(Return to the Table of Contents)

Chapter 3
GRAMMAR 1: PREDICATES

3.1
What Grammar Is 111
3.2
The Divisions of the Grammar 112
3.3
The Simple Predicate 113
3.4
Varieties of Predicates 115
3.5
On the Metaphysics of Predicates 116
3.6
The Simple Tenses pa, na fa 117
3.7
Location with vi va vu 119
3.8
Conversion with nu fu ju 120
3.9
Negation with no 125
3.10
Abstraction with po pu zo 126
3.11
Metaphor: The Modifier-Modified Relationship 129
3.12
Grouped Modifiers with ge 132
3.13
Inverse Modifiers with go 134
3.14
Connected Predicates with e a o u noa 137
3.15
Mixed Predicates with ze 140
3.16
Internally Connected Predicates with ce ca co cu noca 142
3.17
Extending Scope with ci cui 145
3.18
Internally Mixed Predicates with ze 151
3.19
Forethought Connections with ka ke ko ku kanoi 152
3.20
Metaphor and Insight 156

Notes 159

3.1 What Grammar Is

Grammar is the art of stringing words together in understandable ways. You have spoken grammatically, in any language, when your hearers have understood what you said. Thus a grammar is not a collection of rules for speaking elegantly, or correctly, or even sensibly. For much that is nonsense is understandable, and what people usually mean by "incorrect" speech is simply unfashionable. Thus 'Ain't that man coming?' is grammatical in English simply because it is regularly produced in several dialects of that language, and understood in all of them. 'Coming ain't man that' is ungrammatical in every English dialect because it is unfathomable. And this, in turn, is true because there are no rules by which such a string of words can be formed in any English dialect. As a consequence no listener can guess how it was formed, and this is a large part of what understanding really is. We are therefore concerned, in this chapter, not with how people will talk sensibly in Loglan but with how they will talk at all in it; that is, with the rules they will use, or might use, to say anything at all.

Now construed in this modern, scientific way it is clear that the domain of grammatical sentences in any language must be very, very large. For grammars must not only account for what is in fact said in a language, or is likely to be said, but for what might be said under any circumstances at all. Do green ideas sleep furiously?1 Who knows? Is it possible to say that they do? Of course. But is it grammatical to say so? Again, of course. For grammar is the art of the possible. Like language itself it is not exclusively, nor even primarily, concerned with what is.2

The number of rules in Loglan grammar is about 200. If this seems large, it will interest you to know that linguists have devised about 6,000 rules to deal with a very small part of written English. One guesses that they have at least as many more to go. Loglan, then, is reasonably small as human grammars go; yet the domain of its grammatical utterances is very large. Therefore we cannot hope to discuss every possible kind of Loglan utterance in this book, or even all the 200-odd rules that define their domain. A complete list of those rules is given in Loglan 6: Formal Structures, where they are given in a form suitable for writing instructions to machines. Our purpose in this book is a different one, however. It is to explore the possible effects of the human uses of the language on the mind. So only the most instructive of the immense variety of grammatical utterances are discussed informally in this chapter and in Chapters 4 and 5.

In this chapter and the next two, then, we will try to exhibit not the whole grammar of Loglan but the essential part of it. And we will discuss that part in a way designed to increase not your mastery of the grammar but your understanding of it as a whole. In particular we would like to show you why Loglan has the kind of grammatical arrangements it does have, and how these arrangements are related--or may be thought to be related--to the processes of thinking which are our main concern.

3.2 The Divisions of the Grammar

We will divide our discussion of Loglan grammar into three parts, taking up the first part in the rest of this chapter, and assigning the next two chapters to the others. In the first of these parts, we will deal with the fundamental notion of Loglan grammar: the idea of the predicate and its most important elaborations. In doing this, we will keep the designative apparatus of the language very simple: we will use only pronouns to refer to things.

In the second part of our grammatical discussion (Chapter 4) we will describe the variety of ways in which things can be designated in Loglan. We will find that all the designative apparatus of English is present here--pronouns, descriptions, the Loglan equivalent of common and proper nouns--plus a good deal more besides. One of our tasks in that chapter will be to show how the predicate constructions of this chapter are used in the machinery of description.

In the third part (Chapter 5) we will consider the varieties of sentence-forms in Loglan. In particular, we will consider how simple sentences may be combined to express logically complex ideas and how these may be strung together in discourse. Here at last we will be dealing with Loglan at that level of language with which ordinary logic deals.

I will supply either a pronunciation guide or a phonemic transcription for each numbered Loglan specimen you encounter in this book. We'll be using guides for the shorter specimens in the first third of this chapter, then transcriptions for the occasionally longer specimens thereafter. You will learn the language faster if you pronounce each specimen as you come to it and listen carefully to the sound of your own voice. If you do this, you will be supplying yourself with the audible stimuli that are indispensible for sutori (second and subsequent) language learning. A rewarding consequence of such an effort will be that you will hear ever more competent Loglan speech emerging from your mouth each day. As you listen to your own Loglan speech, and then compare what you hear with the "good Loglan" described in the guides and transcriptions, you will find that the difference between them is growing less and less. It's for this reason that I've put the guides after the specimens. Remember that you know all the sounds of Loglan before you begin. They are are just arranged in new patterns and have new associations. And the best way to learn those new patterns is to listen to yourself producing them.

3.3 The Simple Predicate

In the previous chapter you learned that the great bulk of the Loglan vocabulary is composed of its predicate words, and that predicate words in Loglan correspond to the nouns, verbs, adjectives and many of the adverbs and prepositions of English. It is not surprising, then, that the fundamental constructions of Loglan grammar concern the use of predicate words. Let us look at the sentences below:

(1)Da mrenu He is a man.
[dah-MREH-noo]
(2)Da blanu It is blue.
[dah-BLAH-noo]
(3)Da madzo de She makes it (i.e., is a maker of it).
[dah-MAHD-zoh-deh]

It is as if we said in a kind of Pidgin English 'He man', 'It blue' and 'She make it'.3 The Loglan words mrenu, blanu and madzo are, of course, predicates. The little word da means 'he', 'she', 'it', 'they' or 'them', or simply 'X' as in the language of mathematics. In the third sentence, de appears. It too means either 'he', 'she', 'it', 'they' or 'them', or simply 'Y'.4

The important thing to notice is that the meaning of the predicate words in these sentences evidently includes the English notion of a verb. It is now apparent that mrenu and blanu do not really mean just 'man' and 'blue' as we have loosely said, but the whole expressions '...is a man' and '...is blue'. Moreover the word madzo means not only the verb 'to make', it may apparently also mean the whole phrase '...is a maker of...'. In fact, madzo and blanu mean more than that, for look at these sentences:

(4)Da madzo de di X makes Y out of Z.
[dah-MAHD-zoh-deh-dee]
(5)Da blanu de X is bluer than Y.
[dah-BLAH-noo-deh]

If now we are to believe that madzo means '...makes...out of...', and that blanu means '...is bluer than...', as well as the simpler phrase '...is blue', then it is clear that Loglan predicate words mean a great deal more than the individual English nouns, verbs and adjectives with which you will be tempted to equate them. They do. They mean whole sentences. More precisely, they have the meanings of sentences with blanks in them.

This is the fundamental notion of Loglan grammar. Each predicate word or construction represents a potential claim about the world. And it is that whole claim--or the longest of the several claims that might be made with it--that is the meaning of that predicate.5 Thus, the whole meaning of the Loglan word madzo is, in English, '...makes or is a maker of...out of material...'. That's a lot to pack into one word.

Now the devices that fill the blanks in a predicate expression are known as the arguments of that predicate. The word 'argument' is adopted from mathematics, where it means whatever appears between the parentheses of some functional expression. Thus 'x' is the argument of the function 'f(...)' in the expression 'f(x)'. (The parallel between the mathematical function and the Loglan predicate will probably be clear.) The arguments of a predicate designate the persons, objects, or things of which the predicate is claimed to be true. Thus in (4), above, the pronouns da, de and di are the arguments of the predicate expression ...madzo... ... . They are the designations of the three things the sentence is about: a maker X, a made thing Y, and a material Z. The two arguments of the predicate ...blanu... in (5) above are da and de. Clearly they must refer to a bluer thing X and a less blue thing Y if the claim of the sentence is to be true.

Now no one is obliged to say all that he might say every time he speaks. Thus:

(6)Da blanu X is bluer than. (I.e., X is bluer than something...probably some standard patch of blue.)
[dah-BLAH-noo]
(7)Da madzo X is a maker of. (I.e., X makes something from something.)
[dah-MAHD-zoh]
(8)Da madzo de X is maker of Y from. (I.e., X makes Y from something.)
[dah-MAHD-zoh-deh]

are all perfectly permissible, if incomplete, claims. They are called incomplete utterances in Loglan; for in Loglan, unlike English, they are obviously incomplete. People do not say 'It is bluer than' and stop in English. If they did, they would sense what the Loglan speaker means when he says Da blanu. Thus the Loglan forms invite completion, and questions about completion, in open and obvious ways. We can easily imagine the sense of the incompleteness of most ordinary human speech becoming a very powerful aid to the Loglan-user when interacting with machines.

We now see that all by itself, and without inflection or adornment, the Loglan predicate word carries a great deal more specific meaning than the usual natural language word. This accounts for the fundamental simplicity of Loglan grammar, but also for its genuine difficulty for the newcomer. For simple (atomic) sentences do not really have to be "constructed" in Loglan. They already exist in the specific claims embodied in its host of predicate words.6

3.4 Varieties of Predicates

It will be clear from the foregoing that predicates may be classified by considering the largest number of arguments they may take. Thus mrenu takes one argument and never more than one;7 blanu takes either one or two arguments, but never more than two; and so on. We will call predicates that take exactly one argument one-place predicates. Predicates which, like blanu, take at most two arguments, will be called two-place predicates. Among the predicates which take at most three arguments, are of course, madzo, but also words like godzi ('...goes to...from...'), corta ('...is shorter than...by amount...') and, even more surprisingly, matma ('...is the mother of...by father...'). For a predicate may take as many arguments as it needs to make its meaning clear. Finally, there are a few four- and five-place predicates. The word vedma ('...sells... to...for price...') is one of these. There are no six- or higher-place predicates presently defined in the language, although certainly there could be.8

One-place predicates express categorical ideas, or the properties of things viewed in isolation. Many English nouns ('book', 'monkey', 'hammer'), a few English adjectives ('perfect', 'complete') and some intransitive verbs ('sleep', 'sneeze') express categorical ideas in that language. There are relatively few of these one-place predicates in Loglan, because few things are viewed in isolation in that language. Thus two-, three- and four-place predicates are much more common in Loglan, for they express the relations by which things are connected to other things: mothers, children and fathers; travelers, destinations and points of departure; parts and wholes; talkers and the people and things they talk to and about; shorter things and longer things and the amounts by which they differ; seers, seen things, and the backgrounds against which they are seen; and so on. Since Loglan abounds in relational predicates of this kind, it might well be called a relational language. But not because there are in fact more relational ideas in Loglan than in other languages, for probably there are not; but because it is much more obvious in Loglan than in other languages when its predicate ideas are relational. For Loglan grammar makes all its relational notions very plain where the grammatical arrangements of many other languages tend to obscure the relational character of their ideas.9

3.5 On the Metaphysics of Predicates

Now you have probably sensed that a vast simplification of language is achieved by this device. If predicates express both properties and relations, then there is hardly anything in language that cannot be said by means of predicates, for relations and properties are all we usually talk about. Thus the claim of the English transitive verb ('John hit Pete') is always a relation; of intransitive verbs ('John sneezed'), a simple if short-lived property. The claim of most English prepositions is either a relation ('John is in the house') or part of a more complex relation ('John went into the house'). We have seen that the claims made with English nouns and adjectives are either properties ('That was perfect') or relations ('John is the father of Jack'); and so on. If Loglan predicates do all this work in Loglan, then what is there left to talk about?

Actually, quite a lot. For while Loglan is simple in just these content words where the natural languages are complex, Loglan is complex in its handling of little words where natural languages are still rather rudimentary. The point is, it can afford to be. For with the great savings which are achieved in Loglan by regarding each predicate word as a potential sentence--and this is the idea of the propositional function which is the great achievement of modern logic--we can now elaborate the logical functions of the language far beyond their natural limits. In effect, we have simplified the content-handling machinery of language in order to elaborate its machinery for handling thought. But to do this we have paid a price, or rather we have arranged for you to pay one. For if you learn the language you will find that while the mechanics of the predicate grammar are very simple for your tongue to master, its metaphysics are not easy for the mind. For your mind, gentle reader, has almost certainly been shaped by an Indo-European language. It is therefore admirably equipped to deal with a world of enduring objects (nouns), of actions and processes (verbs), of permanent qualities (adjectives), of transitory qualities (one kind of adverb), and of qualities of qualities (another kind of adverb); and it is just this partition of the world you will miss in speaking Loglan. Your world is a time-bound world; it makes its fundamental distinctions on the basis of permanence or change. The world you will gradually come to see in speaking Loglan is time-free; for its fundamental notions contain no hint of time. Your world has hard, categorical boundaries between one thing-class and another; in the Loglan world the classifying qualities of things are more softly viewed. Your world is a world of separate objects; the things of the Loglan world are caught up in a web of relations. In short, the world of Loglan is just that time-free world of continuous qualities and things-in-relation that science has taught us to expect to find under the appearances we see. Perhaps if it helps us see that world a little more directly, it will have been worth the price of these wrenches to our minds.

3.6 The Simple Tenses pa na fa

We have said that the Loglan world is time-free because its fundamental notion--the unadorned predicate--contains no hint of time. But time and events in time must obviously be accommodated. This is simply done. We can now adorn the predicate with the optional apparatus of tense. To begin with, we need only three little words: pa, na and fa. Look at the following sentences:

(1)Da pa madzo de X made Y.

