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Re: TECH: lambda and "ka" revisited

mi joi la .and. cusku di'e

> I know. I was proposing that the official rule be that instead of:
>   tavla fa le nanmu poi cliva fa le ninmu poi kea xi pa cimba kea xi re
>   ("the man such that the woman such that she kisses him leaves spoke")
> the official guaranteed-unambiguous unvague way of doing it is:
>   tavla fa le nanmu poi kea xi xy zou cliva fa le ninmu poi kea xi zy
>   zou kea xi zy cimba kea xi xy

This is certainly a satisfactory device; I would tend to use "poi ke'a
goi ko'a/ko'e zo'u" and then use "ko'a" and "ko'e" thereafter.

> Let me give a somewhat extreme ambiguous example:
>   ka xeu da skicu le ka xeu de cinba xeu di
> - this, I think, is suo 2 ways ambiguous:
> I.  "property of being a describer of the kisser relationship"
>     where you could paraphrase by {ka xeu da skicu koa}
> II. the outermost ka is dyadic, with arguments xeu da and xeu de
>     - "the describer-of-the-property-of-being-kissed-by relaionship"

The meaning as given can only be I, because a da-variable not bound in a
prenex is treated as if bound in the innermost potential prenex, and the
nearest place to attach a prenex would be after the second "ka", so "de"
and "di" are as if bound in it.

> How to disambiguate? I suggest
> I.  {ka xeu da zou da skicu le ka xeu de xeu di zou de cinba di}
> II. {ka xeu da xeu de zou da skicu le ka xeu di zou de cinba di}

Certainly these are the explicit ways, and indeed II cannot be expressed
without a prenex; the most economical form is:

	ka xe'u de zo'u xe'u da skicu le ka de cinba xe'u di

where "da" is implicitly bound by the same prenex as "de", since there is
no other possible prenex, but "di" is bound by the (unexpressed) prenex
after "le ka".

> > PA is a wastebasket category, but the maxim of minimum mutilation
> > tells me that "xe'u" has to go there, considering how late in the
> > game it is being introduced.
> I think that maxim would lead to the use of {kea}, as advocated by
> Jorge & now by me.

Using "ke'a", though, disallows the neat form "xe'u broda" for "xe'u da
poi broda", as in:

	le ka xe'u nanmu cu cinba la djein.
	the property of being a man who kisses Jane

In addition, a special rule for binding "ke'a" implicitly in a prenex would
be needed, rather than piggybacking on the existing rules for da-series.
Lambda quantification binds variables, after all, and we already have
machinery for bound variables.

I am, however, considering a separate selma'o XEhU as proposed by lojbab
in another message; this would act as a quantifier_300 but wouldn't participate
in MEX activities.

> > This fnord is obviously not the way natural fnord fnord languages operate
> > fnord.
> Exactly. No grammarians' rules have ever included one for fnord-insertion.

What about the grammarian Hagbard Celine?

> > > But be that as it may, what does it mean to say {la djan ckaji
> > > le ka xeu da cimba xeu de}?
> > I think it means that John bears the relationship kisser-of-somebody to
> > an unspecified person.  This is why I wanted to give "ckaji" an arbitrary
> > number of places depending on its x2, so that your example would be
> > equivalent to
> >        la djan. ckaji le ka xe'u da cinba xe'u de kei zo'e
> Is that synonymous with "John bears the relationship kissed-by to
> an unspecified person"? If not, how is that said?

Under this schema, it would be

	la djan. ckaji le ka xe'u da se cinba xe'u de kei zo'e

or its transforms

	la djan. ckaji le ka xe'u de xe'u da zo'u da cinba de kei zo'u


	la djan. ckaji zo'e le ka xe'u da cinba xe'u de kei la djan.

But given the existence of "bridi", probably no such extension of "ckaji"
is needed.

> >        bridi le ka xe'u da cinba xe'u de kei la djan. ce zo'e
> >        Something-is-a-proposition-formed-from the-relation (X kisses Y)
> >                and-the-set {John, Whoozis}.
> > or even
> >        le ka xe'u da cinba xe'u de cu zilbre la djan. ce zo'e
> > which means the same thing.
> There's not much call for {zil-}, since the proposition is still there
> is you have saturated predicate. Another example:
>     zo cinba valsi le ka xeu da cinba xeu de

Interesting, although I'm not sure it's quite true.  Using "zil-" makes for
economy; remember that I read "zi'o" as simply removing the place from the
relationship.  IOW, "mi dunda zo'e do" entails "mi dunda zi'o do" but not
vice versa.

Erratum:  "ce" should be "ce'o", since order counts.

> > Besides, how can you be sure that you've filled every argument?
> Only by filling them, at all levels of subordinacy.

And therefore the existence of a separate cmavo "du'u" is useful, because
it guarantees 0-adicity of the intension.

