8) more closely, we see that the order of appearance of the non-designative arguments ba and no be differs in these two sentences in a way that exactly reflects the order of the explicit quantifying expressions in their English translations as sentences (9) and (10). Moreover the negative part of the argument no be is, in a sense, "stuck to" its variable: it may be transformed but it may not be simply moved. The difference in meaning, then, between (6) and (8) inheres essentially in the order of these arguments. So they may not be converted without changing that meaning.
Before leaving the matter of negative arguments, let us go back and qualify something we said about negative predicates in Section 3.9. We said there that if the negative no applied to the entire predicate expression--as it does in Da no pa gudbi mrenu--it could be moved to the head of the sentence without changing the claim of that sentence. And so it may, if the sentence contains no non-designating variables or indefinite descriptions...objects we had not then encountered. Thus, because Da no pa gudbi mrenu ('X was not a good man') is a complete sentence (mrenu is one-place) it does not, therefore, even implicitly contain non-designating variables. The predicate negative may, therefore, be exported without changing its claim: No, da pa gudbi mrenu = 'It is not the case that X was a good man.' But suppose we alter the sentence so that it contains the non-designating variable ba in place of the designating variable da:
| (11) | Ba no pa gudbi mrenu | Something x was not a good man. |
Now the exportation of no produces an entirely different claim:
| (12) | No, ba pa gudbi mrenu | It is not the case that something x was a good man. |
which, as it turns out, makes the same claim as the pauselessly spoken sentence:
| (13) | No ba pa gudbi mrenu | No something x was a good man. |
The difference between (11) and (13) is the same as that between
| (14) | Ba no breba | Something is not bread. |
| (15) | No ba breba | Nothing is bread. |
This is clearly a difference to which every language must attend. In Loglan we attend to them by assigning difference in meaning to different orders of the same small set of words (ba, no, ra, etc.). In English these matters are attended to with a host of different pronomial words and expressions ('nothing', 'no one', 'everything', 'something', 'some', 'none', etc.) as well as by strict rules governing the interpretation of each order: 'Nothing is related to everything' vs. 'Everything is related to nothing.' In both languages negatives tend to be "stuck to" their arguments if that argument is a non-designating word.
The most important thing we have learned in this section is that negatives before arguments may be exported to the head of the sentence if and only if those arguments are of the designating kind. Incidentally we have also learned that negatives before predicates may also be transported to the head of the sentence if and only if that sentence as a whole contains no non-designating arguments such as non-designating variables or indefinite descriptions.55 This restriction is broader than it sounds. We have already noted (Section 4.30, Note 36) that every incomplete sentence implicitly contains a non- designating variable: an existential if the predicate is positive, a universal if it is negative. Thus the innocent claim Da corta ('X is short') implicitly contains the minimal claim that X is shorter than something (Da corta ba) but the negative claim, Da no corta, is really quite extravagant, meaning as it does that X is non-shorter than, i.e., longer than or equal to, literally everything there is (Da no corta raba). From this sentence we may not export the negative, as in No da corta raba = 'It is not the case that X is shorter than every something x', for to do so produces the absurd result that the X that was once claimed to be among the longest things in the world is now satisfied to be anything but the shortest.
The handling of negatives is evidently fairly important in a logical language. We shall complete our discussion of Loglan negatives in Section 5.26 on negative sentences.
Just as we may say Da pa dzoru ze prano ('X walked-and-ran') and mean something quite different by it from Da pa dzoru, e prano, so we can form mixed arguments in Loglan with the same mixing operator ze. The distinction between mixed and connected argument forms need not puzzle us long. It is exactly the same distinction we have already encountered between quantified descriptions made with le and those made with lo in Loglan. Thus the difference in reference between the following pair of sentences,
| (1) | La Djan, e la Pit, pa pinduo [peen-DOO-oh] le hasfa | John and Pete (both) painted (paint-did) the house. |
| (2) | La Djan, ze la Pit, pa pinduo le hasfa | John and Pete jointly painted the house. |
is exactly the same difference as we might have drawn with the quantified descriptions below:
| (3) | Le to mrenu pa pinduo le hasfa | Each of the two men painted the house. |
| (4) | Leu to mrenu pa pinduo le hasfa | The team of two men painted the house. |
For in both (1) and (3) we are talking about two independent events, both of which we assert to be true. Evidently they painted it at different times. Either that or they painted it at the same time while trying to avoid each other's brushes, for each is obliged to paint the whole house if sentences (1) and (3) are both to be true. Sentences (2) and (4) are more sensible. John and Pete now evidently constitute a team, and jointly, by dividing the work, they got it painted. From neither of these last two sentences can we legitimately infer that either of them painted the house.