[dah-pah-MAHD-zoh-deh]

(2)Da fa godzi de X will go to Y.

[dah-fah-GOHD-zee-deh]

(3)Da na blanu X is now blue.

[dah-nah-BLAH-noo]

(4)Da pa mrenu X was a man.

[dah-pah-MREH-noo]

(5)Da fa fumna X will be a woman.

[dah-fah-FOOM-nah]

What could be simpler? Every Loglan predicate may be "inflected" in this way; but no predicate needs to be. Thus, the tense machinery of Loglan is strictly optional. You use it when you are concerned with time; you don't when you are not.10

The optional character of the Loglan tenses permits the direct expression of many things that are hidden in certain arbitrary-seeming usage-patterns of the natural languages. In English there is no "time-less" tense. But we need one; therefore we make one up. We use the present tense of verbs like 'swim', 'dance' or 'fly' and expect our listeners to know when we say 'He swims', 'She dances well', and 'John flies to New York' that we do not mean these remarks literally. For when we use the so-called "present" tense in these sentences we do not intend to claim that he is swimming now, or that she is dancing now, or that John is flying now, but only that he can swim, she can dance well, and that John does fly to New York when he goes there at all. We expect--and get--the cooperation of the listener in these non-literal uses of the English present tense because we need a time-free tense in English and do not have one.11 Loglan has one. Therefore in speaking Loglan you can mean what you say. The difference between the following sentences

(6)Da sucmi X swims (i.e., is a swimmer).

[dah-SOOSH-mee]

(7)Da na sucmi X is swimming (i.e., is now swimming).

[dah-nah-SOOSH-mee]

is just what it seems to be. In the first we are imputing a certain time-free property to X, namely that he can swim if you let him. He is a swimmer. In the second we are asserting that he is exhibiting that property right now. He is swimming.

Note that English usage requires the little verb 'can' to express the time-free sense of its verbs unequivocally. The suffix '-able' also communicates this notion. Thus, problems are solvable, people are lovable, substances are flammable, and so on. In Loglan we assert these properties nakedly and directly; for they are just what the naked predicate is about. Thus, the difference between

(8)Da cabro X burns (i.e., is flammable).

[dah-SHAH-broh]

(9)Da fa cabro X will burn (i.e., will actually burst into flames).

[dah-fah-SHAH-broh]

is again just the difference between the assertion of a time-free property and the prediction of a future event.12 Thus if (9) is to be true, the event of X's burning must actually occur. We now see that Loglan really has four simple tenses; they are formed by putting pa, na, fa or nothing at all in front of any predicate word.13

There are also some compound tenses in Loglan but these are straightforward elaborations of the simple tenses and need not concern us here. Lists of these more complex time-binding operations will be found in Loglan 6 under Lexeme PA.14 We may remark in passing that all European tenses--and some extra ones besides--are easily accommodated in the complete Loglan tense system.

3.7 Location with vi va vu

Words which locate predicated things or events in relation to the speaker--words like 'here', 'there' and 'far away' in English, which are vi va vu in Loglan--are often used in inflecting position in Loglan, that is, like tense operators. Thus

(1)Da vi madzo de X here makes Y.

[dah-vee-MAHD-zoh-deh]

(2)Da fa va cabro X will there burn.

[dah-fah-vah-SHAHB-roh]

(3)Da vu fa vedma X away will sell.

[dah-voo-fah-VED-mah]

are quite normal forms in Loglan. But there are both other positions and other uses of tense and location words in Loglan which we will consider in Chapter 5 on sentence forms.

Just as there are compound tenses so there are compound location operators in Loglan. An account of these is also given under Lexeme PA in Loglan 6. Grammatically speaking, location operators are indistinguishable from tense operators in Loglan. Where no difference is required grammatically, no distinction is drawn. This principle of grammatical parsimony has been a general rule in the construction of Loglan grammar.

3.8 Conversion with nu fu ju

Putting a tense or location word before a predicate is called an operation; and the words that accomplish the operations of Loglan grammar are called its operators. Several operations may be performed on Loglan predicates. The one that we will consider now is called conversion. Look at the following sentences:

(1)Da pa bloda de X hit Y.

[dah-pah-BLOH-dah-deh]

(2)De pa nu bloda da Y was hit by X.

[deh-pah-noo-BLOH-dah-dah]

(3)Da cluva de X loves Y.

[dah-SHLOO-vah-deh]

(4)De nu cluva da Y is loved by X.

[deh-noo-SHLOO-vah-dah]

In sentences (2) and (4) the meanings of the predicates bloda and cluva have been converted into what we call, in English, the "passive voice". But notice that all we have really done is exchanged the meanings of the first and second places of these predicates. Thus 'X loves Y' and 'Y is loved by X' make exactly the same claim about X and Y. All that has happened is that the order of the places in the predicate expression has been changed. The operator '...-ed by' serves notice of this rearrangement in English. The operator nu serves the same function in Loglan.

But the little word nu exchanges the meanings of the first and second places of any Loglan predicate. This includes those with adjectival and noun-like meanings as well as those that behave like verbs. Thus

(5)Da nu blanu de X is less blue than Y.

[dah-noo-BLAH-noo-deh]

(6)Da nu matma de X is an offspring of mother Y.

[dah-noo-MAHT-mah-deh]

are also permissible forms. Thus it will not do to think of conversion as simply the Loglan version of the "passive voice." Any predicate having at least two places can have those places exchanged by the operation with nu. Thus madzo and vedma are three- and four-place predicates respectively, but they too can be converted with nu:

(7)Da pa nu madzo de X was made by Y.
[dah-pah-noo-MAHD-zoh-deh]
(8)Da fa nu madzo de di X will be made by Y from Z.
[dah-fah-noo-MAHD-zoh-deh-dee]
(9)Da pa nu vedma de di X was sold by Y to Z.
[dah-pah-noo-VED-mah-deh-dee]
(10)Da na nu vedma X is now being sold.
[dah-nah-noo-VED-mah]

Notice that the nu-conversion does not disturb the meaning of the third (or higher) places of such predicates. Thus, in (8) di is still the material, and in (9) di is still the buyer. For all nu does is switch the meanings of the first and second arguments. Notice also that incomplete forms of converse predicates, as in (10), are just as sayable as the incomplete forms of normal ones.

Notice also that the word nu, as in pa nu vedma, comes between the tense operator and the predicate word. This is because the operation of conversion may only be performed upon the naked predicate; it should not be applied to the tensed one. It is therefore this converse predicate (nu vedma) that is then tensed (pa nu vedma). English word-order expresses this same conception. Thus, in translating 'X was sold' by Da pa nu vedma, the word pa performs some of the offices of English 'was' and the converse form nu vedma has approximately the sense of the past participle 'sold'. But note that the separation of these two operations is not so neat in English.

In exactly the same way the operators fu, and ju work to bring third-, and fourth-place arguments into the first-place of predicates of higher form. Thus in

(11)Da fa fu madzo de di From X will be made Y by Z.
[dah-fah-foo-MAHD-zoh-deh-dee]

the positions of the material X and the maker Z have been exchanged. So it is the position of the made-thing Y that is now unchanged. In normal form this same claim would be Di fa madzo de da ('Z will make Y from X'). Note that the made-thing Y is in second place in both forms. Again, in

(12)Da pa fu vedma de di do X was sold Y by Z for price H (i.e., X bought Y from Z for H).
[dah-pah-foo-VED-mah-deh-dee-doh]

it is the first and third places which are exchanged. Should we wish to bring the fourth arguments of longer predicates into first place, the little word ju exists to make such conversions. For example:

(13)Da pa ju vedma de di do X was the price of Y to (buyer) Z from (seller) H.
[dah-pah-zhoo-VED-mah-deh-dee-doh]

Should fifth and higher higher places of extremely long predicates be required, then a subscripting system is repaired to. Thus nufe will exchange the first and fifth places of any predicate long enough to have one:

(14)Da pa nufe ketpi de di do du X was the accommodation for travel to Y from Z on carrier H secured by ticket Q.
[dah-pah-noo-feh-KET-pee-deh-dee-doh-DOO]

In this way, the price and the accommodation (seat, cabin, berth, etc.) implicit in the predicates 'sell' and 'ticket', respectively, have been brought into first place.15 In the ju-and nufe-conversions the second- and third-place meanings remain unchanged.16

Now these are complicated notions, in any language. But what is complicated about them is their derivation, not their uses once derived. Thus the Loglan speaker will almost certainly regard ju vedma as a distinct predicate meaning '(is the) price (of some merchandise)', and not just a variant of the predicate meaning 'sell'. We may so regard it, for we are interested in examining the structure of the language. But it may be that to the practiced speaker of Loglan the predicate expressions ju vedma and vedma will seem about as closely related--or as distantly--as 'vocal' and 'vocation' are in English. In any case, he or she will almost certainly regard them as distinct ideas, each with a pattern of uses to be mastered separately. He will certainly not contrive the uses of one from what he knows about the other by "transformations" performed in the course of speech.17

But returning to our structural examination, we now see that the chief practical function of the conversion operation is not to switch meanings around in the complete forms we have been considering, but to bring higher order arguments into prominence in incomplete forms. Here are some examples:

(15)Da pa ju vedma X was a price (of some sold object).
[dah-pah-zhoo-VED-mah]
(16)Da fa fu madzo X will be a material (from which something will be made).
[dah-fah-foo-MAHD-zoh]
(17)Da na nu godzi X is now a destination (a place now being gone to by some unspecified goer).
[dah-nah-noo-GOHD-zee]
(18)Da nu blanu X is less blue (than something else).
[dah-noo-BLAH-noo]
(19)Da nu cluva X is lovable.
[dah-noo-SHLOO-vah]

If the last translation startles you, reflect on this (in a Loglan way): Da cluva de means 'X loves Y'. To say Da cluva (incompletely) must therefore mean that X loves someone or something in a time-free sense--in short, X can love; he or she is a lover. But Da nu cluva de means 'X is loved by Y' in a timeless sense. Whence Da nu cluva must mean--again incompletely--that X is a beloved. That is, he, she or it can evidently be loved; whence X is lovable. Thus we encounter the time-free sense of the Loglan predicate in converse as well as normal form. Here are some other examples of converse potentialities:

(20)Da nu madzo X is makable (i.e., can be made).
[dah-noo-MAHD-zoh]
(21)Da fu ditca X is teachable (i.e., can be taught something).
[dah-foo-DEET-shah]

The complete form of the predicate ditca means '...teaches...to...'; whence the teachable person or animal is normally designated in the third place, thus requiring the fu-conversion. But now notice:

(22)Da nu ditca X is a teachable (i.e., a teach-
able topic or subject).
[dah-noo-DEET-shah]
(23)Da nu titci X is edible (i.e., can be eaten).
[dah-noo-TEET-shee]

Thus titci must be at least in part a two-place predicate meaning '...eats...'. But note that 'X is eaten' and 'X is taught' are not good translations of (23) and (22). These English expressions involve the hint of time; they seem to suggest that the eating and teaching did in fact take place. This is contrary to the spirit of Loglan. For in Loglan the fundamental thing about an object is not whether it has been eaten or taught, but whether it is the kind of thing that can be eaten or taught.

This is a troublesome notion to the English mind. But it can perhaps be clarified by the following example: If I show you a drawing of a tool that has never been made but which I believe can be made, I will impute that property to it in Loglan with the grammatically simple claim Da nu madzo; and I will sense, as I am saying it, that what I have said about this still imaginary thing is somehow more fundamental than the more elaborate claim I might make about it tomorrow, when it has been made. Thus the tensed Loglan form Da pa nu madzo feels more elaborate to me because it is more elaborate, grammatically. The untensed form Da nu madzo feels more fundamental because it is more fundamental, again grammatically. For in Loglan the direction of grammatical simplicity is nearly always the direction of observational simplicity. If something has in fact been burned it must have been burnable; the second state precedes the other observationally. But many burnable things exist which have never been, and will never be, actually burned. In English the direction of grammatical simplicity goes the other way. 'Burnable' is a more elaborate word than 'burned'. Yet you probably now agree that being burnable is a simpler state than being burned. Just so with 'made' and 'makable', 'loved' and 'lovable', and every other property of this still-potential world. Again we see how European grammars are more complicated than they would otherwise need to be by their metaphysical commitment to the idea of time.

3.9 Negation with no

The little word no is called the negative operator in Loglan and is used in a wide variety of ways. Some of these ways will not concern us until we consider negative arguments and sentences in Chapters 4 and 5. For the present, we are only concerned with the ways in which the negation of predicates can be arranged.

There are two such ways. One is when no precedes a tense operator, as in sentences (1) and (2); the other is when it precedes a predicate, as in sentence (3). When no precedes the tense word, as in

(1)Da no pa gudbi mrenu18 X was not a good man.
[dah-noh-pah-GOOD-bee-MREH-noo]

([GOOD] rhymes with 'food', not 'good') and

(2)Da no fa bakso madzo X is not going to be a box-maker.
[dah-noh-fah-BAHK-soh-MAHD-zoh]

it has the effect of negating the whole predicate expression. Thus the claim of (1) is consistent with X's having been a bad woman, or a good butterfly, for that matter, for it is the whole predicate expression pa gudbi mrenu that has been contradicted by no. At any rate, sentence (1) does not mean, as its translation sometimes does in English, that X was a man but not a good one. To say the latter in Loglan, we shift the negative operator to a position immediately before the particular predicate word it is intended to negate. Thus:

(3)Da pa no gudbi mrenu X was a non-good man.
[dah-pah-noh-GOOD-bee-MREH-noo]
(4)Da fa no bakso madzo X will be a non-box maker (i.e., a maker of something other than boxes).
[dah-fah-noh-BAHK-soh-MAHD-zoh]

Here no has the exact sense of English 'non-'. Thus in (4) X is going to make something alright, but not boxes. And in (3) X was a man alright, but not a good one. Precise distinctions of this kind can be clearly made in English--for witness these translations--but it is not the custom of English speakers to do so. Instead, the difference between the meanings of (2) and (4) is usually suggested in spoken English by a shift in stress:

(5)Da no fa bakso madzo X is not going to be a box-maker.
[dah-noh-fah-BAHK-soh-MAHD-zoh]
(6)Da fa no bakso madzo X is not going to be a box-maker.
[dah-fah-noh-BAHK-soh-MAHD-zoh]

In Loglan such logical distinctions are important enough to deserve distinct grammatical arrangements. These will function equally well in both the written and the spoken forms.

