Re: [lojban] non-ka properties

[Jorge Llambías <jjllambias@gmail.com>]

2011/6/25 Felipe Gonçalves Assis <felipeg.assis@gmail.com>:
>
> First, a thought experiment. Imagine you were assigned to define the
> place structure of a gismu based on the idea of "more", or comparatives.
> How would you define it? (Really, think a bit about that before proceeding)

I don't know, but I can tell you how I think the place structure of
"zmadu" came about: Imagine you want a suffix like the English suffix
-er, to make comparatives like "smaller", "prettier", "heavier",
"greener", and so on. Then you end up with the place structure of
"zmadu" (the first three places anyway): x1 is more than x2 in
smallness, x1 is more than x2 in prettiness, etc.

The extension of this to properties that are not derived from a simple
adjective came later, but it's a natural one. "x1 is more than x2 in
how many kids they have". Wait, there is the adjective "prolific", so
that would be "x1 is more than x2 in prolificness", but you would say
"more prolific" rather than "prolificker" in English anyway.  Or "x1
is more than x2 in how many times they travelled to Paris", I don't
think there is an adjective for being a frequent traveller to Paris,
but there is the property "lo ka ce'u xo kau roi klama la paris".

> Now, what I believe my approach would be.
> I would start with "x1 is more than x2..." and think, "we need more places
> to specify in which sense x1 is more than x2". And in which senses may
> something be more than other?
>
> This is no mystery in logic or math. The general idea of "being more" is
> the concept of an order relation. My first proposal would possibly be
>  "x1 is greater than x2 under order relation x3",
> with {zmadu} and {mleca} being the words used to talk generally about
> order relations.

I think "lidne" might be a better candidate for the general word for
order relations. But you can probably convert any "lidne" relation
into a "zmadu" or "mleca" with a suitable choice of property:

abu lidne by lo selyle'u
= abu mleca by lo ka ce'u xo kau moi lo selyle'u

> How can we express an order relation? Straightforwardly:
>  {ko'a zmadu ko'e loka ce'u cnita ce'u}.
> Assuming the place structure of the order relation paralleled that of
> {mleca}, the above sentence would mean precisely
>  {ko'a se cnita ko'e}.

I'm confused. Did you really mean "mleca" and "se" there? I would have
said "ko'a zmadu ko'e loka ce'u cnita ce'u" would have to be "ko'a
cnita ko'e".

But the problem with that is that "cnita" is already, on its own, an
order relation. You gain nothing with "zmadu". "ko'a cnita ko'e"
already says what you wanted to say in the first place. The power of
"zmadu" is that it creates an order relation out of something that is
not, on its own, an order relation. Something like "crino". From the
property "lo ka ce'u crino" you create the order relation "lo ka ce'u
ri'ozma ce'u". But it would be pointless to say "ko'a zmadu ko'e lo ka
ce'u ri'ozma ce'u".

> It turns out, though, that there is another relatively simple way, probably
> much more common, to specify an order relation. Given a general set X,
> an already ordered set Z, and a map f: X -> Z, there is a unique order
> relation in X which makes f monotone. This is the order induced in X by
> Z via f.
>
> This is what we mean when we say "Alice is heavier than Bob". We are
> comparing the folks with the relation induced by the usual real numbers
> ordering via the weight function.
>
> In these cases, it would be much simpler to just make x3 the function.
> It could be argued that this is a sumti raising over the original definition.
> This implicit sumti raising could be made standard with no risk of
> ambiguity.

And that's basically what zmadu does, except you don't put f in the
x3, you put there the properties that the members of X have by virtue
of being mapped by f into Z.

This is convenient because we already have a straightforward way to
refer to these properties using selbri ("lo ka ce'u <selbri>"),
whereas we have no straightforward way of referring to f. The simpleat
I can think of is "lo fancu be fo lo ka ce'u <selbri>" but that just
adds words to what we already had.


> Let us look first at the definition.
> "x1 exceeds/is more than x2 in property/quantity x3 (ka/ni) by amount/excess x4"
>
> Granted, the line of thought of the gismu finti was not the same as mine.
>
> However, you certainly agree that the x3 is meant to specify the kind of
> more-ness being expressed. If you also think that a {zmadu} necessarily
> entails some order relation, you should agree that it is the x3 that allows
> the speaker to specify it.
> (The x4 is a separate issue, addressed at the end)
>
> Now, let us examine current use. In the sentence
>  {ko'a zmadu ko'e loni ce'u clani},
> would you describe the x3 as rather
>  (a) a property abstraction in the same sense that {loka ce'u clani} is?
>  (b) a quantity in the same sense as {loni ko'a clani} is?
>  (c) the length function?
>  (d) something else?
>
> Option (c) is clearly the answer for me.

"ni" (much like "jei") has been used with two different senses. More or less:

(1) ni = ka se la'u ma kau
(2) ni = se klani lo nu

I assume your sense (a) responds to (1), and your sense (b) to (2).

I don't think it has ever been used to describe the length function,
unless you assume that the x3 of zmadu must take a function, and
therefore when "lo ni clani" is used in the x3 of zmadu then it must
be referring to the length function instead of to the properties that
things have by being assigned a length by the length function.

If you assume, like I do, that the x3 of zmadu takes a property, then
when "lo ni" is used in the x3 of zmadu it must be referring to the
property "lo ka se la'u ma kau ce'u clani".

> {fancu} would be more useful were it defined as, e.g.,
>  "[...] defined by expression x4 with free variable x5 (letteral)".
>
> What do you think of my using the undefined x5 like that?
>  {fancu fo lu lo cmene be me'o xy. li'u me'o xy.}

Personally I'm happy with the kau-method, but I would understand what you mean.

>> but there is no cmavo (say "lo'au") that condenses that into
>> something like "lo'au cmene be ce'u".
>
>> I would suggest using a function cmavo, like "lo'au", for that.
>
> Alternatively, the new cmavo could play the role of {ce'u}, and
> bind to the usual descriptors, instead of abstractions:
>  {lo cmene be ce'au}
>  {loni ce'au clani}

As I said, I prefer that any expression that starts with "lo cmene
..." refers to names and not to a function into names, but that's just
my preference.

> As a general note, whatever the means to representing a
> function may be, it should be relatively easy to specify its
> defining expression and range. The precise domain is
> usually unimportant.

The defining expression also usually pretty much determines the range:
you know what kind of thing "cmene" can take as its x1, so it's not
really necessary to specify that the range of the cmene-function is
linguistic expressions of a certain kind (cmevla or selbri in the case
of Lojban names).

But you can also figure out what the function in question is from the
property "lo ka ma kau cmene ce'u", "the property of having whatever
name it has".

> All in all, I am still convinced that functions are not only important,
> but also the right thing to fill some places. Nevertheless, I am not
> sure about how to best express them concisely while still keeping
> in line with current lojban grammar and usage...

Especially difficult are the cases of xokau, such as what I would
express with "lo fancu be fo lo ka ce'u xo kau moi" (the function that
takes something into its position in a sequnce) or "lo fancu be fo lo
ka xo kau da broda ce'u" (the function that takes something into the
number of things that broda it, for example "lo fancu be fo lo ka xo
kau da tunba ce'u", "the function that takes something into the number
of siblings they have").

mu'o mi'e xorxes

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