Chapter 11. Events, Qualities, Quantities, And Other Vague Words: On Lojban Abstraction

The purpose of the feature of Lojban known as “abstraction” is to provide a means for taking whole bridi and packaging them up, as it were, into simple selbri. Syntactically, abstractions are very simple and uniform; semantically, they are rich and complex, with few features in common between one variety of abstraction and another. We will begin by discussing syntax without regard to semantics; as a result, the notion of abstraction may seem unmotivated at first. Bear with this difficulty until Section 11.2.

An abstraction selbri is formed by taking a full bridi and preceding it by any cmavo of selma'o NU. There are twelve such cmavo; they are known as “abstractors”. The bridi is closed by the elidable terminator kei, of selma'o KEI. Thus, to change the bridi

into an abstraction using nu, one of the members of selma'o NU, we change it into

The bridi may be a simple selbri, or it may have associated sumti, as here. It is important to beware of eliding kei improperly, as many of the common uses of abstraction selbri involve following them with words that would appear to be part of the abstraction if kei had been elided.

(Technically, kei is never necessary, because the elidable terminator vau that closes every bridi can substitute for it; however, kei is specific to abstractions, and using it is almost always clearer.)

The grammatical uses of an abstraction selbri are exactly the same as those of a simple brivla. In particular, abstraction selbri may be used as observatives, as in Example 11.2, or used in tanru:

Abstraction selbri may also be used in descriptions, preceded by le (or any other member of selma'o LE):

We will most often use descriptions containing abstraction either at the end of a bridi, or just before the main selbri with its cu; in either of these circumstances, kei can normally be elided.

The place structure of an abstraction selbri depends on the particular abstractor, and will be explained individually in the following sections.

Note: In glosses of bridi within abstractions, the grammatical form used in the English changes. Thus, in the gloss of Example 11.2 we see “my going-to the store” rather than “I go-to the store”; likewise, in the glosses of Example 11.3 and Example 11.4 we see “being-a-soldier” rather than “is-a-soldier”. This procedure reflects the desire for more understandable glosses, and does not indicate any change in the Lojban form. A bridi is a bridi, and undergoes no change when it is used as part of an abstraction selbri.

The following cmavo is discussed in this section:

The examples in Section 11.1 made use of nu as the abstractor, and it is certainly the most common abstractor in Lojban text. Its purpose is to capture the event or state of the bridi considered as a whole. Do not confuse the le description built on a nu abstraction with ordinary descriptions based on le alone. The following sumti are quite distinct:

Example 11.5 through Example 11.9 are descriptions that isolate the five individual sumti places of the selbri klama. Example 11.10 describes something associated with the bridi as a whole: the event of it.

In Lojban, the term “event” is divorced from its ordinary English sense of something that happens over a short period of time. The description:

is an event which lasts for the whole of my life (under normal circumstances). On the other hand,

is relatively brief by comparison (again, under normal circumstances).

We can see from Example 11.10 through Example 11.12 that ellipsis of sumti is valid in the bridi of abstraction selbri, just as in the main bridi of a sentence. Any sumti may be ellipsized if the listener will be able to figure out from context what the proper value of it is, or else to recognize that the proper value is unimportant. It is extremely common for nu abstractions in descriptions to have the x1 place ellipsized:

is elliptical, and most probably means:

In the proper context, of course, Example 11.13 could refer to the event of somebody else swimming. Its English equivalent, “I like swimming”, can't be interpreted as “I like Frank's swimming”; this is a fundamental distinction between English and Lojban. In Lojban, an omitted sumti can mean whatever the context indicates that it should mean.

Note that the lack of an explicit NU cmavo in a sumti can sometimes hide an implicit abstraction. In the context of Example 11.14, the appearance of le se nelci (“that which is liked”) is in effect an abstraction:

which in this context means

Event descriptions with le nu are commonly used to fill the “under conditions...” places, among others, of gismu and lujvo place structures:

(The “when” of the English would also be appropriate for a construction involving a Lojban tense, but the Lojban sentence says more than that the studying is concurrent with the ease.)

The place structure of a nu abstraction selbri is simply:

The following cmavo are discussed in this section:

Event abstractions with nu suffice to express all kinds of events, whether long, short, unique, repetitive, or whatever. Lojban also has more finely discriminating machinery for talking about events, however. There are four other abstractors of selma'o NU for talking about four specific types of events, or four ways of looking at the same event.