The pronunciation guides are now probably supplying you with more phonetic information than you need. So from this point on I shall supply phonemic transcriptions of the numbered specimens instead of phonetic guides--that is, I shall use /e/ rather than [eh] or [eigh], and /da MREnu/ rather than [dah MREH-noo] to show the production of the sentence Da mrenu--and use the guide form only to give the pronunciations of new words as they are introduced. Transcriptions, you will see, are often more compact than the specimens themselves. More important, they will concentrate your attention on the stress- pause contour of the sentence as a whole. It is now time to do this. But you may wish to refer back occasionally to Chapter 2 to assure yourself of the correct pronunciation of an old sound in a new context.

3.10 Abstraction with po pu zo

Abstraction is one of the most powerful devices in natural language. The step from 'red' to 'redness' must have been one of the most important linguistic advances ever made...perhaps as important as the invention of negation. Yet abstraction is logically one of the more obscure linguistic acts. Where are the things created by it, such things as Virtue, Perfection and Democracy? Or, for that matter, where is the color Red? It is hard to know what one is talking about when one uses such words. Yet to be able to see the world in terms of just such properties as "redness," "length" and "mass"--and not merely as endless collections of "red things," "long things" and "massive things"--must have been one of the linguistic requirements for the development of science itself. It is hard to see how a taste for causal analysis could have developed in minds surrounded wholly by concrete particular things. Perhaps it was; we do not know. Science did develop extensively in the hands of the Greeks, and Greek is abundantly furnished with the machinery for talking about abstract ideas. But so were other ancient tongues, for example, Sanskrit, and the ancient Hindus did not raise the questions that led the Greeks to science. In short, language may supply the necessary conditions of cultural events, but the linguistic factor is certainly never sufficient to guarantee some cultural result.

However this may be, it is clear that if Loglan is to be, among other things, a language for contemporary scientific thinking, we must provide it with the apparatus of abstraction. In English that apparatus exists but is most irregular. There is a group of suffixes--like '-ion', '-ship', '-ness', '-ence', '-hood', '-acy', and '-ity'--that sometimes mean properties and sometimes mean states of affairs; and then there are some special words like 'vice', 'wit', 'force', 'mass' and 'evil' that are abstract but show no outward signs of it. One "knows" they are abstractions only by "knowing" that they...well, refer to abstract things. Obviously we must do better than that.

Analysis shows that at least three kinds of abstraction occur in ordinary speech. One is the abstraction of properties ('Honesty is a common trait among Englishmen', 'Mass is an important concept to physicists', and so on). Another is the abstraction of events or states of affairs ('The race was short', 'His childhood was unusually long', 'The singing took place between 8:00 and 8:30', and so on). And the third and currently the rarest form of abstraction is the one which forms the quantitative sense of some predicates ('There is more blue in that picture than in this one', 'His love was greater than hers', 'There were thirteen inches of snow', and so on). There may be other varieties of abstraction in current use and still others may yet be invented. If so, Loglan can easily accommodate them. But at the moment only three abstract operators have been coined. These are pu, which means 'is a property of being (something)', po, which means 'is an event, state or condition of being (something)', and zo, which means 'is an amount of being (something)'. The three operators are used in grammatically identical ways. In translating English, the event operator po will be most commonly used. It may be that translations from other languages will reveal quite different patterns of abstract thought.

Let us look at the following sentences:

(1)Da po mrenu X is a manhood.

/dapoMREnu/

(2)Da po de mrenu X is Y's manhood (i.e., the state of Y's being a man).

/dapodeMREnu/

(3)Da pu gudbi X is a goodness (i.e., a property of something's being good).

/dapuGUDbi/

(4)Da pu de gudbi di X is a/the property of Y's being better than Z.

/dapudeGUDbiDI/

(5)Da zo blanu X is an amount of blue.

/dazoBLAnu/

(6)Da zo de blanu X is the amount of blue in Y (i.e., the amount of Y's being blue).

/dazodeBLAnu/

In each of the odd-numbered sentences an abstract operator is used generally. That is, it generates a predicate expression (po mrenu, pu gudbi, zo blanu) that might be applied to many things. Thus, there are at least as many manhoods as there are men, at least as many goodnesses as good things, and so on. But in the even-numbered sentences the field of application of the predicate has been much narrowed. For the predicate which is the basis of the abstraction has been furnished in each case with one or more arguments. In sentence (4), for example, the operator pu transforms the whole expression pu de gudbi di into a predicate of which da is the first and only argument. Within this predicate expression de and di are the first and second arguments of the predicate gudbi.

We sense that such specified abstract predicates apply to unique things. Of course they may not. In (2) Y may have been a man several times and may thus have had several manhoods; in (4) Y may be better than Z in several ways; and so on. But these are matters of fact, not grammar. Grammatically the predicate expression po de mrenu is a general term; like mrenu itself it may in principle be applied to many things.

We will see in the chapter on arguments how these general abstract notions can be turned into unique designations; how, for example we can translate the English word 'virtue' in 'Virtue is nice'. Obviously the word 'virtue' is some kind of unique designation in this context; but we have clearly not provided for it yet. For we are still talking about predicates, and hence about the claims people make about the world. We have not considered yet how speakers designate the things about which they make those claims. Yet it is true in English at least that the chief use of abstract predicates is in designation. Thus the Loglan names of "Liberty, Equality and Fraternity" have not been constructed yet. We will see, however, in the next chapter how their construction depends essentially on the abstract forms of predicates which we are now considering.19

Before we leave abstract predicates, there is one feature of event-abstraction which needs pointing out. That is that Loglan makes no distinction between short events (happenings) and long ones (states of affairs). Thus the following sentences,

(7)Da po tsani X is a sneeze (i.e., an act of sneezing).

/dapoTSAni/20

(8)Da po mrenu X is a manhood (i.e., a state or condition of being a man).

/dapoMREnu/

are grammatically identical; both are formed with the event-operator po. In Loglan both sneezes and manhoods are events. And a thing X is an event of sneezing, or a manhood, provided it is an interval of space-time in which, or during which, some other thing Y sneezes or is a man. Obviously it cannot matter logically how long Y sneezes, or how short a time he is a man. Again it is worth recalling that neither grammar nor logic is concerned with what is, but only with what might be. Can we say that his sneeze was longer than his manhood? Of course we can. It would be wrong to contrive a grammar which precluded such nonsense, or such irony.

3.11 Metaphor: The Modifier-Modified Relationship

The simplest of operations on the predicate involves no operator at all. Yet it is logically one of the most complicated, and historically, the most important, for it is undoubtedly the major source of language growth. This operation is the one by which a speaker may modify the meaning of one predicate simply by preceding it with another. Thus the meanings of the predicates in the following sentences:

(1)Da corta mrenu X is a short man.

/daCORtaMREnu/

(2)Da gudbi matma X is a good mother.

/daGUDbiMATma/

(3)Da blanu hasfa X is a blue house.

/daBLAnuHASfa/

are as easily interpreted in Loglan as they are in English. Note that the modifier precedes the modified word. This is the most widespread arrangement among the natural languages,21 and therefore we have followed it. In Loglan this order is uniform: it is the order of adjective-like words modifying noun-like ones, and of adverbial ones modifying verb-like or adjective-like predicates. Thus even when the modifier is adverbial in the English sense, the modifying word comes first in Loglan:

(4)Da kukra prano X runs quickly (is a fast runner).

/daKUKraPRAno/

(5)Da bilti sucmi X swims beautifully (i.e., is beautiful as a swimmer).

/daBILtiSUCmi/

There is a way of modifying this order that we will look at in Section 3.13. But we must now inquire more closely into the meaning of such phrases. If X is a short man, does this mean that he is short and a man? Not necessarily; for he might be fairly tall...for a woman, say, or a child. All we can surmise is that he is short for a man; that is, a short type of man. What about blue houses? And beautiful swimmers? Can we expect them to be really blue? And really beautiful? All over? Inside and out? Certainly not; for blue houses and beautiful swimmers, like short men, are blue for houses and beautiful as swimmers. That is, they are blue among houses and not among skies, and it is their swimming that is beautiful, never mind their eyes. And good mothers? Good as mothers, perhaps, but not necessarily good cooks or good wives. And so on.22

Clearly we are dealing here with metaphorical extensions of primitive ideas. We know what a mother is, and a man and a house. And we know what good, blue, beautiful and short mean, as primitive ideas. The first time we hear the metaphor 'good mother' we are in a fair position to guess what the speaker means, from our knowledge of the uses of these simple predicates in the language. But we cannot be sure. Neither--until one has seen one--can one be sure what a blue house is. How blue does a house have to be to be blue? How short is a short man? More puzzlingly, how watery is a water-pistol? How intellectual is an intellectual dwarf? And what is a bicycle pump anyway? Does it pump bicycles? Into what?

In Loglan we surmise, with most logicians, that such questions are unanswerable by direct analysis. We suppose that the meanings of predicate expressions formed of two or more constituent predicate ideas are like the meanings of simple predicates themselves: essentially unitary and unanalyzable.23 A blue house is...well, a blue house. Like houses themselves, or blue things, you have to be shown one to really know. And intellectual dwarfs? Well, here again it is not the art of logical inference, but a sense of irony that helps one to understand this phrase; that and having heard the phrase 'intellectual giant', with which it strongly contrasts. And bicycle pumps? Again, the knowledge that bicycles have pneumatic tires might help the auditor guess what this metaphor means; and so on. But we are doing more than arguing for the utility of use and custom in understanding such phrases; we should also insist that all such modifier-modified pairs are metaphors, the humblest as well as the most exotic and obscure. And that the original occasions of their use represented, at those moments, the extension of the semantic machinery of the language into regions then unknown. Red houses and short men are commonplace, now. But we suppose they were not once. Water pistols are now commonplace. But we know they were not before someone invented and then named that innocent, modern contrivance. Star-sailors are not commonplace; but the word 'astronaut' is and they may be. So language grows. New predicates arise. And we suppose that the first step in that process is the coining of fresh metaphor, and that this always involves the "misuse" of some old word.24

Let us now consider some elaborations of the modification relationship. Look at the sentence

(6)Da mutce corta mrenu X is a very short man.25

/daMUTceCORtaMREnu/

In English, 'very' is an adverb, 'short', an adjective, 'man', a noun. It is not grammatical in English to say 'X is a short very man', or 'X is a man short very'. The reason is that only adjectives modify nouns--or so we say, but nouns do, too--and if adjectives are to be modified, it takes an adverb to do so. Not so in Loglan; for look at these curious remarks:

(7)Da mutce mrenu corta X is a very man-type of short thing (?!).

/daMUTceMREnuCORta/

(8)Da corta mutce mrenu X is a shortly very man (??!!).

/daCORtaMUTceMREnu/

(9)Da corta mrenu mutce X is a shortly man-type very thing (???!!!).

/daCORtaMREnuMUTce/

All these Loglan sentences are grammatical. For any predicate can modify any other predicate in Loglan. Thus the Loglan-speaking mind is free to combine predicates in any way it likes.

We predict that this grammatical freedom in using Loglan modifiers--a freedom that derives from the simple fact that all its predicates belong to a single part of speech--will lead to a great richness of metaphor in Loglan; and that this in turn may be related to the process of insight-formation, in any language. Thus Chinese, which is more like Loglan than English in this regard, is a metaphor-rich language. English, which is burdened with a fairly restrictive set of modification rules, is by comparison metaphor-poor. In fact 'metaphor-poor' is about as flighty a metaphor as you can build in English; for in it a noun has modified an adjective! This is one of the rarer modification styles of English, but its use is probably increasing. Apparently even the European languages are tending to become more like Loglan and Chinese in their increasing freedom of metaphor.

3.12 Grouped Modifiers with ge

Despite its many restrictions, the meaning of a modified predicate is sometimes very unclear in English. A classic case is the sentence 'It's a pretty little girls' school'. What on earth does it mean? A school for pretty little girls? A school for girls who are pretty little? A pretty type of little girls' school? A pretty type of little girls' school? Take your pick. There are at least five equally legitimate grammatical interpretations of this innocent remark.26

The question behind this confusion in English is, of course, what modifies what? In English we cannot be sure.27 In Loglan we can be. For there is an operator ge [geh] which groups the modifiers in a string of modifiers in such a way that what-modifies-what is clear. Look at the following sentences: (In them the word bilti [BEEL-tee] means 'beautiful', cmalo [SHMAH-loh] means 'small', nirli [NEER-lee] means 'girl', and [SHKEH-lah] ckela means 'school'.)

(1)Da bilti cmalo ckela nirli X is a beautifully small girls' school (i.e., a school for girls who are beautifully small).

/daBILtiCMAloNIRliCKEla/

(2)Da bilti ge cmalo nirli ckela X is beautiful for a small girls' school.

/daBILtigeCMAloNIRliCKEla/

(3)Da bilti cmalo ge nirli ckela X is beautifully small for a girls' school.

/daBILtiCMAlogeNIRliCKEla/

(4)Da bilti ge cmalo ge nirli ckela X is beautiful for a small (type of) girls' school.

