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Re: [jboske] Transfinites



At 04:47 AM 1/12/03 +1100, Nick Nicholas wrote:
cu'u la lojbab

OK, I'll try to explain, but since I'm playing And's game, you are
likeliest to consider this all illegitimate.

You may be surprised. I'm not an idiot, and I you have proven to be a superior teacher-to-lojbab than the others.


> At 09:26 PM 1/11/03 +1100, Nick Nicholas wrote:

> >xod was wrong about tu'o.
> Without agreement as to the meaning of tu'o, I can't argue this very
> well.

In *all* the following, assume that tu'o = mo'ezi'o, because that is
what we have *all* been doing: xod, And, Jorge, and me.

Ok, for purposes of this discussion. But then ...


> You seem to jump back and forth as to the meaning of tu'o.

Yes, because there are two senses of mo'ezi'o: one that we have gotten
used to over the past month (uncountably many), which I believe is
wrong, and one that no quantification is pertinent, which I think
handles the intensional readings of entities.

Which suggests that people are using two different meanings for zi'o, which in turn means different meanings of mo'ezi'o which in turn gives different meanings of tu'o.


That there are different meanings of zi'o in play seems further evidenced by my failure to understand And's claim that "zi'o catra ko'a" means "ko'a mrobi'o" (perhaps adding an x3 zi'o on the catra to avoid questions of the corresponding value in the mrobi'o predicate). (Besides the question of zi'o, ultimately it appears that both sentences are trying to be predicates on the single argument ko'a, and it becomes a question of whether a 1-place catra is the same predicate as a 1-place mrobi'o; this cannot be deduced because we have no appropriate rules for deduction or definition of the MEANING of a zi'o'd predicate like 1-place catra; and then even if we say that two predicates have the same set of truth values, we cannot say that they are the same predicate or mean the same, but merely that one entails the other. /end-of-distraction).

My reading of CLL zi'o (which I hit when I looked up CLL zo'e so it is relatively fresh) matches with understanding Cowan's "translated" example and your mo'ezi'o interpretation that "no quantification is pertinent". The meaning I get from the tu'odu'u discussion as explained by And, is that he thinks that zi'o means that "there may be 1 or more quantification values that could be inserted, but none of them are more correct than any other", which sounds to me like answering the "ma catra ko'a with "guns", "bullets", "a specific bullet", "a finger of ko'e that pulled the trigger whether or not ko'e was aware of this", etc. which goes back to questions of causality and "guns don't kill people, people kill people", a question I spent more time on than others when I reworked the Loglan design into Lojban.

At any rate, it seems clear that understanding and resolving the gadri quantification issue rests on clear determining/defining some far more basic questions of Lojban semantics that seem to be up in the air, like the meaning of zi'o, zo'e, tu'o, the definition of a predicate, causality vs. equivalence, etc. I don't expect jboske to drop its current apparently productive line of thought merely because I don't understand it, but I suggest that the byfy needs to tackle things in a different order to build the infrastructure to make these discussions clear to us less-logical types.

Pop the stack. Back to your explanation ...

> >Second. the cardinality of the set is trans-infinite. This is what
> >holds for substances.
> These strike me as incompatible with a zi'o interpretation. 0, 1, and
> aleph are all possible values for quantification, and therefore not a zi'o
> but a zo'e, given the way CLL distinguishes between zi'o and zo'e.

That is my conclusion.

We agree 8-), but I don't think And makes the same distinction between zo'e and zi'o. ...


In particular, as I say, {ro} is intuitively used for transfinite sets;

By transfinite, I assume you mean all forms of ci'i/infinity


and the set of all possible portions of a
substance is demonstrably transfinite.

All accept this as following from the assumed definition of substance, even though I think that we have two kinds of substances, the infinitely subdividable kind and the atomically composed kind. Modern scientific theory seems to reject the possible existence of the former, and we need to be able to disambiguate the two kinds of substances (and I daresay that gadri that reflect scientific reality are more important than those that reflect abstract philosophical analysis that does not match reality, while admitting that we do need to be able to handle infinitesimals, if only for mathematics).


