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Kludgesome Solution #1
The following will be very very very confusing. & and X, bear with it:
it is intended as an SL-compatible accommodation of the excellent
solution. Which has taken five hours out of my life. The rest of you:
it may be hard for you to believe that this is more compatible with
Standard Lojban than the Excellent Solutions --- but it is.
Incompatibly with SL, this solution introduces weird quantifications:
PA lo piPA, ci'ipa lo PA, ci'ipa loi PA, PA loi. These are to be
understood as shorthands of quantifications converting between the
countability types of collective, substance and individual. I mark the
weird quantifications as (Weird 1), (Weird 2) and (Weird 3) below.
This is a response to Excellent Solution 3, and an attempt to be
equally powerful.
Mad Propz to And and all, but I simply could not understand XS4.
Point by point.
1. No drastic redefinitions of cmavo or default quantification should
be required.
2. The Nicolaic properties aren't my idea, they're Johannine. If you're
prepared to make lo Kind, you've already tossed the Fundament out, so
you might as well use lo'e for something else. So you can do as you
please with them in XS. I will keep them mental constructs.
3. lo remains a gadrow for Individual, and loi a gadrow for LojbanMass,
defined as a union of substance and collective. Kind is handled by
non-quantification on the outer quantifier (tu'o).
4. I'm not clear on the difference between extensional and intensional
sets, but the solutions And proposes are compatible with a more
fundamentalist Lojban.
5. The implicit outer PA on any gadri is NOT mo'ezi'o, but mo'ezo'e,
and indeed mo'ezu'i. However, this default *is defeasible*. In
particular, context may dictate a value of mo'ezi'o instead of
mo'ezo'e. All extensional contexts force mo'ezo'e, however. I assume
the Standard Lojban default outer quantifiers.
6. The default inner PA is mo'ezo'e, which is glorked from context. For
an atomic property, it is ro, understood as rosu'eci'ino (at most
aleph-0). For a substance property, it is necessarily rosu'oci'ipa (at
least aleph-1). This captures the fact that substances are
indefinitely subdividable, and atoms and groups-of-atoms are not.
7. Inner quantification does not properly include tu'o, since the set
of all possible portions of substance does have a (transfinite)
cardinality --- which is assuredly not mo'ezi'o. In the following,
however, feel free to substitute tu'o for ci'ipa.
Uncountability is encoded by inner (and outer, as we will see) ci'ipa.
In cases where the property quantified over is atomic, this coerces a
conversion to atom-goo. For atoms, this is also done by fractional
quantification.
lo ci'ipa remna = loi ci'ipa su'osi'e be lo su'eci'ino remna
pisu'o lo su'eci'ino remna = pisu'o loi ci'ipa su'osi'e be lo
su'eci'ino remna
Where su'osi'e is a possible bit of the substance (what I have been
doing in my ontologies as memzilfendi.)
Countability is encoded by inner su'eci'ino: countables have a
cardinality either finite or aleph-0.
These are prolix inner quantifiers, and I will not shed a tear if we
revert to ro and tu'o. But ro clearly applies to transinfinites as
well, so I believe this is kind of cheating.
As an abbreviation ONLY, I will use ro and tu'o below as inner
quantifiers for cisinfinite and transinfinite quantification. Because
they are prolix.
8. In the following, I give in brackets acceptably defaulted-out
quantifiers and gadri.
* pa lo broda [pa broda]: a single broda, whether an atom (pa lo ro
broda) or an indvidual of substance (pa lo tu'o broda= pa lo ci'ipa
broda) (INDIVIDUAL)
Individual of substance is also a coercion:
* pa lo ci'ipa broda = pa lo piro loi broda = pa lo su'eci'ino spisa be
piro loi ci'ipa broda (INDIVIDUAL OF SUBSTANCE)
Where spisa refers to a physically discrete portion of the substance.