/daBILti.geCMAlo.geNIRliCKEla/28

In the absence of other markings of the predicate string--like go and cue which we will take up presently--the operator ge groups everything that comes after it into what may then be regarded as the modified term. Thus in (2) what bilti modifies is the whole expression cmalo nirli ckela; X is evidently beautiful for a small girls' school. In (3) bilti modifies just the word cmalo, whence X is a beautifully small something. The ge operator groups nirli ckela into the single idea which remains to be modified, and we see that that something is a girl's-school. Thus the whole claim of (3) is that X is beautifully small for a girl's-school, or slightly rephrased, a girl's-school that is beautifully small. Sentence (4) has both the groupings that occur separately in sentences (2) and (3). Thus it claims that X is a beautiful type of small type of girls'-school. Notice that the English phrase 'type of', while sometimes leading to awkward translations, is nevertheless the best all-around translator of the Loglan operator ge. If English speakers regularly used such a phrase to indicate how they meant their modifiers to be grouped, we could more often understand what they say. But they do not. And therefore what they say can often be interpreted in several equally correct ways.29 This is, of course, just the problem of syntactic ambiguity. The operator ge removes a large potential source of it from the language.

Normally the scope of ge runs to the end of the predicate string in which it appears. But sometimes a speaker needs to limit the scope of one of da's ge's. For this purpose the optional right-mark, cue, exists. In effect, cue serves as a right parenthesis that cuts off the scope of the last ge that has been spoken. Thus in

(5)Da bilti ge cmalo nirli cue ckela X is a beautiful small-girls' school (a school for beautiful small-girls).

/daBILtigeCMAloNIRli.cueCKEla/

the grouping effect of ge is limited by cue to the two words cmalo nirli, which thus form a single unit. It is as if cmalo nirli had been joined into a single hyphenated word that meant 'small-girl'. As such it is the modificand of bilti, and the whole expression bilti ge cmalo nirli cue is then the modifier of ckela. (As we shall see later, in Section 3.17, there is a hyphen-like mark that can effect this same modification structure with one stroke instead of two.)

There is one caution to be observed in using ge: it can occur meaningfully between any two predicates in a string of predicates except the last two. Thus, cmalo ge nirli ckela is good Loglan, but cmalo nirli ge ckela is not. The reason is that there is nothing left to group; the last word, ckela, is already a single idea. So while nirli ge ckela is not ungrammatical in Loglan, it is redundant. Once you understand ge you will not be tempted to use it in this way. It is like saying that something is 'a red type of house'. Of course. But isn't that exactly what a "red house" is?

3.13 Inverse Modifiers with go

In addition to grouping some of the modifiers in a string of modifiers into something that functions as a single term, it is sometimes useful to produce a normally early portion of a string of modifiers last. This is especially useful if one wants to specify an argument of one of the modifying words, or wishes to surprise one's listeners by withholding mention of an unexpected modifier until last. As an example of the first and more common usage, suppose I want to say that X is a shorter-than-Y type of man. If we start with a sentence in normal word order,

(1)Da corta mrenu X is a short man.

/daCORtaMREnu/

it is difficult to make this specification of the modifying predicate corta. (It can be done; but just as in English it is awkward to do.) So we first "invert" the predicate with go, as below:

(2)Da mrenu go corta X is a man who is short (i.e., a man of the short type).

/daMREnugoCORta/

and then specify the modifying predicate corta which is now conveniently last:

(3)Da mrenu go corta de X is a man of a type which is shorter than Y.

/daMREnugoCORtade/

In all these sentences, phrasing pauses before go are natural but optional. So we might have:

(4)Da hasfa, go blanu de X is a house of a type that is bluer than Y.

/daHASfa.goBLAnude/

When a pause is used, note that a comma appears in the corresponding text.

(5)Da prano, go kukra de X is a runner of a type who is faster than Y (i.e., X runs faster than Y).

/daPRAno.goKUKrade/

In each case, inversion with go reverses the normal modifier-modified word order; and the modifying word is then conveniently last.

Now there is a deceptive simplicity in all this, deceptive because the only short English translations we can contrive for these Loglan remarks do not quite mean what the originals do in Loglan. Consider the sentence:

(6) Da matma go gudbi de
/daMATmagoGUDbide/

The simplest English translation of this sentence is 'X is a mother who is better than Y.' But better in what? As a mother? Or in general? Of the English, one cannot be sure. Of the sense of the Loglan, we can be sure, for we know how the sentence was formed. Thus just because we know that gudbi is a displaced modifier of matma, we know that the phrase gudbi de--in this sentence at least--means 'better-as-a-mother than Y'. If we wanted to say that X is a mother and better-in-general than Y, we could easily do so. And we shall see how presently. But this is not the way.

Here are other examples of modifier strings inverted with go:

(7) Da nirli ckela go cmalo
/daNIRliCKElagoCMAlo/

What does it mean? Exactly what Da cmalo ge nirli ckela means; for it is nothing but an inverted form of the same remark. Thus (7) means exactly what we mean in English when we say that it's a girls' school that is small. From this it follows that (7) must be equivalent to

(8)Da ge nirli ckela go cmalo X is a girls' school that is small.

/dageNIRliCKElagoCMAlo/

with its redundant ge. And it is clear that it is. For (8), in turn, is equivalent in meaning to

(9)Da cmalo ge nirli ckela X is small for a girls' school.

/daCMAlogeNIRliCKEla/

as required. Good usage in Loglan requires that we not use punctuation words like ge redundantly. So we will not ordinarily speak sentences like (8) unless we want to point something out in them...as we just have. And of course we would usually use inversion on sentences like (9) only if we then wanted to specify an argument of the modifier cmalo after doing so, as in the sentence below:

(10)Da nirli ckela go cmalo de X is a girls' school of a type that is smaller than Y.

/daNIRliCKElagoCMAlode/

Note that it is often impossible to translate such Loglan constructions literally into English. The little word ge frequently defies exact translation. But perhaps by this time it doesn't matter. For you may have begun to sense what the Loglan sentences mean directly, without the intervention of these English approximations of its very precise operations.30

As we shall see in a later section, there are still other Loglan meanings to be teased out of the English sentence 'It is a pretty little girls' school'. But these require the notion of "connected" predicates, to which we now turn.

3.14 Connected Predicates with e a o u and noa

One of the simplest--and yet ultimately most powerful--devices of natural language is the one that enables us to make remarks about the connections between ideas. In English the words which permit us to talk about connections are called "conjunctions," and the most popular of them is 'and'. Thus in the sentence,

(1)X is a teacher and a father. Da ditca, e farfu

/daDITca.eFARfu/

the predicate ideas 'is a teacher' and 'is a father' are connected with the conjunction 'and' and with the Loglan word e. (The pause before e is obligatory, by the way, as before all such connecting words.) In Loglan, words of this kind are called connectives, and the simplest of them are the four one-letter words e, a, o, and u. (The fifth one-letter word i has a special connective role between sentences which we will not discuss until Chapter 5.) Making connections in Loglan is very similar to using conjunctions in English, as the following examples show:

(2)Da gudbi mrenu, e sadji farfu X is a good man and a wise father.

/daGUDbiMREnu.eSADjiFARfu/

(3)Da groda bakso, a cmalo hasfa X is a large box or a small house, and possibly both.

/daGROdaBAKso.aCMAloHASfa/

(4)Da na clivi, o na brute X is now alive if and only if it is now breathing.

/danaCLIvi.onaBRUte/

(5)Da na clivi, u na brute X is now alive whether it is now breathing or not.

/danaCLIvi.unaBRUte/

Notice how simply the Loglan connections are made in contrast to the rather elaborate forms of the English connecting phrases. This is because connecting predicates is a grammatically simple operation in Loglan whereas frequently in English it is not.

In all these sentences the speakers of both languages are making claims not about properties but about the connections between properties. With the connective e in (2) the predicates 'good man' and 'wise father' must both be true of X in order for the claimed connection to be true. Thus (2) claims what we will call the logical conjunction31 of two ideas. With a in (3) either or both of the connected predicates may be true of X if the claimed connection is true, and the connection is false only if both predicates are false of X. Thus only if X is neither a large box nor a small house is (3) false. This is the inclusive sense of English 'or', a sense which we sometimes express in English with the odd expression 'and/or'. We will call this second kind of connection alternation, for it expresses the relation between alternatives...but remember that these are alternatives that may be taken several at a time.

The connections made with o and u in (4) and (5) represent sharply different claims about the same two predicates. In (4) the connection with o is true just in case the individual predicates are either both true or both false of X; thus X must be either dead and not breathing, or alive and breathing, for the sentence as a whole to be true. This kind of connection is called equivalence. In a certain rather formal sense, equivalent predicates "mean the same thing."32 In (5), however, the sentence as a whole is true whenever the first predicate clivi is true of X, and false otherwise, no matter what may be the case for the predicate na brute. Thus we may describe the u-connection by saying that X's aliveness is "independent" of its breathing. So we call the u-connection independence.

Independence, equivalence, conjunction and alternation are the four elementary logical operations of Loglan; and the simple one-letter words that express them are the building blocks out of which the whole system of Loglan connectives is constructed. For these four ways are obviously not the only ways two properties may be connected. There are, in principle, sixteen possible ways of talking about two things simultaneously and fourteen of them are linguistically useful. English provides for all fourteen by one circumlocution or another. Loglan provides for all fourteen with single words, though sometimes these words are compounds constructed from one of the elementary connectives a e o u combined with either nu or no. We will defer a more comprehensive discussion of the derivation of compound connectives until we encounter them again in connecting arguments and sentences. Since the Loglan system of connectives is perhaps the most intricate part of the language, it is best to consider it little by little rather than all at once. For the moment, a single example of the derivation of a compound connective will suffice to illustrate the method.

One of the most useful connections between ideas is the one we will call implication: the connection we often assert in English with the conditional expression 'If...then...'.33 For example,

(6) If it is rained on, then it will be wet.

is a conditional remark. It doesn't have to be rained on for the sentence to be true; neither does it have to be wet. For the sentence is false only in the joint event of its being rained on and not being wet. Now it turns out that every implication is equivalent to an apparently more complex statement involving alternatives. Thus (6) is equivalent to:

(7) Either it won't be rained on or it will be wet, and possibly both.

The equivalence of (6) and (7) can be sensed by reflecting that all instances of rain produce wetness but wetness can occur without rain; the sprinkler may have been left on. Therefore, if it is not rained on, then the lawn may be wet anyway and the claims of both (6) and (7) will still be true. Similarly, if it's not wet and it didn't rain then (6) is still true--and so, even more obviously, is (7). Apparently all we deny with (6) is that it could be rained on and not be wet. But this is exactly what we deny with (7).

For what (7) denies is that both its alternatives are false. And this denial means that it will both fail to not be rained on and fail to be wet. But to fail to not be rained on is to be rained on. Thus what (7) denies is identical to what (6) denies, namely that it is rained on and fails to be wet. And we have already seen that both (6) and (7) are true in all other cases. Thus the connection each makes between rain and wetness is the same connection, no matter how different they sound in English.

Now let us look at the Loglan. The Loglan connective meaning 'if...then...' or '...implies...' is noa [noh-ah]. This compound word is derived from the elementary connecting expression no...a..., an alternation whose first term is negated. The predicates for 'is rained on' and 'is wet' are crina [SHREE-nah] and cetlo [SHET-loh]. Thus (6) becomes:

(8)Da fa crina, noa fa cetlo34 That X will be rained on implies (that it) will be wet.

/dafaCRIna.noafaCETlo/

We now use the simple connective a for inclusive 'or' to translate (7):

(9)Da no fa crina, a fa cetlo X will not be rained on and/or will be wet.

/danofaCRIna.afaCETlo/

A great change has been wrought in these ideas. For we now immediately sense that the Loglan sentences in (8) and (9) mean exactly the same thing. For to the speaker of Loglan, the very word which expressed the connection of implication (noa) exhibits its derivation from the words for alternation and negation (no and a) as a matter of immediate perception. Thus to use the connecting scheme da no...a... in Loglan is just another way of using the connection da...noa... in Loglan; and it is clear to the speaker of Loglan that it is. It is as if speakers of English used the curious phrase 'not-and-or' instead of 'if...then...' when they wanted to talk about conditional ideas. Would it then be difficult to see that 'It rained not-and-or it's wet' meant exactly the same thing as 'It did not rain and-or it's wet'?

We suppose that it would not. We suppose that it will not be difficult for speakers of Loglan to make this same transformation between ideas. For in Loglan, as in English, the connections made with no...a... and ...noa... are simply different expressions of the same idea. In English it is devilish difficult to see this. In Loglan it will be difficult not to see it. For in Loglan the derivation of all complex connectives from simple ones is always plainly hinted in the structure of the words themselves.35

Now the connected expressions we have been discussing in this section are not the only ways in which connectives may be used. Nor are predicates the only expressions which may be connected. For not only may arguments and sentences be similarly connected, but so may the predicate modifiers of other predicate words. We will take up this last variety of predicate connection in a later section of this chapter, while connected arguments and sentences will be dealt with in later chapters.

3.15 Mixed Predicates with ze

Some expressions of the natural languages look like connections but are not. Consider the following sentence in English. Speaking, perhaps, of a child's ball we say:

(1) It is red and blue.

Now if we are not cautious we will translate this expression into Loglan with e, getting the connected predicate in:

(2)Da redro, e blanu X is red and blue.

/daREDro.eBLAnu/

But (2) means that X is red and X is blue. For if a claim made with e is to be true, then both the connected parts of the predicate must be true of their common argument independently. This may be true of some X's, but it is not normally true of children's toys. If we say--in English--that a physical object is red and blue, what we usually mean is that its surface is striped, or mottled, or checkered, or that in some other way the two predicated properties are mixed up in it. In carefully written English we sometimes express this claim about a mixture of properties by linking up the words in the "mixed predicate" with hyphens:

(3) X is red-and-blue.

