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Date: Fri, 2 Dec 2011 22:24:56 -0500
From: Martin Bays <mbays@sdf.org>
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Subject: Re: [lojban] No title, since the subject will have changed by the
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* Friday, 2011-12-02 at 09:20 -0800 - John E Clifford <kali9putra@yahoo.com=
>:
> ----- Original Message ----
> From: Martin Bays <mbays@sdf.org>
> Sent: Mon, November 28, 2011 7:34:42 PM
> > * Sunday, 2011-11-27 at 22:59 -0600 - John E. Clifford <kali9putra@yaho=
o.com>:
> >=20
> > > On Nov 27, 2011, at 10:36 AM, Martin Bays <mbays@sdf.org> wrote:
> > >=20
> > > > * Friday, 2011-11-25 at 12:38 -0600 - John E. Clifford=20
> > ><kali9putra@yahoo.com>:
> > > >=20
> > > >> On Nov 24, 2011, at 9:44 PM, Martin Bays <mbays@sdf.org> wrote:
> > > >>=20
> > > >>> * Wednesday, 2011-11-23 at 13:34 -0800 - John E Clifford=20
> > ><kali9putra@yahoo.com>:
> > > > OK. So we need a meaning for {zo'e} which has each of these two as
> > > > special cases. This could be "particular quantifier over a domain
> > > > I (could) have in mind" - a special case being that it's quantifica=
tion
> > > > over a singleton domain, so equivalent to it just being a constant
> > > > I (could) have in mind.
> > > >=20
> > > But making it a quantifier makes it subject to quantifier rules.  To
> > > be sure, if it is restricted to some single object, the difference
> > > between some and all disappears.  The problem is ensuring that the
> > > thing at the end of{poi} is in fact a predicate with a single (and the
> > > right)referent.  Actually, the single requirement doesn't generally
> > > need to hold, since we have plural reference, presumably -- unless you
> > > want a single bunch, which you are pretty much sure to get.  But, of
> > > course, the particular and universal quantifiers don't collapse under
> > > negation.  In short, I don't think this works.
> >=20
> > Well, what I really meant was the dreaded close-scope existentially
> > quantified plural variable - "close-scope" dealing with the interaction
> > with other quantifiers, and "plural" dealing with the bunch issue (i.e.
> > I did mean a domain of quantification consisting of a single bunch
> > when I said "singleton domain").
>=20
> Not sure why dreaded, they just don't fit sometimes.

Could you give an example?

> As near as I can figure out, you intend that all blanks be filled by
> {zo'e} which you would define as {su'o da poi ...} where '...' is
> filled by either {du jo du} (though, I am unclear why this complex
> form with {du}, leaving four places to explain, rather than something
> with a one-place predicate} or with {du lo ....} where '....' is to be
> filled with some predicate I (would have) had in mind.

I think {su'o da} is a singular quantifier.

I'm not sure that the two options you give for filling the '...' are
sufficient, though I'd be happy if they were.=20

{du jo du} is because we couldn't find an appropriate one-place
predicate.

> In the one case,=20
> this gives a particular quantifier over the whole universe of discourse. =
 In the=20
> other, it is over a unit set, so gives the individual, lo .... .  The lat=
ter is=20
> to allow for the indifference of this term to passage of negations and pe=
rhaps=20
> other things.  But, of course, either of these hidden values may be a bun=
ch and=20
> thus the question of how it relates to the basic predicate returns.  And =
it=20
> appears -- though I haven't worked out the details -- that modes of predi=
cation=20
> are also subject to the influence of negation.  So. ultimately, you will =
not=20
> achieve the results you want, which would have been somewhat closer, I th=
ink,=20
> with using just {su'o da} and {lo ....} directly.  Your further disiderat=
um,=20
> that this {su'o da} is in the scope of all preceding quantifiers but does=
 not=20
> have any succeeding ones in its scope is even harder to do when moving ba=
ck to=20
> traditional form.  You could ease the first problem a bit by saying that =
the=20
> mode was always collaborative, at least one interpretation of which cover=
s all=20
> the others.

I have no modes. In your terminology, this probably does means that
I assume the mode is always collaborative.

> For the second, I don't see much hope, except, as you say, introducing
> a Skolem function -- and even that may not workm depending on the
> rules.

