Re: [lojban] non-ka properties

[John E Clifford <kali9putra@yahoo.com>]

I'm still puzzled but at least now maybe I have something to work with that is a 

bit more concrete.  Let's take 

ko'a zmadu ko'e lo ka clani  
(ignoring that {clani} is one of those predicats whose place structure needs 
reworking -- the second place is just to distinguish width from height from 
length and the third place  -- which ought to be second -- ought to be a 
measurement)
x is greater than y in length
x is longer than y
Now, as far as I understand all this, there arise three questions;
Can/should {lo ka clani} be replaced by a function expression, and, if so, what 
expression?
Can function expressions occur as arguments to {zmadu} etc.?
What does a function expression look like anyway

To look at the second question first, what would it mean for a function to be 
greater than another function?   I suppose something like that for their mutual 
domains the value of the first function for an argument from that domain is 
always greater than that of the second function for that same argument. With 
this understanding we could  write that f1 is greater than f2, using function 
expressions, though the full form is more informative, if longer.

Ok, so function expressions can be sumti and so could go in place of the 
property expression in the third place of {zmadu}.
What function would that be? The one that assigns to each thing a length, 
presumably (see problems above) something with the same output as (lo ni [ce'u] 
clani}, so we could use it as the function (not just the value, since the 
argument covaries).  Of course, we could skip the roundabout and just say 
(longer, alas) {lo ni ko'a clani cu zmadu lo ni ko'e clani}.
And that  does make more sense (as does the "function") since lo ka ko'a clani 
is not greater (or less) than loka ko'e clani.







----- Original Message ----
From: Felipe Gonçalves Assis <felipeg.assis@gmail.com>
To: lojban@googlegroups.com
Sent: Sat, June 25, 2011 8:41:51 PM
Subject: Re: [lojban] non-ka properties

2011/6/25 Jorge Llambías <jjllambias@gmail.com>:
> 2011/6/23 Felipe Gonçalves Assis <felipeg.assis@gmail.com>:
>>
>> Could you point me where this general meaning of {kau} is explained?
>
> I don't think there is any detailed explanation of "kau" anywhere,
> largely because we haven't agreed on one. There has been a lot of
> discussion about it on this list, if you have the patience to search
> the archives.
>

I have actually been examining them, but there are just so many years
of discussion... It was only not clear to me how settled the issue was,
but as far as I can see, {kau} is really only documented as part of an
indirect question with {du'u}, and the point is what the logic behind an
indirect question is.

ta'onai
Thank you very much for all your careful considerations, xorxes.

> (2) do "zmadu" and "jibni" require functions as their third argument.

Having clarified the situation, allow me to try to attract you to my
point of view.

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)

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.

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}.

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.

{jibni} is a similar case, requiring a metric to specify the kind of
closeness, which on its hand might be specified as induced via
a map into a metric space.

> As for (2), while it would have been possible to define "zmadu" and
> "jibni" that way, they just weren't defined that way as far as I
> understand them.

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.

This means that the idea of a map in this position is not new.

Unfortunately, the {ni} approach is limited, besides being a part of the
grammar that might not please xorxes:
> [...] Personally I
> don't like it, because I think something that starts with "lo cmene"
> should refer to names, and the function that maps people to names is
> not itself a name.
zo'o

zo'onai
I should have mentioned the ni-cehu case in the first message.


(About the x4 in {zmadu}: This place appears to imply that our
actual {zmadu} reflects the general structure of ordered metric
spaces, rather than simple posets. This may be a consequence
of the gismu finti having numbers in mind rather than general
ordered sets. Anyway, the structure can still be induced via a
suitable map. Also, the trivial metric is compatible with any
poset.)


Let us now proceed to the question of how to represent functions
more generally, and in a practical way.
> (1) how do we refer to a function in Lojban

> You could refer to the function in the longwinded fashion: "lo fancu
> be lo prenu bei lo valsi bei lo ka makau cmene ce'u", "the function
> from people to words by the rule of what their name is"

I would feel relieved if able to use at least that kind of construction,
but even the nature of the x4 is unclear to me. I noticed you used
the ka-kau, which I still consider messy.

{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.}

> 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}

You will probably say that the function is not the territory,
but unless there is serious consideration for an experimental
cmavo, we should not argue about that.


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.


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...

mu'o
mi'e .asiz.

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