* Saturday, 2011-11-05 at 02:36 +0000 - And Rosta <and.rosta@gmail.com>:
> Martin Bays, On 04/11/2011 23:37:
> > Let me try to clarify the basic problem I see with kinds, which
> > I understand xorxes' dialect of lojban to suffer from. Then we can ask
> > whether yours does too.
> >
> > Since we don't know exactly what we mean by 'kinds' (I certainly don't
> > claim to), let me call the kind of kind which suffers from the problem
> > a 'malkind'; the following description of the problem should be taken
> > as a definition of malkinds.
> >
> >
> > Suppose we have a forall-exists statement. Any at all will do;
> > let's consider
> > "every French person wears a beret"
> > and render it in lojban as
> > (A) {ro faspre cu dasni su'o ransedyta'u}.
> >
> > Then with malkinds, if (A) is true it would also be true that
> > (B) {su'o ransedyta'u cu se dasni ro faspre},
> > i.e. we can just swap the quantifiers over and get another true
> > statement.
> >
> > How does that work? For (B) to be true, we need something which
> > ransedyta'us and which every French person wears. With malkinds, (A)
> > being true implies that there is such a thing - namely the malkind
> > corresponding to berets.
> >
> > (Various terms have been used which I take to refer to such a malkind,
> > amongst them "berets", "the kind 'berets'", "Beret", and "Mr. Beret")
>
> Hmm. This is well set out.
>
> As I understand things, (B) is a legitimate entailment of (A) only if
> there is only one beret, i.e. that all frenchmen wear the same beret.
> I think that's the crucial point.
>
> As for whether all frenchmen do wear the same beret, that depends on
> beret differentiation criteria. By the usual beret differentiation
> criteria, they don't wear the same beret. But given that it is
> possible to say that we all admire (the same) Obama and that millions
> of children each play with (the same) Barbie, I think that it would be
> possible to think of a Barbie-like Beret that pops up on the heads of
> many different frenchmen. I leave open whether the Barbie-like
> Beretrequires a different predicate from the berets that each pop up
> on only one head.
Yes, that's exactly the issue. Your Barbie-Beret is a malkind in the
above sense if it satisfies "is a beret".
> I note that natural language appears to be rampantly malkindful:
> "What's *the hat that every frenchman wears*? *It* is a beret. *It* is
> worn by every frenchman."
Yes, indeed.
You can't literally deduce "there is a beret which every french person
wears" from "every french person wears a beret", but you *can* deduce
"there is a hat which every french person wears". So the situation is
barely better than that described above.
Relatedly, no-one would call English a logical language.
> If I may be permitted to impute thoughts to you, I think your basic
> objection is to being able to consider Barbie-like Beret to be
> a beret. You don't object to "Every American should vote for an Obama"
> entailing "An Obama should be voted for by every American", since you
> are happy to accept that there is only one Obama. But you don't accept
> that there is only one beret.
Correctly imputed.
> > So in the sense that if we would say that one is true then we'd also say
> > that the other is true, (A) and (B) are equivalent in malkindful lojban.
>
> Do you mean they are truth-conditionally equivalent, or simply that
> each, when supplemented by auxiliary assumptions, can be inferred from
> the other?
Something like both... see "metatruth" in my reply to xorxes (which is
clumsy, but I don't see a better way to describe the situation).
> If Barbie-like Beret is a malkind, then (B) is derivable
> from (A) only if it is also the case that all frenchmen wear the same
> beret; if they all wear different berets, you can't derive (B).
Hmm? Doesn't (A) imply that all french people wear Barbie-Beret? And
doesn't that imply (B) (in a domain containing Barbie-Beret and new new
french people)?
> So it seems to me that either (A) doesn't entail (B) malkindfully or
> that xorxesianism is not malkindful.
I don't see what you've done here.
> > If xorxes says (B) - or {ro faspre cu dasni lo ransedyta'u}, which
> > appears to be approximately equivalent - I don't know how, beyond my
> > prior knowledge of which was more likely, to tell whether he really means
> > to make the surprising statement that all french people share a single
> > beret, or just the (za'a also false!) statement that every french person
> > wears a beret.
>
> I think (B), at least with {pa ransedyta'u} rather than {su'o
> ransedyta'u}, means they share a single beret.
Again: Barbie-Beret seems to mean you can't deduce that from either.
> And I think {ro faspre cu dasni lo ransedyta'u} means almost the same
> thing, except that it does not exclude the possibility that there is
> more than oneberet worn by every frenchman.
>
> > Generally, with malkinds, the order of quantifiers in a sentence gives
> > *no* information, at least until you bring in informal things like
> > emphasis and convention.
> >
> > It seems to me rather obvious that this should be considered a problem!
> >
> > Can we agree on that much?
>
> As said above, either malkindfulness is a problem but is not
> xorxesian, or malkindfulness is xorxesian but is not a problem
> (because the order of quantifiers does matter in xorxesianism).
>
> > It's more that you take your things and divide them up into sections,
> > and consider two things to be equivalent if they're in the same section.
> >
> > The 'imaginaries' bit implies that the sections shouldn't be chosen just
> > arbitrarily, but should be following some rule.