I don't know what problem you're seeing here. The rules for having the
quantifiers be "innermost" are simple: given a lojban sentence, work
with any {zo'e}s as if they were constant terms; once we have translated
the sentence to a sentence in an appropriate logic, handle {zo'e}s
by replacing an atomic formula of e.g. the form
"broda(zo'e,a,b,zo'e,c,...)" with
"EX X:P(X). EX Y:Q(Y). broda(X,a,b,Y,c)".


Anyway, I am unhappy to note that without allowing either a disjunctive
mode or kinds (and they come to approximately the same thing in this
case), I don't see a way to understand {lo tadni} in {lo tadni goi ty cu
sruri lo dinju}. Presumably it isn't assumed that they all study the
same thing, nor that they otherwise collectively study anything, and yet
we are claiming {ty tadni zo'e}.

> > > >>>> 3. Bunches relate to predicates in a variety of ways,
> > > >>> Right, this is the part of your approach I'm unhappy with. I'm lo=
ath to
> > > >>> give up the simple version of plural semantics, whereby a selbri =
is
> > > >>> interpreted in a given world just as a relation on the set of bun=
ches.
> > > >> But as far as I can see, you are the one who has given that up.
> > > >> I certainly have not.
> > > > Ah, so it looks like I have been misunderstanding you. I understood=
 you
> > > > as having the truth value of a predication (in a world) depend on t=
hree
> > > > things - the predicate, the bunches which are its arguments, and the
> > > > mode(s) of predication. Now I'm understanding you as saying that it
> > > > depends only on the first two, with the mode(s) merely being a way =
of
> > > > describing how it is that the truth value is related to the truth v=
alues
> > > > of the various predications where the bunches are replaced by their
> > > > subbunches. Is that right?
> > > >=20
> > > I'm not sure what this means, but it should mean something like "the
> > > truth value of a predication depends, inter alia, on the way the
> > > subbunches of the bunch which is the argument relate to the
> > > predicate."  Does the bunch have the property because all of it's
> > > subbunches do or because of them do or because none of them other than
> > > the whole do, or is predicate applied to the bunch in some
> > > "statistical" way, and so on.  Clearly, the students wear green ties
> > > in a way quite different from the way they surround a building or come
> > > from several countries or live at home or have above average
> > > intelligence or are civil.
> > > [...]
> > > >> ) will help with the modes of predication issue.  A few
> > > >> nice adverbs seem to be the most natural way to proceed.
> > > >=20
> > > > So this would be explicitly marking which mode of predication is me=
ant
> > > > to be in use, hence giving joint information about the precise pred=
icate
> > > > intended (when there's vagueness in that) and the bunches intended.
> > >=20
> > > So far as I  can see, the predicates nor the bunches change, just the=
 mode.
> >=20
> > Now I'm quite confused. You seem in the first quoted paragraph to be
> > saying that the truth value is determined wholly by the bunches and the
> > predicate, and that the mode is merely a way of describing the reasoning
> > which gives the truth value. But in the second quote, you seem to be
> > suggesting we add adverbs which specify the mode but which give no
> > information about the predicate or the bunches. If the mode doesn't
> > affect the truth value once the predicate and bunches are fixed, what
> > information can this adverb be giving?
>=20
> I intend that all three are involved, since the same bunch and predicate =
can be=20
> related in a number of ways, with differing results.

Right. Then my original statement was pertinent after all: I'm loath to
give up the simple version of plural semantics, whereby (conceptually,
at least) a selbri is interpreted in a given world just as a relation on
the set of bunches.

> That the boys move the piano collectively is very different from that
> they move it conjunctively or disjunctively, for example  (and we
> won't look inside to see just how the collaboration was carried out in
> the first case).  So, the mode does affect the truth value and the
> adverbs are there (as in English) to specify the mode, which Lojban
> does not now do.  Leaving them out is the usual Lojban trick of not
> stating the obvious or "don't care" position -- necessary for
> languages, frustratingly not for logics.

If we want to state conjunctive or disjunctive mode, we can use
quantifiers. If I understand you correctly, {ko'a [conjunctive] broda}
is equivalent to {ro ko'a broda}, and {ko'a [disjunctive] broda} to
{su'o ko'a broda}.

The idea that plain {ko'a broda} be ambiguous between these two
possibilities amongst others is surely utterly abhorrent?

Martin

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