> > > My objection to {duu} is that it is always singleton in extension,
> > > so should have sumti rather than selbri status.
> John:
> > Not quite: you omit the x2 of "du'u", which is a text expressing the
> > proposition which is x1.
> Okay. True. But if we agree that the contents of duu..kei (plus requisite
> pragmatics) is sufficient to uniquely determine the proposition, then
> x1 is always singleton in extension, irrespective of what's in the x2.

Right.  I simply meant that

	du'u mi klama le zarci kei be lu mi klama le zarci li'u


	du'u mi klama le zarci kei be zoi gy. I go to the market .gy.

are distinct selbri, even though they are true of the same object.

> So duu is really a one place predicate, denoting a class of sentences.
> Or rather, duu is used in a range of one-place predicates, each of
> which denotes a class of sentences.

Or rather still, "du'u" is used in a range of two-place predicates, each
of which relates a class of propositions (not sentences) to the sentences
which express the proposition.  (Again, "proposition" = "0-adic intension".)

> > > (4) Could you explain why propositions are 0-adic intensions?
> > Because an n-adic intension, in Quine's sense, is an abstract object
> > derived from an open sentence in n variables (a propositional function
> > of n variables, in older jargon).  If n = 0, the open sentence becomes
> > a closed sentence, and a proposition is the abstract object derived from
> > a closed sentence.  (Note that in this jargon "proposition" is not the
> > same as "sentence"; sentences are linguistic behaviors, and are concrete;
> > propositions are abstractions from those behaviors.  This account is
> > is modulo the systematic type-token ambiguity that is pervasive in Lojban
> > as elsewhere.)
> I see no role for "proposition" as distinct from "state-of-affairs",
> "a way the world is", "an it-being-the-case-that". So I do wish to
> distinguish "proposition" from "sentence", but I don't see them as
> "abstractions" from sentences.

I don't have enough brain today to make my point coherently, but W&O
may provide some insight.

> It is very naughty of Lojban to exhibit type-token ambiguity. It of
> all languages should be well-behaved. It's why I say such-and-such
> a selbri shd be a sumti, and vice versa.

Well, consider:

	mi cusku zo djan.

where "djan." is a token, versus

	mi se cmene zo djan.

where "djan." is more like a type: I do not mean that my name is a specific
>instance< of the word "djan."

> > There is a kind of implicit "du'u" underlying "jei", which is the truth
> > value of the proposition that <bridi>.  To say you know the truth value
> > of a proposition is indeed the same as knowing whether it is true or
> > false.
> This is the fallacy Jorge was meaning to expose. If the truth value of
> p is 1, and you know the truth value of p, then you know 1 - whatever
> that means. But from knowing 1 it does not follow that you know which
> propositions 1 is the truth value of.

I concede; the frame "mi djuno le jei <bridi>" is not a good representation
of "I know whether <claim>".

> > What exactly ["su'u"] means is specified by its x2 place, so you get
> > "x1 is an abstraction of <p> of-type x2 (e.g. an asserter, {lo xusra})".
> > Less mundanely, we have the book titled "Abstraction of (Jesus Christ
> > is crucified) of-type a downhill-motorcycle-race".  "su'u" allows for
> > expansion of the abstraction set.
> I think I'd like to argue that "abstraction" has no meaning, at least
> not beyond the n-adic ka/duu.
> I don't know which book you're talking about.

"The Crucifixion of Jesus Christ Considered As A Downhill Motorcycle Race."
(Arguably my translation doesn't render the word "considered".)
The point is that every other abstraction can be expressed as a "su'u"
with an appropriate x2:  "nu" is "su'u ... kei be lo fasnu", "jei" is
"su'u ... kei be lo niljetnu", etc.

> > > Right. A major property is temporality - nu are associated with times
> > > and duu arent.
> > Well, that's shaky.  "le nu li re su'i re du li vo" is probably the same
> > as "le du'u li re su'i re du li vo", although both are equally temporal
> > or atemporal or totitemporal or what you will.
> I don't think such atemporal or omnitemporal things can be nu. For me,
> all nu must be terminable.

I think that this point need not be prescribed: "nu" certainly covers
space-time events, and its application to abstract events can be left
open.  But see below.

> > "Physical" is a sticky notion. There is no problem with "nu" objects
> > that aren't actualized, like "le nu le djordj. .ualas. cu merko gugde
> > ralju" even though George Wallace wasn't ever U.S. President.
> There is every problem with such nu objects. {nu la djordj ualas cu
> merko gugde ralju} is false.

I assume that by "false" you meant that it is predicated of {noda}.

In that case, how do you say "I desire George Wallace to be etc."?
Certainly "mi djica le nu ..." is traditional here.  There is a difference
between what contingently didn't happen, but could have, and what is
not a happening at all.

John Cowan					cowan@ccil.org
		e'osai ko sarji la lojban.