Re: lojban predicates

[John Cowan <cbmvax!UUNET.UU.NET!snark.thyrsus.com!cowan>]

la bab. tcySEL. cusku di'e:

>       2 + 2
>
> In this example, the plus-sign is the equivalent of a lojban gismu.

It is analogous to a gismu, but it is not the equivalent of a gismu.
(Failure to grasp this point was one reason why the mekso part of Lojban
was so late to be worked out.)

A gismu expresses a >relation< (or, if it has only one place) a >property<
which is either true or false.  "2 + 2" is neither.  Only the full equation
"4 = 2 + 2" expresses a relation, one which holds between three terms.
Lojban can treat this sentence either as a regular bridi with a 3-place
selbri, or as an identity between two mathematical sumti.

> (But note that the complete arithmetic expression consists of two
> predicates, the plus-sign and the equals-sign; the lojban expression
> using "klama" is an expression with only one predicate, asserting a
> relationship among five objects/states/processes/entitites in the
> universe.)

"2 + 2 = 4" also has just one predicate.  Expressed as a regular bridi, it
reads:

        li vo nu'asu'i li re li re
        the-number 4 is-the-sum-of the-number 2 and-the-number 2

As a mathematical identity, it is:

        li vo du li re su'i re
        the-number 4 equals the-number 2 + 2

"su'i" is the "+" operator, and the "nu'a" prefix converts it into a selbri.

--
cowan@snark.thyrsus.com         ...!uunet!cbmvax!snark!cowan
                e'osai ko sarji la lojban