> >Since xod, we have been limiting the denotation of {ro} to countable
> >numbers,
> Which if I had understood, I would have disagreed with on the spot.
> That
> is why proposals need to be translated into English.

xod said in English "if only you guys hadn't hijacked tu'o to mean
Unique, we could use it to indicate the inner quantifier of
substances." And immediately said "good idea." I now think it isn't.

I am coming back to the hijacking of tu'o for Unique/Kind,

which is Mr. Rabbit, right? The terminology changes so rapidly that non-jboske types can't keep straight what the current meaning is, much less relate it to non-jboske language. I think this is part of what turns off people who are less than full-blooded jboske - miss or misunderstand a single message where the words got redefined and you are lost forever.


but now I
think for different reasons: tu'o signals that unlike su'o da, the
quantifier does not appear in a prenex.

However "ci'i da" would appear in a prenex? And you think now that ci'ida is, or is not, the appropriate quantifier for philosophical "substances"?


> >The kind divorces
> >the quantificand from any prenex. So I contend tu'o lo mikce --- a
> >non-counted, not an uncountable doctor --- is meaningful as an
> >individual, not a substance: it is the intensional doctor, the
> >doctor-kind.
>
> You've been talking about inner quantifiers, and then suddenly use an
> outer.
> mi na jimpe

Bob, you are slow (and I have personal experience of that), but I am
also moving very fast here. I have just concluded that tu'o is
illegitimate for inner quantifiers, since our sets of substances do
have a cardinality (albeit transinfinite). However, I am now saying
tu'o is legitimate for outer quantifiers, because it suppresses
quantifying the entity in the (outermost) prenex --- which is how we
think of intensionals.

OK. You jumped usages of tu'o without explaining. I get the explanation. Even while not entirely getting intensionals, I recognize that there is a difference between what you are calling intensionals and whatever the others are called ("extensionals"? the in-/ex- opposition seems unexplained here, but whatever; I know less Latin than I do logic).


> The following almost makes sense, except that the lack of the broda leaves
> me lacking a referent, and the tu'o again seems incompatible with zi'o

*All* the tu'o in these examples are indicating "suppress prenex
quantification":

> >pa lo ci'ino Atom
> >tu'o lo ci'ino Kind of Atom

As in, if this is one of aleph-null entities (actually, sueci'ino),
this is an individual (not just an atom -- I refined that later).

Can I suggest using either '(mathematical) point' or 'infinitesimal'? If these are too much of a pain to type, a Lojban word would be even better. I tend to do much better when Lojban words are coined for concepts that cannot be presumed to mean what they normally do in English usage.


If this is [quantification is irrelevant] out of aleph-null, this is a
Kind of Individual, or an Intension of Individual: ^lx.Individual(x).

I presume that you could come up with an example sentence using points on a line intensionally, even though I have no idea what such a sentence would be, since I can't keep intension and extension straight (there are at least 3 different meanings of "intensional/intentional" in use in Lojban and cross-pond spelling convention issues that make me certain that I don't know which is being used.


intention ->planned, semu'i/seri'a
intent/sion - something to do with tense and modality that pc often uses (and there may be two ways that pc uses it), and the implied relationship between the root "tense" referring to the tense system as well as to whatever pc means by intensional makes it only worse
intension vs extension - the meaning that applies here


Please make sure these words are well defined for byfy use, and again I suggest we coin some lojbanisms.

> >The majority of properties are inherently atomic, group, or substance.
> This last sentence suggests that the above are quantifiers on different
> sorts of ka broda, not on broda. I don't know what else you might mean
> by "properties".

Again, you've missed some episodes. Property in the Montague sense is
defined as ^lx.P(x): it is a predicate, abstracted over possible times
and worlds. If you would rather read 'predicate' where I say
'property', go ahead.

I read your explanation as expanding your above statement to mean.


"The majority of ce'u roles in ka ce'u broda properties are inherently atomic, group, or substance."

