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Re: [jboske] Digest Number 160

1. Back to mass mails.
2. I'm leaving town Monday, like I say, and doing my printouts Friday night. I'm going to have to take time off just to digest all the arguments that have flown on my topic.

Message: 7
Date: Sun, 12 Jan 2003 16:07:04 -0000
From: "And Rosta" <a.rosta@lycos.co.uk>
Subject: RE: Kludgesome Solution #1


The signs are encouraging. I have little idea about what is and isn't
consistent with current SL, because that seems so hard to decide.

I don't think SL is that opaque or that difficult to reconcile with. The problem is it is underdifferentiated in many aspects.

There are some axioms of kludginess I abide by.

* unmarked lo broda must be consistent with su'o lo broda
* a collective and a substance must both be expressible with loi (be masses)
* lo broda must denote an individual in the unmarked case (whatever else it may denote)

> > > 4. I'm not clear on the difference between extensional and 
> intensional
> > sets, but the solutions And proposes are compatible with a more
> > fundamentalist Lojban
> Two extensional sets are identical if they have the same membership
> Two intensional sets are identical if they have the same defining
> feature (the same membership criterion)

Oh. Got it. As in, the former is the denotation of lx.P(x); the latter
is, more or less, the expression lx.P(x). OK, I'll try and incorporate
this


One possibility for intensional sets is {tu'o (lo) du be lV'i},
but this only works if tu'o IS treated as having scope over
lV'i. Otherwise, there is no difference between:

tu'o du be lo'i jboskepre

and

lo'i jboskepre ku goi ko'a zo'u tu'o du be ko'a

whereas the intention is that only the latter should be equivalent
to:

tu'o du be la xorxes ce la nik ce la xod ce la djan ce la and...

I still don't fully grok this (Mr set of Lojbanists, whose extensions (avatars) may be different across worlds and times, but is inherently the same individual?), but I think this can simply be

tu'o lo piro lo'i

since this exploits (a) the fact that piro lo'i == lo'i ; (b) lo piro lo'i is consistent with how KS1 indviduates non-individuals as entireties --- as opposed to lu'a, which *extracts* individuals.

> > > 7. Inner quantification does not properly include tu'o, since the set 
> > of all possible portions of substance does have a (transfinite)
> > cardinality --- which is assuredly not mo'ezi'o
> Okay, but I can't promise that we won't find differences between
> "is water" and "is a portion of water"

Well, there are three things one can speak of:

1. substance(x): x contains at least one bit that is P, but x contains
no atom of P

2. bit of substance(x): the transinfinitely many bits of x.
Transinfinitely means uncountable because, if you think you have
counted all the possible portions of the substance (top 16/th cube,
middle 16/th cube, central 19/th sphere), you can always come up with a
portion you haven't accounted for. Just as with Real numbers and the
diagonalisation proof


(I still wouldn't know what the difference between 'transinfinite'
and 'transfinite' is, but at least I understand the two sorts of
infinity found in the natural and real numbers.)

'transfinite' is the proper term, 'transinfinite' is my mangling of it.

> In fact, since bits of substance are delimited by 3D space, which are 
delimited by 3D points, which are specified by real numbers, that
cardinality is necessarily the same as real numbers


I hope this talk of '3D space' is prototypical rather than strictly
definitional.

I've started to move on from this. In my ontology, I had only covered physical objects. Now that I've looked at real numbers, I see I have to make the memzilfendi broader, and not define it only in 3D space. In particular, the notion of spisa (what does lo broda mean) is domain-specific: in 3D objects, it's physically distinct objects, in numbers, it's "= x". I guess it's more psychological than anything else: what do we regard as singletons.

> So no, there are countable bits of the substance. It's just that they 
are not all the possible bits of the substance. Just as natural and
rational numbers are countable subsets of the uncountable set of real
numbers. So I believe the analogy holds. A substance is something with
aleph-1 bits, a non-system has at most aleph-0 bits


The difference is that any bit of substance will still contain
aleph-1 bits. Similarlay a *portion* of the number line, say
the stretch between 2 and 4, will contain aleph-1 bits. BUT
we can say that {2, 3, 4} has cardinality 3 -- it contains 2 numbers,
whereas if you take some bits of substance and try to say how many
you have, then the cardinality is always aleph-1.

It depends on the ve memzilfendi. Sorry, but it does. If you don't have a fixed ve memzilfendi (the way of cutting up the stuff), then of course you will have aleph-1 bits. If you do fix it, you'll have finite.