> >
> > So we decide that even though we were considering all the things to be
> > different, we no longer care about some of the differences, and consider
> > certain things to be the-same-as-for-present-purposes other things.
> >
> > We can then go one step further and consider these sections
> > ("equivalence classes") as things in themselves ("imaginary elements").
> >
> > So this may not be quite what you seem to be saying, but it may be
> > close.
>
> It strikes me as very close or else bang on. I would consider
> everything to be an imaginary element.
Excellent. Another repurposed technical term for lojban to abuse!
I might as well give the full definition: an imaginary is an equivalence
class for a *definable* equivalence relation, which just means that the
notion of equivalence used to split up the classes should be one we can
express in the language - i.e. we can write it down in the form {ce'u
broda ce'u} (where broda is standing in for some possibly quite
complicated expression).
(In the original context, we'd be working purely in first-order logic,
where definability is a rather strong condition... in lojban, which is
highly expressive by design, it isn't such a strong condition. But it
indicates the idea that our notion of equivalence shouldn't be too
unnatural, e.g. we can't just carve our domain into arbitrary subsets
and call each an imaginary)
> >> Sure, we know what the difference between one lion and two lions is.
> >> But there are these cases where you can't tell the difference. And
> >> I think that these cases in which the speaker can't tell the
> >> difference should be generalized into a case where for whatever reason
> >> the speaker doesn't tell the difference.
> >
> > But do we really need to create a new entity to do that? In examples
> > like the "lion(s) in your garden every day", we can just give a vague
> > count - {su'o cinfo}, in that case.
>
> Yes, but it looks like one lion, not like a group of one or more
> lions.
Then {pa ju'o ru'e cinfo}?
> Contrast "the candidate your friends are going to vote for",
> which means they each vote for only one candidate, albeit not
> necessarily the same one, with "the candidates your friends are going
> to vote for", which allows that they each vote for more than one
> candidate.
Hmm. I think we actually do speak different dialects of english! For me,
"the candidate your friends are going to vote for" only makes sense if
my friends are all going to vote for the same candidate. You said
something similar with lions in a previous email which also didn't fit
with my understanding of english.
Not that this really matters, since it's lojban we care about, but
I thought I should mention it in case it leads to any crosstalking.
> >>>> If the difference between (i), (iii) and (iv) is that in (i)
> >>>> disambiguation is by tense, in (iii) disambiguation is by special
> >>>> individuating cmavo, and in (iv) disambiguation is solely by glorking,
> >>>> then I reject (i) because I don't see how it could work,
> >>>
> >>> Do you see that it couldn't work?
> >>
> >> Yes. If {ko'a broda ko'e} you'd want to disambiguate both the criteria
> >> by which ko'a counts as a single broda (be ko'e) and the criteria by
> >> which ko'e counts as a single se broda (be ko'a). I don't see how the
> >> tense system could do that.
> >
> > i.e. it works only on unary predicates?
>
> Yes.
>
> > But we're talking about using it on a descriptor, which takes a unary
> > predicate anyway. In {lo broda be ko'e} there's only one place to
> > deal with; similarly for {lo se broda be ko'a}.
>
> So the same problem doesn't arise with {pa da broda pa de}? What
> I mean is, yes we talking about {lo}, but if you need to indicate
> differentiation criteria on the unary predicate complement of {lo},
> why wouldn't you also need to indicate differentiation criteria on
> predicate places in general?
The idea here ((i)) was not to have differentiation criteria, but
instead just use bunches. You can get appropriate bunches using {lo} and
tenses; then e.g. instead of saying something about Barbie-Beret, you
say it about the bunch of all possible berets.
> > So one solution (similar to something I've suggested in different
> > language before) might actually be to allow these imaginaries in
> > addition to bunches, and allow that those e.g. deriving from lions do
> > themselves cinfo, *but* require that (usual singular) quantifiers do not
> > pick them up.
> >
> > {lo}, meanwhile, could be defined to be allowed to pick up any of them.
> >
> > We might also define/clarify other quantifiers and gadri to be allowed
> > to pick up various combinations of bunches and imaginaries.
>
> Since I think everything is an imaginary, in the sense of being
> a generalization over potential subtypes, something that doesn't pick
> up imaginaries doesn't pick up anything.
>
> > Other than the fact that I doubt I've made sufficiently clear what
> > I mean by an 'imaginary', and the issue that I'm not really sure that
> > what I mean by it covers all the cases you and xorxes want to be
> > covered, I suppose your main problem with this would be that it still
> > singles out a particular "layer" of e.g. lions to be the things picked
> > up by {su'o cinfo}.
>
> Yes.
>
> >But I don't see a way around that if we want to
> > solve the quantifier-swapping issue (which I really think we do).
>
> I don't think there is a quantifier-swapping issue.
Let's see how that plays out, then, before discussing what to do with
imaginaries.
> There's only disagreement on beret-counting. Or Obama-counting: if
> I don't agree that there is only one Obama, then I'd object to you
> claiming that "ro prenu cu prami su'o Obama" and "su'o Obama cu se
> prami ro prenu" are equivalent.
If you were happy to choose once and for all whether you want multiple
berets (one for each french person, say) or just Barbie-Beret, there
wouldn't be such a problem. But you want both, in different situations,
don't you? With all of them ransedyta'uing?
Martin
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