While the distinction between mixed and connected arguments is now plain to us--for we have learned to see it as potential speakers of Loglan--it is surprising how frequently the unmodified word 'and' is used in English to report a designation of a set and not a true connection at all. Thus all the following sentences almost undoubtedly contain pairs of arguments that the typical English speaker would intend to be regarded as a single designation of something composed of several parts: 'John and Mary own their own house', 'Joe and Sally are good at mixed doubles', 'Roger and Carl went downtown', 'He sold the horse and saddle to the boy.' In every case the most usual interpretation of the word 'and' would certainly be that it formed a lump of two things which, taken together (e.g., 'the horse-and-saddle'), behaved in a certain way (e.g., was sold in a single transaction). But note that this way does not necessarily, or even very frequently, characterize the two things taken separately. Thus Joe may not be good at mixed doubles when he is teamed with anyone but Sally.
The truth is that while the English phrase '...and jointly...' can be used to replace 'and' in each of these sentences, it does not occur to the ordinary English mind to do so. For the metaphysical orientation of English suggests no such distinction. Therefore the word 'and' does not really mean e in Loglan; nor does it mean ze. Instead it means some curious unresolved blending of the ideas of connection and mixture which are in Loglan utterly distinct. Just what this idea is, would be hard to describe. But it is probably a mistake to think that the Loglan distinction is implicit in English. It can be made, and some careful English speakers do sometimes make it; but it is evidently not natural in English to think about the differences between lumps of things and sets.
But we have seen in this chapter that in Loglan the distinction between lumps or masses of things, on the one hand, and two or more individual things of which some same thing may be true or sets of things, on the other, is the most fundamental distinction in the Loglan grammar of arguments. And we have just now seen that the fundamental operation underlying this distinction is the connection of arguments with e as opposed to their consolidation into sets and teams with ze. Then by repeated applications of this set-forming operation with zewe arrive eventually at a single designation of all the butter there is. And this is exactly what we mean by lea batra. We then see that the distinction between lea batra and ra batra can be logically generated for every predicate in the language. In doing so, we become systematically alert to a very important matter that is only dimly felt in the natural languages. Are we talking about sets? Or about individuals who happen to share some property? This distinction is implicit in English at just one point: in the difference between the grammatical treatment of its mass and collective nouns, like 'butter' and 'team', and its countable nouns, like 'men' and 'books'. In Loglan this important distinction is fully generalized, and is available to us whenever we talk or think.
Again we see how Loglan metaphysics is sharply different from that of English...indeed, from the metaphysical assumptions of all the natural tongues. For the Loglan world starts with pieces of butter and bits of better-than, and by successive applications of the machinery of abstraction and set description, all the elementary predicate notions of the language can be raised to any level of conceptual intricacy that we desire. At the highest levels are such familiar individuals as virtue and butter. But they are joined, in the Loglan view of things, by such surprising abstract entities as "butterness," "bookness", "enoughth-ness", and "the set of all the burrowing owls." Thus the Loglan world of individuals is a larger world than is commonly accessible to the natural tongues, for it accommodates by vastly exceeding the old. What this may finally mean for the observing eye and the thinking mind can only be guessed. But one thing is certain. For any given size of vocabulary, there will be more in Loglan to think about.
1 Throughout this chapter I will use the word 'designate' in the approximate sense of 'purport to name, identify, or single out', a sense that does not entirely accord with either philosophic or linguistic usage (cf. Morris 1946, Carnap 1948, Ziff 1960, Quine 1961a). I do this because there is no well-established single word in English that permits one to refer to just this species of linguistic behavior, and I need to. For in the system of semantics I am about to develop, the act of "designation" contrasts with that of "predication," and both are ways of referring to the "external", i.e., non-linguistical, world. In adopting this terminological scheme, I am closest, among logicians, to the analyses if not the usages of Quine. The distinction he draws between "singular" terms and "general" ones, i.e., between that which purports to name X, and that which is true of X (see Quine 1961a:205ff), is very nearly what I take to be the distinction between designating and predicating, though my emphasis is naturally a different one. (For example, I do not think, as Quine does, that the former activity can be eliminated in favor of the latter.) Both acts refer; we would agree on that. But that they do so in entirely different ways is the main point of this chapter. Morris and Carnap, in contrast, use 'designate' in approximately my sense of 'refer'; Ziff uses 'refer' in approximately my sense of 'designate'; some writers use 'denote' where I use 'designate'; others use 'designate' where I use 'predicate'. Still others call predicates "names." And the names of what? Why, of "properties", of course. In short, semantical terminology is in something of a muddle. There is more on this matter in Chapter 8 of Loglan 2 (Brown 1969b).
2 The need for toi toa and tio tao was discovered during Loglan conversations with Prof. John Parks-Clifford, a logician, in December 1977.
3 If Christopher had visited the King of Spain, and we had been told that he had persuaded him that the Earth was round, we would be in a similar quandary.
4 More than suffice, evidently. As mentioned in the text, experience has suggested that any three among the replacing variables, for example, da de do, can be assigned and kept track of in this "LIFO" way ("Last In, First Out"), but that assigning more than three in the course of speech is probably too much for the human temporary memory. Usage has added two new conventions since 1975 which supplement the da de di do du system. The first is to use an identifying clause on the first use of a fourth or later replacing variable, e.g., di ji la Pit = 'Y, who is Pete', a practice which allows one to ignore order of occurrence. The second is to use the letter variables discussed in Section 4.6 as abbreviations, e.g., to use fei (f) to replace le fumna, whenever the context gets too complicated for the da de di do du system to handle. Indeed, the use of letter variables already seems to be so problem-free as to suggest that it may supplant the free variable system entirely. Both systems are still optional. The learner may use either or both. Again we will "let usage decide".