Glasses single out water. Picking discrete numbers singles out numbers. These substances are atomic in singled-outedness, which makes them individuals.

But the nature of a real number is that you can always pick a malicious memzilfendi, the x <= n/2, x > n/2, to chop it into two bits, indefinitely. Numbers are choppable under that ve memzilfendi. That makes them stuff in my book (other than 0; so the predicate namcu can denote both an atom and a stuff.)

Like I said at the start, a entity x can be stuff w.r.t. one pred, and an atom w.r.t. another. 5 is stuff w.r.t. namcu-hood --- an individual of stuff, but an atom w.r.t. 5-hood. A glass of water is stuff w.r.t. waterhood, but an atom w.r.t. a piromeihood. Ergo, when I say lo namcu, I am speaking of an individual of stuff, just like lo djacu, but when I say li 5, I am necessarily speaking of an atom. When I speak of a glass of water as water, I can call it loi djacu as well; but when I call it piromei, it's lo piromei.

The catch is that whatever you can say of an atom, you can say of a mass: 5 is indeed pisu'o loi namcu. But it's not piro loi namcu. It is (I *think* I'm claiming) piro of the stuff (x <= 5). Where piro is *not* "every bit of", but "maximum bit of".

This is an abstruse point, but it's important for my ontology. Then again, it turns out the ontological types only dictate countability/uncountability, and what we're really interested in (gadri and outer quantifiers) refer instead to individual vs. collective vs. "substance" (mass). So that I should call numbers stuff is not ultimately all that germane; we can simply call stuff "anything with transfinite cardinality" and be done with it...

This was my objection, which amounts to saying that numbers aren't
substance. {ci fi'u ro ci'i pa} can quantify over numbers, but
in quantifying over substance the numerator and denominator
if treated as cardinalities would always be {ci'i pa fi'u ro ci'i pa},
so instead we have to use {pa ci'i re} ("1 in every 2 bits") or
{me'i fi'u ro} or {su'o fi'u ro}, or whatever.

Which, I've tried to convince you, is no more applicable for real numbers than to substances (lots of email before I can get to your response.)

> 3. physically distinct bit of substance. I defined this at the end of 
Ontology #3 as spisa. This is a portion of substance of P, wholly
surrounded in 3D space by non-P. The glassful of water, physically
separated by the glass from the pitcherful of water. These spisa are

> countably many
Fine, so long as the 3-D space is the prototype rather than strictly
definitional.

It's clearly not applicable to all sets with transfinite cardinalities, now that I've noticed real numbers. It is applicable to the usual sets with transfinite cardinalities -- material objects.

My concern is that you don't give us a way to do (1). For example,
take "my fondness for Nick". I certainly can't count my fondnesses
for Nick, but nor do know how to quantify over bits of fondness
-- I don't even know how to distinguish ro bits from me'i bits.

(Where (1) is &-Substance.) And, you'll get your Kind. One way or another.

> I believe it is. When the founders said a substance was pisu'o loi ro
> (and they did), the substance was ro of something. This can't just be

ro of spisa (because you can say half the glass is irradiated, and so
the spisa is not atomic.) So I contend it is quantificaation over bits

> of substance
The Founders said that jbomass was pisu'o loi ro. So what that means,
there is no definite way of telling.

But I have a story that explains it. ro is by definition the cardinality of the set of minimum atomic bits, if this is a collective, else aleph-1 (the cardinality of the transfinitely many bits), if not. For humanity, the cardinality is 6G. So ro lo ro remna is 6G out of 6G; for pisu'o loi ro remna qua collective, it's one bit (the maximal) of a population with 6G bits. For djacu, piro loi djacu is one bit (the maximal) of a population with ci'ipa bits.

It's true that djacu and similar gismu are defined not as "is water"
but "is an amount of water". But the fact remains that we might want
to define predicates whose argument is a substance, not a bit of
substance.

You know my answer by now. :-)

> > > {tu'o lo broda se pamei} = {tu'o lu'i loi pa lo broda} = Mr One Broda 
> > {tu'o lo broda se remei} = {tu'o lu'i loi re lo broda} = Mr Two Broda
> > (the members of Mr Pair of Broda)
> > {tu'o lo broda se romei} = {tu'o lu'i loi ro lo broda} = Mr All Broda

> > > (the members of Mr Collective of All Broda)
> > We need to quantify over members of Mr Broda Pair. How do we do that?
> {PA lu'i tu'o lo(i)}?

