My last will and testament on lo'e

[Nick Nicholas <opoudjis@optushome.com.au>]

Guys, I give up. I thought about this really hard for three hours, 
and I just don't have that many spare hours. So I'm going to write 
here what I scribbled down and did work out; if it is helpful, fine.

I am now also finding that my eyes are glazing over when I read 
others' contributions on this topic, so I doubt I have anything left 
to contribute anyway.

If this is a solved problem in formal semantics, can someone *please* 
find out? Does either pc or And have any formal semanticist friends 
they could ask? If this is a problem with several schools of thought, 
could we identify them and just pick one? I find it exceedingly hard 
to believe that we here now are breaking new ground that noone has 
worked on for the past 100 years. I'll go further. I find the fact 
that no jboskeist has ever gone out and referred to papers written by 
semanticists that might discuss these recurring issues to be 
incompetence. How can I defend the jboske enterprise to others (hi 
xod :-) as benefitting from 2 millenia of logic, when I don't see 
anyone trying to benefit from the last 50 years?

So.

Let us assume that we know what lo'ei (Llamban lo'e, the intensional 
article in general) is.

Let us call my version of lo'e (typical intension) lo'e'au

lo'ei cinfo is an intension, an abstraction. It is sense without 
denotation. It is "satisfied" by any instance of {lo cinfo}. (The 
notion of 'satisfying' is one that has me worried, and I'll come back 
to it.)

lo'e'au cinfo is also an intension. But inasmuch as it is 'satisfied' 
--- as it has a corresponding extension --- that extension is not all 
lions, as with lo'ei cinfo. It is a subset: all typical lions.

I claim:

lo'e'au cinfo =
lo'ei fadni be lo'i cinfo

So: lo'ei generates an intension out of all lions.
lo'e'au (and I content, lo'e) generates an intension not out of all 
lions, but out of all typical lions.
Typical as to what? As to the trait under discussion, whatever is 
being predicated of lo'e'au cinfo

What does it mean when we say that something is an ordinary lion?
What does it mean (thank you for bringing it up, pc) when we say 
something is an ordinary unicorn?

I believe ordinary is ultimately extensional: survey all the lions 
out there, find where most of them (and the most representative ones 
among them) live, and that's where the typical lion lives.
But what of unicorns? Or dragons?

Giles of Putney, 1300 AD has a mental construct of the universe which 
actually is populated by dragons. He can potentially enumerate them. 
They are all evil. So as far as he's concerned, the typical dragon is 
evil. That dragon St George knocked off is evil, that dragon in 
Beowulf is evil, etc.

Weng Shui, 1300 AD has a different mental construct: still populated 
by dragons, but they are mostly benevolent.

As far as Giles is concerned, {lo'e cridrdrakone cu palci gi'enai 
vrude}. As far as Weng Shui is concerned, {lo'e cridrdrakone cu 
vrude gi'enai palci}. Both are things that need to be sayable in 
Lojban, even if we thing both Giles and Weng are full of crap.

Similarly for unicorns. The typical unicorn is white. What does that 
mean? That I am positing a universe where unicorns really exist (and 
we're getting into possible worlds here --- sorry xod), and in that 
world, most of them are white.

So it should be possible to make claims of typical entities, even 
when those entities are fictional. But that means they have to be 
enumerable. Which means they *do* have to have denotation. So I'll 
set up a parallel world. Have to count unicorns somewhere, after all.

That's one. Two, the notion of typicality is not limited to numerical 
supremacy. A claim is typical if most representative of germane 
classes of the entity in question display it. Say there are 10 
flavours of chocolate. I like chocolate, not just if I would like 80% 
of all chocolates in the world if presented with them. (Presentation 
is of course the problematic 'satisfying' referred to above.) Rather, 
that is a generic claim if I like instances from most classes of 
chocolate.

Now, what is the defining characteristic of these classes? If you 
like eating choc, it's different flavours. If you are identifying 
where lions live, OTOH, it's not different places where they live, 
but more germane classes cutting across them. I haven't worked this 
bit out yet. for now, I'll quantify that as {rau klesi} too --- 
though not {rau su'o so'e}.

So I think fadni means something like this:

da fadni lo'i broda ==

su'o py. poi ve djuno
su'o my. poi munje ku'o
rau su'o so'e da
rau su'o so'e de
su'o di poi broda
zi'e poi di klesi da de
zi'e poi di se vasru my. ku'o
rau ty. poi temci ku'o
rau sy. poi stuzi ku'o
zo'u:

veju'o py. ca ty. vi sy.
di broda

I'll note that the {te klesi}, and therefore the precise denotation 
of {di poi klesi}, will vary from broda to broda.