5 As remarked in Chapter 3, Note 3, Loglan has a grammar which is in many respects like those of the natural pidgins and creoles. This augers well for its possible closeness to the human language biogram; see Bickerton (1981). According to this writer, the similarities between child speech and pidgin are not accidental.
6 A Whorfian from Mars might assume from this fact that England had the least developed class-system among the European nations. How wrong da would be! The English class system is probably the most highly developed among those of the European nations. We may be warned by this example of the dangers of over-simplifying Whorf's ideas.
7 The anaphoric use of letter variables was first suggested by Stephen Smith on a visit to The Institute in 1979.
8 The logical theory of descriptions, following Russell (1905), gives a slightly different account of these matters, namely that the description '(i)Fx' purports to name (i.e., designate) the one and only object of which 'F' is true, 'F' being some predicate expression which allows this interpretation, e.g., 'is an author of Waverly' (see, for example, Quine 1961a:222). On this interpretation 'the author of Waverly' (Russell's classic example) is taken to contain the covert claim 'There is an x such that x is an author of Waverly and, for any y, if y is an author of Waverly, then y is identical to x.' But the uniqueness claim is patently false for the majority of expressions commencing with 'the' in everyday speech, e.g., 'the man', 'the red thing', etc. What is common to all such expressions is the intention of the speaker to single out however crudely (e.g. 'the whachamacallit') the unique object, or set of objects, about which da has something to say. That such expressions use predicates is apparently misleading, for they do not use them predicatively; any more than names used vocatively actually name. On the view taken in this book, no claim whatever is made by a description. What is signified by the use of one is (among other things) the speaker's readiness to help the listener locate the unique object about which da has something to say. We may say that this implies that da believes that such objects exist, but this is a different matter. No one may be accused of claiming everything that da's words imply. There is more on this in Loglan 2, Chapter 8 (Brown 1969b, reprinted in TL2:31-41).
9 Marking a string of words with a leading asterisk (*) in this way will serve hereafter to notify the reader that the string so marked is not acceptable, either not a correct parse, or not grammatical, or not good usage. This one is grammatical, i.e., the utterance will parse; but it will not parse in this way.
10 This intimate glimpse of the machine's rather fussy parsing behavior is probably nothing that human users of the language need to worry about...unless they aspire to be Loglan grammarians. We frankly doubt that descriptions like that in (8) will have much currency in human Loglan. It is, after all, an exception to the general analogical rule that "Whatever works in one context should work in another." The converse rule "Whatever doesn't work in one context is probably not worth trying in others" is probably also built into human grammar learning behavior. So unless we are taught by machines to make sentences like (8) it is unlikely that human users will ever try to make them...knowing, as they surely will, that sentences intended to parse like (7') always fail. Analogical rules like the one defeated here may, in fact, be quite generally invoked in human grammar learning. If they are, they are probably responsible for a great deal of the syntactic ambiguity in natural language. Scott W. Layson is responsible for this particular bit of grammar programming. It was done during the first, 1978-82 assault on the "macgrammatical mountain", the one that resulted in Notebook 1 (Brown 1982a). Its purpose was to make these unambiguous sentences machine intelligible...whether humans would ever be tempted to use them or not. An interesting scientific question raised by this particular provision of Loglan grammar is whether the analogical rule by which the use of new grammatical structures is extended from one context to another--sometimes leaving a trail of new ambiguities in its wake--is hard-wired in the human central nervous system or not? With Loglan, language scientists should be able to tease answers to such important questions out.
11 This discussion of the mass term owes much to Quine (1960) in which he makes ingenious use of the distinction between mass terms and general terms in discussing certain philosophical difficulties in the way of coming to understand totally unknown languages. In particular, Quine examines the difficulty that will be experienced by a philosophically wary investigator--one who has presented a series of different rabbits, say, to a certain informant--in deciding whether that informant's uniform linguistic response to this series of stimuli means that da's language has a general term for 'rabbit', of which da recognized each new rabbit as an instance, or whether da's language has only a mass term, roughly equivalent to 'Mr. Rabbit', say, of the designatum of which da recognizes in each presentation simply a reappearance. Quine shows that the resolution of this difficulty involves linguistic transformations of a surprisingly high logical order; and that these, in turn, involve ontological assumptions about the language in question which one would have hoped to be among the findings, rather than the presuppositions, of linguistic inquiry. My own reflections on this matter persuade me that in the mass term/general term distinction we are probably dealing with a fundamental biological feature of the human speech apparatus...differently exploited in learning different languages, to be sure, but always there. For example, my own observations of the speech behavior of very young (pre-English speaking) children suggests that the mass term may be developmentally the earliest semantic mechanism to appear in human speech behavior--far earlier, for example, than the mastery of the detailed use of mass terms as a special class of nouns in English--and that it is, therefore, the meaning of the general term that is ontogenetically secondary in the biological development of the human semantic scheme. Goodman (1951) also discusses the "arbitrary" ways in which the primitive predicate may be invested with meaning under a wide variety of ontological schemes. On this view, the basic semantic mechanism of Loglan could have been a Trobriand-style 'X is a manifestation of Mr. Y.' type of predicate relation rather than the, to us, "simpler" semantic relation between designations of particular concrete individuals and some general term ('X is an instance of Y'). The same considerations apply to the difference between "abstract" and "concrete" predicate meanings. Thus we could have invested the unadorned Loglan predicate with the abstract meaning that is in fact its meaning now with po and pu. The concrete particular meaning we now hold simple would in that case be derived from some grammatically complex operation on the linguistically "simpler" notion of an event or quality. Such hypothetical languages are fascinating to contemplate; but the choice among them may be more than a pragmatic one, and actually turn out to be partly rooted in some intractable streak of Nature that, by evolving us to do so, "insists" that we first regard her from some particular, favored side. For the mechanism of that "insistence" could, of course, only be the evolution of the rewarding apparatus in language-using animals so as to favor just that side. There is more on the lo operator and its ontological implications in Brown (1977a).