From such remarks we do not normally grant either of the inferences 'Then it's red' or 'Then it's blue'. For we normally want to distinguish between red balls, blue balls and red-and-blue balls. Thus (2) is false of any X if (3) is true of it.

In Loglan we use the operator ze to form mixed predicates of this kind. Thus, the Loglan translation of (3) is:

(4)Da redro ze blanu It is (mixed) red-and-blue.

/daREDrozeBLAnu/

The linkage with ze is not a connection in the logical sense at all. For a connection, we have seen, involves a claim about (at least) two other claims about the world, and sentence (4) asserts only one claim, namely that X is red- and-blue. There are many mixtures of properties in nature. In Loglan we use mixed predicates to talk about them:

(5)Da pa dzoru ze prano de X walked-and-ran to Y.

/dapaDZOruzePRAnode/

Did he walk to Y? No. Did he run to Y? No. For let us suppose his behavior was a mixture of the two activities. He walked for a while, ran for a while, then walked again, and so on, and finally got to Y. He walked and ran...well, intermittently, as we might helplessly say in English. Sentence (5) says the same complex thing tersely and unmistakably in Loglan.

A final example. Suppose someone wishes to characterize an offspring of a tiger and a lioness in Loglan (in English, the single word 'tiglon' has been coined):36

(6)Da tigra ze simba It's a mixture of a tiger and a lion.

/daTIGrazeSIMba/

And again, the crucial test. Is it a tiger? No. Is it a lion? No. It is a literal--in this case, biological--mixture of the two.

Now the crucial logical property of the mixing operator ze is that it disallows just those inferences that e allows. If you make this mistake about tiglons, by assuming that they are also lions, you may be caught up in some unsuspected tigerish quality of the beast. Again Loglan makes an important logical distinction in both speech and writing that is easily neglected in English. One can make the distinction in English, of course, for we have just done so. But the point is, it is not easy to do so both briefly and in a way that will be easily understood. In Loglan, it is both easy to do so and impossible to be misunderstood. For the little word ze means nothing else, and is as easy to use as 'and'.

3.16 Internally Connected Predicates with ce ca co cu noca

Suppose we want to say that someone is a father who is both good and wise. We want therefore to make a connection between the two predicates in 'He's a good father' and 'He's a wise father'. We have already considered one way of forming such connections in Loglan.

Thus we say:

(1)Da gudbi farfu, e sadji farfu X is a good father and a wise father.

/daGUDbiFARfu.eSADjiFARfu/

But the word farfu seems unnecessarily repetitive here. Is there any way to say 'He's a good and wise father' in Loglan as clearly as we do in English?

Of course. But to do so unambiguously--which is the constant aim of Loglan grammar--requires an entirely different series of Loglan connectives, namely ce ca co and cu [sheh shah shoh shoo].37 Recall that the connectives e a o and u were used between predicate expressions, as in Da gudbi, a sadji ('X is good and wise'). We will now see how this new series of connectives is used only within predicate expressions. Thus they form connections inside what is grammatically a single, if elaborate predicate, expression. Yet we will also see that the connections they assert are of the same logical type. Thus ce, like e, asserts conjunction; ca, like a, asserts alternation; co, like o, asserts equivalence; and so on. The same claim that is made with e in (1) can be made with ce in (2) below:

(2)Da gudbi ce sadji farfu X is a good and wise father.

/daGUDbiceSADjiFARfu/

We will now call expressions like gudbi ce sadji farfu internally connected predicates. They represent internally complex ideas. Note that we do not pause before ce and kin.38

Here are some other sentences with internally connected predicates:

(3)Da groda ce redro bakso X is a big, red box (i.e., big and red).

/daGROdaceREDroBAKso/

(4)Da kamla ca godzi, trena X is a coming or going (pause) train.

/daKAMlacaGODzi.TREna/

Note that a pause before trena would be quite natural...in both languages. In Loglan, as in English, such "phrasing pauses" are, of course, optional. In the haste of rapid speech, pauses of this kind are often omitted. But whenever pauses are intended in the spoken form, they are represented in the written form by commas. Remember that, unlike other languages, Loglan is audio-visually isomorphic. This means that a writer of Loglan, like a composer of music, may compose his text in a way which will indicate how he intends it to be read aloud.

In English we would prefer the inverse form 'It's a train which is coming or going' for sentence (4). It is possible of course to invert the predicate in Loglan, too. Thus for (4) we may say:

(5)Da trena, go kamla ca godzi X is a train which is coming or going, and possibly both.

/daTREna.goKAMlacaGODzi/

It is hard to find instances of equivalence and independence used internally in English. Here are some rather strained examples:

(6)Da forli cu kukra, prano X is a strong--whether fast or not--runner.

/daFORlicuKUKra.PRAno/

(7)Da clivi co brute, nimla X is a living--if and only if a breathing--animal.

/daCLIvicoBRUte.NIMla/

Again, all these pauses are optional. Note that to forge such internal connections in English it is often useful to pause rather definitely on both sides of the internally connected word or phrase. This is suggested by the use of dashes (--) in the English translations given above. In contrast, the Loglan forms are simple and swift, although a pause before the modificand of such connected modifiers is often helpful to one's auditor. Moreover, the Loglan forms accommodate the rarer forms of internal connection--like equivalence, independence and implication--just as easily as they do the more common forms. As a consequence, internal equivalence, independence and implication may not be so rare in Loglan.

Here is an example of internal implication which is easy to say in Loglan but difficult to be clear about in English:

(8)Da crina noca denli cetlo X is a rainy--only if a wet--day.

/daCRInanocaCETloDENli/

For just as noa is derived from no...a, so the internal connection noca is derived from no...ca. One can easily imagine logically intricate predications of this kind becoming far more frequent in spoken Loglan than they have ever been in natural speech.

So far we have considered only internally connected modifiers, such as gudbi ('good') and sadji ('wise'). But the modified parts of metaphors, that is, their "modificands", may also be connected. Thus the external connection in:

(9)Da gudbi mermeu [mehr-MEIGH-oo], e gudbi farfu X is a good husband (married-man) and a good father.

/daGUDbimerMEu.eGUDbiFARfu/

may be as easily transformed into an internal connection as the connection between modifiers.

(10)Da gudbi mermeu ce farfu X is a good husband and father.

/daGUDbimerMEuceFARfu/

Notice that in all the cases we have considered so far the internal connection formed with ce, ca, co, etc., is assumed to connect only the two immediately adjacent predicate words. Thus, in the string gudbi mermeu ce farfu, the connective ce connects just mermeu and farfu, and each of these must then be taken to be modified by gudbi. If we meant to say that X is a good husband and father, without wishing to commit ourselves to the goodness of X's fatherhood, we would not use an internal connective at all but the external connective e: Da gudbi mermeu, e farfu. In this sentence the predicate expressions gudbi mermeu and farfu act in parallel, so to speak, as coordinate predicates of their common argument Da. But suppose we wish to connect a two-word modifying phrase to a one-word one as internal modifiers of a common modified term. Suppose, for example, we wished to say that someone is a very good father and a wise father without repeating the word 'father'. But Da mutce gudbi ce sadji farfu does not say that. It says that X is a very good father and a very wise one; for ce connects only gudbi and sadji, each of which must then be taken both to be modified by mutce and to modify farfu.

In English text we use punctuation with commas, dashes, hyphens or underlining to make such subtle distinctions, and in English speech, an elaborate combination of intonation, stress and pause. But even then we cannot be certain of conveying such ideas with precision.

3.17 Extending Scope with ci cui

In Loglan we have another pair of spoken punctuation words ci [shee] and cui [shwee] which we may use to extend the scope of an internal connective beyond the immediately adjacent predicate word. Ci has an effect rather like that of an English hyphen, but the kind that is used between words, not within them...a distinction that is difficult to make in English but obvious in Loglan, where our hyphens are of different kinds. The interverbal hyphen ci may be used in many other contexts than extending connective scope, however. For example, the claim of sentence (5) of Section 3.12 may be more economically written with ci:

(1)Da bilti cmalo ci nirli ckela X is a beautiful small-girls' school (a school for beautiful small-girls).

/daBILtiCMAlociNIRli.CKEla/

When connectives are in the neighborhood, their scope may be extended in either direction by ci:

(2)Da mutce ci sadji ce gudbi farfu X is a very-wise, and a good, father.

/daMUTceciSADjiceGUDbiFARfu/

(3)Da mutce ce gudbi ci sadji farfu X is an extreme, and a wisely good, father.

/daMUTceceGUDbiciSADjiFARfu/

In contrast, cui is like a left-parenthesis: it announces the beginning of a string of two or more predicate words which will ultimately be connected to an ensuing word or string of words. Thus the sense of (2) can be equally well conveyed by:

(4)Da cui mutce sadji ce gudbi farfu X is a (very wise) and a good, father.

/dacuiMUTceSADjiceGUDbiFARfu/

If we wish to extend the scope of an internal connective beyond both of the single predicate words adjacent to it, we may either use ci's on both sides (the pauses are phrasing pauses and optional and nurmue [NOOR-mweh] is derived from nu mutce and means 'moderate' or 'moderately'),

(5)Da nurmue ci gudbi, ce mutce ci sadji farfu X is a moderately-good, and very-wise, father.

/daNURmueciGUDbi.ceMUTceciSADjiFARfu/

or a cui on the left and a ge...cue pair on the right:

(6)Da cui nurmue gudbi, ce ge mutce sadji cue, farfu X is a moderately good, and a very wise, father.

/dacuiNURmueGUDbi.cegeMUTceSADjicue.FARfu/

Some Loglanists prefer the hyphen-like word ci over the parenthesis-like cui and ge...cue because linking with an infix like ci is usually more economical. But there are some things that cannot be said with ci. These can always be said with the bulkier apparatus of cui and ge...cue. In the interests of logical completeness, then, as well as multiplying our options, these two systems of grouping words and extending the scope of connectives exist side by side in Loglan.

Consider a final example. In this one the Loglan pattern of spoken hyphens is very similar to a rare but unequivocal style of written English:

(7)Da sadji, ce mutce ci gudbi junti ci mermeu, ce farfu X is a wise and very-good young-husband and father.

/daSADji.ceMUTceciGUDbiJUNticimerMEu.ceFARfu/

This grouping of elements--which the hyphens show so clearly in both Loglan and written English--is difficult to express unmistakably in spoken English. If we wanted to uses parentheses and brackets to show this grouping, we could rewrite (7) as

(7') Da [sadji ce (mutce ci gudbi)] [(junti ci mermeu) ce farfu]

This is, of course, exactly the way machines or other knowing auditors will parse (7).

There is a style of "punctuated" Loglan text in which hyphenating y's are represented by hyphens (-), number-words by numerals, letter-words by letter-characters, and in which the logical connectives are sometimes represented by their symbols. In this style the word ci may be replaced by a low hyphen (a hyphen dropped to the baseline:

(7") Da sadji ce mutce_gudbi junti_mermeu ce farfu

The interverbal hyphens are pronounced [shee] as before. But from this written formulation it is immediately clear to the eye what the ear may only have guessed, namely that we may infer the conjunction of four separate claims from this sentence: (i) Da sadji junti_mermeu, that X is wise for a young husband; (ii) Da mutce_gudbi junti_mermeu, that X is very good for a young husband; (iii) Da sadji farfu, that X is a wise father; and (iv) Da mutce_gudbi farfu, that he is also a very good father. Incidentally, in sentences (ii) and (iv) the ci's between mutce and gudbi have become redundant. Good usage would therefore dictate (ii') Da mutce gudbi junti_mermeu and (iv') Da mutce gudbi farfu, for "grouping left" is what unmarked predicate strings in Loglan do automatically.39

This is perhaps more than one can say univocally with an internally-connected predicate expression in spoken English. Note however that in written English this rare hyphenating style would do the clarifying job just as well as the Loglan hyphen does in Loglan. The only difference is that the Loglan hyphens are spoken. So their clarifying role is available to the speaker as well as to the writer of Loglan.40

Let us now consider some of the English ambiguities that are resolved by these devices. Suppose someone says 'It's a fast bicycle pump'. Does he mean that it's a pump for fast bicycles? A fast type of bicycle pump? Or a pump which is both fast and for bicycles? These meanings are almost impossible to distinguish in spoken English, no matter what intonation or pause-stress pattern one adopts. In fact we rely almost wholly on plausibility inferences from the context in which the speech occurs to resolve such meanings in English. As a consequence there is a limit to the new meanings we can produce with any hope of being understood.

Not so in Loglan. The word for 'pump' is dampa [DAHM-pah]. 'Bicycle' is a complex notion in Loglan, as it is in English, being derived from two elementary notions: the combining form of to ('two'), which is tor- [tawr], and the word for 'wheel' which is krilu [KREE-loo]. So torkrilu [tawr-KREE-loo] is the required word. (The English word 'bicycle' is also derived from two primitive roots, but one is Latin 'bi-' and the other Greek 'cycle'!) And 'fast', we already know, is kukra. With this trio of predicates we can now assert the three possible meanings of 'It's a fast bicycle pump.' The version which is grammatically simplest in Loglan is:

(8)Da kukra torkrilu dampa X is a fast bicycle pump (that is, a pump for fast bicycles).

/daKUKratorKRIluDAMpa/

Here, as we learned in the section on metaphor, each predicate modifies the next word in the string. Like 'pretty little girls' in English, the first word modifies the second, which so-modified modifies the third. The next most simple construction can be made either with the grouping operator ge:

(9)Da kukra ge torkrilu dampa X is fast for a bicycle pump.

/daKUKragetorKRIluDAMpa/

Or with the phrasing hyphen ci:

(10)Da kukra torkrilu ci dampa X is a fast bicycle- pump.