Lojban attempts to question the assumption that such ce'u roles are inherently anything, even while the prescribed place structures GENERALLY dictate a particular kind of sumti has to fill the role (though of course the terminology we've used has been set/mass/individual alternation rather than atomic/group/substance) This suggests that your model has an underlying different structure than the fundamental Lojban one, but for once I won't object till I see where it leads.

so we have unresolved issues: the assumption of inherency of place structure role types (which seems to contradict the concept of predicate), the set of inherent roles that is applicable (which I keep trying to relate to the variety of possible objects that can exist in OOP), and the overall structure. These sound like incredibly difficult issues.

But OK, let's move on %^)

> >So the innermost quantifier, aleph-0 or aleph-1, is usually left out
> >with impunity. Illustrating with djacu as substance and remna as
> >atomic, Standard quantifier defaults, and tu'o meaning ci'ipa:
> You've lost me again - I thought you were arguing for your "third
> reason"
> which is compatible with tu'o=mo'ezi'o (in which case it cannot mean
> ci'ipa
> which is a value).

No, this is to make myself intelligible to other discussants, who in
the past month have treated tu'o as ci'ipa. I do so in the Kludgesome
Solution too, but in brackets. The convention shall be, outermost tu'o
is Kind; non-outer tu'o should be understood as ci'ipa.

Why not just say ci'ipa, after defining that you think it means what they have been using tu'o for?


> >loi remna Collective of Individual
> >tu'o loi remna
> The inner quantifier of these is presumably the number of people,
> which is
> somewhere around 6 billion. I don't understand how tu'o fits.

I'm being elliptical: loi remna: Collective; tu'o loi remna: Kind of
Collective (Intension of Collective.)

If you had put the inner quantifier in, and had also indicated that you were doing pairs of extensional/intensional forms, I might have gotten it (given all the above explanation). Remember this need to be explicit when you have to explain it to the next non-jboskeist (as you will eventually if it works)


> >loi djacu Substance
> >tu'o loi djacu
>
> The inner quantifier of djacu substance would seem to be a countable
> large but less than aleph null number of portions of djacu, all larger than
> atomic size, which could be formed out of the mass of all water.

Bull. As I've been saying in my ontologies, the point of a substance is
that it is infinitesimally subdividable. Water is not truly
infinitesimally subdividable, but is always linguistically treated as
subdividable, because atomic theory has not yet influenced human
language.

I hate the example. "Water" may be treated as if atomic theory doesn't exist, but "djacu" then may not mean "water" linguistically, because the Lojban inventors and most users KNOW atomic theory exists, and they also know that real-world "water" as opposed to the linguistic stuff, has emergent properties like wetness that even individual molecules do not have. Thus "ka ce'u djacu" is precisely an example of a sumti role that is NOT inherently atomic group, or substance, but may be any of these or something disjoint/overlapping all of them that hasn't been covered. I really think you have to go back to mathematics to come up with pure concepts that fit these ideals, and even then I have trouble (a line-of-point requires at least two points, so it is a substance composed of an infinite number of two-adjacent-point-atoms that all display the same properties as the whole).


The inner quantifier is all possible amounts of water, not
just all possible physically separate amounts of water; if you mix
together green and red water, you can say that some of the water is red
and some green, but you will not be able to physically separate them. A
substance by definition has aleph-one (maybe aleph-two) as its inner
quantifier.

This sounds more akin to Lojbanmass-of-substance(goo), but OK.


The atomic theory, by making the inner quantifier finite,
makes water a collective of molecules.

OK


> >pisu'o remna Substance of Individual
> No idea.

You know this as "sailor-Goo"

Got that. But I don't know whether you are assuming "Q remna" ?= "Q da poi remna" ?= "Q lo remna"


Different Lojbanists seem to have different opinions as to how each of these relate to the other, and I can't keep the CLL story (which I accepted without agreeing to in the "Great jboske Debate on gadri of 1994") straight from my "founder's intent" version, from whatever version you are assuming.

Not knowing what the semantics of Q remna meant, I did not understand what you were trying to say about sailor-goo.

