* Friday, 2011-11-04 at 18:34 +0000 - And Rosta <and.rosta@gmail.com>:
> Martin Bays, On 03/11/2011 23:49:
> > * Saturday, 2011-10-29 at 20:59 +0100 - And Rosta<and.rosta@gmail.com>:
> >> Martin Bays, On 29/10/2011 18:28:
> >>> * Saturday, 2011-10-29 at 17:05 +0100 - And Rosta<and.rosta@gmail.com>:
> >>>> Martin Bays, On 29/10/2011 01:14:
> >>>>> I'm saying that the definition of {cinfo} is
> >>>>> "x1 is a lion/[lioness] of species/breed x2", and that I wouldn't want
> >>>>> to change this.
> >>>> We're all saying this much.
> >>> If you were actually saying that Lion is a lion, it would be the meaning
> >>> of English we were disagreeing on! So I hope you aren't.
> >> Given that English allows us to speak of "a lion" that you would
> >> consider to not count as a lion, and to speak of "an Obama" that you
> >> would not consider to count as an Obama, we do seem now to be
> >> disagreeing about the meaning of English.
> > OK, so I agree that "is a lion" can sometimes be used of kinds of lions.
> > I was forgetting this.
> > I'm not sure it can be used of Lion itself, though.
>
> A difficulty I have in this discussion is that you have defined
> various notions, such as 'Lion', 'kinds', 'mundanes', but we lack
> a clear mutual understanding of them. Furthermore, you are using these
> notions metalinguistically but arguing they don't have a place in
> Lojban and are supposing me to be arguing that they do have a place in
> Lojban, whereas I don't really understand the import of the
> metalinguistic terms, and hence don't believe myself to be arguing the
> notions have a place in Lojban.
OK!
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")
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.
What's more, this works with *any* forall-exists statement. If {ro broda
su'o brode cu brodi} is true, then with malkinds, {su'o brode ro broda
cu se brodi} is true.
More generally, this allows us to permute universal and existential
quantifiers however we like - e.g. if an AEEA sentence is true, then so
is the corresponding EAEA sentence, hence so is the EAAE sentence, and
so on.
Now there's a subtle issue I've glossed over thus far, which is *where*
these sentences are true. What follows from an AE sentence like (A)
being true in a given domain is not that the corresponding EA sentence
(like (B)) is true in *that* domain, because that domain may have
omitted the malkind. But it's true in some other domain, namely one
which contains the malkind, e.g. Beret, and doesn't introduce e.g. any
new french people.
Does this domain-switching save us?
I think not. If someone says (B) to us, we have no way, other than our
knowledge that it would otherwise be false, of knowing that we are meant
to interpret it in a domain containing the malkind Beret.
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.
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?
> >> 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. We have a load of things, say lions, and we decide to consider
some of them to be equal-for-present-purposes to others; e.g. we might
decided that any two lions of the same sex are
equal-for-present-purposes. This leaves us (glossing over the
complexities of gender in real life) with two things - which we might
refer to as male lions and female lions, but which we think of as
individuals rather than as sets/bunches.
> > (Although I'm not sure this wouldn't end up being effectively equivalent
> > to considering them as bunches)
> >
> > In any case: as I'm understanding it, Lion is an entity which somehow
> > corresponds to the unary predicate "x is a lion" (where recall that
> > I mean by this that x is an actual lion, not a kind of lions!). I'm
> > a bit vague on what its properties should be, but xorxes' usage seems to
> > agree with the simple rule: if "lions [do/are something]" is true in
> > english, then Lion does/is it too.
>
> As I suggested in my last message, maybe your Lion is, in my terms,
> what you get when you take the bunch of all lions, but don't know or
> choose not to say whether or not they're all the same lion. I'd say
> all bunches work that way: you don't know or choose not to say whether
> or not they're all the same individual.
>
> >> And the one you'd want is where the speaker is
> >> certain how many distinct lions there are, based on maximizing
> >> spatially distinct lions, minimizing temporally distinct lions, and
> >> whichever other criteria deal with cases like "the lion(s) we each
> >> spoke about" (where we each speak about one lion) and so forth.
> >
> > Something like that. Whether or not we can define it precisely, and
> > whether or not we'd agree on edge-cases, I think we both know what the
> > difference between one lion and two lions is.
>
> 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.