/daKUKratorKRIluciDAMpa/

In (9), the operator ge causes all that follows to be treated as a single term; and in (10) ci links torkrilu ci dampa into a single term. Thus in both utterances kukra modifies not torkrilu, but the unified phrase, either torkrilu ci dampu or ge torkrilu dampa depending on which grouping option the speaker has chosen. Accordingly, from either (9) or (10) we may infer that X is fast among bicycle-pumps. This is the meaning that plausibility inference would probably most often assign to the original English phrase. The difference between the two Loglan renderings is a matter of personal style. Some loglanists use ge in preference to ci in these kinds of structures, others use ci in preference to ge.41

Finally, the third and most complicated interpretation of 'It's a fast bicycle pump' involves an internally connected modifier:

(11)Da kukra ce torkrilu dampa X is (both) a fast (pump) and a bicycle pump.

/daKUKracetorKRIluDAMpa/

Here both kukra and torkrilu modify dampa. In written English we would have some chance of communicating this implausible notion (after all, no bicycle pump is really very fast among pumps) with a comma between the two modifiers--thus 'It's a fast, bicycle pump'--hoping that, on the model of 'It's a big, red box' and many other sentences of this form, the reader would understand what we meant. But there is no guarantee of the reader's making the right guess even in written English. For 'It's a fast bicycle pump'--which now seems oddly ungrammatical--can also be thought to have the meaning of Loglan sentence (8).

The point is that English is ambiguous, and rather wonderfully so. Loglan is not. Therefore, for most English sentences, there is no hope of translating them into Loglan with any exactness, simply because to find an exact translation of an ambiguous remark one must find a sentence in the target language which has exactly the same set of possible meanings as the original sentence has in the source language. This objective can be approximately met when the source and target languages are closely related natural tongues. And therein lies a large part of the translator's art. But it is not possible in Loglan. To translate into Loglan is like doing a philosophical analysis: One must decide what the original sentence "really means." This is not always possible, if only because the speakers of natural languages often "really mean" things that are really ambiguities! It is perhaps an appalling thought that our minds may be helplessly filled with grammatical puns. But it is just this possibility which analysis of this kind reveals.

Let us look once more at the intriguing remark 'It's a pretty little girls' school' from the point of view we have just uncovered. On the pattern of 'It's a big, red box' (Da groda ce redro bakso) it is clear that we must now count certain connections amongst these modifiers as among the possible legitimate interpretations of this sentence. In a previous section we considered the various ways in which the string of modifiers in a corresponding Loglan sentence might be grouped or not grouped with ge and its optional right-mark cue. There were five such ways: (i) Da bilti cmalo nirli ckela, (ii) Da bilti ge cmalo nirli ckela, (iii) Da bilti ge cmalo nirli cue ckela, (iv) Da bilti cmalo ge nirli ckela, and (v) Da bilti ge cmalo ge nirli ckela. We must now consider whether certain internal connections with ce may not yield equally plausible interpretations of this remark. (The other logical connections seem not to occur implicitly in English.) In fact ce does permit several new interpretations of the original remark:

(12)Da bilti ce cmalo nirli ckela It's a beautiful and small girls' school (that is, a school for girls who are beautiful and small).

/daBILticeCMAloNIRliCKEla/

(13)Da bilti ce cmalo ge nirli ckela It's beautiful and small for a girl's school.

/daBILticeCMAlogeNIRliCKEla/

Now a speaker of 'It's a pretty little girls' school' might easily intend either of these two additional constructions. But how many more are there? It turns out that there are twenty-two clear and distinct ways in which the four Loglan predicate words may be strung together in this order and either connected with ce, or grouped with ge and cue or ci, or both. Only thirteen of these twenty-two Loglan sentences are legitimate interpretations of 'It's a pretty little girls' school', however; for the other nine constructions, while clear enough in Loglan, simply cannot be the intended meanings of the English remark. Still, thirteen is rather a lot. The English sentence is richer in interpretations than one at first suspects. On the other hand, that there are so many equally legitimate interpretations of any English sentence means that there is a substantial amount of ambiguity in that language, much more than we are ever aware of in speech.42

In any case we have found in these examples an area of Loglan grammar which not only accommodates the rich intricacy of a great natural tongue, but far exceeds it. For simply by recognizing these two grammatical operations among modifiers--conjunction with ce and grouping with ge or ci, both of which we evidently if unconsciously perform in speaking English--and then making all the logically possible combinations of these operations explicitly available to the speaker of Loglan (as well as the full battery of logical connections instead of only one) we may surmise that we have exceeded the modification provisions of all the natural tongues. What that may mean, in time, to the speaker of Loglan, is hard to guess. But there are some interesting possibilities which we will consider in the closing section of this chapter. First, however, we must consider briefly how internally mixed modifiers are formed.

3.18 Internally Mixed Predicates with ze

Just as we found that it is possible to confuse a connected predicate with a mixed one, so it is possible to confuse an internally connected pair of modifiers with a mixed pair. Thus

(1) It is a red-and-blue ball.

presents the same problem in analysis as

(2) It is red-and-blue.

for both sentences involve mixed predicate notions. Thus it is incorrect to translate (1) by Da redro ce blanu balma (balma means 'ball') for the same reason that it was incorrect to translate (2) by Da redro e blanu. The same ze we use to mix whole predicates, as it were, we may now use without ambiguity to mix their parts. Thus with a phrasing pause (1) becomes

(3)Da redro ze blanu balma X is a red-and-blue (pause) ball.

/daREDrozeBLAnuBALma/

from which, as from (2), we may not infer either Da redro balma or Da blanu balma. The modified parts of metaphors may also be mixed:

(4)Da pelto tigra ze simba X is a yellow (pause) tiger-and-lion.

/daPELtoTIGrazeSIMba/

Or both modified and modifying parts may be mixed:

(5)Da pelto ze nigro tigra ze simba X is a yellow-and-black (pause) tiger-and-lion.

/daPELtozeNIGroTIGrazeSIMba

If all this seems reminiscent of the structure for forming internal connections with ce ca co and cu, what you have probably guessed is correct. The grammar of ze is modeled on that of ce. But logically its meaning is quite different.

3.19 Forethought Connections with ka ke ko ku kanoi

The connective words with which we have so far dealt are essentially "afterthought" connectives. They permit a speaker to insert connections in his speech as he goes along, so to speak. One starts to say 'Bob is a student of Greek' and having got the word 'student' out, one remembers that John teaches Greek, too, and continues '...and a teacher of Greek'. This is convenient; but there are certain things that cannot be said in this careless way. For example, it takes forethought to say 'John is both a student of Greek and either a lecturer or a tutor of mathematics.' The 'both...and...' and 'either...or...' forms of English imply forethought. Moreover they permit us to deal with structures of a higher order of logical complexity than would be possible without them. We need a series of such forethought connectives in Loglan. So let us build one.

We generate the new forethought connectives in the following way. We put the consonant /k/ in front of the simple (one-letter) afterthought connectives we already know. These are the four one-letter words a e o u; and we know that they mean 'and/or', 'and', 'if and only if' and 'whether'. Moreover, we know that they are used as infixes in the schemata ...a..., ...e..., ...o... and ...u.... Putting /k/ in front of them gives us the series of prefixes ka ke ko ku [kah keh koh koo]. We will speak this k-marked prefix ahead of any pair of predicate expressions we wish to connect in a forethoughtful way. Finally, we will separate the two connected predicates with the special k-marked infix ki [kee]. The result is the four schemata ka...ki..., ke...ki..., ko...ki... and ku...ki.... We can now translate these four Loglan schemata into the four English forethought forms 'either...or..., and possibly both', 'both... and...', 'if and only if...then...' and 'whether..., ...', respectively.

So much for the four simple connections, the ones that do not involve negation or conversion. But what about the noa-connection, implication, which does involve negation? Well; we recall that the afterthought schema ...noa... ('...only if...') "really means" (was derived from) no...a... ('not...and/or...'), which is just another way of saying that an implication is an alternation with its first term negated. How do we express this important notion forethoughtfully? Simple. We go back to what implication really means, that is, to its deriving schema. When we do this, we see immediately that at least one way of saying no...a... forethoughtfully is ka no...ki..., which is the same as saying 'either not...and/or..., and possibly both' in English. Having got this far, all we have left to do is weld the phrase ka no into a single word; and we do this by replacing the negative no with the negative suffix -noi. The result is kanoi...ki..., which I expect the reader will now agree is an extraordinarily transparent rendering of the logical meaning lying behind English 'if...then...'.43

Now let us use these k-marked connectives to join some predicates. Here is a forethought conjunction of predicates: ke prano ki sucmi. It might be used in such a sentence as

(1)Da ke prano ki sucmi X both runs and swims.

/dakePRAnokiSUCmi/

as might be said of an athlete, say. In Loglan the same two predicates may be joined in an implication:

(2)Da kanoi prano ki sucmi *X if runs, then swims (i.e., If X runs, then X swims).

/dakanoiPRAnokiSUCmi/

As the English part of the example discloses we do not use forethought implications between predicates in English. In Loglan, we often do.

Given this forethought way of speaking, we can make any intended grouping pattern within a sequence of connected predicates unmistakably clear. For example,

(3)Da ke prano ki ka sucmi ki valti X both runs and either swims or jumps.

/dakePRAnokikaSUCmikiVALti/

Clearly this means that X runs, and, in addition, that X either swims or jumps...presumably the speaker has forgotten which. With ordinary afterthought connectives, this particular grouping of terms cannot be conveyed...at least not when spoken in that order. Thus

(4)Da prano, e sucmi, a valti X runs and swims, or jumps.

/daPRAno.eSUCmi.aVALti/

means that X both runs and swims, or X jumps...and again the speaker has apparently forgotten which. Notice that the trailing expressions a valti and 'or jumps' are genuine afterthoughts in both languages...always in Loglan and usually in English. By this we mean that they are added onto already complete thoughts. Thus, in the following sentence, Da prano was complete before e sucmi was added.

(5)Da prano, e sucmi X runs, and swims.

/daPRAno.eSUCmi/

And in (4), Da prano, e sucmi was complete before a valti was added. It is in this sense that the a e o u noa series are afterthought connectives. They add connections to already completely formed ideas. Thus,

(6) X runs...and swims or jumps.

cannot be the sense of Loglan sentence (4) no matter how one pauses in it. The reason is that the connectives in (4) are afterthought connectives and will not group that way. To obtain the sense of English (6), which is of course the sense of (3), one must use at least one forethought connective. Here is the sense of (3) and (6) as minimally marked:

(7)Da prano, e ka sucmi ki valti X runs, and either swims or jumps.

/daPRAno.ekaSUCmikiVALti/

When used with predicates, connectives of the ka-series are assumed to connect whole predicate expressions--not just predicate words--unless they occur non-initially in a predicate string, that is to say, inside one. Thus, ke...ki... in

(8)Da ke nurmue ckano ki sadji farfu X is both moderately kind and a wise father.

/dakeNURmueCKAnokiSADjiFARfu/

will be taken to embrace nurmue ckano ('moderately kind') on the left--nurmue may be pronounced either [NOOR-mweh] or [noor-MOO-eh], as you prefer--and sadji farfu ('wise father') on the right. But in

(9)Da nurmue ke ckano ki sadji farfu X is moderately both kind and wise as a father (i.e., a moderately kind father and a moderately wise father).

/daNURmuekeCKAnokiSADjiFARfu/

the ke...ki... connection embraces only the two predicate words ckano and sadji. In other words, inside predicate strings, ke...ki... has the same one- word scope as the internal connectives of the ca-series. Outside them, it has the scope of a-connectives.

One consequence of this arrangement is that the first term in a predicate string cannot be k-connected...unless that string is the operand of a description; see Section 4.8. But among the predicate strings we are considering in this chapter, the ke...ki...-pair in the following sentence

(10)Da ke nurmue ki ckano sadji farfu X is both a moderate (person) and a kindly wise father (a father who is wise in a kindly way).

/dakeNURmuekiCKAnoSADjiFARfu/

connects the whole predicate expressions nurmue and mrenu sadji farfu. So it cannot mean 'X is both a moderately and a kindly wise father.' The sense of the latter can be expressed in Loglan, of course, and indeed very simply:

(11)Da nurmue ce ckano sadji farfu X is a moderately and kindly wise father.

/daNURmueceCKAnoSADjiFARfu/

But it cannot be done with ke...ki... . In the vernacular of Loglan grammarians, the "head predas of pred-strings may not be kekked" unless they are to be used in descriptions. We will see what this restriction means when we study descriptions in Section 4.8.

3.20 Metaphor and Insight

We have seen in the last few sections how the devices for reporting the internal structure of one's metaphors are in Loglan unusually clear. Moreover, the freedom with which one can modify any predicate word of the language with any other predicate word should lead, in Loglan, to an unusually large store of potential metaphors in which to clothe one's ideas. Through both these characteristics, the structure of Loglan should facilitate the coinage of new ideas. For because the speaker of Loglan will be able to speak clearly although metaphorically, there will be some point in doing so, the point of being understood. And because any predicate which occurs to him is a legitimate modifier of any other predicate, there will be some ease in doing so, the ease of unbridled choice. We can, I think, confidently expect the play of metaphor to be rich and strong in Loglan speech.

But what has metaphor to do with thought? If it were our purpose to construct a language that would best serve the poetic impulse in man, then to enlarge the veins of metaphor in that language would perhaps be our chief concern. But it is not. Our purpose is to facilitate thought, whatever thought may turn out to be. If, in doing so, we also enrich other functions of the language, so much the better. But our hand must first be moved by the requirements of thought.

For a long time philosophers believed that there were, in the main, just two varieties of thought: deduction, or the movement of the mind from the general to the particular, and induction, or its movement from the particular to the general. By deductive thinking we prove our mathematics and grind out the consequences of our theories. By inductive thinking we survey data, examine trends, and form new hypotheses by extending what we find beyond those data and those trends. Viewed this way, thinking is a single, two-way street. We deduce going one way; we induce going the other.

