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Nick:
> 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
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.
> Second. the cardinality of the set is trans-infinite. This is what
> holds for substances
What does "trans-infinite" mean?
> 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.
> 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
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'.
> 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
With caveats about my possibly missing your point, I don't think
you correctly characterize our idea about tu'o and ro. We can
count namcu, I take it: {ci namcu} is meaningful, isn't it. So
{ro namcu} means (or is equivalent to) "every namcu", because
ro gives you the cardinality of the set of all namcu. So for
{ro -real-number}, ro = aleph-1, whatever the thuc that is.
But {tu'o broda} was to be used where the contrast pa/re/ci/../ro
made no sense -- how do you count something that has no boundaries
or fixed size? You can't. Can mathematicians?
If 'broda' were 'bit of substance' rather than just 'substance',
then we could quantify. The cardinality would always be infinite,
but the quantification can be done as a proportion of all the
bits that exist.
> 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.)
I have no idea what the penult para means, but looking at the last
para, we weren't restricting ro to countably many things. We were
restricting ro to the cardinality of sets of countable things.
{(LE) tu'o broda} was understood to mean that it was meaningless to
try to distinguish between pa/re/ci broda.
That said, ci'i makes sense on the 'bit of broda' interpretation.
> 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
I thought I was proposing Q for both collectives/sets and substances?
Q set/collective = Q members of. Q substance = Q bits of.
> 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
Sure. When we were proposing to use tu'o as an outer quantifier, this
is what it meant (though see comments to first reason above). As
an inner quantifier that states a cardinality, tu'o would mean
that there is no cardinality (not because the set is infinite, but
because there is no criterion for defining what counts as a single
member).
> So..
>
> pa lo ci'ino Atom
> tu'o lo ci'ino Kind of Atom
So how do we say the equivalent of SL "lo ci broda"? I guess
the sensible answer is that you can replace ci'ino but not
ci'ipa by the actual cardinality.
> 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
If "pi mu loi ci'i no" gives you the collective of one in
every 2 people, how do you get the distriutive?
How do you get "a certain Q of". This question applies to
all your examples.
> pisu'o loi ci'ipa !=
> su'o fi'u ro loi ci'ipa Substance
> tu'o loi ci'ipa = Kind of Substance
Why "!="?
> 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
Where "su'o" is the total number of individuals of substance?
> The majority of properties are inherently atomic, group, or substance.
> So the innermost quantifier, aleph-0 or aleph-1, is usually left out
> with impunity.
So how do we state the actual cardinality? Surely the cardinality of
the set of my parents is not ci'ino.
> 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
I have glossed over this, because I can't keep up and because it
doesn't cover +specific.
> 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
This is all great stuff, but it'll be a long haul.
--And.