Hm. Hm. I have only introduced lu'i as a last minute thing, and so I
didn't really think this through, but I suspect the answer is yes. I'll
> need to revisit the INDIVIDUALS IN COLLECTION definition

I misused lu'a for lu'i (that is, misused by my standards, used by your standards). I have accepted that lu'a is quantifiable. So yes:

One out of a pair of broda: pa lu'a loi re lo broda
Kind of one out of a pair of broda: tu'o lu'a loi pa lu'a loi re lo broda

I don't know if you *can* say PA lu'i tu'o loi. Can you extract quantities out of intensions like that?

You know, this tu'o really is too prolix to be really worth it. For real human use, I think I'll give you a LAhE, with some tolerable paraphrase rule, so that LAhE-Kind pa lu'a loi re lo broda can turn into something even more prolix...

Furthermore, zero quantification is not always the same as kind.
Take the collective of {nitcion, xorxes, xod}, or the collective
of all jboskepre. Since there is only one of them, quantification
over collectives of all jboskepre or of n,x,x is redundant and
unnecessary. Yet there is still a distinction between kind and
nonkind versions of these things.

Wait, 'cause you're losing me again. Of the collective of which you speak,

Mr n,x,x has one avatar in any possible world (so we can speak of it extensionally with impunity)
It's a Kind (all its avatars are the same) trivially, because there's only ever one avatar.

all jboskepre has one avatar per time and world.
It has lots of avatars across times and worlds.
Hence, intensionally vs extensionally defined collective.

I can zero quantify both; with the former that's trivial and pointless (since the extension already gives you the same truth conditions in all possible worlds); with the latter... OK, are you saying the Kind is different in different worlds, and tu'o loi jboskepre gives you only Kind of jboskepre-in-this-world?

I don't mind zi'o-quantification breaking down, and in fact nothing in the machinery of tu'o did elevate the Kind to something independent of world and time; but please help out here.

> > > I clean up a logical confusion between tu'o = uncountably many and 
> tu'o
> > = uncounted
> That's not a logical confusion. It's a confusion about the meaning
> of substance selbri ('substance' vs 'bit of substance')

Well, it's a confusion, anyway 

I think a KS solution would be to take the gimste at close to face
value and read "is an amount of" as "is a bit of".

Bit of, not just physically separate bit of (spisa)?

But that doesn't
mean that "is stuff" is not a possible predicate, and your scheme
needs to accommodate this.

When I understand it. :-)

Message: 8
Date: Sun, 12 Jan 2003 16:07:10 -0000
From: "And Rosta" <a.rosta@lycos.co.uk>
Subject: RE: Ontology #3

> And, I am not John. :-) I want to do everything extensionally, because 
I believe that is Lojban nature (we are bound to the prenex). But I
also agree that the intension must be possible, and would rather kludge
that by just switching the damn quantification off


Unfortunately, kinds are only one instance where quantification can
be switched off. The reason why switching off quantification sort
of works for kinds is that there is only one of them. So a rigidly
extensionalist treatment would still insist on quantifying over
Mr Broda ("x1 is Mr Broda").

In fact, you've been quantifying subkinds yourself. But *only* as inner, not as outer quants; that's the difference, right?

The reason I switched of quant wasn't the "is only one", it was the "prenexes give me de re, and I want de dicto." But it would help all of our sanities if I did as you say:

So I wish there to be a way to switch off quantification -- and tu'o
is acceptable for that in a kludgesome solution, though any sort of
overt zi'o is rather galling for reasons we all feel. But tu'o alone
is not sufficient to give us kinds. A KS is at liberty to propose
a new gadrow for kinds, and that might be a more workable solution.

In fact, this would make Kinds immune to brute force extensionalism: sure, put LAhE-Kind lo broda into the prenex for all I care! You'll still only ever get 1 out of it. And 1 means no differentiation between avatars of broda, ever ever ever.

(A property they share with the naughty use of the lojbanmass -- the if (any) 1, then all: the pisu'omei, linking the claim with an unspecified bit of the collective. This is de dicto in a way, but at the expense of sacrificing quantity. (Although if the cardinality is known to be finite {ro}, fi'u ro loi broda gives us the right answer, if we accept that fi'u ro loi is intensionally quantifying --- "any one 1/ro" --- in intensional contexts. But not in extensional contexts. Which is an ugly ambiguity: we're right back where we were with English.) And since this naughty use would be itself chronically confused with the 2 (or 16) other uses of the lojbanmass, I'll leave it as an emergency kludge, if anything.)

