# UserWiki:Ilmen/two paradigm candidates for amount abstraction predicates

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## TWO PARADIGM CANDIDATES FOR AMOUNT PREDICATES

Let us call "amount predicate" any predicate that involves an amount abstraction, such as {mutce}, {traji}, {zenba}, {zmadu}, {cnano}, {zilzena} and so on.

By the past, Lojbanists used to use them in the following manner:

Ⓐ {mi mutce lo ni ce'u tatpi}, {mi traji lo ni ce'u certu}.

But this usage of {ni} was conflicting and incompatible with another usage thereof, namely a relation between a pure number and a proposition:

Ⓑ {li no ni mi tatpi}, {lo mitre be li re ni ta rajycla}

Those sentences are equivalent to ones using a numeric amount predicate such as the hypothetical "rajyclalai": "x1 has a tallness of x2 (number)". For example:

Ⓒ {ta rajyclalai li re}

The current trend is to use {ni} only with that second meaning, and thus, by the Lojban design rule that cmavo shall not display any polysemy that the syntactic environment cannot resolve, the usage of {ni} with amount predicates as illustrated in Ⓐ should be forbidden.

That raises the question of what kind of argument should be provided to amount predicates.

There are two competing possible paradigms, we shall introduce them below.

Amount slots can be any of the following depending on the predicate's definition:

• An abstract relation between an entity and a number, for example {lo ka ce'u se majga ce'u}, "the relation [___ is the mass of ___]" (that would be suitable for mutce-x2, zenba-x2, traji-x2 etc.) ;

• An abstract property of a number, e.g. {lo ka ce'u majga ti} ("the property [___ is the mass of this]" (that would be suitable for zilzena-x1).

Example of usage:

Ⓓ {mi zenba lo ka ce'u tiljylai ce'u}, "I increase in weight",

``` {lo ka do rajyclalai ce'u cu zilzena}, "your tallness increases",
{mi traji lo ka ce'u citka mo'e ce'u da}, "I'm the one who ate the greatest number of things".
```

The downside of this paradigm is that there are often two {ce'u}s, which can make things longer, and Lojban doesn't have many numeric amount predicates like {rajyclalai} with a number slot directly in their argument structure. Using {la'u} together with a regular relative greatness predicate (rajycla instead of rajyclalai, tsali instead of tsalai…) is an alternative: {mi mutce lo ka ce'u tsali se la'u ce'u}. {lo ka ni…} has also been sometimes used.

The upside of this paradigm is that having a numeric ce'u-slot allows saying things like {zenba lo ka ce'u viska mo'e ce'u da}. Giving a formal definition for amount predicates becomes fairly easy, for example {zmadu} can be defined as follow: {lo se ckini be x1 bei x3 cu dubmau lo se ckini be x2 bei x3}, "what x1 is in relation x3 with is a number greater than what x2 is in relation x3 with".

Furthermore, the number slot can appear arbitrarily deeply nested in the abstraction.

Amount slots are either properties or propositions. No pure number slot is directly involved, the predicate in the abstraction is a "greatness predicate" such as {tsali}, {rajycla}, {glare} and so on, as opposed to their numeric amount predicate equivalents, {tsalai}, {rajyclalai}, {glalai} respectively, as is the case with Paradigm 1.

Example of usage:

Ⓔ {mi zenba lo ka ce'u tilju}, "I increase in weight",

``` {lo du'u do rajycla cu zilzena}, "your tallness increases",
{mi traji lo ka ru'o se citka be ce'u cu sormei}, "I'm the one who ate the greatest number of things".
```

(Note that the third example in Ⓔ is worded significantly differently from its equivalent in Ⓓ.)

The upside of this paradigm is that less {ce'u} slots are necessary, which makes for more succintness, and it directly makes use of the Lojban stock of greatness predicates, without requiring {la'u} or the creation of equivalent numeric amount predicates as is the case with Paradigm 1.

The downside is that giving a formal definition for amount predicates under this paradigm is more challenging. There seems to be a need for some sort of magical predicate that would allow converting any proposition or property with a greatness predicate (e.g. tsali, rajycla…) as its main predicate into something that allow extracting a concrete number out of it for making comparisons (e.g. for defining {zmadu}).

A possible formal definition for {zmadu} under this paradigm could be: {lo *** be x3 cu poi'i lo se ckini be x1 bei ke'a cu dubmau lo se ckini be x2 bei ke'a}, "with R being the numeric predicate relation corresponding to the greatness property x3, what x1 is in relation R with is a number greater than what x2 is in relation R with". («***» here stands for the aforementioned magical conversion predicate.)

Whether the necessity of such a conversion predicate really poses a significant problem for e.g. developping interpretation software remains to be investigated. That might be no more troublesome than interpreting other magical-looking predicates such as {bridi}, after all.

(Ilmen, 2018-01-19)