So {lo fadni} is still extensional: it still enumerates instances of 
lions, albeit typical ones. {lo'e'au} extrapolates from those to the 
intensional abstraction "the typical lion", in a way parallel to how 
{lo'ei} abstracts from the denotation of 'lion' to 'The lion'. And 
that's why it is utterly meaningless to say {re lo'e cinfo}.

Now. What does it mean to satisfy an intension, and generate the 
corresponding extension? Since extensions are real, and intensions 
are, uh, less real, we need to be able to do this. pc said that "if 
presented with a given chocolate, I will like it." And says "if 
presented with a given lion, I will tame it".

(A1) .i mi sisku leka ce'u broda
(A2) .i mi sanji ledu'u da broda
(A2') .i mi sanji ledu'u leka ce'u broda cu ckaji da
(A3) .i mi facki ledu'u da broda

(A2') is there because that's how you fill in the value of ce'u.

What you want, in going from *kaircitka (I eat intensions, I would 
eat x if presented with it), to citka, is something like:

(B1) .i mi kaircitka leka ce'u cakla
(B2) .i mi sanji ledu'u leka ce'u cakla cu ckaji da
(B2a) .i mi jdice la'edi'e
(B3) .i mi ca'a citka da
(B3?) .i mi kaircitka ledu'u da cakla

I have no idea if (B3) and (B3?) are the same thing. I also know that 
when (A1) is satisfied by (A3), we completely changed predicates, 
from sisku to fatci. In going from B1 to B3, we're not changing 
predicates really. This makes me conclude that sisku/fatci is not 
really illustrating what's going on; And has said this here earlier 
(intrinsically intensional concept.)
I tame lions => I tame lion X
!= I seek lions => I find lion X

I will add that for Jorge to speak of buska was a spectacularly inept 
move, because we have no intuitions about buska --- it's not Lojban, 
after all. And I really cannot see how to generalise it to predicates 
like {citka} and {xabju} at all.

Moving on, then. Can we define lo'ei without paraphrasing between 
preds that exist and preds that don't? I'd rather we did. I have no 
idea if this will work, but I will suggest:

mi tinbygau lo'ei cinfo =
su'o ka ce'u goi ko'a cu ckaji su'onoda zo'u
mi tinbygau ko'a

or maybe

mi tinbygau ko'a poi loka ce'u goi ko'a cu ckaji su'onoda

or just maybe

mi tinbygau lo jai ka ce'u cinfo

I know that {lo jai ka ce'u cinfo} sure ain't countable, and sure has 
something to do with an intension -- the intension being {ka ce'u 
cinfo}. I'm just not sure it's actually meaningful. But I doubt 
{buska} is meaningful either.

Present our lion-tamer with a lion, and he'll tame it.

(C1) .i mi tinbygau lo jai ka ce'u cinfo
(C2) .i mi sanji ledu'u le ka ce'u cinfo cu ckaji xy
(C2a) .i mi jdice lenu tinbygau xy
(C2b) .i node fante lenu tinbygau xy
(C3) .i mi tinbygau ko'a poi loka ce'u goi ko'a cu ckaji xy
(C4) .i mi tinbygau xy

(C3) to (C4) is murky to me. But it needs to be doable formally, for 
the intension to be real to me.

I can't go any further. pc is right that there's more of le'e than 
lo'e in what I'd said: le'e needs to emphasise speaker discretion in 
which classes are 'rau', lo'e needs to pretend to be more objective. 
*Perhaps* rau belongs to le'e and not lo'e at all.

But parting shot: xod is right.
John has been hitting men all week?

su'o da poi nanmu zo'u:
ca'o le prulamji jetfu
la djan. cu darxi da

Why must the men being struck have been Mr Man, typical men, or 
pieces of lambda calculus? This *is* an intrinsically extensional 
claim.

Moreover, I abided by And's ban on ka'e and ca'a, but I wish I hadn't:

(D1) .i mi nu'o facki ledu'u ce'u broda
(D2) .i mi sanji ledu'u da broda
(D2') .i mi sanji ledu'u leka ce'u broda cu ckaji da
(D3) .i mi ca'a facki ledu'u da broda

The doublet {nu'o facki/ca'a facki} tells me a lot more about the 
difference between lion-tamers yet to tame a lion, and people 
actually taming lions right now. Sorry, but it does.
--
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* Dr Nick Nicholas, Linguistics/French & Italian nickn@unimelb.edu.au *
University of Melbourne, Australia http://www.opoudjis.net
* "Eschewing obfuscatory verbosity of locutional rendering, the *
circumscriptional appelations are excised." --- W. Mann & S. Thompson,
* _Rhetorical Structure Theory: A Theory of Text Organisation_, 1987. *
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