12 Strong quotation began with J.S. Prothero's (1979) suggestion and was further developed by me in Brown (1979g).
13 The designative use of quotation marks in English should not be confused with their use to serve notice on the reader that certain words or phrases are being used non-literally, i.e., "horror" quotes, as they are sometimes called. Thus, a pair of horror quotes (double-quotes in my idiolect) appears around the word 'horror' in the preceding sentence, while a genuinely designative use of (single) quotes appears around the same word in this one. To perform the notice-serving function of quotation marks in English, there is another operator, namely the metaphorizer jo, which has the function of marking figurative expressions, especially on the first occasion of their use in some passage or discourse; for more on jo and kin, see Loglan 6.
14 Single word quotation with liu was proposed by William Mengarini in (1977c). See Brown (1979f) for further development.
15 The appeal of nonsense to logicians is curiously widespread and in some cases monumental (for example, in Lewis Carroll). The affinity is not accidental. It is often nonsense that reveals the logical structure of ideas most nakedly. One test of a logical language, then, is that in it one should be able to speak nonsensically and still be understood. Thus if I want to say that John is a short word I do not wish the blind forces of "common sense" and "usage" to defeat me whichever way I turn this phrase.
16 These French quotation-marks have the advantage over the English ones of being clearly directional. As this is a useful feature in analyzing quotations within quotations, I have adopted them. Note that li and lu, being distinct words, are also "directional".
17 Or at least they are in all languages of which we know; but see Note 11, above, for considerations which argue the logical possibility of languages in which such abstract mass individuals are the elementary objects of the linguistic scheme, and hence elementary to just such hypothetical "minds" as had been exclusively exposed to such languages. Whether human minds would react in this way to such exposure is, of course, a biological question of some interest.
18 Quine (1958) offers an interesting conjecture as to how abstract singular terms might originate by analogy with concrete ones as a solution to one of the ontological problems of the child. Supposing (as seems likely) that children commence their linguistic careers with an ontology, i.e., a view of existence, which sees the world as composed of mass individuals and their reappearances (Mummy, Hunger, Warmth, and the like), and graduate to countable objects and general terms (boys, dogs, glasses of water, and the like); there would then emerge the ontological problem of what kind of individuals "stand behind" those general terms which have spotty, streaky or superficial manifestations, like 'is red'. For a red thing is not red clean through, as a boy is a boy clean through and as every drop of water is wet. Quine suggests, therefore, that on analogy with some word like 'water', which survives ontologically as the mass individual Mr. Water lurking behind the predicate 'is water', a new individual Mr. Red is mistakenly conjured up to be the simple, concrete massification of the predicate 'is red'. Mistakenly, because in fact the mass individual composed of all red things is not all red, as water is all water, but mostly white (apples), pink (Injuns), green (plums), and so on; and of course the child knows this. So what the child really means to designate by the mass term 'red', in such sentences as 'Red is my favorite color', is not the same kind of mass individual da alludes to in 'Water is my favorite drink.' Instead, it is the abstract mass individual composed of all the red parts, spots, or streaks of red by virtue of which red things are red, the same individual we designate in Loglan with lopu redro. Hence attributes arise on the basis of a false analogy; and red becomes as "pure" and "liquid" a thing as water is, though oddly less substantial, by virtue of the shifting ontological scenery in the child's mind.