> >> I don't see there being a simple dichotomy between kinds and
> >> nonkinds, though.
> >
> > Is a lion a kind? If so, what are its exemplars?
> >
> > Ah, I recall your answer: lion-stages.
> >
> > OK; is a lion-stage a kind? If so, what are its exemplars?
>
> Further lion-stages. Or, as xorxes suggested in his reply, different
> spatial aspects. Or, the lion-stage-that-I-described and the
> lion-stage-that-you-described. And so on -- subtypes may be
> differentiated in all sorts of ways, not just spatiotemporal ones.
I see, maybe.
> >>> OK, so it seems we now have three proposed methods of handling this kind
> >>> of situation:
> >>>
> >>> (i) JC's bunches approach - there are only lions and other perilous
> >>> objects; Lion and Perilousness are maximal(ish?) bunches of such;
> >>> disambiguation is through the tense system (e.g. {lo ka'e ckape},
> >>> maybe)
> >>> (ii) Using abstractions - e.g. Perilousness doesn't ckape, but it does
> >>> ka ckape; Lion doesn't cinfo, but it does ka cinfo and it does
> >>> ckape; lions cinfo and ckape.
> >>> (iii) (being my probably inaccurate understanding of your suggestion)
> >>> Like (ii) but the other way up: Lion is basic; an individuating
> >>> cmavo gets us down to lions. Similarly Perilousness is basic, and
> >>> (multiple? repeated?) cmavo can get us down either to Lion or all
> >>> the way to lions. Sometimes (i.e. in some contexts) only Lion
> >>> cinfos, while sometimes it's lions which cinfo; both ckape when
> >>> they're around, but sometimes only Perilousness ckapes (presumably
> >>> only when neither Lion nor any lions are around, although
> >>> individuating cmavo can summon them into being).
> >>>
> >>> But am I understanding correctly that you actually favour:
> >>>
> >>> (iv) Like (iii) but without the individuating cmavo - we can glork from
> >>> context whether we're talking about lions or Lion or Perilousness.
> >>> ?
> >>
> >> Let me leave Perilousness to one side, since I'm not sure what it means here.
> >>
> >> I'm not advocating (ii).
> >
> > Do you see anything particular wrong with it?
>
> I think it remains to be decided if something that *is* the property
> of being a lion is dangerous, which is what (ii) seems to say. My
> current position is that the property of being a lion is not
> dangerous.
>
> If Lion is not a lion, but is the property of being a lion, then I can
> only conclude that "Lion" does not denote anything that I am arguing
> in support of.
It's more that my understanding of xorxes' Lion, which for him
is a possible referent of {lo cinfo}, has its properties being deducible
(not necessarily straightfowardly) from the properties of lo ka cinfo.
But they're not the same - in particular Lion cinfos, whereas no-one
would want {lo ka cinfo cu cinfo} to hold.
> >> 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? 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}.
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? Theoretically plausible, but do you
have any example where this would be an issue (i.e. where we can't get
ko'a or ko'e some other way)?
> >> and favour (iii)
> >
> > There is a reason to prefer a bottom-up approach like (i) or (ii) to the
> > top-down approach of (iii). Although the path may in some cases be
> > tortured, it does seem that the properties of kinds are eventually
> > derived from the properties of their exemplars; but the converse is
> > false.
>
> I understood the difference between (i) and (iii) to principally
> involve whether it is the predicate/predication that is marked with
> a disambiguator or whether it is the predicate-place that is marked
> with a disambiguator.
>
> Any disambiguation schmeme also faces the problem that wWhere broda(X)
> and broda(Y), there is a potentially infinite number of different ways
> of deciding that X is or is not Y, so I guess the scheme would need to
> be suitably open-ended and expandable.
So perhaps it would be helpful to think about it like this:
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.
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}. But I don't see a way around that if we want to
solve the quantifier-swapping issue (which I really think we do).
> >> if only because you have thought deeply about (iv) and find it
> >> unsatisfactory. If i were to consider only my needs and not yours,
> >> (iv) would suffice.
> >
> > Then again, maybe you have a (v) to suggest?
>
> I don't have a clear enough sense of what would satisfy you. I think
> for lions and Obama I might have a clear sense, but I don't know how
> to generalize that to a usable scheme.
Nevermind, it sounds like I have a (v). Maybe I'll try to present it
more cleanly in a later mail.
Martin
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