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.cuse risnazo'e
That-namedJohn has-as-heartsomething-unspecified.

John has a heart.

has the same truth conditions as

Example 11.22. 

That-namedJohn has-the-property
lekase risna[zo'e][kei]

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. 


You are new to me in redness.

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

Information from the property in an "aspect" place can often be raised to another place, leaving a dummy, often omitted, property behind:

Example 11.24. 

lenudoxunre[kei]cucninomi[le ka se sanji mi]
Theevent-ofyoubeing-red  is-newto me[in that I am aware of it]

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. 


is quite different from

Example 11.26. 


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

Example 11.27. 

That-namedJohn exceedsthat-namedGeorge

I love John more than I love George.

Example 11.28. 

That-namedJohn exceedsthat-namedGeorge
leka pramimi
in-theproperty of(Xlovesme).

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 11.1. 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. 

That-namedJohn exceedsthat-namedGeorge

and of Example 11.28 is:

Example 11.30. 

That-namedJohn exceedsthat-namedGeorge

This convention allows disambiguation of cases like:

Example 11.31. 

theproperty-of givingthehorse


Example 11.32. 

lekace'udundalexirma [zo'e][kei]

the property of being a giver of the horse

which is the most natural interpretation of Example 11.31, versus

Example 11.33. 

leka[zo'e]dundalexirma ce'u[kei]

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)