19 Another clarifying provision is the pause rule that distinguishes the compound operator lepo and kin from the corresponding phrases le po and kin with which they might sometimes be confused. Le po phrases are rare but when they do occur are always distinguished by internal pauses which lepo and kin never show. For example, the phrase le po in (i) le po sucmi ditca = 'the swimming teacher (i.e., a teacher of the activity of swimming)' is always pronounced with a pause between the le and the po, and, in addition, the le is often stressed. Thus /LE.poSUCmiDITca/ is a typical utterance of (i). In contrast, both syllables of the word lepo are usually unstressed and there is never a pause between them. The utterance /lepoSUCmiDITca/ therefore uniquely resolves as (ii) lepo sucmi ditca = '(the state of) being a swim(mer) teacher, i.e., a teacher of swimmers', which is a much more common way of speaking in Loglan. Expressions like (i) are said to involve short-scope po, for in them, the force of abstraction extends over exactly one predicate, the next predicate word. Expressions like (ii) are said to involve long-scope -po, for in them the force of the abstraction runs over the entire sentence serving as the operand of the event description. When short-scope po occurs non-initially in a predicate string, as in (iii) le corta po sucmi ditca = 'The short swimming-event teacher' (i.e. a teacher of swimming-events of short duration), no pause is required: /leCORtapoSUCmiDITca/. It is only when short-scope po follows a descriptor that it needs to be set off from that descriptor by an intervening pause. Other stress patterns than those described here are, of course, quite permissible.
20 This move may have some bearing on the phenomenon that Quine calls "referential opacity" (1961b:139ff). For example, when recast with a Loglan-like event-description the troublesome sentence 'Philip believes that the capital of Honduras is in Nicaragua' (p.141) becomes 'Philip believes that the state of affairs of the capital of Honduras being in Nicaragua obtains.' This second formulation relieves Philip of the responsibility of ever having listened to, or uttered, such a remark, and yet clearly designates the non- existent object in which Philip believes. How different this is from a third formulation: 'Philip believes that the sentence 'The capital of Honduras is in Nicaragua' is true.'! About this third sentence, we should certainly agree with Quine that its deduction from 'Philip believes that the sentence 'Tegucigalpa is in Nicaragua' is true' and the true identity 'Tegucigalpa is the capital of Honduras' is not justified. But contexts within quotation marks are always and everywhere referentially opaque. But are descriptions always similarly opaque? Clearly not. For 'the village ten miles north of Tegucigalpa' and 'the village ten miles north of the capital of Honduras' both succeed, for a person in possession of this identity, in designating the same presumably existent thing. The difficulty that is residual in Philip's believing in the object we have designated 'the state of affairs of the capital of Honduras being in Nicaragua' is that it is non-existent; and how indeed do we locate such objects for the sake of testing the truth of sentences in which their designations occur? This is, of course another and a quite different problem; but certainly it is not incapable of solution. For how do we determine whether or not Philip believes in the flatness of the Earth, or in the flights of Pegasus? We ask him; and in doing so we do not have first to locate a flat Earth or a winged horse to present to him; for a picture or a model, or even a carefully constructed sentence delineating this non-existent thing, will clearly do for ascertaining the truth or falsity of any claim that da believes in it.
21 For humans. The ga-rule is not awkward for machines. The machine grammar sees ga as just another allolex of the PA Lexeme. Machines will observe that human speakers evidently use it when they have no particular time or place or mode in mind but want to mark their predicate expressions anyway. (The motive of the mark-using speaker may remain unknown to the machine.) The machine would not regard the use of ga when contextually unnecessary as ungrammatical, or even odd. Thus, *Da ga mrenu is a perfectly grammatical expression to the machine. (If you have LIP--the "Loglan Interactive Parser"--try it. It will parse. But I have starred it because it is bad usage...from the point of view of human users of the language.) That in fact human speakers, being sensitive to such matters, do not produce such unnecessarily marked sentences is a distributional matter, a matter of usage, not grammar. Machines may remain context-insensitive, in short, and still parse the productions of context-sensitive human beings. When our machines begin to speak Loglan back to us, we may of course then teach them whatever humanoid practices we wish them to observe. When we do that, we will perforce be teaching them a kind of context-sensitivity. For in a certain sense all usages are context-sensitive in that they are selected by the user as appropriate to the contexts in which they are to appear.
22 The noun/verb distinction does this work in English, as in all the Indo-European languages. Thus the distinction made with various English suffixes between the description 'the man singer' and the sentence 'The man sings' is made in Loglan by the presence or absence of the predicate marker ga: Le mrenu gritu vs. Le mrenu ga gritu. From this and similar experiments it emerges that the chief syntactical work of the noun-verb and adjective-verb distinctions in the natural languages may be to distinguish the predicative from the designative parts of sentences. The PA operators and the LE and NI operators do this work in Loglan, and, as in Da preda, they may be omitted when no ambiguity can arise.
23 See Brown (1977a) for an informal discussion of the ontology of the lo-operator.
24 Technically, we might say that the description 'my book' uses the vague claim that there exists a two-place, or higher order, predicate P such that I and my book are apparently related by P, in the same non-committal way that it uses the explicit claim that my book is apparently a book. Thus the listener is helped to locate my book by a conjunction of two presumable predicate relations: one vague but with a specified second argument, the other concrete but unspecified.
25 Work on the special designators may be found in Darwin (1978a), Rosenberger (1978) and Brown (1979c,d).
26 One counts in Loglan either by separating the integers by the continuation connective I (see Section 5.1), as Ne. I to. I te (/NE.iTO.iTE/) means literally 'One. And two. And three' or by pausing between the quantifiers: ne, to, te (/ne.to.te/). So the word netote cannot be heard, as English 'one-two-three' might, as a short burst of counting instead of the integer '123'.