For some time now we have known that this traditional schema is too neat. Where do we get the theories from which we then happily deduce? From what do we derive the fresh insight with which we look again at the old world and happily find new data in it? How, in short, does novelty in either thought or perception arise? For neither new premises nor new facts can be got either from deduction or from induction, as these processes are presently understood.

The fact is the mind creates bold new hypotheses, fresh hunches, new ways of looking in old corners of the world in ways which we as yet only dimly understand. And when it does, it seems to obey no law of logic that we yet understand. In fact, insight-formation seems to be a wholly illogical process on our present understanding of that word. Even so, the American philosopher, C. S. Peirce, once called this third variety of thinking "abduction" to distinguish it from the other two, and hoped to found a logic for it that would be distinct from, and yet joined to, the logics of deduction and induction that we know so well. So far that new abductive logic has not developed far beyond the rudimentary state in which Peirce left it, though the mathematician Polya (1954) has perhaps gone as far as anyone toward that new logic with his analysis of the art of plausible reasoning in the mathematical domain. But at the present time we can only report that while very much is known about the arts of deductive and inductive thinking, almost nothing is known about the art of generating insight. For this, in the end, is what Peirce's abductive logic will be about.

Yet we have insight, and insights about insight. And one of them is that scientific and mathematical hypotheses arise by the same, or by a very similar, mental process as the one by which a poet coins new metaphor; and that is apparently by the free combination of old elements in new patterns. Let us see how this might arise. (But first let us borrow the Loglan variables da, de, di, etc., and use them as genderless, numberless and caseless English pronouns hereafter.)

Let us note that poets are not content with red houses and tall men. Whatever a poet's business is, it forces da outside the domain of stale metaphor which is the "good usage" common in da's time. What da wants to write about, and us to see, is evidently what we have not seen before. And da will use language we have not heard before to make us see it. Like the logician, the poet is intent on taking our linguistic blinkers off. But unlike de, da makes no new languages, but simply sets off boldly for the unused regions of the old. Convinced that we are blinded by usage, da transcends that usage by coining new images, new predicates, new ways of looking at new worlds. That the number of predicates in every language seems implacably to grow may be in large measure the result of da's poetic labors; or that our stock of predicate ideas is now immensely large may be the accumulated result of the poetic impulse in us all.

The second thing to notice is that poetry tends to be ungrammatical. For not only does the poet's search for metaphor drive da outside the bounds of ordinary usage, but it apparently also sends da out to look for new methods of constructing sentences as well. There is little that is "good English" in e.e. cummings or Emily Dickinson. For these poets invented new parts of speech and new methods for combining them, as well as coining new ways of using what they found at hand. Evidently the domain of English as it stood was not large enough to contain the vision of these poets. English was the tool de used; but English was also the prison from whose walls de broke.44

Why is this? And what does the linguistic law-breaking of the poet have to do with thought?

The accounts of scientific and mathematical invention set down long afterward by the scientists and scholars who made them seem to suggest that there is a lawlessness in scientific creation that is strikingly similar to the linguistic prison-breaking of the poet. Orderly, careful surveys of the possibilities seem not to lead in any regular way to new theorems, new hypotheses, new concepts or new hunches about the world. Instead, the process of invention seems to look something like this: The worker steeps da's mind in what is known about some unsolved problem that interests da. Then da relaxes, plays, toys with ideas, or better yet, forgets about them for a time. Then, one day while boarding a train (Poincare), taking a bath (Archimedes), huddling by a stove (Descartes), or watching a falling apple (Newton), the new idea flashes, descends, strikes. The person who is now to become renowned hastens to write it down. Nearly everybody to whom such an experience has occurred is convinced that the unconscious mind played a great role in de's invention. To be sure, it is the conscious mind that verifies the new idea, works out its consequences, joins it solidly to the old; and these activities all involve the most disciplined departments of the mind. But it is apparently the unconscious mind that, once supplied with the elements with which it toys, seems to do the actual abductive work of inventing new ideas.

The unconscious part of the human mind is, as Freud told us, among other things a law-breaker. Not only does it break moral laws (the dreamer murders) but also physical laws (the dreamer flies). Is it not also possible that among the laws it breaks are the laws of linguistic usage? The laws of plain- speaking? The canons of "common sense"? Ultimately the laws of grammar itself? If so, then what has happened unconsciously in the thinker may be very similar to what happens consciously in the poet: the fancied flight; the illegal leap; in short, the contrivance of new metaphor.

A new metaphor, if it is a good one, points to some hitherto-unnoticed corner of the world. What is in this corner may not be important; or it may be. If it is important, beautiful, or permanently interesting to its hearers, it supplies a new predicate: the wine-dark sea, or the "uncuttable" atoms with which the poet-scientists of ancient Greece endowed our modern world. If it is not, the unconscious thinker or the conscious poet tries again; for da is unembarrassed by the bizarre, the unseemly, the "illogical" content of the creative mind.

If there is, then, this profound but unconscious connection between scientific invention and the linguistic law-breaking which goes on semiconsciously in the poet's mind, then a language which encouraged the poetic art of metaphor might also encourage the growth of Peirce's logical art of abductive reasoning in strange, new ways. Loglan, by its very nature, will almost certainly encourage metaphor. It may also encourage thought in these as yet unfathomed ways.45

Notes

1 This specimen of weird but grammatical English is a shortening of an even longer one built by N. Chomsky. It has the interesting property that all adjacent pairs of its words ('green ideas', 'ideas sleep', etc.) have extremely low probabilities of co-occurrence. The probability of the string as a whole occurring naturally must therefore be vanishingly small.

2 Linguists will recognize that the definition of grammaticality implied in these remarks is broader than the ones currently favored by natural language grammarians. However, in the absence of facts about usage it may be the only reasonable view to take of grammaticality in a constructed language. That it may also be a theoretically defensible view is suggested by McCawley (1979:236) when he says that the "sentences universally judged to be 'grammatical'" in a given language "are simply those for which no one has any difficulty in thinking of uses".

3 Loglan is similar to the languages called pidgins in many ways. This fact may have an important bearing on its cross-cultural learnability, for it may mean that Loglan's grammatical arrangements are closer to the biological "bone" than those of more elaborate tongues. Bickerton's (1981) hypothesis is that the grammar of pidgins is the product of children being left to their own linguistic devices by parents who have been transplanted from their native cultures to work-settings dominated by foreign employers. The employed parents are so involved in the struggle to acquire enough of the dominant language to work effectively that they do not take the time to create the linguistic atmosphere that will teach their native language effectively to their own children. So it is the children of transplanted laborers, according to Bickerton, who build the world's pidgins. The vocabulary of each pidgin comes in the main from the language of the dominant people in its region; but its grammar, on Bickerton's hypothesis, comes from the human genome.

4 In European mathematical usage, the standard three variable sequence is X, Y, Z as it is in Loglan. It is also the early part of the longer sequence X, Y, Z, W, Q which we require to translate the Loglan third-person variables da de di do du into the logically-flavored English favored in this book.

5 The technical problems connected with this view of meaning are discussed in Loglan 2, Chapters 8 and 9.

6 The student of logic will recognize the propositional function in this description of the basic grammar of the Loglan predicate.

7 Except when its place-structure is extended metaphorically, as in the metaphorical use of the English word 'man' in 'He was a man about it'. But such "metaphorical misuse" of a well-established predicate is often a first step toward shaping a new literal meaning for it in its language. We will assume in this book, however, that Loglan is holding still while we describe it, which among other things will mean that the places of its predicates are as described.

8 See Note 15 for a possible sixth place of the predicate ketpi = 'is a ticket to travel to...from...on carrier...with accommodation...'.

9 For example, that 'mother' is a noun in English, and one which seems superficially to behave like the noun 'man', obscures the fact that the first expresses a relational idea and the second does not.

10 Or when the time-frame of the discourse has already been established. In one recommended style of Loglan story-telling the narrator uses unmarked predicates once the pastness of the action has been established. Explicitly tensed predicates are needed only when the time-frame shifts again; see Parks-Clifford (1980b:21-7).

11 It is probably a mistake to call the English "present" tense a time-binding tense at all. For by giving up its time function to the present progressive, it has acquired something of the sense of the unadorned predicate in Loglan. This is not true in languages like French and Spanish, where the present tense still functions as a genuine indication of present time. Thus English is better equipped than these languages to accommodate the time-free tense of Loglan.

12 The English-trained mind yearns for a third alternative: 'X will be flammable' as of something that is presumably not flammable now. In truth, this cannot be said easily in Loglan. But the notion of an emerging time-free property not present now is either self-contradictory or redundant. If something will be flammable, then it is flammable "now" in the time-free sense; and if something is not flammable in this same time-free sense, then no circumstantial change can make it flammable later. If an English-speaker tells us that a piece of wet wood is such an object, then he has simply added drying the wood to the list of steps which, like lighting a match, must be taken in order to ignite it. On the Loglan view wet wood is flammable, just as cold wood is. Never mind that the conditions for its actual burning (dryness, temperature, the presence of oxygen, etc.) have not in fact been met. Oddly enough, this means that such expressions as English 'X will be flammable' may be translated into Loglan simply as Da cabro. Other meanings suggested by the English phrase are usually contradictory, e.g., that a time-free property can come and go like a flashing light. There is more on the potentiality question in McCreight and Brown (1978) and McCreight, Brown and Parks-Clifford (1979).

13 Occasionally the punctuation word ga is used in place of "nothing at all" to signify the time-free sense of the predicate. See Section 4.14 for the uses of ga.

14 A lexeme, in the technical language of Loglan linguistics, is a class of grammatically interchangeable words, often called a "syntactic category". We need a single word since we use it so frequently in our grammatical work; so the word 'lexeme' was coined about 30 years ago as an analog of 'phoneme' and 'morpheme'. See Loglan 6 for more exact definitions of this and related terms.

15 The speaker who wishes to use a sixth place of ketpi for the price of the ticket, on the grounds that vehicular travel accommodation on this planet is never gratis, is free to do so. Sixth place conversion would of course be accomplished with nuso (so = 6). Thus Loglan provides such speakers with an infinite series of conversion compounds formed of the principal allolex nu of this lexeme suffixed by any integer: nufe, nuso, nuse, nuvo, etc., sometimes spelled nu5, nu6, nu7, nu8, etc. Usually this series of numbered compounds commences with the integer nu5. But for certain purposes nu itself may be replaced by nuto (nu2), fu by nute (nu3) and ju by nufo (nu4). For the rest of the integers see Section 4.21.

16 It is one of the limitations of Loglan that one cannot speak of the first and third arguments of a predicate without also speaking of the second; and this is true even of converse forms. But vague references to intervening arguments can be made by dummy variables just as we do in English; thus 'something' in 'He made something out of it' is such a variable. In the same spirit we can say Da pa madzo ba de in Loglan, for ba is also a "dummy variable", i.e., a word that occupies the position of an argument without referring to anything. By using ba in this way we permit the third argument de, which does refer to something, to be accurately specified. Other uses of dummy variables are discussed in Section 4.30.

17 The linguist will recognize in this remark my differences with the Chomskian, or transformational, approach to human grammar. Nothing in my own research with grammars over the past 30 years has suggested that speakers actually do make grammatical transformations in the course of speech, however elegant this contrivance may be for the description of a grammar. My own approach to grammar-writing has been simulative and experimental rather than descriptive, and so not directly concerned with formal economy. But then Loglan grammar is much smaller than English grammar, which has been Chomsky's chief concern, and does not require "compaction devices" to be completely described. More on this problem will be found in Loglan 2, Chapter 7.

18 The word gudbi in this position modifies mrenu, as bakso modifies madzo in sentence (2). The modifier-modified relation is discussed in Section 3.11.

19 Philosophical analysis tends to ignore the role of abstract predicates as general terms and to leap immediately to the more interesting problem of what it is that "abstract singular terms" like 'virtue' name; see Section 4.11 for this naming apparatus in Loglan. What I will show, however, is that providing the machinery for abstract predication now, before considering how abstract entities are to be named, very much simplifies the latter problem...even if it means discussing a type of predication of which little use is made in English.

20 When an initial consonant-pair is completely new to you, as [ts] probably was, it may help to split the two consonants between two syllables, for example, to practice saying them as [dah-poht-SAH-nee]--as if the sentence were *Da pot sani--for awhile. What such practice does, however, is inform your tongue that these C-pairs are possible for it to pronounce. Once it learns that, it will naturally slip back into the standard syllabifications given in the text and you will be saying (and hearing) [dah-poh-TSAH-nee] again.

21 That is to say, it is the standard modifier-modified arrangement in 6 of the 8 most widespread languages: English, Chinese, Hindi, Russian, Japanese and German. Only Spanish and French have modifiers last; and even these prefer the modifier-modified word-order for their most common modifiers. But see Loglan 2, Chapter 6, The Word-Order Problem, for data supporting other views.

22 Quine (1960) calls these relationships "syncategorimatic" and regards them as the atypical case of the modifier-modified relationship. He argues that most modifier-modified predicate pairs can be analyzed as conjunctions, thus that whatever is a red house is red and a house. We oppose this view, arguing that scarcely any modifier-modified pairs in English (and, by fiat, none in Loglan) can be properly analyzed as conjunctions. In fact, we would go further and argue that the predicate 'is red' in the sentence 'That house is red' is not used literally at all, but as an abbreviation for 'is a red house'; in short, that the speaker means to claim that the house in question is red for and as a house. On this view the two sentences 'That house is red' and 'That's a red house' have identical truth-conditions provided their designata are the same. Weinreich (1966) gives an analysis of the modifier relationship that accords with this view.

