Chapter 11: Events, Qualities, Quantities, And Other Vague Words: On Lojban Abstraction
The following cmavo are discussed in this section:
ka NU property abstractor ce'u KOhA
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,
✥4.1 la djan. cu se risna zo'e John has-as-heart something-unspecified. John has a heart.
has the same truth conditions as
✥4.2 la djan. cu ckaji le ka se risna [zo'e] [kei] John has-the-property the property-of having-as-heart something. John has the property of having a heart.
(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:
✥4.3 do cnino mi le ka xunre [kei] You are-new to-me in-the-quality-of-the property-of being-red. You are new to me in redness.
(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 ✥4.3, producing:
✥4.4 le ka do xunre [kei] cu cnino mi The property-of your being-red is-new to me. Your redness is new to me.
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:
✥4.5 ka mi prami [zo'e] [kei] a-property-of me loving something-unspecified
is quite different from
✥4.6 ka [zo'e] prami mi [kei] a-property-of something-unspecified loving me
✥4.7 la djan. cu zmadu la djordj. le ka mi prami John exceeds George in-the property-of (I love X) I love John more than I love George. ✥4.8 la djan. cu zmadu la djordj. le ka prami mi John exceeds George in the property of (X loves me). John loves me more than George loves me.
The “X” used in the glosses of Examples 4.7 through 4.8 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 c11-§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 ✥4.7, with no ellipsis, is:
✥4.9 la djan. cu zmadu la djordj. le ka mi prami ce'u John exceeds George in-the property-of (I love X).
and of ✥4.8 is:
✥4.10 la djan. cu zmadu la djordj. le ka ce'u prami mi John exceeds George in-the property-of (X loves me).
This convention allows disambiguation of cases like:
✥4.11 le ka [zo'e] dunda le xirma [zo'e] [kei] the property-of giving the horse
✥4.12 le ka ce'u dunda le xirma [zo'e] [kei] the property-of (X is-a-giver of-the horse to someone-unspecified) the property of being a giver of the horse
which is the most natural interpretation of ✥4.11, versus
✥4.13 le ka [zo'e] dunda le xirma ce'u [kei] the property-of (someone-unspecified is-a-giver of-the horse to X) the property of being one to whom the horse is given
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, a resource of the language that has not yet been explored.
The place structure of “ka” abstraction selbri is simply:
- x1 is a property of (the bridi)