(Weird1)
This introduces the non-canonical quantification PA lo piPA, which I
define as equivalent to PA lo su'eci'ino spisa be piPA:
pisu'o loi djacu = some water
re lo pisu'o loi djacu = two pieces of some water
= re lo djacu
* piro loi ci'ipa broda [piro loi tu'o broda]: the substance of broda
(SUBSTANCE)
* pisu'o loi ci'ipa broda [piro loi tu'o broda]: some of the substance
of broda
* piro loi re lo broda [loi re broda]: a collective consisting of two
broda, whether atomic (loi re lo ro broda) or substance (loi re lo tu'o
broda) (COLLECTIVE OF ATOM, COLLECTIVE OF SUBSTANCE)
* piro loi ro lo broda [loi ro broda]: the collective consisting of
every broda, whether atomic or substance
* piro lei re lo broda [lei re broda]: a certain collective (described
as) consisting of two broda
* piro loi ci'ipa lo re lo broda (loi tu'o lo re lo broda, piro lo re
lo broda) =
piro loi ci'ipa su'osi'e be pisu'o loi ro lo re lo broda: the substance
of two broda (SUBSTANCE OF INDIVIDUAL)
* piro loi ci'ipa loi re lo ro broda (loi tu'o loi re lo broda, piro
loi re lo broda) =
piro loi ci'ipa su'osi'e be loi re lo ro broda: the substance of a
couple (SUBSTANCE OF COLLECTIVE)
(Weird2)
The last two definitions use ci'ipa lo re, ci'ipa loi re; this is a
conventional abbreviation of ci'ipa su'osi'e be pisu'o loi ro lo re.
ci'ipa su'osi'e be pisu'o loi re --- since the x2 argument of si'e must
be a lojbanmass.)
Stepping through the substance of collective:
re lo ro broda: two people (INDIVIDUAL)
loi re lo ro broda: a couple (COLLECTIVE)
piro loi ci'ipa loi re lo ro broda: all of the uncountably many bits of
a couple
expanding to
piro loi ci'ipa su'osi'e be loi re lo ro broda
all ofthe uncountably many bits of a couple of all people
So foursome-goo is
piro loi ci'ipa loi re lo remna (or if you like, piro loi tu'o loi re
lo remna
If we use le, we can kill the inner quantifer, and refer to: {loi tu'o
lei re remna} -- the goo of the two people.
* re lo ro loi re lo broda = re lo ro girzu befi lu'i re lo broda : two
pairs of broda (INDIVIDUAL OF COLLECTIVE) (That is, a collective
treated as an individual, not an individual taken out of a collective.)
* piro loi ro loi re lo broda = piro loi ro girzu befi lu'i re lo broda
: a collective of pairs of broda (COLLECTIVE OF COLLECTIVE)
(Weird3)
The last two definitions use ro loi; this is a conventional
abbreviation of ro lo girzu befi lu'i --- since the x2 argument of si'e
must be a lojbanmass.
Stepping through the individual of collective:
re lo ro broda: two people (INDIVIDUAL)
loi re lo ro broda: a couple (COLLECTIVE)
re lo ro loi re lo ro broda: two couples = two out of all couples,
which expands to:
re lo ro lo girzu befi lu'i re lo ro broda
two out of all of the groups of the sets of two out of all broda
So two quartets of people are:
re lo ro loi vo lo remna
Now, since vomei is by default a collective rather than a substance as
a lojbanmass,
ro loi vo lo remna == ro lo vomei be lo'i remna
re lo ro loi vo lo remna = re vomei be lo'i remna = re remna vomei
This makes Wierd3 advantageously map {vomei} to {ro loi vo lo}
This runs counter to the XS mapping {PA loi} = "PA members of". Since
PA counts things, I would rather it count collectives than members of
collectives. However, I need to be able to extract members from
collectives --- the counterpart of {se vomei} rather than {vomei}. In
the current kludge, I will infuriate Jorge by making this lu'i. So:
* lu'i piro loi re lo broda [loi re broda]: the members of a duo of
broda (INDIVIDUALS IN COLLECTIVE)
This covers our combinations: Individual (of Atom), Substance,
Individual of Substance, Collective of Atom, Collective of Substance,
Substance of Individual. (Collective of Substance is inherently
Collective of Individuals of Substance), Substance of Collective,
Individual of Collective, Collective of Collective, Individuals in
Collective.
Relative to {remna} and {djacu}, these can be glossed as: one or more
humans; some water, a glass of water, a bunch of people, a bunch of
glasses of water, Human-Goo, Beatles-Goo, one or more bunches of
people, a bunch of bunches of people, the people in the bunch.
We can also have tertiary constructs:
* ci lo ro loi ci'ipa lo re lo broda (ci lo tu'o lo re broda, ci lo
piro lo re broda): three scoops of the goo formed by putting two broda
through the universal grinder (Individual of Substance of Individual)
* loi ro lo ci'ipa lo re lo broda (loi ro lo tu'o lo re broda, loi ro
lo piro lo re broda): the collective of all the scoopfuls of goo formed
by putting two broda through the universal grinder (Collective of
Substance of Individual == Collective of Individuals of Substance of
Individual)
* pisu'o loi ci'ipa lo pa lo ci'ipa broda: Substance of Individual of
Substance (some of the scoopful of broda).
