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Re: [jboske] Transfinites

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.

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.

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.

>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. In particular, as I say, {ro} is intuitively used for transfinite sets; and the set of all possible portions of a substance is demonstrably transfinite.

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

>There is a third reason to use tu'o: if there is no quantification
>going on at all. No quantification means no prenex.

This seems consistent with mo'ezi'o.

>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.

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

>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.

>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.

>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.)

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

>pisu'o remna Substance of Individual
No idea.

You know this as "sailor-Goo"

>lo djacu Individual of Substance

You know this as "a piece of"

>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.

>* 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. (Embryos don't count.) loi ro remna is a collective, 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], and the default interpretation of {loi ro remna} is collective.

>* 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.) 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. 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.

>... 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.

> 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? 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).

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.

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 --- 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'.)

--
ÎÎ ÎÎÎÎÏÎ ÎÏÎÎ ÏÎ ÏÏÎÎÎÎ ÏÎ ÎÎÎÎÎÎÎÎÎ#Nick Nicholas, French/Italian,
ÏÎÎ ÎÎÎÏÎÎ ÏÎÏ ÏÎ ÎÏÏÏÎÎ ÎÎÎÎÎÎÎÏÎ #University of Melbourne
ÏÎÎ ÏÏÎ ÏÎÏ ÎÎÎÎÎÎÎ ÎÏÎÎÏÏÎ, ÏÎÎÎÎÎ! # nickn@unimelb.edu.au
ÏÏÎÏ ÎÏÏÏÎÎÎÏ ÎÎÎ ÏÏ' ÎÎÎÎÏÎÎÎÎ ÎÎÏÎ.# http://www.opoudjis.net
-- Î. ÎÎÎÎÎÏÎÎÎÎÏ, ÎÎÏÏÏÎÎÎÏ: ÎÏÎÏÏÏÏ# 

===
O Roeschen Roth! Der Mensch liegt in tiefster Noth! Der Mensch liegt in
tiefster Pein! Je lieber moecht' ich im Himmel sein! --- _Urlicht_
nickn@unimelb.edu.au http://www.opoudjis.net
Dr Nick NICHOLAS, French & Italian, Univ. of Melbourne, Australia