27 There is more on the quantification privileges of various kinds of descriptions in Rosenberger (1978) and Brown (1979c).
28 Indefinite description has had a checkered history in Loglan. The first widely published account of the language, the 1960 Scientific American article (Brown 1960), included a provision for speaking universals and existentials by indefinite description much as is here described. But six years later this option had already been removed from the language. It had been replaced in Brown (1966), the first book on the language and the 1st Edition of this one, by the requirement that the quantificational machinery of modern logic always be used. The latter option had been present in 1960 but was not obligatory. So, as early as 1966, expressions such as Ra humni ga razdou had been outlawed and were to be replaced by expressions like Raba humni, noa razdou ('Every something x is human only if it reasons'). (The latter sentence is still good Loglan and its construction will be explained in Section 4.30.) Indefinite description reappeared after a 21-year absence in Notebook 3 (Brown 1987). My reasons for reinstalling it were three-fold: (1) Learners whose native languages include indefinite articles used the corresponding Loglan words (su and ne) in indefinite descriptions anyway, whether it was "grammatical" for them to do so or not. (2) Translating natural language texts that contained indefinite articles into a style of Loglan that eschewed them often imposed an alien formality on those texts. Without indefinite description, the translater had to render all instances of existential and universal claims by the heavily logical- ized Loglan forms. For example, da would have to replace every genuinely existential 'a' in an English text with a ba jio-clause ('something x which is a...') and every 'all' with raba...noa ('every something x is...only if...'). Such a requirement, if adhered to, would certainly mar Loglan's performance as a translation instrument. But (3) quite the most important consideration was the fact that Loglan had become, since 1975, a language of optionalities. It is fair to say that Loglan is now not so much a logical language as one in which the option of "talking logic" elegantly and swiftly is available to the speaker should da wish to use it. Moreover, logicality-alogicality is not the only pair of stylistic choices now built into the language. There has always been the optionality of its tense system, for example; and there are now optional case tags. Yet the existence of a system of case-tags (which may be found in Section 4.31) in no way interferes with the basic caselessness of the unadorned Loglan argument. This, like the equally basic tenselessness of its unadorned predicates, remains as it was before the case option was added. I believe (but cannot of course yet know) that the logicality function will be similarly unimpaired by the side-by-side existence of pre-logical linguistic forms. Besides, each option-pair is, in effect, a provision for running a natural experiment. The existence of the fully logicalized but nevertheless speakable ba and raba forms alongside the evolutionarily older, and hence more natural, su and ra forms will provide for just one more such experiment, in this case a vital one for the Whorf hypothesis. Does the use in speech of logicalized verbal forms, like the predicate calculus, facilitate the thinking of the speakers? Or hinder it? Who chooses to use these logical devices? Under what circumstances? We would like to know. With a fully optionalized experimental language such as Loglan now is, it ought to be possible to find out.
29 The use of the syllable /ra/ as the quantifier word meaning 'all' and also as the numerical suffix meaning '-some' or '-ad' may seem to introduce homonyms into the language. But the grammar is so arranged that these two uses of the same syllable will never be confused. For example, the word ra can never follow a number word; so if /ra/ is heard after a number word it is not the word ra but the suffix -ra one is hearing. Semantically, the two uses of /ra/ are related. The cardinal number of a set is found by counting all its members.
30 Alternatively this could be said by first making the complex predicate fergalno from fe + r + galno; whence Ta fergalno veslo = 'That's a five-gallon container.' Loglanists have not yet faced such situations frequently enough to have developed distinct preferences for one form over another.
31 Again the quantifier ri meaning 'several' and the ordinal suffix -ri have non-overlapping distributions, and so will never be confused.
32 This is true of the broad group of languages of which I and my manuscript readers know. But I would be most grateful if a reader who knows of one which uses this order would apprise me.
33 The system of measurement statements described in this section was, in all essentials, proposed by Scott W. Layson in (1979). See also Brown (1980c) for additional development.
34 Lae and sae were proposed by William Mengarini in (1976) and further discussed by John Parks-Clifford in (1980b:48-50).
35 Me was invented in early 1978 during the stay at The Institute of Scott W. Layson. It was he who coined the figure that there had been "a me-shaped hole in the language". Me was first described in TL2:114 in February 1978 and further discussed by Parks-Clifford (1980b:20-21).
36 Note that Ba pa ditka mi lemi barma ('Something bit me on my arm') makes the same claim completely as the incomplete form Mi pa nu ditka ('I was bitten') makes, and that this last statement contains no reference to the biter at all. But in fact all incomplete forms of multiplace positive predicates implicitly claim the existence of at least one whole set of participants in the predicated relationship even though some of them remain unmentioned. Thus Mi vedma ('I sell') is, strictly speaking, an abbreviation of Mi vedma ba be bo ('I sell something to someone for something') and may be so expanded when desired. Sentences with negative predicates, on the other hand, require universally quantified non-designating variables for their completion; see Note 37 below. Thus Mi no vedma becomes Mi no vedma raba rabe rabo ('I do not sell anything to anyone at any price'); see Section 5.25 on negative sentences for further discussion of this point.