Let's step by step the last one:
There's uncountably many bits of broda. (Substance)
I take a countable piece of the broda. (Individual of Substance)
This piece itself has uncountably many bits. (Substance of Individual
of Substance)
I refer to some of the mass of them.
As a consequence of the pragmatically conditioned defaults given in (6),
if broda is inherently atomic, lo broda is by default an atom, and loi
broda a collective of atoms
if broda is inherently substance, loi broda is by default substance,
and lo broda an individual of substance ('portion')
if broda is unmarked, lo broda is by default an atom, and loi broda a
substance.
9. {tu'o lo broda} = Mr Broda (with no notion of quantity: the
reification of the property on its own}
Collectives:
{tu'o lo broda pamei} = {tu'o loi pa lo broda} = Mr Single Broda
{tu'o lo broda remei} = {tu'o loi re lo broda} = Mr Pair of Broda.
{tu'o lo broda romei} = {tu'o loi ro lo broda} = Mr Collective of All
Broda.
{tu'o le broda remei} = {tu'o lei re lo broda} = a certain Kind
embodying what is described as the property of being a pair of broda.
This follows, since lo broda remei (a collective of two broda) is
identical to {loi re lo broda}, and includes in its denotation all
possible pairs of broda. Extensionally, we would refer to a particular,
individual pair as {pa lo ro loi re lo broda} = {pa lo ro lo girzu befi
lu'i re lo broda} ("one out of all the [groups that are] two people") =
{pa lo broda remei}. (By Weird 3)
Intensionally, this is "any of all the [groups that are] two people"),
{tu'o lo ro loi re lo broda}
But if {pa lo ro broda} == {pa broda},
then {tu'o lo ro loi re lo broda} == {tu'o loi re lo broda}.
This is a notational convenience which I'm not sure people will like;
since at the moment {re loi} is undefined, however, I'm going to use it
as a coercion of "two collectives of".
Substances:
{tu'o loi broda} = Mr Broda
I correlate loi with piPA and lo with PA outer quantifiers. Absent an
outer quantifier, I believe tu'o lo broda and tu'o loi broda refer to
the same Kind.
{tu'o loi broda gumna} = {tu'o lo pisu'o loi ci'ipa broda}: Mr Some
Substance of Broda
(We dealt with the kind of collective as being an individual of
collective with an outer quantifier of tu'o. We deal with the kind of
substance as an individual of substance, with its outer quantifier as
tu'o:
An extensional particular individual of substance ("this water here")
is: {pa lo pisu'o loi broda}. The corresponding intension is {tu'o lo
pisu'o loi broda}.
{tu'o loi broda gumna piromei} = {tu'o lo piro loi ci'ipa broda} [tu'o
lo piro loi tu'o broda]: Mr All Substance of Broda
Individuals:
{tu'o lo broda remei} is a couple of mermaids, not two mermaids. When
you speak to {lo remna remei}, you speak to a collective, it is when
you speak to {lo remna se remei} that you speak to the individuals {ro
lo remna se remei = re lo remna}. So to force an individual,
distributive rather than collective notion of quantified Kind:
{tu'o lo broda se pamei} = {tu'o lu'i loi pa lo broda} = Mr One Broda
{tu'o lo broda se remei} = {tu'o lu'i loi re lo broda} = Mr Two Broda
(the members of Mr Pair of Broda)
{tu'o lo broda se romei} = {tu'o lu'i loi ro lo broda} = Mr All Broda
(the members of Mr Collective of All Broda)
So, with the old time mermaids,
De dicto:
I seek mermaid(s): mi buska tu'o lo fipni'u (= tu'o lo su'o lo fipni'u)
I seek a mermaid onesome: mi buska tu'o loi pa lo fipni'u
I seek a mermaid couple: mi buska tu'o loi re lo fipni'u
I seek the totality of mermaids: mi buska tu'o loi ro lo fipni'u
I seek one mermaid: mi buska lu'i tu'o loi pa lo fipni'u
I seek two mermaids: mi buska lu'i tu'o loi re lo fipni'u
I seek all mermaids: mi buska lu'i tu'o loi ro lo fipni'u
I seek some xodium: mi buska tu'o lo pisu'o loi marjrxodiumu
I seek all the xodium there is: mi buska tu'o lo piro loi marjrxodiumu
De re:
I seek mermaid(s): mi buska su'o lo fipni'u
The de dicto {tu'o loi Q} reduces to de re {pa Q}, and de dicto {tu'o
lo Q} to de re {pa lo Q}. I presume that the Unique Kind, being used de
dicto, establishes a relation between the seeking and a single thing.
