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xod was wrong about 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.
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.
The set of natural numbers has cardinality aleph-0 The set of real numbers has a cardinality, and it is aleph-1.That means that there are proper subsets of real numbers that are countable: N is a subset of R. It also means it is feasible to speak of 'all' over a transfinite set. It's just that the set is not countable.
Since xod, we have been limiting the denotation of {ro} to countable numbers, and tu'o to transinfinte numbers. This would mean we cannot speak of ro namcu with respect to the set of Real numbers. This is bogus.
The amount of possible portions of substance (not physically separated) as physical objects in 3-D space is at least as great as the number of possible 3-D spaces, since such a space can uniquely contain a given portion of substance.
A 3-D space can be delimited by at the very least four real numbers: an origin (3 numbers as coordinate) and a radius, forming a sphere. The number of possible spheres in a 3-D space is aleph-1 ** 4. The number of possible parallelepipeds is constrained by 3 points, and is aleph-1 * 9. The number of possible spaces of arbitrary shape will be determined by at least alpeh-0 points, and is thus aleph-1 * aleph-0 (I forget if that's aleph-1 or aleph-2).
We can choose to restrict ro to countably many things, but I doubt we should. So we're still stuck, if so. In the following, I'll use not tu'o as an inner quantifier, but ci'ino and ci'ipa for aleph-0 and aleph-1. I retain tu'o for its true meaning (see below.)
The cardinality of collectives is the number of possible subsets of a set. If the set is countably infinite, the number of subsets is 2 ** aleph-0 = aleph-0. I am limiting myself to collectives of atoms; if I allow collectives of collectives of collectives, I may end up transinfinite again, but I'll treat those as not basic ontologically.
The cardinality of Q, the rational numbers, is also aleph-0. And I see why And wants Q to fraction-quantify collectives, and R to fractional-quantify substances. It may be too late for Standard Lojban to demand this though.
There is a third reason to use tu'o: if there is no quantification going on at all. No quantification means no prenex. 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.
So... 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'ipaThe majority of properties are inherently atomic, group, or substance. 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:
lo remna Individual tu'o lo remna loi remna Collective of Individual tu'o loi remna loi djacu Substance tu'o loi djacu pisu'o remna Substance of Individual 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 loi su'o lo tu'o remna Collective of Substance of Individual = loi su'o lo pisu'o remna pisu'o djacu =pisu'o lo djacu Substance of Individual of Substance [pisu'o = pisu'o lo]
(cf. pisu'o loi djacu = Substance)
And for blanu as a property ambiguous between substance and atom:
lo blanu Individual
loi blanu Substance
loi su'o blanu Collective of Individual
loi su'o lo pisu'o loi blanu Collective of Substance
lo pisu'o loi blanu Individual of Substance
pisu'o lo blanu Substance of Individual
pisu'o loi blanu Substance
pisu'o blanu Substance of Individual (pisu'o = pisu'o lo)
lo pisu'o lo blanu Individual of Substance of Individual
loi su'o lo pisu'o blanu Collective of Substance of Individual
pisu'o lo pisu'o lo blanu Substance of Individual of Substance
This reverts to pragmatics after all. Well, pragmatics as in knowledge
about the world.
* 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.
... Later (sigh), I will try and see how I wedge this into something compatible with the Excellent Solution. 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.
---------------------------------------------------------------------- Dr Nick Nicholas; University of Melbourne, http://www.opoudjis.net nickn@hidden.email Dept. of French & Italian Studies No saves, Antonyo, lo ka es morirse una lingua. Es komo kedarse soliko en el silensyo kada diya ke el Dyo da --- Marcel Cohen, 1985 (Judezmo)