* Saturday, 2011-08-13 at 08:45 -0700 - John E Clifford <kali9putra@yahoo.com>:
> Well, picky picky, but 1) ain't no sets here (in the usual meaning of
> sets -- and, for xorxes, in any sense at all). There are just the
> things (or the whole they comprise)
I didn't really mean to import any set theoretical baggage with the term
'set'... if a sumti has referents, which you and xorxes seem to agree
on, then we can consider the set of its referents.
> 2) it would be better, rather than having an Ambiguous flag, either to
> have a case without a flag at all or allow both flags to fly so that
> we could pick the one that fit the situation.
I'm not sure what you mean here. What would be difference between
'neither' and 'both'?
> 3. careful with gunma, as always: the referents take on the bridi
> collectively, but there is nothing else there (xorxes view).
> 4.
> external quantifiers of lo, loi, and probably the rest all
> shift to distributive mode (and fractional quantifiers are fine, just as "half
> the students wore red ties is). Otherwise (and this is mainly about how what
> you meant was expressed) your summary is fine,
> i. ro lo broda cu broda is not a tautology, since the individuals in lo broda
> may be broda only collectively (lo sruri be lo dinju, e.g.), in which case, the
> sentence is false.
> ii. ditto
> iii. this is probably a definition of sorts, otherwise a tautology -- or would
> be if 'gunma' were actually defined in some appropriate way.
> de falso omnia so no contradiction we need worry about (the gunma of all
> non-gunma would probably lead to some sort of problem, though maybe not, since,
> for me, every gunma is in itself).
[These points dealt with / rendered obsolete by other parts of this
thread]
> again,, 'ro lo broda' need not be the same as 'ro broda', which is, at best, 'ro
> lo ro broda'.
This is another issue... the current gadri proposal quite explicitly
equates PA broda with PA lo broda. There is already a comment about this
at the bottom of the page.
> ----- Original Message ----
> From: Martin Bays <mbays@sdf.org>
> To: lojban@googlegroups.com
> Sent: Sat, August 13, 2011 7:47:39 AM
> Subject: Re: [lojban] xorlo and masses
>
> * Saturday, 2011-08-13 at 05:41 -0600 - Jonathan Jones <eyeonus@gmail.com>:
>
> > On Sat, Aug 13, 2011 at 2:29 AM, Martin Bays <mbays@sdf.org> wrote:
> >
> > > * Friday, 2011-08-12 at 23:04 -0600 - Jonathan Jones <eyeonus@gmail.com>:
> > > > On Fri, Aug 12, 2011 at 9:29 AM, Martin Bays <mbays@sdf.org> wrote:
> > > > > So in all cases, the referents of {lo/loi broda} are entities which
> > > > > individually broda?
> > > >
> > > > No, just loi. lo is completely non specific.
> > >
> > > I'm not sure what "non specific" means, but...
> >
> > Non specific means that {lo broda} is not specific as to whether the
> > referents are being referred to collectively or distributively. As J. Cowan
> > said, to specifically refer to them collectively, use {loi}, to specifically
> > refer to them distributively, use {PA lo} (where PA is any cmavo or cmavo
> > cluster of selma'o PA) or {lu'a lo}.
> >
> > {lo} is completely generic, and distributive or collective reference when
> > using only {lo} must be determined via context. This is why in {lo tadni cu
> > sruri le dinju gi'e krixa}, {lo tadni} are collectively {sruri le dinju},
> > but distributively {krixa}, because {lo tadni} does not specify whether
> > those which {tadni} are distributive or collective.
>
> OK. I would like to semi-formalise this understanding as follows:
>
> The interpretation of a sumti (or more accurately: a sumti-6) consists
> of a set of referents and a distributivity flag. The distributivity flag
> has three settings: Distributive, Collective, and Ambiguous. When used
> in a bridi, the bridi is respectively claimed of each referent, or of
> the referents as a gunma, or ambiguously between the two options.
> {lo broda} and {loi broda} both return Sumti6 whose referents each
> satisfy broda; the difference is just that the flag is set to Ambiguous
> in the first and Collective in the second. lu'a and lu'o reset the flag,
> but have no other effect. When quantifying (non-fractionally) over
> a sumti, the flag is ignored.
>
> Does this accurately capture the intention of xorlo?
>
> > > all I'm claiming is that
> > > {ro lo broda cu broda} is a tautology, where {ro lo broda} quantifies
> > > distributively over the referents of {lo broda}. Is this controversial?
> >
> > How could it be controversial?
>
> Good.
>
> My point then was that the following three assertions are inconsistent:
>
> (i) {ro lo broda cu broda} is a tautology
> (ii) {ro loi broda cu broda} is a tautology
> (iii) loi broda == lo gunma be lo broda (i.e. have the same referents)
>
> Indeed, we can derive a contradiction with broda set to {na'e gunma}:
>
> ro loi na'e gunma cu na'e gunma (by (ii))
> ro lo gunma be lo na'e gunma cu na'e gunma (by (iii))
> su'o gunma cu na'e gunma (by (i))
>
> > Also, IIRC, if you are using an outer quantifier, you don't actually need
> > lo. ({PA lo broda} = {PA broda})
>
> (sure, I'm just leaving the 'lo' in to emphasise that the {lo broda} in
> {ro lo broda} has a meaning of its own, with the {ro} then quantifying
> over its referents)
>
> Martin
>
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