37 The logician will miss the existential quantifier in these expressions. In the language of logicians (1) would normally be rendered '(Ex)Fxy', in which '(Ex)' is the existential quantifier and may be read 'There is an x such that'; (2) by '(Ex)(Ey)Fxy'; and so on; for example as in the notation of Quine (1961). If we really are to "talk symbolic logic" in speaking Loglan, why not follow this well-established linguistic route? But Loglan is a spoken language, not a notation meant for visual inspection, nor yet a way of reading notational expressions aloud; for surely this is the origin of the logician's version of spoken English. In every spoken language the most frequently used expressions have the briefest forms, and the existential claim is surely one of the most frequently used devices in the natural languages...more frequent, for example, than universals. We should expect this rule to hold in Loglan, too. Therefore we set aside a series of "non-designating" variables to be used exclusively with quantified sentences in Loglan and say that any unquantified instance of such a variable implicitly expresses the existential claim, while any instance of such a variable preceded by the quantifier ra ('all') implicitly expresses the universal claim; there is more on the Loglan system of implicit quantification in Section 5.24 on quantified sentences.
38 Logicians, but not other people, are likely to feel that this sentence requires explicit mention of an existential quantifier with sentence-long scope, as in schema (i) '(Ex)(Fx · Gx)', in order to distinguish it from the two short-scope quantifiers of schema (ii) '(Ex)Fx · (Ex)Gx'. For if it were an instance of (ii) as ordinarily interpreted by logicians--say by Quine (1961)--then the discovery that there was something x that was a man and something else x that came would satisfy the claim of (7) in a way that is plainly contrary to our intention. But we construe (7) in such a way that it does not require this embellishment; for recurring instances of any given non- designating variable in the same Loglan sentence are all taken to refer to the same indefinite someone or something. Thus ba implicitly recurs in (7), for (7) may be expanded into the connected sentence (7a) Ba mrenu, ice ba pa kamla (literally, 'x is a man; and x came') by means of the sentence connective ice which we have not come to yet (see Section 5.23 on connected sentences); but the two instances of ba which occur in it may not be interpreted as referring to different objects. If we want to make the distinction in Loglan which is imputed to the difference between schemata (i) and (ii) in contemporary logic, we must use different variables: (7b) Ba mrenu ice be pa kamla (literally 'x is a man and y came'). The Loglan convention here is that while ba and be do not have to be distinct somethings, they may be. Again note that it is the more interesting of the two claims (7a) and (7b) that can be more briefly said in Loglan. We should also note that these arrangements necessitate some changes in the schematization of logical law as applied to Loglan; thus, for Loglan sentences, schemata (i) and (ii) are equivalent, and a third schema (iii) '(Ex)Fx · (Ey)Gy' would have to be introduced to accommodate their former difference. As far as I know, the other adjustments are equally harmless; but the matter has not been studied exhaustively.
39 To see that the word 'man' in 'A man came' does make some kind of claim against the world--and is therefore not a designation--suppose that we found out, by exhaustive search, that only one thing came and that one thing was a woman. Would we not then regard our previous remark 'A man came' as false? This contrasts rather strikingly with the fate of 'The man came' under the same circumstances; for in that case all we should care about would be whether the woman that came was in fact the person designated by the speaker whether camouflaged or not.
40 The very least that we should require of a designation is that it function, even if temporarily, as a name: that is, that there be exactly one thing or set of things about which the speaker is saying whatever da is saying and of which some portion of da's speech functions as a verifiable label. 'John came' says the speaker. 'Is this John?' we ask, working our way down the list of Johns. Somewhere, sometime the speaker must say yes; for there must be at least a quasi-John which satisfies da's intentions. For if there is not, da is not playing the two-handed game we have here called "designation" according to its rules. Now names, descriptions, and the free, demonstrative and personal variables all satisfy this strict behavioral criterion. Words like 'someone', however, do not. If we make the mistake of thinking that they do and ask of someone who says 'Someone came', 'Is this someone?' we may be told yes or no indiscriminately with every presentation; for everyone we present is someone and no one we present will be the intended someone the speaker "has in mind." In short, the speaker has made a zero-order designation: a most peculiar and powerful maneuver which enables da to predicate something of the world without committing daself to locating anything in it. That so fastidious an act should lurk behind every "universal" claim is one of the most curious and far-reaching discoveries of modern logic.
41 This explains why 'someone' and 'something' are among the favorite words of children. 'Someone broke it' gives nothing away. Closely related is the strange intransitive sense of such verbs as '(to) break' in such sentences as 'It broke', which is a kind of suppressed passive: 'It was broken by someone or something (and I'm not saying who or what).'
42 Again we assume that the implicit quantifier has sentence-long scope, i.e., that sentence (11) is an instance of schema (i) (x)(Fx --> Gx) and not of schema (ii) (x)Fx --> (x)Gx, see Note 38 above. For the system of implicit quantification foreshadowed here, see Section 5.24.