Message: 9
Date: Sun, 12 Jan 2003 16:08:26 -0000
From: "And Rosta" <a.rosta@lycos.co.uk>
Subject: RE: Transfinites

[snipped bits where I disagreed then and now over inner quant of fract quants]

> If there is only one all-of-humanity, what's the 6G doing in there (or 
for that matter the ro?) The inner quantifier isn't telling you the
cardinality of groups, the way lo 6ki'oki'o tells you the cardinality
of individual humans. No, the inner quantifier tells you how many
possible atomic bits there are to quantify over, using the fractional
quantifier

So the inner quantifier of a lojbanmass gives you not the cardinality
of the mass, but of the bits of the mass.


Right. But the same is true of sets. {lo'i ci broda} doesn't tell
you how many sets of broda there are; it tells you how many broda
there are.

... Yes. So what's the problem? Sets and Masses behave consistently: it is the nature of fract quant that the inner quant is the cardinality over which the portions are glommed.

> piro means you are picking, not all 
possible fractions of the collective, but the fraction of the
collective which contains all the individual bits


Yes. So really it's functioning as an inner quantifier and
means "lu'o ro fi'u ro".

I'd accept that if I also accepted that pimu loi djacu means {lu'o ro fi'u re} (I think). But the extra stipulation of equal volume makes me think this is simply more intricate.

Eh. I'm starting to spin my wheels here...


Message: 21
Date: Sun, 12 Jan 2003 17:47:07 -0000
From: "And Rosta" <a.rosta@lycos.co.uk>
Subject: RE: Subject: RE: Transfinites

Nick: 
And:
> > There are three reasons you might count something as tu'o
> >
> > First, there's only 0 or 1 of them. Dumb reason. Something like this
> > may have been attempted with ledu'u
> > I'm not sure what you have in mind here, but if the reference to 
> ledu'u is a clue then the argument was that when in the mass of
> all worlds there is exactly one of something, it is undesirable
> (for reasons that I can spell out yet again, if necessary) to
> *have* to quantifier over all broda in order to refer to the one
> broda. So this would really by like your third case

You may not have to, but there is one there: you can put a quantifier
in the prenex, su'osu'epa da. In the third case, you can't: the prenex
is simply sidetracked. Nothing alike. But let's not dwell on that


I'm not convinced that su'osu'epa is the right number. Maybe
{mo'e tu'o lo namcu} is the right number.

You've spelled this out more recently (as one of yr Mr Numbers), right?

At any rate, I accept the important distinction between
{vei mo'e tu'o lo namcu ve'o lo broda} and {tu'o lo broda}. So
we are making progress. However, the way I think this should
be done is:

{vei mo'e lo-kind namcu ve'o broda} (Substance)
{lo-kind broda} (Kind)

or, if you insist:

{vei mo'e lo-kind namcu ve'o lo-kind broda} (Kind)

but this gives rise to infinite recursion unless there is a
PA that means "mo'e lo-kind namcu").

I'll make sense of this in your later email; can't now...

> > > In my ontologies, I have been quantifying with prenexes over 
> substances
> > and bits of substances. I can say that if x is water, all conceivable
> > bits of x are water --- so I am saying all. Similarly, I can speak
> of x
> > + y being a real number, for all real numbers x and y
> Quantifying over a substance is not the same as quantifying over
> bits of substance. The latter makes sense, and to me at least, the
> former doesn't

I now see why. But our inner quantifier for collectives quantifies over
bits of collective (lei re prenu), not over the collective.


I understood it to be {ro fi'u PA} where the numerator is the number
of members in the collective, PA is the number of things with the
te memzilfendi, and ro = denominator.

So in lei pare prenu, it's actually (at least some of) loi (ro/16)? Icky. May buy you some compositionality, but very icky, if so.

> So I 
believe our inner quantifier for substances quantifies over bits of
substance. Of which there are uncountably many, by definition. So
aleph-1 is an appropriate and distinctive inner quantifier. This is not
just tu'o


As I have said in other messages today, if the predicate means
"is a bit of broda-stuff" then the inner quantifier is {ro fi'u
ci'i no}. If the predicate means "is broda-stuff" then the
inner Q is {ro fi'u vei mo'e lo-kind namcu ve'o} (ideally
shortened by a PA meaning "vei mo'e lo-kind namcu ve'o").


So, for a set with 16 individuals
indiv. inner quant: 16
collective inner quant: all/16
pimu loi collective: 1/2 out of all/16 = 8/16 out of all/16 ?
pimu loi substance inner quant: all/Mr Number

I balk at this. I don't think I get it, or that I will like it when I do. I don't think I got it, either...