An event considered as a point in time is called a “point-event”, or sometimes an “achievement”. (This latter word should be divorced, in this context, from all connotations of success or triumph.) A point-event can be extended in duration, but it is still a point-event if it is thought of as unitary, having no internal structure. The abstractor mu'e means “point-event-of”:

An event considered as extended in time, and structured with a beginning, a middle containing one or more stages, and an end, is called a “process”. The abstractor pu'u means “process-of”:

An event considered as extended in time and cyclic or repetitive is called an “activity”. The abstractor zu'o means “activity-of”:

An event considered as something that is either happening or not happening, with sharp boundaries, is called a “state”. The abstractor za'i means “state-of”:

The abstractors in Example 11.17 through Example 11.20 could all have been replaced by nu, with some loss of precision. Note that Lojban allows every sort of event to be viewed in any of these four ways:

Further information on types of events can be found in Section 11.12.

The four event type abstractors have the following place structures:

The following cmavo are discussed in this section:

The things described by le nu descriptions (or, to put it another way, the things of which nu selbri may correctly be predicated) are only moderately “abstract”. They are still closely tied to happenings in space and time. Properties, however, are much more ethereal. What is “the property of being blue”, or “the property of being a go-er”? They are what logicians call “intensions”. If John has a heart, then “the property of having a heart” is an abstract object which, when applied to John, is true. In fact,

has the same truth conditions as

(The English word “have” frequently appears in any discussion of Lojban properties: things are said to “have” properties, but this is not the same sense of “have” as in “I have money”, which is possession.)

Property descriptions, like event descriptions, are often wanted to fill places in brivla place structures:

(The English suffix “-ness” often signals a property abstraction, as does the suffix “-ity”.)

We can also move the property description to the x1 place of Example 11.23, producing:

It would be suitable to use Example 11.23 and Example 11.24 to someone who has returned from the beach with a sunburn.

There are several different properties that can be extracted from a bridi, depending on which place of the bridi is “understood” as being specified externally. Thus:

is quite different from

In particular, sentences like Example 11.27 and Example 11.28 are quite different in meaning:

The “X” used in the glosses of Example 11.27 through Example 11.28 as a place-holder cannot be represented only by ellipsis in Lojban, because ellipsis means that there must be a specific value that can fill the ellipsis, as mentioned in Section 11.2. Instead, the cmavo ce'u of selma'o KOhA is employed when an explicit sumti is wanted. (The form “X” will be used in literal translations.)

Therefore, an explicit equivalent of Example 11.27, with no ellipsis, is:

and of Example 11.28 is:

This convention allows disambiguation of cases like:

into

which is the most natural interpretation of Example 11.31, versus

which is also a possible interpretation.

It is also possible to have more than one ce'u in a ka abstraction, which transforms it from a property abstraction into a relationship abstraction. Relationship abstractions “package up” a complex relationship for future use; such an abstraction can be translated back into a selbri by placing it in the x2 place of the selbri bridi, whose place structure is:

The place structure of ka abstraction selbri is simply:

The following cmavo is discussed in this section:

Amount abstractions are far more limited than event or property abstractions. They really make sense only if the selbri of the abstracted bridi is subject to measurement of some sort. Thus we can speak of:

because “blueness” could be measured with a colorimeter or a similar device. However,

makes very little sense in either Lojban or English. We simply do not have any sort of measurement scale for being a mother.

Semantically, a sumti with le ni is a number; however, it cannot be treated grammatically as a quantifier in Lojban unless prefixed by the mathematical cmavo mo'e:

Mathematical Lojban is beyond the scope of this chapter, and is explained more fully in Chapter 18.

There are contexts where either property or amount abstractions make sense, and in such constructions, amount abstractions can make use of ce'u just like property abstractors. Thus,

is not the same as

Example 11.37 conveys that the blueness comes and goes, whereas Example 11.38 conveys that its quantity changes over time.

Whenever we talk of measurement of an amount, there is some sort of scale, and so the place structure of ni abstraction selbri is:

Note: the best way to express the x2 places of abstract sumti is to use something like le ni ... kei be. See Example 11.62 for the use of this construction.

The “blueness of the picture” discussed in Section 11.5 refers to the measurable amount of blue pigment (or other source of blueness), not to the degree of truth of the claim that blueness is present. That abstraction is expressed in Lojban using jei, which is closely related semantically to ni. In the simplest cases, le jei produces not a number but a truth value:

is equivalent to “truth”, and

is equivalent to “falsehood”.

However, not everything in life (or even in Lojban) is simply true or false. There are shades of gray even in truth value, and jei is Lojban's mechanism for indicating the shade of grey intended:

Example 11.41 does not imply that George is, or is not, definitely a criminal. Depending on the legal system I am using, I may make some intermediate decision. As a result, jei requires an x2 place analogous to that of ni:

Abstractions using jei are the mechanism for fuzzy logic in Lojban; the jei abstraction refers to a number between 0 and 1 inclusive (as distinct from ni abstractions, which are often on open-ended scales). The detailed conventions for using jei in fuzzy-logic contexts have not yet been established.

