kau, take 2

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

Once again, I'm going to make a fool of myself.

I mean, what I'm going to say, people here have presumably said years 
ago, and it's my fault for tuning out of discussion. And the discussion 
has also presumably moved miles ahead or away or whatever. But I'll do 
this anyway.

What is the difference between "I know someone killed Laura Palmer", 
and "I know who killed Laura Palmer"?

Well, the intuitive thing is to break the second claim down into two 
claims: "I know someone killed Laura Palmer" and "I know who that 
someone is". So we might try {mi djuno ledu'u da zo'u: da goi xy catra 
la lauras.palmer.} and {mi djuno ledu'u da mintu de}

But of course, that's not quite enough (as the very lame use of {de} is 
meant to indicate.) The 'who' has to be extensionally defined (pinpoint 
a particular individual), not intensionally (give a description of the 
individual, say a predicate they match). Otherwise you get this:

-- I know who killed Laura Palmer!

-- Yeah, who?

-- The same guy who killed Theresa Banks!

No, that's not an answer; we want a name.

I knew for a while that eggheads speak of extension and intension in 
terms of variable scope, and didn't quite know why. It occurred to me 
today. This is not news to you, but let's go:

Intension:

Dale Cooper knows that, for some X, X killed Laura Palmer
=> Dale knows someone killed Laura

Extension:

For some X, Dale Cooper knows that X killed Laura Palmer
=> Dale knows who killed Laura

The difference? "BOB killed Laura" and "someone killed Laura" are two 
distinct claims; the first entails the second, of course.

Now, say Coop knows about BOB and I don't. In the intensional reading, 
Coop just knows that there's some blank who did it; he knows the claim 
with the blank in it, because the job of the prenex is to insert the 
blank. In the extensional. the identity of X is a blank as far as I'm 
concerned, but not as far as Coop's concerned. The X has already been 
filled in by the time we get to his knowledge. Compare:

For some X, Dale Cooper is in love with X.

I don't know how that X is. But we're strongly implying Coop knows.

Instantiating X -- that is, filling X in with a value --- make sense in 
the extensional reading and not the intensional:

Extension:

For some X, Dale Cooper knows that X killed Laura Palmer
=> X = BOB: Cooper knows that Bob killed Laura Palmer

Intension:

Dale Cooper knows that, for some X, X killed Laura Palmer
=> Dale knows that, for some BOB, BOB killed Laura Palmer
... Bzzt.

So what's {kau}? {kau} is simply an instruction that, when you embed 
the current bridi into someone's epistemology, you swing the prenex 
before the knower rather than after:

.i la deil.kuper. djuno ledu'u ma kau catra la lauras.palmer.
.i su'o no da zo'u: la deil.kuper. djuno ledu'u da catra la 
lauras.palmer.

(There's a little trick with {ma} and 0 quantification we're doing 
there; move along, nothing here to see.)

If {kau} has meaning, then obviously the absence of {kau} has meaning. 
The absence of {kau} --- which I think can legitimately be indicated 
with {kaunai} --- indicates that the prenex stays where the hell it is:

.i la deil.kuper. djuno ledu'u da kaunai catra la lauras.palmer.
.i la deil.kuper. djuno ledu'u su'o pa da zo'u: da catra la 
lauras.palmer.

Now, there is an intuitive sense in which {du'u ... kau} has a meaning 
distinct from any embedding knower. That sense is that the variable 
flagged is instantiated or uninstantiated. But, in this take at least, 
instantiation is something that you need a knower around to do. So to me

.i da kau catra la lauras.

is identical to:

.i su'o da zo'u: mi djuno ledu'u da catra la lauras

whereas the default

.i da (kaunai) catra la lauras.

is identical to:

.i mi djuno ledu'u su'o da zo'u: da catra la lauras

The linguists in the audience will at this point grimace at the 
performatives. (That's the assumption that any sentence X can be 
paraphrased as "I say X" or "I know X".) The performative hypothesis 
was big in the early '70s, and blew up spectacularly by the end of the 
decade. I don't remember how, which is why I'm using it. :-)

But, you might retort, then {kau} becomes meaningless outside of a 
knower and a predicate. Yes, and that's no big problem. In cases like 
this, we pull out the lambda salvator. :-) If the only real things are 
numbers, "+" doesn't mean anything. It needs two numbers either side of 
it to mean something -- a number. So + is \lx\ly.x+y. x means 
something; y means something; and x+y means something. But + on its own 
doesn't.

Same thing in Lojban ce'u. We only allow the existence of predications 
and entities --- bridi and sumti. So what's a quality? A quality is 
something that needs a referent (what will go into ce'u) to turn into a 
predication (du'u). We know what {le du'u mi xunre} means: it has a 
concrete reference to me and an attribute of me. What does redness 
refer to? On its own, nothing; you need to plug a referent in to 
evaluate it. But that's OK; sometimes pieces of language need to able 
to float like that. So redness is \lx.xunre(x) : leka ce'u xunre. It's 
not du'u, so it's not meaningful in itself. It's meaningful when it 
gets turned into du'u: it's du'u in waiting.

So I would claim (again, getting all '70s linguistics --- categorial 
grammar, if you must know), that semantically kau is a lambda 
expression, taking an entity, a predication containing that entity, and 
a knower:

kau = \lX\lY(X)\lZ."su'o no X zo'u: Z djuno ledu'u Y(X)

In swinging prenexes around, {kau} obviously has scope issues. Multiple 
knowers do indeed lead to ambiguity:

la kup. djuno ledu'u la xaris. cusku ledu'u da kau catra la lauras.

