11.4. Property abstractions

The following cmavo are discussed in this section:



property abstractor



abstraction focus

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,

Example 11.21. 

la djan. cu se risna zo'e
That-named John   has-as-heart something-unspecified.

John has a heart.

has the same truth conditions as

Example 11.22. 

la djan. cu ckaji
That-named John   has-the-property
le ka se risna [zo'e] [kei]
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:

Example 11.23. 

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 Example 11.23, producing:

Example 11.24. 

le ka do xunre [kei] cu cnino mi
The property-of your being-red     is-new to me.

Your redness is new to me.

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:

Example 11.25. 

ka mi prami [zo'e] [kei]
a-property-of me loving something-unspecified

is quite different from

Example 11.26. 

ka [zo'e] prami mi [kei]
a-property-of something-unspecified loving me

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

Example 11.27. 

la djan. cu zmadu la djordj.
That-named John   exceeds that-named George
le ka mi prami
in-the property-of (I love X)

I love John more than I love George.

Example 11.28. 

la djan. cu zmadu la djordj.
That-named John   exceeds that-named George
le ka   prami mi
in-the property of (X loves me).

John loves me more than George loves me.

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:

Example 11.29. 

la djan. cu zmadu la djordj.
That-named John   exceeds that-named George
le ka mi prami ce'u
in-the property-of (I love X).

and of Example 11.28 is:

Example 11.30. 

la djan. cu zmadu la djordj.
That-named John   exceeds that-named George
le ka ce'u prami mi
in-the property-of (X loves me).

This convention allows disambiguation of cases like:

Example 11.31. 

le ka [zo'e] dunda le xirma [zo'e] [kei]
the property-of   giving the horse


Example 11.32. 

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 Example 11.31, versus

Example 11.33. 

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. 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:

bridi x1 is a predicate relationship with relation x2 (abstraction) among arguments (sequence/set) x3

The place structure of ka abstraction selbri is simply:

ka x1 is a property of (the bridi)