> > Bearing in mind that I know next to no maths, so am probably talking 
> out of my netherparts, I am guessing that 'all' means 'every member
> of' or 'every subset of', and not 'everything that is a set of real

> > numbers'
> Correct. I can say "all real numbers'. I can say "all possible bits of

water" -- whether they are physically separate or not. They are {ro}.
They are {ro su'e ci'ipa}. By analogy with collectives, that, not tu'o,
is the inner quantifier of substances as lojbanmasses


Okay, if you are saying that loi coerces Substance into Bit of Substance.
{PA-kind (lo PA-kind) broda} should do for Substance.

Excellent progress.

I'm happy you're happy; but once again, I don't get it yet.

You CAN count real numbers. Give me a list of n real numbers and
I will tell you what n is. But you can't give me a list of bits
of substance, because they aren't individuable (if you tried
to give me a list, you'd be giving me a list of Individual of
Bit of Substance). Numbers are (if I remember your scheme correctly)
atoms, while Bits of Substance are Substance. (If I haven't got that
quite right, I think you'll at least know what I mean.) What you
can't do is count the real numbers in a number-span -- that is, if
you count them, you always get to ci'ipa.


So this is what X means by quantifiable: there is something one can start to count with delimited bits of substance and numbers (if one has decided on a ve memzilfendi --- has aportioned it into bits, and therefore individuals), there is nothing to start to count with stuff, it's just stuff. Yes? If I ever give you a cis-finite list of substance, it's a particular ve memzilfendi and se memzilfendi (n).

> By the time we get to PA lo tu'o lo ... , you've got tu'o ambiguous
between Kind and Substance. You don't want that

No. I want PA-kind and lo-kind. Then all is hunkydory.

And this PA-kind is some wierd quantifier, like tu'o but not quite, which asserts the impossibility of quantification, as opposed to the absence from the prenex? Heh. You know, I'd rather give you the separate gadrow for Kinds, and leave tu'o for this PA-kind (if that's what's going on.)

> > I have glossed over this, because I can't keep up and because it
> doesn't cover +specific

Right now, I think +specific is fine print 

Not really, because in my own workings towards XSs I have found that
one of the pitfalls is an excessive asymmetry between o-gadri
and e-gadri, whereas -- elliptizabilites apart -- they ought to
be symmetrical.

Not looking fwd to it them.

> .... basically, do what you want done with gadri (or at least, that
which we both want done), but violating as little of CLL as possible

Damn it, this is fun.. 

I do know what you're doing. I knew it was what you were going to
do. And I am confident that you can succeed.

I'm less so.

The only real difference between KS and XS is that the former
favours SL-compatibility over elegance and the latter favours
elegance over SL-compatibility.

That's what I have in mind.

Message: 25
Date: Sun, 12 Jan 2003 20:28:51 +0000
From: "Jorge Llambias" <jjllambias@hotmail.com>
Subject: Re: Substance vs Bit of Substance


la nitcion cusku di'e

The bits of substance that I've been talking about (anything from "the
top quarter of" to {pi ro}) are, I would claim, extensionally defined
notions of substances.


I agree. You're not really talking about Substance as such but
a quantifiable derivation ("bits of substance"). That bits
can physically contain or overlap other bits is not really
relevant to their quantifiability. Quantifiablility is not
the same as countability.

And whensover we put a fractional quantifier or divide up anything, we introduce quantification in somethat that was otherwise just sludge and unquantified.

Real numbers are quantifiable: you can talk of "each real number",
"no real number", "at least one real number", "not all real
numbers". That the cardinality of the set is aleph-one does not
make them into Substance. If you can single out the members of
the set then you can quantify over that set, whatever the
cardinality.

Numbers are quantifiable bits of number-sludge. :-)

OK, I think I see. No chopping, just sludge. Still call that a Kind.
--
**** **** **** **** **** **** **** **** **** **** **** **** **** **** ****
* Dr Nick Nicholas, French & Italian Studies nickn@unimelb.edu.au *
University of Melbourne, Australia http://www.opoudjis.net
* "Eschewing obfuscatory verbosity of locutional rendering, the *
circumscriptional appelations are excised." --- W. Mann & S. Thompson,
* _Rhetorical Structure Theory: A Theory of Text Organisation_, 1987. *
**** **** **** **** **** **** **** **** **** **** **** **** **** **** ****