The following cmavo is discussed in this section:

There are some selbri which demand an entire predication as a sumti; they make claims about some predication considered as a whole. Logicians call these the “propositional attitudes”, and they include (in English) things like knowing, believing, learning, seeing, hearing, and the like. Consider the English sentence:

How's that in Lojban? Let us try:

Not quite right. Events are actually or potentially physical, and can't be contained inside one's mind, except for events of thinking, feeling, and the like; Example 11.43 comes close to claiming that Frank's being-a-fool is purely a mental activity on the part of the speaker. (In fact, Example 11.43 is an instance of improperly marked “sumti raising”, a concept discussed further in Section 11.10).

Try again:

Closer. Example 11.44 says that I know whether or not Frank is a fool, but doesn't say that he is one, as Example 11.42 does. To catch that nuance, we must say:

Now we have it. Note that the implied assertion “Frank is a fool” is not a property of le du'u abstraction, but of djuno; we can only know what is in fact true. (As a result, djuno like jei has a place for epistemology, which specifies how we know.) Example 11.46 has no such implied assertion:

and here du'u could probably be replaced by jei without much change in meaning:

As a matter of convenience rather than logical necessity, du'u has been given an x2 place, which is a sentence (piece of language) expressing the bridi:

and le se du'u ... is very useful in filling places of selbri which refer to speaking, writing, or other linguistic behavior regarding bridi:

Example 11.48 differs from

because Example 11.49 claims that John actually said the quoted words, whereas Example 11.48 claims only that he said some words or other which were to the same purpose.

le se du'u is much the same as lu'e le du'u, a symbol for the predication, but se du'u can be used as a selbri, whereas lu'e is ungrammatical in a selbri. (See Section 6.10 for a discussion of lu'e.)

The following cmavo is discussed in this section:

There is an alternative type of sentence involving du'u and a selbri expressing a propositional attitude. In addition to sentences like

we can also say things like

This form is called an “indirect question” in English because the embedded English sentence is a question: “Who went to the store?” A person who says Example 11.51 is claiming to know the answer to this question. Indirect questions can occur with many other English verbs as well: I can wonder, or doubt, or see, or hear, as well as know who went to the store.

To express indirect questions in Lojban, we use a le du'u abstraction, but rather than using a question word like “who” (ma in Lojban), we use any word that will fit grammatically and mark it with the suffix particle kau. This cmavo belongs to selma'o UI, so grammatically it can appear anywhere. The simplest Lojban translation of Example 11.51 is therefore:

In Example 11.52, we have chosen to use ma as the word marked by kau. In fact, any other sumti would have done as well: zo'e or da or even la djan.. Using la djan. would suggest that it was John who I knew had gone to the store, however:

Using one of the indefinite pro-sumti such as ma, zo'e, or da does not suggest any particular value.

Why does Lojban require the kau marker, rather than using ma as English and Chinese and many other languages do? Because ma always signals a direct question, and so

means

It is actually not necessary to use le du'u and kau at all if the indirect question involves a sumti; there is generally a paraphrase of the type:

because the x3 place of djuno is the subject of knowledge, as opposed to the fact that is known. But when the questioned point is not a sumti, but (say) a logical connection, then there is no good alternative to kau:

In addition, Example 11.56 is only a loose paraphrase of Example 11.52, because it is left to the listener's insight to realize that what is known about the goer-to-the-store is his identity rather than some other of his attributes.

The following cmavo are discussed in this section:

There are three more abstractors in Lojban, all of them little used so far. The abstractor li'i expresses experience:

The abstractor si'o expresses a mental image, a concept, an idea:

Finally, the abstractor su'u is a vague abstractor, whose meaning must be grasped from context:

All three of these abstractors have an x2 place. An experience requires an experiencer, so the place structure of li'i is:

Similarly, an idea requires a mind to hold it, so the place structure of si'o is:

Finally, there needs to be some way of specifying just what sort of abstraction su'u is representing, so its place structure is:

The x2 place of su'u allows it to serve as a substitute for any of the other abstractors, or as a template for creating new ones. For example,

can be paraphrased as

and there is a book whose title might be rendered in Lojban as:

Note the importance of using kei after su'u when the x2 of su'u (or any other abstractor) is being specified; otherwise, the be lo ends up inside the abstraction bridi.