> >lo djacu Individual of Substance

You know this as "a piece of"

"selci of" or "pagbu of" or "spisa" of (which I note uses "substance" in the gismu definition - we better fix it to match whatever is appropriate).


We WILL need gismu or brivla clearly defined for all of these fundamental concepts and consistently stated with reference to those concepts. They can be among the ones we define for the dictionary. I accept that place structure rewording to make such consistency is quite within the fundamentalist byfy charter.

> >This reverts to pragmatics after all. Well, pragmatics as in knowledge
> >about the world.
> ... I need some context indicating how you might use each of these
> concoctions, to know enough about what they mean in order to test
> whether
> they fit my sense of pragmatics.

Oh, I'm sure they won't: I simply mean real world knowledge.

And "my sense of pragmatics" has nothing to do with "real world knowledge"? Gee thanks %^)


> >* If a property is inherently atomic, loi ro is the collective, and loi
> >piro the substance. The default is loi is the collective.

People are atoms; they don't contain other people.

Individual remna are atoms (use remna, not "people" which is ambiguous between remna and prenu, and in English is some sort of mass, since it has no singular)


(Embryos don't count.)

If an embryo is a remna then it is not part of mother remna. If it is part of mother remna, it is not an individual remna itself. (lojban solves the abortion terminology debate, at least semantically %^)


loi ro remna is a collective,

Assuming that lojbansets are not collectives, OK.


loi piro remna (which I introduce
later as shorthand for {loi ci'ipa su'omei be su'o lo ro remna} is a
substance [People-goo],

I would have thought that the latter would be (using your above definition of sailor-goo as pisu'o remna)


loi ci'ipa su'omei be [pisu'o remna]

But I do get

loi ci'ipa su'omei be su'o lo ro mokca as being a "line-of-points" quasi-substance (but see above note on the unit infinitesimal selci of a line be two adjacent points)

As for your label, you have two different things called "substance": substance of individual (sailor-goo) which you said was pisu'o broda and this new "people(human)-goo" which is "loi piro remna, or is the latter "humanity-goo", as opposed to "human-goo".

and the default interpretation of {loi ro remna} is collective.

I said OK to that above.


> >* If a property is inherently substance, lo is the individual, loi
> >su'o/ci'ino/(ro) (countable) is the collective, and loi tu'o/ci'ipa
> >(uncountable) is the substance. The default is loi is the substance.

Water is substance: all quantities of water contain smaller quantities
of water (ignoring the atomic theory.)

ci'ino being a countable infinity, while ci'isu'opa is an uncountable infinity, right?


Lines-of-adjacent-point-pairs are therefore a collective of countable infinity size, and lines-of-any-point-pairs is a substance of uncountable infinity smaller lines, with or without atomic theory. I'm using it to try to understand you. Then lo is a line (or is it a line-selci(point-pair)) ignoring its internal structure.

You can make loi djacu mean
either a collective of individual portions of water (traysful of
glasses of water), or just the substance of water. Obviously the
default should be the substance of water. So water and people will
behave differently as to what the default inner quantification of their
lojbanmasses is.

I think I see this.


A lojbanmass of people is by default a collective. A
lojbanmass of water is by default a substance. This is a defeasible
default, but a sensible default nonetheless.

OK.


> >... Later (sigh), I will try and see how I wedge this into something
> >compatible with the Excellent Solution.
> Which excellent solution, and why do we want compatibility with it?

And's topsy-turvy reconfigurations of the gadri, which you've dismissed
as frivolous and which have indeed paid little mind to traditional
distinctions, but which also make differentiations you still have no
inkling of.

The question is whether Lojban should be trying to add new differentiations that are not already inherently built into the language. Does Lojban need to make unambiguously all distinctions that metaphysicians can come up with even though no natural language can unambiguously do so?


I see a purpose in trying to do so: Lojban strives for metaphysical neutrality. But since at any point someone could invent a new metaphysics that counters all of the accommodations Lojban has built in, at some point metaphysical neutrality becomes an argument for an open-ended and ever-changing language, and we have two fundamental design principles (metaphysical neutrality, and speakable/learnable/more-or-less-unchanging language) in conflict.

