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Re: [jboske] Transfinites



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

I almost understand this enough to comment. Since I don't fully, consider my comments to be groping in the dark.

xod was wrong about tu'o.

Without agreement as to the meaning of tu'o, I can't argue this very well. You seem to jump back and forth as to the meaning of tu'o. Thus the exact meaning of tu'o should be settled first before we consider a particular gadri proposal; then introduce something new if what you want doesn't match that tu'o.

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.

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.

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.

and tu'o to transinfinte numbers.

This again is incompatible with tu'o meaning mo'ezi'o, which requires that there be NO number.

This would mean we cannot
speak of ro namcu with respect to the set of Real numbers. This is
bogus.

Agree.

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

So...

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

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

pisu'o loi ci'ino =
su'o fi'u ro loi ci'ino   Collective of Individual
tu'o loi ci'ino   =       Kind of Collective of Individual

pisu'o loi ci'ipa !=
su'o fi'u ro loi ci'ipa   Substance
tu'o loi ci'ipa   =       Kind of Substance

pisu'o lo ci'ino =
pisu'o loi ci'ipa nysi'e be pa lo ci'ino   Individual-Goo (Substance of
Individual)

pa lo ci'ipa =
pa lo ci'ino selci be piro loi ci'ipa    Individual of Substance

pisu'o loi ci'ino lo su'o lo ci'ipa =    Collective of Substance
loi su'o lo ci'ipa

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".

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).

lo remna      Individual
tu'o lo remna

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. Depending on what you mean by collective, the maximum outer quantifier is either the number of individuals, or 1 or the number of proper subsets of the set of people, which is a combinatoric much larger than 6 billion but less than aleph null.

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.

pisu'o remna  Substance of Individual

No idea.

lo djacu      Individual of Substance

loi su'o djacu  Collective of Substance

lo tu'o remna  Individual of Substance of Individual
= lo pisu'o remna

If tu'o = pisu'o in the latter, then again it is not zi'o. If any value is meaningful, then it is not zi'o.

By now I'm lost so I won't say any more. It is nice of you to put specific words in here, but ...

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.

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

I think I know what you are trying to say, but I get stymied by the problems noted above, so that the fallen trees are masking the forest.

... 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?

 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.

--
lojbab                                             lojbab@hidden.email
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