The single thing becomes de re a single avatar. So when you seek de
dicto, you seek any one of the n possible couples of mermaids. When you
seek de re, you seek one particular couple of mermaids.
pa loi PA = pa lo girzu befi lu'i PA = lu'o PA = loi PA
lu'i pa loi PA = lu'i pa lo girzu befi lu'i PA = lu'i lu'o PA = lu'i
loi PA = PA lo
pa lo piPA => piPA
I seek a mermaid onesome: mi buska pa loi pa lo fipni'u = mi buska loi
pa lo fipni'u
I seek a mermaid couple: mi buska pa loi re lo fipni'u = mi buska loi
re lo fipni'u
I seek the totality of mermaids: mi buska pa loi ro lo fipni'u = mi
buska loi ro lo fipni'u
I seek one mermaid: mi buska lu'i pa loi pa lo fipni'u = mi buska pa lo
fipni'u
I seek two mermaids: mi buska lu'i pa loi re lo fipni'u = mi buska re
lo fipni'u
I seek all mermaids: mi buska lu'i pa loi ro lo fipni'u = mi buska ro
lo fipni'u
I seek some xodium: mi buska pa lo pisu'o loi marjrxodiumu => mi buska
pisu'o loi marjrxodiumu
I seek all the xodium there is: mi buska pa lo piro loi marjrxodiumu =>
mi buska piro loi marjrxodiumu
If {lu'i tu'o loi re lo fipni'u} looks like a mouthful for "any two
mermaids", well, be grateful for propositionalism...
10. {pimu loi su'eci'ino broda} [pimu loi ro broda] = a collective
consisting of one in every two broda.
11. {tu'o lo pimu loi su'eci'ino broda} [tu'o lo pimu loi ro broda] =
Mr One in Every Two Broda.
12. broda is halved as follows, depending on ontological type:
Substance: {pimu loi ci'ipa broda}
Atom: {pimu loi su'osi'e be lo ro broda} = {pimu lo broda} (by coercion)
Collective is ambiguous: is half a collective subcollectives (still
consisting of individuals), or is it collective-goo? If half the
Beatles John and Paul, or bits of John, Paul, and George? I deem the
default to be the former:
{pimu loi su'o lo ro broda}
The latter is expressible as a substance of collective (since
collective-goo is indeed a substance):
{pimu loi ci'ipa lo su'osi'e be piro loi su'o lo ro broda} =
{pimu loi tu'o loi su'o lo ro broda}
So, if a quartet is {loi vo lo remna},
half a quartet = two people = {pimu loi vo lo remna}
half a quartet, as halved by chainsaw = {pimu loi tu'o loi vo lo remna}
where tu'o anywhere but on the outermost quantifier is understood as
signalling uncountability, and is actually equivalent to "the
uncountably many portions of" (ci'ipa loi su'osi'e be piro...)
13. I have already killed XS {PA loi} = "members of", replacing it with
{lu'i}.
PA Kinds of the Kind expressed by {tu'o lo broda}... would need to be
expressed by {PA lo tu'o lo broda}. But since this introduces ambiguity
(I've been using non outermost tu'o to mean ci'ipa = ci'ipa loi
su'osi'e be), and it is messy anyway, I would prefer it to be expressed
by bridi.
I haven't written this cleanly, I fully admit. But I think this is more
SL-compatible than the Excellent Solution. In particular,
lo broda remains an individual rather than a kind. Or rather, lo broda
expresses both an individual and a kind, but the latter is marked as
tu'o lo broda.
I clean up a logical confusion between tu'o = uncountably many and tu'o
= uncounted.
I have a mechanism for secondary and tertiary combinations of
collective, substance, and individual.
I retain the default quantifications as much as possible.
& and X, over to you. It's butt-ugly, sure. But does it work? If not,
how not? I suspect X had already proposed tu'o once for Kind and
abandoned it; why? Because if we define outer quantifier as "what goes
in the outer prenex", and the Kind never goes in the outer prenex,
isn't zi'o exactly what is going on here?
----------------------------------------------------------------------
Dr Nick Nicholas; University of Melbourne, http://www.opoudjis.net
nickn@unimelb.edu.au 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)