The following cmavo are discussed in this section:

It is sometimes inconvenient, in a situation where an abstract description is logically required, to express the abstraction. In English we can say:

which in Lojban is:

which has an abstract description within an abstract description, quite a complex structure. In English (but not in all other languages), we may also say:

where it is understood that what I try is actually not the door itself, but the act of opening it. The same simplification can be done in Lojban, but it must be marked explicitly using a cmavo. The relevant cmavo is tu'a, which belongs to selma'o LAhE. The Lojban equivalent of Example 11.66 is:

The term “sumti-raising”, as in the title of this section, signifies that a sumti which logically belongs within an abstraction (or even within an abstraction which is itself inside an intermediate abstraction) is “raised” to the main bridi level. This transformation from Example 11.65 to Example 11.67 loses information: nothing except convention tells us what the abstraction was.

Using tu'a is a kind of laziness: it makes speaking easier at the possible expense of clarity for the listener. The speaker must be prepared for the listener to respond something like:

which indicates that tu'a le vorme cannot be understood. (The terminator for tu'a is lu'u, and is used in Example 11.68 to make clear just what is being questioned: the sumti-raising, rather than the word vorme as such.) An example of a confusing raised sumti might be:

This must mean that something which John does, or which happens to John, occurs frequently: but without more context there is no way to figure out what. Note that without the tu'a, Example 11.69 would mean that John considered as an event frequently occurs – in other words, that John has some sort of on-and-off existence! Normally we do not think of people as events in English, but the x1 place of cafne is an event, and if something that does not seem to be an event is put there, the Lojbanic listener will attempt to construe it as one. (Of course, this analysis assumes that djan. is the name of a person, and not the name of some event.)

Logically, a counterpart of some sort is needed to tu'a which transposes an abstract sumti into a concrete one. This is achieved at the selbri level by the cmavo jai (of selma'o JAI). This cmavo has more than one function, discussed in Section 9.12 and Section 10.22; for the purposes of this chapter, it operates as a conversion of selbri, similarly to the cmavo of selma'o SE. This conversion changes

into

In English, the subject of “cause” can either be the actual cause (an event), or else the agent of the cause (a person, typically); not so in Lojban, where the x1 of rinka is always an event. Example 11.70 and Example 11.71 look equally convenient (or inconvenient), but in making descriptions, Example 11.71 can be altered to:

because jai modifies the selbri and can be incorporated into the description – not so for tu'a.

The weakness of jai used in descriptions in this way is that it does not specify which argument of the implicit abstraction is being raised into the x1 place of the description selbri. One can be more specific by using the modal form of jai explained in Section 9.12:

This section is a logical continuation of Section 11.3.

There exists a relationship between the four types of events explained in Section 11.3 and the event contour tense cmavo of selma'o ZAhO. The specific cmavo of NU and of ZAhO are mutually interdefining; the ZAhO contours were chosen to fit the needs of the NU event types and vice versa. Event contours are explained in full in Section 10.10, and only summarized here.

The purpose of ZAhO cmavo is to represent the natural portions of an event, such as the beginning, the middle, and the end. They fall into several groups:

All these cmavo are applicable to events seen as processes and abstracted with pu'u. Only processes have enough internal structure to make all these points and spans of time meaningful.

For events seen as states and abstracted with za'i, the meaningful event contours are the spans pu'o, ca'o, and ba'o; the starting and ending points co'a and co'u, and the achievement contour co'i. States do not have natural endings distinct from their actual endings. (It is an open question whether states can be stopped and resumed.)

For events seen as activities and abstracted with zu'o, the meaningful event contours are the spans pu'o, ca'o, and ba'o, and the achievement contour co'i. Because activities are inherently cyclic and repetitive, the beginning and ending points are not well-defined: you do not know whether an activity has truly begun until it begins to repeat.

For events seen as point-events and abstracted with mu'e, the meaningful event contours are the spans pu'o and ba'o but not ca'o (a point-event has no duration), and the achievement contour co'i.

Note that the parts of events are themselves events, and may be treated as such. The points in time may be seen as mu'e point-events; the spans of time may constitute processes or activities. Therefore, Lojban allows us to refer to processes within processes, activities within states, and many other complicated abstract things.

An abstractor may be replaced by two or more abstractors joined by logical or non-logical connectives. Connectives are explained in detail in Chapter 14. The connection can be expanded to one between two bridi which differ only in abstraction marker. Example 11.74 and Example 11.75 are equivalent in meaning:

This feature of Lojban has hardly ever been used, and nobody knows what uses it may eventually have.

The following table gives each abstractor, an English gloss for it, a Lojban gismu which is connected with it (more or less remotely: the associations between abstractors and gismu are meant more as memory hooks than for any kind of inference), the rafsi associated with it, and (on the following line) its place structure.