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Re: [lojban] {zo'e} as close-scope existentially quantified plural variable

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.

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."
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. 


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? 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).

So it seems to me that either (A) doesn't entail (B) malkindfully or that xorxesianism is not malkindful.


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. 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'd be the individuative cmavo. I guess the one you call "Lion" is
used where X is a lion and Y is a lion but you don't know (or don't
say) whether X = Y.


Err. Maybe. I don't think I understand you there.


Well, I was just groping towards trying to get an understanding of
what Lion is.


But if you mean to consider kinds as equivalence classes of mundanes
("imaginary elements", in mathematical logic jargon), I may be with you.


Explain a bit further, and then I might be able to say whether this is
what I mean.

I don't know what equivalence classes and imaginary elements are, but
if they're what you get in situations where broda(X) and broda(Y), but
you don't know or choose not to say whether X=Y, then maybe I'm saying
that whenever you say broda(Z), Z is one of these equivalence classes
thingos.


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.


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. 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.

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?


Do you mean that there's then a bootstrapping issue - we need ko'a to
get ko'e and need ko'e to get ko'a?


No.


Given e.g. a binary predicate P(x,y), which let's say is to start with
defined only when x is a foo and y is quux,
(i) has us define what P(X,Y) means where X is a bunch of foos and Y is
a bunch of quuxs (here a bunch of foos corresponds to a set of foos);
meanwhile, (iii) (or something like it) has us define what P(x/~, y/~)
means, where x/~ is an imaginary foo - i.e. one of the new things we get
when we consider a new, coarser notion of equality of foos - and y/~ is
an imaginary quux.

So we need to consider the properties of these new beasties X and x/~.
One possible, arguably natural, scheme for this in the case of x/~ leads
to the quantifier-permuting ambiguities discussed at the top of this
post.

Why is X better? Actually, it isn't - they're pretty much dual. The
difference is *just* that we're allowing {su'o da} and {ro broda} to
pick up things like x/~, but not to pick up things like X.

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. 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.
--And.

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