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Date: Sat, 3 Dec 2011 11:06:46 -0800 (PST)
From: John E Clifford <kali9putra@yahoo.com>
Subject: Re: [lojban] No title, since the subject will have changed by the
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Example: {xu do klama le zarci} (mi klama), which, under Gricean rules has to be 
either x2 = {le zarci} or is terribly rude.


The whole distinction between singular and plural quantifiers is suspect.  It 
may mean that the whole system has to be taken as second order, though I think 
that can be avoided.  On the other hand, it is sometimes important to 
distinguish the atoms from the molecules in these bunches.  Happily we can 
always do that with the predicate "is an individual" or, spelling it out, "it's 
the only thing in it".  


 for {du jo du}, since all the work is done by {jo}, any one place predicate 
would do.

What cases do you expect other than "something" and "what I have in mind"?  I 
can't think of an example that doesn't fit those two, though I haven't thought 
very hard.

Using collaborative as the default mode rather weakens the force of 
collaboration, by allowing all sorts of extraneous (a value judgement) items 
in.  In this sense, "We won" shouted by a drunken baseball fan here after the 
world series this year would be literally true, despite his never even having 
gome to a game or watched one.  To be sure, we do sometimes want to bring in 
ancillary folk, but we usually set some limits.  Of course, this is not so much 
a logical matter as a matter of what constitutes a 'real group'.  


Problem with Skolem functions.  Some definitions only require mention of all 
universal quantifiers, others require all terms (the resulting proofs go 
somewhat differently).  If we go the first route, we cannot keep the little 
buried particular out of having scope over subsequent quantifiers.  It is not 
easy even with the second solution, since, in normal form, this particular will 
then bbe in the scope of subsequent quantifiers, which isn't right either.

I'm not quite sure how kinds have much to do with disjunctive mode (nor what 
kinds are doing here at all).

The problem with {lo tadni be zo'e} is back to the interplay of modes and 
quantifiers and all that.  {zo'e} can perfectly well be a buried particular 
here, provided it is not allowed to be pulled across the conjunctive mode of the 
predication (here is a place where quantifiers can't do the work modes do; I 
think there are others).  But that sort of restriction is hard to do in standard 
logic, where all quantifiers have to be prenex at least to the smallest wff in 
which they occur.

Curiously, I see your maneuvering as exactly complicating a simple system.  We 
have to have the various modes of predication just to handle plural reference 
and then some more to deal with generalizations of various sorts. So the only 
problem, given that, is how to fit modes into the satisfaction rules.  
Apparently, that requires either another set of rules (replacing the usual set) 
or a replcation of various predicates or some other complication.  But that is 
unavoidable with plural reference, so it is just a cost to the system. Anything 
else, though, seem prodigal. And, if we don't mark somehow, the different modes 
then we have either ambiguous claims or we have a default value.  Ambiguous 
claims sound terrible logically, but aren't usually too bad practically.  We 
have gotten along with out explicit markers so far, so we can usually work 
things out from context, using common sense (and the Grice rules, if 
necessary).  Picking a default is more difficult, unless we use the weakest for 
of collaborative predication (which I don't really like at all, preferring one 
in which the members of a collaborative group actually participate -- still 
vague, of course -- in whatever they are said to do/be collectively).


----- Original Message ----
From: Martin Bays <mbays@sdf.org>
To: lojban@googlegroups.com
Sent: Fri, December 2, 2011 9:24:56 PM
Subject: Re: [lojban] No title, since the subject will have changed by the time 
it gets there

* 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@yahoo.com>:
> > 
> > > On Nov 27, 2011, at 10:36 AM, Martin Bays <mbays@sdf.org> wrote:
> > > 
> > > > * Friday, 2011-11-25 at 12:38 -0600 - John E. Clifford 
> > ><kali9putra@yahoo.com>:
> > > > 
> > > >> On Nov 24, 2011, at 9:44 PM, Martin Bays <mbays@sdf.org> wrote:
> > > >> 
> > > >>> * Wednesday, 2011-11-23 at 13:34 -0800 - John E Clifford 
> > ><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 quantification
> > > > over a singleton domain, so equivalent to it just being a constant
> > > > I (could) have in mind.
> > > > 
> > > 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.
> > 
> > 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").
> 
> 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. 

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

> In the one case, 
> this gives a particular quantifier over the whole universe of discourse.  In 
>the 
>
> other, it is over a unit set, so gives the individual, lo .... .  The latter is 
>
> to allow for the indifference of this term to passage of negations and perhaps 

> other things.  But, of course, either of these hidden values may be a bunch and 
>
> thus the question of how it relates to the basic predicate returns.  And it 
> appears -- though I haven't worked out the details -- that modes of predication 
>
> are also subject to the influence of negation.  So. ultimately, you will not 
> achieve the results you want, which would have been somewhat closer, I think, 
> with using just {su'o da} and {lo ....} directly.  Your further disideratum, 
> that this {su'o da} is in the scope of all preceding quantifiers but does not 
> have any succeeding ones in its scope is even harder to do when moving back to 

> traditional form.  You could ease the first problem a bit by saying that the 
> mode was always collaborative, at least one interpretation of which covers all 

> 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 loath 
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 bunches.
> > > >> 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 three
> > > > 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 values
> > > > of the various predications where the bunches are replaced by their
> > > > subbunches. Is that right?
> > > > 
> > > 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.
> > > > 
> > > > So this would be explicitly marking which mode of predication is meant
> > > > to be in use, hence giving joint information about the precise predicate
> > > > intended (when there's vagueness in that) and the bunches intended.
> > > 
> > > So far as I  can see, the predicates nor the bunches change, just the 
mode.
> > 
> > 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?
> 
> I intend that all three are involved, since the same bunch and predicate can be 
>
> 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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