I think that ultrafundamentalism requires that we make no accommodating changes for new metaphysics that were not conceived of when the baseline was specified. I am willing to relax on this, especially if you can fit the basics of something that is apparently as widely accepted as Montague semantics into Lojban with relatively minor accommodations. But those differentiations that I have no inkling of would otherwise seem to require experimental cmavo or more longwinded forms under any sort of fundamentalism. I get upset when And pushes not merely for formalism (which you are trying but conservatively) but open-ended formalism that lets him posit new abbreviations for metaphysical differentiations that were NOT part of the baseline language.

So if you can use differing default quantifiers, and the surfeit of gadri that we have, in order to make new metaphysical distinctions that cover more/most/all of Montague, and not break the usage tradition more than we'll have to in order to resolve messes like tu'o and zi'o, then I can probably be convinced.

> > Under this scheme, if the outer
> >quantifier is truly defeasible, then the distinction between kind and
> >avatar is also defeasible. Whatever is true of su'o lo broda is true of
> >tu'o lo broda. So lo broda can be interpreted as su'o lo broda. In
> >intensional contexts, people will need to distinguish between de dicto
> >and de re, by saying su'o lo broda vs. tu'o lo broda, or leave it vague
> >--- *precisely as in natlangs* -- by saying lo broda. However, if they
> >want any two doctors, they'll have to say (tu'o) lo mikce remei.
> Uncommentable due to lack of clear definitions.

Kind and avatar?

And defeasible and de dicto and de re (and their interaction with intensional) and vague and intensional. Too many in one paragraph that I don't clearly understand.


If you eat fish and chips, and I eat fish and chips,
we both eat the same Mr Fish'n'chips (Kind), but difference instances
of Mr Fish'n'Chips (avatar).

So there are TWO kinds of Mr. Rabbit %^) Which one is the mythical Trobriander version of JCB-ism?


If something is true of any individual, and the individual is an avatar
of a Kind, then that something is also true of the Kind. By definition.

Net personae Nicks are avatars of Nick-kind who sits at a keyboard.


I'm not going to define de dicto and de re for you as well; that's been
bandied once too often for me to think you don't know it

I don't - Latin goes through me without cognition, and I've usually skipped the messages that dealt with them - I don't read every jboske message. I know that there is a distinction, but I can't remember a defining pair, and if I did would mix the two up as to which was which. I also get the impression that they interact with but may or may not be the same as opaque/transparent.


Just too damn many features to keep straight. Lojban cannot handle all of them as equally important or we end up with a thousand different gadri or gadri-modifiers depending on whether we supports And's desire for abbreviations or just merely make it possible to say anything in any metaphysical way.

byfy may need a wiki (or to reference the main wiki) in providing easily accessible definitions of key terms with examples (and preferably with Lojban brivla for each for those of us who want to remove ourselves from the problems of English/Latin jargon to Lojban jargon). I understand Xod started to do something like this independent of the wiki on a web page. It needs to be part of the wiki.

--- resolving
it in all contexts is a crucial problem, which Lojban simply hasn't
dealt with, since it assumes propositionalism (you can always find an
inner nested prenex to quantify an intensional sumti --- something not
true for 'draw', and misleading even for 'want'.)

Is this what pc was referring to in his statement that we fixed sisku but forgot the fix with "seeks an instantiation of property x" vs. "seeks property X", or something more?


There! Took me a few hours but I got through it. And I didn't find it illegitimate, but not completely understandable, and it begs so many questions that I can't imagine the average Lojbanist ever understanding whatever it is that you come up with. And if Lojbanists in general cannot understand it, then there becomes a schismatic AL that more resembles Nalgol/guaspi than Loglan/Lojban in lack of understanding/lack of use.

lojbab

--
lojbab lojbab@lojban.org
Bob LeChevalier, President, The Logical Language Group, Inc.
2904 Beau Lane, Fairfax VA 22031-1303 USA 703-385-0273
Artificial language Loglan/Lojban: http://www.lojban.org