23 Proposals have been made, however, that would change this for Loglan. In response to suggestions by R.W. Meijer (1977) and R.W. Johnson (1979), I proposed in 1979 (Brown 1979e) that studies be made of human metaphor-production, or, what amounts to the same thing, of the varieties of predicate modification in the world's languages, with a view to designing a descriptively exhaustive set of "modification infixes"--including the null infix, which we all use now --which would allow the speaker to specify, when da chose to, the "modification pathway" between the terms of a given metaphor. Optional, as always, such a system would permit a coiner of fresh metaphor--say the ironist who first said 'intellectual dwarf'--to indicate to da's listeners the way in which da meant its terms to be imaginatively combined. Da would do so by choosing among the set of infixes the one that best matched da's intended meaning. Those studies have still to be made. When they are made, and a set of infixes has been accordingly designed, Loglan grammar will accommodate them easily; and yet another extension of the domain of the "logically analyzable" will have been made. Readers are invited to contribute to our growing catalog of modification pathways.

24 The Brown and Greenhood scenario of language evolution (1985, 1988) makes explicit use of this hypothesis. See Note 7 for another sense in which new predicate meanings are generated by apparent misuse, i.e., by place-structure extension.

25 Where three or more predicate words occur in a string, Loglan, like normal English, is left-associative. That is, such strings parse by grouping to the left: (mutce corta) menru. What this means is that unless we are otherwise informed, the first term modifies the second ('very short'), the second so-modified modifies the third ('very-short man'), and so on. Section 3.12 shows how other patterns of association can be obtained. See Note 40 for more on associativity in Loglan.

26 Many more than five if we count implicitly connected modifiers, like 'pretty (and) little for a girls-school'. We will consider this source of equivocation in Section 3.17.

27 The main source of this ambiguity in English is, of course, that 'pretty' may be an adverb meaning 'moderately' as well as an adjective meaning 'attractive'. But it is the confusion caused by its uncertain grammatical role (adverb vs. adjective) rather than the semantic confusion between the ideas of moderateness and attractiveness with which we are mainly concerned in this section. For this reason we have translated the Loglan word bilti in what might be called its "adverbial" position in sentences (1) and (3) with the English word 'beautifully'; for the English suffix '-ly' helps to clarify the grammatical role played by the corresponding Loglan word in the Loglan sentence.

28 It is easier to speak a long string with multiple ge's by pausing before each ge as shown. These pauses are not obligatory. With practice it is possible to speak such sentences pauselessly.

29 The fact that stress, pause and intonation help to sort out some of these ambiguities in spoken English is not really relevant; the point is that no method of pronunciation will remove all of them.

30 Formally, ge and go are closely related, as the following transformations and their parsings show. Case I: To go an un-ge-ed and un-go-ed string without changing its meaning: (1) write the last word, (2) write go, (3) write the rest of the string. Thus ABCD, which parses as ((AB)C)D, inverts in just one way, namely as DgoABC, which then parses as Dgo((AB)C) and is thus of meaning equivalent to ABCD. Case II: To go a go-ed string that has at least one un-go-ed joint: (1) write the front part of the string through the last go, (2) treat the remainder as an un-go-ed string under Case I. Thus DgoABC, which parses as Dgo((AB)C), inverts again as DgoCgoAB, which parses as Dgo(Cgo(AB)) and inverts yet again as DgoCgoBgoA--thus using up the last un-go-ed joint--which now parses as the completely inverted right-grouped string Dgo(Cgo(BgoA)). This parse, by inspection, has the same meaning as the parse ((AB)C)D of the original left-grouped unmarked string ABCD. Case III: To go a ge-ed string: (1) write the portion after the first ge, (2) write go, (3) write the portion that precedes ge. Thus the first of the three ge-ings of ABCD, namely AgeBCD, which parses as Age((BC)D), inverts as BCDgoA, which in turn parses as ((BC)D)goA. The second ge-ing, namely ABgeCD, parses as (AB)ge(CD) and inverts as CDgoAB, which parses of course as (CD)go(AB); and the third ge-ing, which gives AgeBgeCD, parses as Age(Bge(CD)) and inverts as BgeCDgoA, which in turn parses as (Bge(CD))goA and is thus of meaning equivalent to AgeBgeCD. Inverting at other points produces strings of non-equivalent meaning. For example, wrongly inverting ABCD, with structure ((AB)C)D, as CDgoAB produces (CD)go(AB). From this we see that CDgoAB has the same meaning as ABgeCD, with its parse of (AB)ge(CD), of which it is, therefore, the proper inversion. These notes are for readers interested in the formal behavior of the ge/go system, which can be further explored with LIPTM, the Loglan Interactive Parser.

31 This is a different sense of the word 'conjunction' than the English grammarian uses.

32 In that they have the same "truth-conditions." Thus the two sentences 'X is unmarried and a man' and 'X is a bachelor' are either both true or both false for any X. Their predicates are therefore equivalent in the precise sense that the extensions of those predicates are the same. That their intensions differ, however, may be seen by the fact that it is informative, when learning English, to be told 'Whatever is a bachelor is unmarried and a man' while it is not informative to be told 'Whatever is a bachelor is a bachelor'.

33 The word 'implication' is reserved by some logicians for the relationship between a sentence and any other sentence which may be validly derived from it by a logical law of the 'if...then...' form. Among these logicians the 'if...then...' connection itself is usually called the "conditional." Thus 'Fx' is said to imply ' (Ex)Fx' because 'Fx => (E)Fx: is a valid conditional, i.e., true under all possible interpretations of its terms; see, for example, Quine (1961). In this same language the connection we have called equivalence is called the "biconditional." I have elected not to follow this strict technical usage because I find it stylistically awkward. For example, it would deprive us of such an ordinary use of the word 'implies' as occurs in sentence (8). Moreover, there is no English noun, on a par with 'conjunction' or 'alternation', say, by which to refer to the linguistic act of speaking conditionally or biconditionally. Do we call it "conditionalization," for example? But we need to make such references. So we have used the words 'implication' and 'equivalence' to round out our list of fundamental connective forms and acts.

34 In reading this sentence aloud one should leave a distinct pause before noa. This recognizes the connective character of the new word and its derivation from the pause-bearing elementary connective a. It is as if the pause built into a were not lost in this construction, but simply promoted to the head of the new word: thus /no.a/ becomes /.NOa/.

35 The reader who is impatient to see the other derivations of the system may turn to Appendix B, The Fourteen Logical Connectives.

36 Leaving 'liger', astonishingly enough, for the offspring of a male lion and a tigress. I am indebted to G. P. Esainko for this intelligence.

37 John Parks-Clifford, the first editor of The Loglanist, dubbed these c-adorned connectives "sheks" and the act of using them "shekking". These words are still used in the Loglan technical literature, e.g., in Loglan 6.

38 The internal connectives are not preceded by obligatory pauses. They sustain rather than interrupt the flow of sound. Thus [GOOD-bee-shah-SAHD-zhee] contrasts with [GOOD-bee . ah-SAHD-zhee] as a minor vs. a major move in the logic game.

39 The associativity rules are these: (1) Unmarked predicate strings group left: ABCD parses as ((AB)C)D. (2) Ce-ed strings group left: AceBceCceD => ((AceB)ceC)ceD. (3) Ge-ed strings group right: AgeBgeCD => Age(Bge(CD)); in fact ge is a left-parenthesis. (4) Go-ed strings also group right: AgoBgoCgoD => Ago(Bgo(CgoD)), which is equivalent in meaning to the unmarked string DCBA with its left-grouped parse ((DC)B)A. And (5) Ci-ed strings also group right: AciBciCciD => Aci(Bci(CciD)). Ci's are used, therefore, when normal left-grouping is to be departed from, as in (A(BC))D, which can be expressed as ABciCD => (A(BciC))D or as AgeBCgeuD => (Age(BCgeu))D as the speaker chooses. That all these systems work unambiguously together in Loglan speech and writing is one of the astonishing things about its grammar. It still astonishes me, at any rate, when I think of the massive ambiguity of the natural languages and how it has been reduced to zero in this constructed one.

We may note in passing that there is yet another optionality lurking in these associativity arrangements, for the choice between the left-associativity (or "left-branching", as it is sometimes called) of the unmarked form and the right-associativity ("right-branching") of the fully inverted string with multiple go's matches two apparently quite natural proclivities. Some languages, like English, Chinese and Loglan, are left-branching; others, like French, are right-branching. So a French speaker of Loglan has the option of using right-branched speech like Da ckela go nirli go cmalo go bilti ('It's a school for girls who are small in a beautiful way') if da is willing to use the Loglan inversion operator go to its maximum extent. The above sentence parses as Da (ckela go [nirli go [cmalo go bilti>]) and means exactly the same thing as the unmarked string Da bilti cmalo nirli ckela, with its parse Da ([[bilti cmalo> nirli] ckela), which is the left-branched (go-less) form that will probably be preferred by native English- and Chinese-speaking loglanists. Of course the French-style, go-laden Loglan will pay the penalty of being marked; so our prediction is that fewer francophones than would otherwise be expected to will follow the right-branching route. That unmarked Loglan is left- branching reflects our hypothesis that the human head is naturally a left- grouper, an idea supported by the fact that the most widespread human languages are A-N ("adjective-noun" in word-order), which I take to be strong evidence that they are left-branching in other particulars as well. But there are other scholars, notably Bichakjian (1988), who disagree.

40 The positional and size differences between the ordinary, short, "high" hyphens used to replace y in words like mek-kiu and the long, low hyphens used to replace ci in phrases like junti_mermue are supported by a contextual difference as well. The long low hyphens always occur between well-formed predicate words, while the short high hyphens usually occur between fragments like mek and kiu. Even when y does occur between apparent words, as it does, for example, in Xai-kreni (which is the spelling out of Xai-kre = 'X-ray), the words so joined are never both predicates. Thus Xai (upper-case 'X') and kreni ('radiates/produces rays') are both words, but only one of them is a predicate. So quite apart from considerations of its size and position we know that this hyphen is inside a word formed by joining a letter-word to a predicate. This joint is always made with y, never with ci.

41 Here again Loglan's optionality will provide a kind of natural experiment for language scientists. Will loglanists prefer prefixing with ge or infixing with ci? Will they do this from all linguistic backgrounds, or just from some? If only from some, what does the pattern of distribution mean about their native languages? If from all, what does that result suggest about either some non-biologically fixed but nevertheless universal pattern in human languages or, more likely, about the biological wiring of the human head? In short, we are likely to find out a good deal from Loglan's optionality if the language spreads cross-culturally. Wherever as language designers we have said 'Let usage decide', later observers will have an opportunity to observe and then reflect on the patterns of human usage that actually emerge.

42 Susumo Kuno (1963) found that the average number of legitimate syntactical interpretations of a group of English sentences with an average length of 20 words was about 10. Thirteen for a seven-word sentence ('It's a pretty little girls' school') is on the extreme side, according to this standard, but not so far from the mean as to suggest rarity. Our sentence is more than usually ambiguous but not improbably so.

43 The logician will recognize a variant of the Polish, or "parenthesis-free," notation in this device. The reason we use kanoi...ki... for 'if...then...', and not *noka...ki... is two-fold. First, there is a learning advantage to be gained in preserving the derivational parallel between the marked and unmarked forms of each connective, e.g., between kanoi...ki... and ...noa... through their intermediate forms ka no...ki... and no...a.... Second, there is a transformational advantage in being able to move a negation operator from the left connectand to the suffix position on the prefix, as in transforming ka no preda ki prede into kanoi preda ki prede, and from the right connectand to the suffix position on the infix, as in changing ka preda ki no prede into ka preda kinoi prede. Both advantages would be lost if words like noka were used prepositionally. Note that a medial marker of some kind--ki or kinoi in our system--is necessary to separate strings of which the boundaries are not clear. This is true of both predicate expressions and of sentences in Loglan, though not of arguments, where ki is in a certain sense superfluous except as an occasional bearer of -noi.

44 My English usage of the Loglan free variables is well-illustrated in this paragraph. The rules I follow are these: (1) I regard each new paragraph as a fresh field in which to redeploy them, that is, to reassign them if they have been used earlier in the same document. (2) The first one I introduce is 'da'. In this paragraph 'da' replaces 'the poet', that is, the "mass poet", all the poets there are. (3) The one I use next is 'de'. Here it replaces 'these poets', a phrase which refers in turn to Cummings and Dickinson. (4) I would continue with 'di', 'do' and 'du' if required. (5) I try to make each backward reference span the shortest possible interval consistent with English style. In none of this am I as rigorous as I expect loglanists will be in their use of this same apparatus in the language for which it was designed; see Section 4.4.

45 The grammar of predicates which may have liberated these ways in Loglan has turned out to be one of the more stable parts of Loglan grammar. Since 1975 the grammar of the predicate has changed in only three ways: (1) A former distinction, ze/zea, between mixing within predicates and between them turned out to be unnecessary. Ze now serves in both contexts and zea is unassigned. (2) The use of the old commas gi and gu as scope-delimiters, both between predicates and within them, turned out to generate ambiguities, so the new delimiters cui and cue were adopted for use within them. (3) Closely related to (2), the grouping operator ge turned out to require a rightward delimiter for logical completeness, and the new delimiter, geu, was originally adopted for this role. The incompleteness that precipitated the last two changes was that there was no way, in the 1975 language, to express the four-term grouping (A(BC))D and other longer expressions like it. This was the "Missing 18th Case" in the 'Pretty Little Girls' School' paradigm that appeared in the 3rd Edition. This problem led to a flurry of papers in the Spring of 1977. The solution that led to the present arrangements emerged very quickly from this published work, and has remained in force ever since. In fact, one might say that the entire grammar of predicates has proved hyperstable since 1977 despite considerable movement in other departments of the grammar. In short, the Loglan predicate seems to have settled into place fairly early. The analytic work that gave us this happy result was done by J.R. Brown (1977a,b), D. Hickerson (1977), R.W. Meijer (1977a,b,c), W. Mengarini (1977a,b), J. Parks-Clifford (1977b,c,d,e,f,g), R. Thomas (1977), K. Wright (1977) and myself (J.C. Brown 1977b,c).

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