43 In 1975 Loglan the word raba was the phrase ra ba. In this it was like the phrase le po, one of whose senses also ascended to wordhood during this period while another retained the meaning of a distinct two-word phrase. I do not yet know what causes some phrases to become words while other, even very common phrases do not. One is haunted by the evident histories of such natural words as 'nevertheless' and 'understand'. By what process do these strings of once-separable elements consolidate and become, to speakers of that language, single items in the speechflow? I have no idea what is happening here. But with Loglan, we will probably have a chance to observe this event fairly frequently. It has already occurred more than once.
44 The argument for preserving the logicality-alogicality option in Loglan is summarized in Note 28.
45 Such as no...a..., as in Raba no mrenu, a mitro titci ('Each something is a non-man or a meat-eater').
46 This is not an accident. Whenever a complete English predicate may be expressed with unmarked arguments, such as 'give' may be in '...gives... ...', we have adopted that order as the dictionary order of the places of the corresponding Loglan predicate. In these cases we have learned our lesson, as it were, about the behavior of unmarked arguments from this one natural language. The operative word, however, is 'complete'. Very few multiplace English predicates can be completely expressed without prepositions. So for these far more numerous cases, other considerations have been used to determine the dictionary order of the corresponding Loglan predicates; see Brown (1969b, Ch.9) reprinted in TL1:101-9.
47 Linguists will recognize in this tagging system a means of translating the sentences of any natural language into Loglan in unaltered order. By tagging them, the elements in the source sentence may be kept in their original order no matter what the order type of the source language is. For example, specimen (15) might translate a sentence from a VSO language ("Verb-Subject-Object"); specimen (13), a sentence from an SOV language; while specimen (10) is in fact a translation from our own SVO language. Loglan-normal word order is SVO as well, of course, because that order is the normal (unmarked) order in the languages spoken by 83% of Loglan's "source population", i.e., 83% of the speakers of the eight most populous languages of the world; see Brown (1969b), Ch.6, The Word-Order Problem, reprinted in TL1:54-61. Still, it is important to note that once again Loglan's pervasive optionality makes departure from these statistical norms quite easy. Loglan may be spoken in either of the other two standard word orders, VSO or SOV, if one chooses...in fact, in any of the three abnormal orders OVS, VOS and OSV (in which the object precedes the subject) as well. Again Loglan has made an important, and this time highly variable, feature of the natural languages plainly imitable; and it has done this without departing from our rule of keeping the weight of the disambiguation burden on the Loglan listener at precisely zero.
48 The Loglan case system was developed during the years 1984-87 and announced in Brown (1987). Developmental studies were performed during those years by a visiting Latinist, who wishes to remain anonymous, by my daughter, Jennifer Fuller Brown, and by myself. With optional cases we hope to be able to test Fillmore's (1968) theory on the naturalness of case, as well as to solve certain practical problems of everyday Loglan speech that have arisen since 1975...problems which in a small way tend to confirm Fillmore's theory. But obviously more systematic observations are required.
49 We predict that this will be true in Loglan as well. This is because the negative clause of the noa-sentence will have gone past by the time the infixed noa (no + a) appears. So the listener must go back over the clause da has just heard as a positive one in order to re-understand it as negated. In anoi-sentences the clause to be negated still lies ahead when the no-bearing connective appears, so no back-parsing is required. This observation is due to John Parks-Clifford (personal communication).
50 I suspect that this is true in English as well. But as English usage alternates rather less decisively between what I am calling "marked" and "unmarked" connected forms, it is difficult to be sure what unmarked strings of English connectives mean.
51 The system of marked connectives described in this and earlier sections differs from the 1975 system in ways proposed by John Parks-Clifford in (1980:59-62).
52 It will probably be clear by this time that I am using the notion of sameness of claim in the logician's sense of having the same truth-values under all imaginable circumstances. Thus any given claim may be expressed in many ways; but however it is expressed, the truth-values of any pair of those ways will remain the same under any given set of circumstances, and this will be true of all of its expressions under all sets of circumstances. So construed, sameness of claim is obviously not the same as sameness of meaning; nor is it a condition that we yet know how to measure empirically. Unfortunately linguists have so far not developed behavioral criteria by which to assess either of these matters. So we are as yet confined to the analytic methods of philosophers if we are to talk about what a sentence claims at all. Most linguists, of course, choose the Draconian horn of this dilemma and banish the topic altogether. There is, however, no escaping the problem of what a sentence "claims" if we are to talk about what happens to meaning under the transformations generally called logical.
53 In fact they must be exported before any implicit quantifiers may be made explicit; see Sections 5.24 and 5.25 on quantified and negative sentences.
54 Sentences with non-designative arguments may be converted if and only if all such arguments are of the same type (all universal or all existential) and sign (all positive or all negative).
55 This is a special case of the "rule of reversal" given in Section 5.25. By that rule, if a sentence contains no non-designating arguments, the signs of both the sentence and its predicate may be simultaneously reversed. Thus a positive sentence with a negative predicate may be transformed into a negative sentence with a positive predicate; and this is exportation.