We have three possibilities:

(1) Coop and Harry both know it, and Coop knows that Harry said it
(2) Coop knows that Harry blurted out the name of the killer; Harry has 
no idea what he just said
(3) Harry knows the killer. Coop is aware that Harry knows the killer. 
Coop doesn't know the killer himself.

(1) corresponds to:
su'o da zo'u: la kup. djuno ledu'u la xaris. cusku ledu'u da catra la 
lauras.

So da has scope over the whole sentence

(3) corresponds to:
la kup. djuno ledu'u su'o da zo'u: la xaris. cusku ledu'u da catra la 
lauras.

So da has local scope

(2) I have no idea about, and this may make the whole thing tumble; I'd 
rather leave it for another day.

So how to distinguish between (1) and (3)? In such ambiguities of 
scope, Lojban normally employs subscripts; but subscripted UI is very 
very bad news.

But we do have a solution that can be pressed into service: attitudinal 
scope. It's a hack, but I think we should be able to get away, in the 
long-range case, with:

la kup. bu'okau djuno ledu'u la xaris. cusku ledu'u da kau catra la 
lauras.

where we understand bu'okau, which would be literally meaningless, to 
delimit knowers. It could delimit what is known instead, but I think it 
would be more useful here.

In the objections:

xod says I'm saying that in ma kau, ma retains its meaning, and in da 
kau, da retains it meaning. I don't mind saying that; and it's already 
known that ma kau means su'o no , not su'o pa, consistent with the 
behaviour of ma on its own.

xod asks what the diff is between makau and ko'a. I kind of concur with 
what he's hinting: other than the quantification being by default su'o 
no rather than su'o pa, and the fact that ko'a must be assigned (which 
is a *big* stumbling block), ko'a is by definition instantiated --- its 
prenex is way outside, same as any name's. So they're basically similar.

I am unditching djuno in the definition, which is of course not really 
what xod wanted.

I think this is consistent with what little CLL says on it.

Jordan doesn't see what the point of the question is, and why 
formalise. The reason is, I have no idea what Jorge means when he uses 
{kau}, and that's a problem.

And now, Jorge:

> {mi tolmorji le du'u makau zukte}, "I forgot who dunnit". Is that
> the same as "I forgot that {someone dunnit, for a known someone}"?
> I can remember that someone dunnit, for a known (to someone else)
> someone, and yet forget who it was that dunnit.

So by first principles:

mi ca'o djuno ledu'u su'o da zo'u: da zukte

su'o da zo'u: ge da zukte gi naku mi djuno ledu'u da zukte

su'o da zo'u: ge da zukte gi mi mo'u djuno ledu'u da zukte

The way I've just described kau, gives you:

su'o da zo'u: mi tolmorji le du'u da zukte

which is not the same as

mi tolmorji ledu'u su'o da zo'u: da zukte

since you still remember someone did it, just not someone known.

If this means I was wrong about saying "known", I retract; I hadn't 
thought it through. It's not just "known", it's "known to the current 
salient knower".

> The way we sorted it out is to say that {lo'i du'u makau broda}
> is the set of answers to {ma broda}. It is not absolutely clear
> whether negative answers are included, that's why I'm in doubt
> about the instantiation bit, but I think they are. If I know
> that nobody did it, can I say "I know who did it: nobody"? I
> think yes.

Obviously you have to be able to say that. (I won't get into whether 
answers should be propositions or entities, because you can argue for 
both, and I don't see that argument as pertinent here.) So, how do you 
say "I know that noone did it?" Let's redo the lot:

"I know someone or noone did it"
.i mi djuno ledu'u su'o no da zo'u: da zukte

"I know who did it (and it might have been noone)"
.i su'o no da zo'u: ganai da zukte gi mi djuno ledu'u da zukte

"I know noone did it"
.i mi djuno ledu'u no da zo'u: da zukte

And if (as I suspect) that means the same as:

.i no da zo'u: mi djuno ledu'u da zukte

then we're still OK.

The other thing is, Jorge quite conversationally said:

> i mi nitcu lo'e tanxe "I need a box."
> i ma skari ty "Of what colour?"
> i makau skari "Of any colour." "(Of whatever colour.)"

Not defending it, because he was illustrating something completely 
different; but as an assumed fact about the language. So while I've 
been away :-) , {kau} has turned from an indirect question marker to a 
focus marker?

A, I hate this.
B, this does not follow from CLL.
C, how many people are doing this?
D, linguistics conflates focus and indirect questions; but I do not 
currently think this reflects semantics; I think this is just 
methodological convenience on their part, because the two do tend to be 
coextensive in the world's languages. And focus ain't about semantics 
at all, but discourse organisation --- whereas there is definitely 
something semantic going on with indirect questions, the whole issue of 
identity and instantiation. "I know who killed Laura P." does not mean 
the same as "I know !!!***SOMEONE***!!! killed Laura P."
E, my God do I hate this.

I don't have the energy or the time for another flamefest, and there's 
lots of other Lojban stuff to do, and even more non-Lojban stuff. But 
this is the kind of thing that I regard as contrary to the intention of 
CLL, and I would frown on broadening the sense of {kau} in this way. 
Sorry, Jorge, but I do. I would relent if I knew that a significant 
proportion of other Lojbanists use kau in this broader meaning. And 
that it is being presented as a fait accompli unnerves me.

OK, back to you guys. Jorge, when you explain what you've been doing, 
could you please type very slowly for the jboske-impaired like myself? 
:-)

--
Life Dr Nick Nicholas, Dept of French & Italian Studies
Is a knife University of Melbourne, Australia
Whose wife nickn@unimelb.edu.au
Is a scythe http://www.opoudjis.net
--- Zoe Velonis, Aged 14 1/2.